Systems and methods to predict drug penetration and exposure in the human brain and brain tumors

Abstract

The current disclosure provides systems and methods for predicting drug penetration and exposure in the brain and brain tumors. Systems and methods disclosed herein can be used to predict heterogeneous drug pharmacokinetics in the human brain and, in certain instances, in brain tumors. Particular implementations can be used to predict drug concentration in two regions of the brain mass, three regions of a brain tumor, three regions of cerebrospinal fluid, and brain blood.

Description

SYSTEMS AND METHODS TO PREDICT DRUG PENETRATION AND EXPOSURE IN THE HUMAN BRAIN AND BRAIN TUMORS CROSS-REFERENCE TO RELATED APPLICATION

[0001] This application claims priority to U.S. Provisional Patent Application No.63 / 684,242 filed on August 16, 2024, which is incorporated herein by reference in its entirety as if fully set forth herein. FIELD OF THE DISCLOSURE

[0002] The present disclosure provides systems and methods to predict drug penetration and exposure in the human brain and brain tumors. Systems and methods disclosed herein can be used to predict heterogeneous drug pharmacokinetics in the human brain and in brain tumors. BACKGROUND OF THE DISCLOSURE

[0003] Drug delivery to the brain is restrained by the blood-brain barrier (BBB), a physical and biochemical barrier separating the brain parenchyma from the circulatory system. The structure and function of the BBB, and the blood-brain tumor barrier (BBTB) in brain tumors, is disrupted to varying extents, leading to large intra- and inter-individual variability (heterogeneity) in drug distribution, consequently affecting clinical outcome. The knowledge of drug penetration and exposure (e.g., pharmacokinetics) in the human central nervous system (CNS) is critical to the rational development of new drugs and optimal use of current drugs for effective treatment of brain cancer and other disorders. However, the CNS pharmacokinetics of many new and existing drugs remain understudied and poorly understood because of the difficulty in accessing human brain specimens and the lack of in vitro assays or animal models that reliably predict BBB permeability, drug penetration, and drug exposure in the human brain. Thus, it is imperative that innovative approaches are developed. SUMMARY OF THE DISCLOSURE

[0004] The current disclosure provides systems and methods to predict drug penetration and exposure in the brain. Various implementations of the current disclosure enable prediction of heterogeneous drug penetration and exposure in different regions of the normal human brain tissue (e.g., parenchyma) and CSF system as well as in different regions of a brain tumor following systemic drug administration. Various implementations of the current disclosure can improve the ability to more readily and reliably predict the spatial pharmacokinetics of drugs in the human brain and, when applicable, brain tumors, thus providing an invaluable computational tool to assistdrug developers and health care providers in the development of more effective drugs and optimal use of current therapies to treat brain disorders. BRIEF DESCRIPTION OF THE DRAWINGS

[0005] Some of the drawings submitted herein may be better understood in color. Applicant considers the color versions of the drawings as part of the original submission and reserves the right to present color images of the drawings in later proceedings.

[0006] FIG.1 illustrates an example environment for predicting drug concentration in one or more brain regions.

[0007] FIG.2 illustrates an example method for predicting the concentration of a drug in one or more brain regions.

[0008] FIG.3 illustrates an example method for generating one or more input parameters used to predict the concentration of a drug in one or more brain regions.

[0009] FIG. 4 shows an example computer architecture for a computer capable of executing program components for implementing the functionality described herein.

[0010] FIGs.5A-5C illustrate (5A, 5B) example 9-compartment brain models and (5C) the 4Brain compartment model structures included in the SpatialCNS-PBPK software.

[0011] FIGs.6A-6D illustrate (6A, 6B) percentile plots and (6C, 6D) the scatter plots of the mean concentration profiles generated from Simcyp and the SpatialCNS-PBPK software.

[0012] FIGs. 7A-7C illustrate exemplary (7A, 7B) input panels, and (7C) download options available under the disclosed 9 compartment brain model.

[0013] FIGs. 8A-8D illustrate results of a simulated mean concentration-time profile of total abemaciclib in individual compartments of the 9-CNS model.

[0014] FIGs. 9A-9C illustrate simulation outputs of an individual simulation under the 9- compartment brain model, including (9A) example simulation output tabs and (9B, 9C) example concentration plots.

[0015] FIGs.10A-10D illustrate (10A) output selections available in the sensitivity analysis and (10B-10D) sensitivity plots of the selected parameter PSB1B2, simple diffusion rate between adjacent and deep brain parenchyma.

[0016] FIGs. 11A-11C illustrate simulated concentration-time profiles (in common logarithmic scale) of total abemaciclib in the nine CNS compartments for individuals.

[0017] FIGs.12A-12C illustrate simulated mean, 5th and 95th percentiles of the concentration- time profiles of total abemaciclib in individual compartments of the 9-CNS model from five individuals.

[0018] FIGs.13A-13C illustrate a sensitivity analysis of the impact of PSB2 (passive permeability clearance at the BBB between the blood and deep brain parenchyma compartments) on the total abemaciclib concentration—time profiles in individual CNS compartments.

[0019] FIGs.14A-14C illustrate a sensitivity analysis of the impact of PSB2 (passive permeability clearance at the BBB between the blood and deep brain parenchyma compartments) on the total abemaciclib drug exposure (i.e., AUC) in individual CNS compartments.

[0020] FIGs. 15A, 15B illustrate (15A) calculated PK parameters correspond to the selected inputs, and (15B) area under the curve (AUC) scatter plots generated for the selected parameter PSB1B2.

[0021] FIGs. 16A, 16B illustrate example population plasma pharmacokinetic profiles of abemaciclib, ribociclib, pamiparib, olaparib, temuterkib, and ceritinib.

[0022] FIGs.17A-17C illustrate example total and unbound drug concentration predicted by a 9- compartment brain model disclosed herein, including time profiles for abemaciclib, ribociclib, pamiparib, 3laparib, temuterkib, and ceritinib, in 9 brain regions using the population mean plasma concentration – time profile as the input function.

[0023] FIGs. 18A-18C illustrate example predicted and observed total and unbound drug concentration using a 9-compartment brain model disclosed herein, including time profiles in the CSF for abemaciclib, ribociclib, pamiparib, 3laparib, temuterkib, and ceritinib.

[0024] FIGs. 19A-19C illustrate example predicted total and unbound drug concentration predicted by a 9-compartment brain model disclosed herein, including time profiles in the deep brain parenchyma and 3 tumor compartments for abemaciclib, ribociclib, pamiparib, 3laparib, temuterkib, and ceritinib.

[0025] FIGs. 20A, 20B illustrate the 9-CNS model-predicted and observed unbound drug brain / tumor / CSF-to-plasma partition ratio (Kp,uu) for abemaciclib, ribociclib, pamiparib, olaparib, temuterkib, and ceritinib.

[0026] FIGs.21A, 21B illustrate the 9-CNS model-predicted and observed unbound drug steady- state concentrations in the brain, tumor, and CSF for abemaciclib, ribociclib, pamiparib, olaparib, temuterkib, and ceritinib. DETAILED DESCRIPTION

[0027] The development of drugs that target different areas of the brain (e.g., brain tumors) face many challenges, including limited understanding of drug pharmacokinetics in the brain and drug design to penetrate the blood-brain barrier (BBB) and, in some cases, the blood-brain tumor barrier (BBTB). Once a drug crosses the BBB into the brain, it may distribute heterogeneouslythroughout the brain and surrounding regions (e.g., cerebrospinal fluid (CSF), brain blood, etc.). Data on the spatial distribution of a drug within the brain and on drug pharmacokinetics in the brain remains largely limited, in part due to the difficulty of collecting this data experimentally. Quantitative knowledge of drug penetration and exposure in the human central nervous system (CNS) is critical to rational development of new drugs and optimal use of existing drugs for the treatment of brain disorders.

[0028] Physiologically based pharmacokinetic (PBPK) modeling provides an innovative computational approach for mechanistic prediction of the CNS pharmacokinetics, given its capability of incorporation of drug-specific and biological system-specific parameters into a pharmacokinetic model and prediction of in vivo kinetic processes based on mechanistic scaling of in vitro data (e.g., in vitro cellular permeability and transporter kinetic data) (Zhao et al., Clin Pharmacol Ther. 2011;89(2):259-67; Poulin and Theil. J Pharm Sci. 2002;91(5):1358-70). Currently, the brain is often modeled as a homogenous structure in drug distribution models, which does not account for the heterogenous nature of the brain. When cancer is present, these models do not account for the heterogenous nature of the brain and of brain tumors. Improving the understanding of drug pharmacokinetics in the brain can improve the efficacy of treatments targeting particular sites in the brain, facilitate the development of brain-targeted treatments, and improve the design and safety of clinical trials.

[0029] The current disclosure provides systems and methods for predicting the heterogenous distribution and exposure of a drug in the brain and, in certain examples, in brain tumors. In particular implementations, the disclosed systems and methods can be used to predict the exposure of a drug in one or more brain mass regions, such as the brain tissue adjacent to a CSF tract (also referred to as the “adjacent brain parenchyma” or “CSF adjacent brain tissue”) and the deep brain tissue (also referred to as the “deep brain parenchyma”). In particular implementations, the disclosed systems and methods can be used to predict exposure of a drug in one or more brain tumor regions, such as the tumor rim, the bulk tumor, and the tumor core. In particular implementations, the disclosed systems and methods can be used to predict the exposure of a drug in one or more CSF regions, such as the ventricular CSF, the cranial CSF (also referred to as the “cranial subarachnoid CSF”), and the spinal CSF (also referred to as the “spinal subarachnoid CSF”). In particular implementations, the disclosed systems and methods can be used to predict the exposure of a drug in the brain blood. The systems and methods described herein can predict the exposure of a drug in 1, 2, 3, 4, 5, 6, 7, 8, or 9 brain regions.

[0030] The systems and methods described herein utilize input data that includes drug-specific parameters, system-specific parameters (e.g., parameters related to the brain and body), and thetime-dependent plasma concentration of the drug. Particular implementations described herein relate to generating and validating the drug-specific parameters and the system-specific parameters to improve the accuracy of predicting the drug distribution and exposure. Particular implementations described herein may utilize patient-specific parameters to provide a personalized prediction of a patient’s response to a drug.

[0031] Implementations of the present disclosure will now be described with reference to the accompanying figures and the Experimental Example.

[0032] FIG.1 illustrates an example environment 100 for predicting drug concentration in one or more brain regions. As shown, a prediction system 102 includes a first brain region model 104 and a second brain region model 106. The prediction system 102 is also referred to herein as a “brain model,” a “CNS model,” or a “CNS PBPK model.” The first brain region model 104 is configured to predict concentration-time profile of a drug (e.g., a concentration of the drug over time) in a first brain region. The second brain region model 106 is configured to predict the concentration-time profile of the drug in a second brain region. The prediction system 102 may be implemented in hardware (e.g., one or more processors), software (e.g., instructions executed by the processor(s)), or a combination thereof.

[0033] In various cases, it may be beneficial to determine the concentration of a drug in more than one region of the brain. For instance, a drug targeted to deep brain tissue may reach therapeutic levels in brain tissue that is adjacent to a CSF tract but may not reach therapeutic levels in the deep brain tissue. Modeling the brain mass as a heterogenous structure (e.g., a structure that contains multiple regions, each region having distinct drug exposure parameters) can enable a more accurate prediction of drug distribution of the brain. Accordingly, the efficiency of drug design for brain disorders may improve due to the ability to predict drug concentration in a targeted region of the brain. Clinical trials can be designed to include drug dosages that are predicted to be safer and more efficacious for trial participants. In various cases, it may be beneficial to determine the concentration of the drug in a brain tumor. For instance, an anticancer drug may reach therapeutic levels in the brain mass (e.g., normal brain tissue) but may not reach therapeutic levels in the brain tumor. The ability to optimize drug concentration in the brain tumor and in the brain mass can improve efficacy of treatment of brain cancers.

[0034] These issues can be addressed, for example, by using the first and second brain region models 104 and 106 to predict drug concentration in regions of the brain mass and / or the brain tumor following systemic administration of the drug. For instance, the first and second brain region models 104 and 106 may be configured to predict the concentration of the drug in a first and a second region of the brain mass, respectively. In some examples, the first brain region model 104is configured to predict the concentration-time profile of the drug in a region of the brain tumor, and the second brain region model 106 is configured to predict the concentration-time profile of the drug in a region of the brain mass. In various implementations, regions of the brain mass include CSF adjacent brain tissue and deep brain tissue. CSF adjacent brain tissue is defined, in some examples, as brain tissue within 2 millimeters (mm) of a CSF compartment (e.g., a CSF tract). Deep brain tissue is defined, in some examples, as brain tissue more than 2 mm of a CSF compartment. Regions of the brain tumor include a tumor rim, a bulk tumor, and a tumor core. The normal brain parenchyma is characterized by intact tight junctions at the BBB, protein expression abundance of ABCB1 (3.38 pmol / mg) and ABCG2 (6.21 pmol / mg) at the BBB (determined from isolated microvessels of human normal brain by targeted proteomics) (Teschl G. Ordinary differential equations and dynamical systems; 2021), brain interstitial pH 7.2 (Brannan and Boyce. Differential equations: An introduction to modern methods and applications; 2015; Nagle et al., Fundamentals of differential equations and boundary value problems; 1996; Radhakrishnan and Hindmarsh. Description and use of LSODE, the Livermore solver for ordinary differential equations.1993), and estimated average paravascular bulk flow rate of 0.15 µL / min / g in normal brain parenchyma (Lambert JD. Computational methods in ordinary differential equations. 1973). As compared to normal brain parenchyma, the 3 tumor compartments are characterized by leaky tight junctions, reduction or loss of ABCB1 / ABCG2 expression, relative acidic tumor interstitial pH, and change of paravascular bulk flow. Tumor rim is defined, in some examples, as a brain tumor region with the following characteristics: 2-fold leaky tight junctions at the BBTB compared to the normal level, efflux transporter protein abundance at the BBTB reduced to 50% of the normal level, tumor interstitial pH of 6.8, and double the paravascular bulk flow rate compared to the normal level (due to edema-induced expansion of tumor extracellular water volume). Bulk tumor is defined, in some examples, as a brain tumor region with the following characteristics: 10-fold leaky tight junctions at the BBTB compared to the normal level, efflux transporter protein abundance at the BBTB reduced to 10% of the normal level, tumor interstitial pH of 6.5, and paravascular bulk flow rate decreased by 25% compared to the normal level (due to increased interstitial pressure). Tumor core is defined, in some examples, as a brain tumor region with the following characteristics: 20-fold leaky tight junctions at the BBTB compared to the normal level, loss of efflux transporter protein expression at the BBTB, tumor interstitial pH of 6.2, and paravascular bulk flow rate decreased by 50% compared to the normal level (due to increased interstitial pressure). The implementations described herein can enable improvements in drug design, clinical trial design, and treatment of brain disorders and brain cancer.

[0035] In various implementations, the prediction system 102 is configured to predict the drugconcentration by analyzing a system of equations. In some examples, the system of equations includes one or more ordinary differential equations (ODEs). The prediction system 102 may be configured to apply at least one of Euler’s method, Runge Kutta methods, Adam’s method, a Livermore solver for ordinary differential equations (LSODE), or the like to the system of equations. In some implementations, the prediction system 102 applies the LSODE to analyze the system of equations.

[0036] While FIG. 1 illustrates the prediction system 102 including two brain region models, implementations of the present disclosure are not so limited. In various implementations, the prediction system 102 includes 1, 2, 3, 4, 5, 6, 7, 8, or 9 brain region models. These implementations may be referred to as a N-compartment brain model or as a N-CNS model, where N is the number of brain region models in the prediction system 102. Each of the brain region models are, for instance, configured to predict the concentration of the drug in a region of the brain mass, a region of the brain tumor, a region of the CSF, or brain blood following systemic administration of the drug. Systemic administration may include oral administration, intranasal administration, transdermal administration, intravenous injection, intravenous infusion, intramuscular injection, subcutaneous injection, or the like. Regions of the CSF include ventricular CSF, cranial CSF, and spinal CSF. Ventricular CSF includes CSF in the ventricles of the brain, cranial CSF includes CSF in the cranial subarachnoid space, and spinal CSF includes CSF in the subarachnoid space of the spinal cord.

[0037] In some examples, the prediction system 102 may include one brain region model configured to predict drug concentration in the tumor rim, the bulk tumor, or the tumor core.

[0038] In some examples, the prediction system 102 includes 2 brain region models. For instance, the first and the second brain region models 104 and 106 may be configured to predict drug concentration in a first region of the brain tumor and a second region of the brain tumor, respectively. For instance, the first region of the brain tumor may include the tumor core, and the second region of the brain tumor may include the bulk tumor. In some examples, the first and the second brain region models 104 and 106 may be configured to predict drug concentration in a region of the brain tumor and a region of the brain mass, respectively. For instance, the region of the brain tumor may include the bulk tumor, and the region of the brain mass may include the deep brain tissue. In some examples, the first and the second brain region models 104 and 106 may be configured to predict drug concentration in a region of the brain tumor and a region of the CSF, respectively. For instance, the region of the brain tumor may include the tumor core, and the region of the CSF may include the ventricular CSF. In some examples, the first and the second brain region models 104 and 106 may be configured to predict drug concentration in brain bloodand a region of the brain tumor, respectively. In some examples, the first and the second brain region models 104 and 106 may be configured to predict drug concentration in a first region of the brain mass and a second region of the brain mass, respectively. For instance, the first region of the brain mass may include CSF adjacent brain tissue, and the second region of the brain mass may include deep brain tissue.

[0039] In some examples, the prediction system 102 includes 3 brain region models (e.g., the first brain region model 104, the second brain region model 106, and a third brain region model). In some examples, the three brain region models may be configured to predict drug concentration in CSF adjacent brain tissue, a deep brain tissue, and a region of the brain tumor, respectively. In some examples, the three brain region models may be configured to predict drug concentration in CSF adjacent brain tissue, a deep brain tissue, and a region of the CSF, respectively. In some examples, the three brain region models may be configured to predict drug concentration in CSF adjacent brain tissue, a deep brain tissue, and brain blood, respectively. In some examples, the three brain region models may be configured to predict drug concentration in a region of the brain mass, a first region of the brain tumor, and a second region of the brain tumor, respectively. In some examples, the three brain region models may be configured to predict drug concentration in a region of the brain mass, a region of the brain tumor, and a region of the CSF, respectively. In some examples, the three brain region models may be configured to predict drug concentration in a region of the brain mass, a region of the brain tumor, and brain blood, respectively. In some examples, the three brain region models may be configured to predict drug concentration in a region of the brain tumor, a first region of the CSF, and a second region of the CSF, respectively. In some examples, the three brain region models may be configured to predict drug concentration in a region of the brain tumor, a region of the CSF, and brain blood, respectively.

[0040] In some examples, the prediction system 102 includes 4 brain region models (e.g., the first brain region model 104, the second brain region model 106, the third brain region model, and a fourth brain region model). For instance, the four brain region models may be configured to predict drug concentration in CSF adjacent brain tissue, deep brain tissue, a first region of the brain tumor, and a second region of the brain tumor, respectively. In some examples, the four brain region models may be configured to predict drug concentration in CSF adjacent brain tissue, a deep brain tissue, a region of the brain tumor, and a region of the CSF, respectively. In some examples, the four brain region models may be configured to predict drug concentration in CSF adjacent brain tissue, deep brain tissue, a region of the brain tumor, and brain blood, respectively. In some examples, the four brain region models may be configured to predict drug concentration in CSF adjacent brain tissue, deep brain tissue, a region of the CSF, and brain blood, respectively.In some examples, the four brain region models may be configured to predict drug concentration in a region of the brain mass, a first region of the brain tumor, a second region of the brain tumor, and a region of the CSF, respectively. In some examples, the four brain region models may be configured to predict drug concentration in a region of the brain mass, a region of the brain tumor, a first region of the CSF, and a second region of the CSF, respectively. In some examples, the four brain region models may be configured to predict drug concentration in a region of the brain mass, a region of the brain tumor, a region of the CSF, and brain blood, respectively.

[0041] In some examples, the prediction system 102 includes 5 brain region models (e.g., the first brain region model 104, the second brain region model 106, the third brain region model, a fourth brain region model, and a fifth brain region model). The fifth brain region model may be configured to predict drug concentration in CSF adjacent brain tissue, deep brain tissue, tumor rim, bulk tumor, tumor core, ventricular CSF, cranial CSF, spinal CSF, or brain blood. For instance, the 5 brain region models may be configured to predict drug concentration in CSF adjacent brain tissue, deep brain tissue, tumor rim, bulk tumor, and tumor core, respectively. In some examples, the 5 brain region models may be configured to predict drug concentration in CSF adjacent brain tissue, deep brain tissue, a region of the brain tumor, a region of the CSF, and brain blood, respectively. In some examples, the 5 brain region models may be configured to predict drug concentration in CSF adjacent brain tissue, deep brain tissue, a first region of the CSF, a second region of the CSF, and brain blood, respectively. In some examples, the 5 brain region models may be configured to predict drug concentration in a region of the brain mass, ventricular CSF, cranial CSF, spinal CSF, and brain blood, respectively.

[0042] In some examples, the prediction system 102 includes 6 brain region models (e.g., the first brain region model 104, the second brain region model 106, the third brain region model, a fourth brain region model, the fifth brain region model, and the sixth brain region model). The sixth brain region model may be configured to predict drug concentration in CSF adjacent brain tissue, deep brain tissue, tumor rim, bulk tumor, tumor core, ventricular CSF, cranial CSF, spinal CSF, or brain blood. For instance, the 6 brain region models may be configured to predict drug concentration in CSF adjacent brain tissue, deep brain tissue, tumor rim, bulk tumor, tumor core, and ventricular CSF, respectively. In some examples, the 6 brain region models are configured to predict drug concentration in CSF adjacent brain tissue, deep brain tissue, ventricular CSF, cranial CSF, spinal CSF, and brain blood, respectively. In some examples, the 6 brain region models are configured to predict drug concentration in CSF adjacent brain tissue, deep brain tissue, a first region of the brain tumor, a second region of the brain tumor, a region of the CSF, and brain blood, respectively.

[0043] In some examples, the prediction system 102 includes 7 brain region models (e.g., the first brain region model 104, the second brain region model 106, the third brain region model, a fourth brain region model, the fifth brain region model, the sixth brain region model, and a seventh brain region model). The seventh brain region model may be configured to predict drug concentration in CSF adjacent brain tissue, deep brain tissue, tumor rim, bulk tumor, tumor core, ventricular CSF, cranial CSF, spinal CSF, or brain blood. For instance, the 7 brain region models may be configured to predict drug concentration in CSF adjacent brain tissue, deep brain tissue, tumor rim, bulk tumor, tumor core, ventricular CSF, and brain blood, respectively. In some examples, the 7 brain region models are configured to predict drug concentration in CSF adjacent brain tissue, deep brain tissue, a region of the brain tumor, ventricular CSF, cranial CSF, spinal CSF, and brain blood, respectively. In some examples, the 7 brain region models are configured to predict drug concentration in a region of the brain mass, tumor rim, bulk tumor, tumor core, a first region of the CSF, a second region of the CSF, and brain blood, respectively.

[0044] In some examples, the prediction system 102 includes 8 brain region models (e.g., the first brain region model 104, the second brain region model 106, the third brain region model, a fourth brain region model, the fifth brain region model, the sixth brain region model, the seventh brain region model, and an eighth brain region model). The eighth brain region model may be configured to predict drug concentration in CSF adjacent brain tissue, deep brain tissue, tumor rim, bulk tumor, tumor core, ventricular CSF, cranial CSF, spinal CSF, and brain blood. For instance, the 8 brain region models may be configured to predict drug concentration in CSF adjacent brain tissue, deep brain tissue, tumor rim, bulk tumor, tumor core, ventricular CSF, cranial CSF, and spinal CSF, respectively. In some examples, the 8 brain region models are configured to predict drug concentration in CSF adjacent brain tissue, deep brain tissue, a first region of the brain tumor, a second region of the brain tumor, ventricular CSF, cranial CSF, spinal CSF, and brain blood, respectively. In some examples, the 8 brain region models are configured to predict drug concentration in a region of the brain mass, tumor rim, bulk tumor, tumor core, ventricular CSF, cranial CSF, spinal CSF, and brain blood, respectively.

[0045] In some examples, the prediction system 102 includes 9 brain region models (e.g., the first brain region model 104, the second brain region model 106, the third brain region model, a fourth brain region model, the fifth brain region model, the sixth brain region model, the seventh brain region model, the eighth brain region model, and a ninth brain region model). In various examples, the nine brain region models are configured to predict drug concentration in CSF adjacent brain tissue, deep brain tissue, tumor rim, bulk tumor, tumor core, ventricular CSF, cranial CSF, spinal CSF, and brain blood, respectively.

[0046] The prediction system 102 is configured to predict drug concentration in the first and second brain region models 104 and 106 based on input data 108. The input data 108, in various examples, includes system parameters 110, drug parameters 112, and a plasma concentration 114 of the drug.

[0047] The system parameters 110 include parameters associated with the first region of a brain mass and the second region of the brain mass or of a brain tumor. In various implementations, the system parameters 110 include at least one of: parameters associated with one or more regions of the brain mass, parameters associated with one or more regions of the brain tumor, parameters associated with one or more regions of the CSF, or parameters associated with brain blood. The system parameters 110 may be selected or generated based on the number of brain region models and / or the brain regions associated with the brain region models in the prediction system 102. The system parameters 110 may include at least one of: a region volume, a cerebral blood flow, a CSF absorption rate, a CSF flow rate, a CSF back flow rate, a paravascular bulk flow rate, or a convective flow rate.

[0048] The region volume may include at least one of: a volume of brain blood, a volume of adjacent brain tissue, a volume of deep brain tissue, a volume of tumor rim region, a volume of tumor bulk region, a volume of tumor core region, a volume of ventricular CSF, a volume of cranial CSF, or a volume of spinal CSF. The CSF absorption rate may at least one of: include an absorption rate of cranial CSF into blood circulation through arachnoid villi, an absorption rate of spinal CSF into blood circulation through arachnoid villi, an absorption rate of cranial CSF via olfactory mucosa and cranial nerve sheaths, or an absorption rate of spinal CSF via spinal nerve sheaths. The CSF flow rate may include at least one of: a CSF flow rate from the ventricular space to cranial space, a CSF flow rate from the ventricular space to spinal space, a CSF flow rate from the spinal space to cranial space, or a CSF flow rate from the cranial space to spinal space. The CSF back flow rate may include a CSF back flow rate from the cranial space to ventricular space and / or a CSF back flow rate from the spinal space to ventricular space.

[0049] In some examples, the paravascular bulk flow rate includes a paravascular bulk flow rate from a region of the CSF to a region of the brain mass and / or a paravascular bulk flow rate from a region of the brain mass to a region of the CSF. For instance, the paravascular bulk flow rate may include at least one of: a paravascular bulk flow rate from the cranial CSF to CSF adjacent brain tissue, a paravascular bulk flow rate from CSF adjacent brain tissue to cranial CSF, a paravascular bulk flow rate from the ventricular CSF to CSF adjacent brain tissue, a paravascular bulk flow rate from CSF adjacent brain tissue to ventricular CSF, a paravascular bulk flow rate from cranial CSF to deep brain tissue, or a paravascular bulk flow rate from deep brain tissue tocranial CSF. In some examples, the paravascular bulk flow rate includes a paravascular bulk flow rate from a region of the CSF to a region of the brain tumor and / or a paravascular bulk flow rate from a region of the brain tumor to a region of the CSF. For instance, the paravascular bulk flow rate may include at least one of: a paravascular bulk flow rate from cranial CSF to tumor rim, a paravascular bulk flow rate from tumor rim to cranial CSF, a paravascular bulk flow rate from cranial CSF to tumor bulk, a paravascular bulk flow rate from tumor bulk to cranial CSF, a paravascular bulk flow rate from cranial CSF to tumor core, or a paravascular bulk flow rate from tumor core to cranial CSF.

[0050] In various cases, the convective flow rate includes a convective flow rate from a region of the brain mass to a region of the brain tumor and / or a convective flow rate from a region of the brain tumor to a region of the brain mass. For example, the convective flow rate may include at least one of: a convective bulk flow rate from CSF adjacent brain tissue to deep brain tissue, a convective bulk flow rate from deep brain tissue to CSF adjacent brain tissue, a convective bulk flow rate from deep brain tissue to tumor rim, a convective bulk flow rate from tumor rim to deep brain tissue, a convective bulk flow rate from tumor rim to tumor bulk, a convective bulk flow rate from tumor bulk to tumor rim, a convective bulk flow rate from tumor bulk to tumor core, or a convective bulk flow rate from tumor core to tumor bulk. The system parameters 110 may include any of the system parameters listed herein. In some examples, the system parameters 110 include all of the system parameters listed herein.

[0051] The drug parameters 112 include parameters associated with the drug. In various implementations, the drug parameters 112 include at least one of: a passive permeability clearance, a simple diffusion rate, a transporter-mediated clearance, a metabolic clearance in a region of the brain mass, an unbound fraction in a region, or a unionized drug fraction in a region.

[0052] In some examples, the passive permeability clearance includes a passive permeability clearance at the BBB. For instance, the passive permeability clearance may include a passive permeability clearance at the BBB between brain blood and CSF adjacent brain tissue and / or passive permeability clearance at the BBB between brain blood and deep brain tissue. In some examples, the passive permeability clearance includes a passive permeability clearance at the blood-brain tumor barrier (BBTB). For instance, the passive permeability clearance may include at least one of: a passive permeability clearance at the BBTB between brain blood and tumor rim, a passive permeability clearance at the BBTB between brain blood and bulk tumor, or a passive permeability clearance at the BBTB between brain blood and tumor core. In some examples, the passive permeability clearance includes a passive permeability clearance at the blood-CSF barrier. For instance, the passive permeability clearance may include a passive permeabilityclearance at the blood-CSF barrier between the brain blood and ventricular CSF and / or a passive permeability clearance at the blood-CSF barrier between the brain blood and cranial CSF.

[0053] The simple diffusion rate may include at least one of: a simple diffusion rate between cranial CSF and CSF adjacent brain tissue, a simple diffusion rate between ventricular CSF and CSF adjacent brain tissue, a simple diffusion rate between CSF adjacent brain tissue and deep brain tissue, a simple diffusion rate between deep brain tissue and tumor rim, a simple diffusion rate between tumor rim and bulk tumor, or a simple diffusion rate between bulk tumor and tumor core.

[0054] In some examples, the transporter-mediated clearance includes an efflux transporter- mediated efflux clearance and / or an uptake transporter-mediated uptake clearance. In some examples, the transport-mediated clearance includes a transporter-mediated clearance at the BBB and / or a transporter-mediated clearance at the blood-CSF barrier. For instance, the transporter-mediated clearance may include at least one of: an efflux transporter-mediated efflux clearance at the BBB between the brain blood and CSF adjacent brain tissue, an uptake transporter-mediated uptake clearance at the BBB between the brain blood and CSF adjacent brain tissue, an efflux transporter-mediated efflux clearance at the BBB between the brain blood and deep brain tissue, or an uptake transporter-mediated uptake clearance at the BBB between the brain blood and deep brain tissue.

[0055] In some examples, the transport-mediated clearance includes a transporter-mediated clearance at the BBTB. For instance, the transporter-mediated clearance may include at least one of: an efflux transporter-mediated efflux clearance at the BBTB between the brain blood and tumor rim, an uptake transporter-mediated uptake clearance at the BBTB between the brain blood and tumor rim, an efflux transporter-mediated efflux clearance at the BBTB between the brain blood and bulk tumor, an uptake transporter-mediated uptake clearance at the BBTB between the brain blood and bulk tumor, an efflux transporter-mediated efflux clearance at the BBTB between the brain blood and tumor core, or an uptake transporter-mediated uptake clearance at the BBTB between the brain blood and tumor core.

[0056] In some examples, the transport-mediated clearance includes a transporter-mediated clearance at the at the blood-CSF barrier. For instance, the transport-mediated clearance may include at least one of: an efflux transporter-mediated efflux clearance at the blood-CSF barrier between the brain blood and ventricular CSF, an uptake transporter-mediated uptake clearance at the blood-CSF barrier between the brain blood and ventricular CSF, an efflux transporter- mediated efflux clearance at the blood-CSF barrier between the brain blood and cranial CSF, or an uptake transporter-mediated uptake clearance at the blood-CSF barrier between the brainblood and cranial CSF.

[0057] The metabolic clearance in a region of the brain mass may include a metabolic clearance in the CSF adjacent brain tissue and / or a metabolic clearance in the deep brain tissue. The unbound fraction in a region may include at least one of: an unbound fraction in plasma, an unbound fraction in the CSF adjacent brain tissue, an unbound fraction in the deep brain tissue, an unbound fraction in tumor rim, an unbound fraction in bulk tumor, an unbound fraction in tumor core, an unbound fraction in ventricular CSF, an unbound fraction in cranial CSF, or an unbound fraction in spinal CSF. The unionized drug fraction in a region may include at least one of: a unionized drug fraction in the brain blood, a unionized efficiency in the CSF adjacent brain tissue, a unionized efficiency in the deep brain tissue, a unionized efficiency in tumor rim, a unionized efficiency in bulk tumor, a unionized efficiency in tumor core, a unionized efficiency in ventricular CSF, a unionized efficiency in cranial CSF, or a unionized efficiency in spinal CSF. The drug parameters 112 may include any of the drug parameters listed herein. In some examples, the drug parameters 112 include all of the drug parameters listed herein.

[0058] The plasma concentration 114 is indicative of, in some examples, a plasma concentration- time profile of the drug (e.g., the concentration of the drug in plasma over time). In some cases, the plasma concentration 114 is based on experimental data 116 collected from a population of individuals. The experimental data 116 may include plasma concentration-time profiles of the drug of each of the individuals. The experimental data 116, in some examples, includes one or more pharmacokinetic parameters (e.g., a peak plasma concentration, a time for peak plasma concentration, an area under the curve, an onset time of a minimum effective concentration, a termination time of the minimum effective concentration, a therapeutic time window, an onset time of the maximum safe concentration, a termination time of the maximum safe concentration, or another parameter associated with the plasma concentration-time profile of the drug). In some examples, the plasma concentration 114 includes a mean, a median, a standard deviation, or another metric associated with the experimental data 116.

[0059] Based on the input data 108, the prediction system 102 may be configured to determine a first predicted concentration 118 of the drug in the first brain region and a second predicted concentration 120 of the drug in the second brain region. The first and second predicted drug concentrations 118 and 120 may include a concentration-time profile of the drug and / or one or more pharmacokinetic parameters (e.g., a peak plasma concentration, a time for peak plasma concentration, an area under the curve, etc.).

[0060] In some examples, the prediction system 102 is configured to determine a mean profile simulation result. The mean profile simulation result may include, for instance, at least one of: aconcentration table, a concentration plot, a concentration log plot, or a pharmacokinetic parameter. In various cases, the prediction system 102 is configured to determine a parameter sensitivity simulation result. The parameter sensitivity simulation result may indicate, for example, an impact of at least one parameter on the output (e.g., the concentration-time profile, a pharmacokinetic parameter, etc.). In some instances, the parameter sensitivity simulation results includes at least one of: a concentration table, a concentration plot, a concentration log plot, a pharmacokinetic parameter, or an AUC scatter plot.

[0061] In some examples, the prediction system 102 is configured to receive an input from a user 124. The user 124 may be a researcher, a clinical trial designer, a clinician, a data scientist, a regulatory specialist (e.g., a regulatory agency employee, an employee of the Food and Drug Administration, etc.), or the like. For instance, the prediction system 102 may receive, via an input device 122, an indication of a time period from the user 124. The prediction system 102 may be configured to determine the concentration-time profile during the time period and / or the pharmacokinetic parameter(s) during the time period. In various cases, the prediction system 102 receives, via the input device 122, an indication of a number of simulated individuals from the user 124. The prediction system 102 may be configured to determine a concentration-time profile of the drug and / or one or more pharmacokinetic parameters for each simulated individual. For instance, the prediction system 102 may determine a generated parameter list for a given inter- individual variability (IIV), a concentration table, a concentration plot, a concentration log plot, a percentile data table, a percentile plot, or a percentile log plot. In some examples, the user 124 provides an indication, via the input device 122, of the selected model parameters included in the mean profile simulation result. In some examples, the user 124 provides an indication, via the input device 122, of the at least one parameter included in the parameter sensitivity simulation result. For instance, the user 124 may provide an indication of at least one of: a minimum value for one or more parameters, a maximum value for one or more parameters, a number of points to generate within a range of one or more parameters, a minimum time point for one or more parameters, or a maximum time point for one or more parameters. In some examples, the user 124 provides an indication, via the input device 122, of a particular IIV, and the prediction system 102 may determine a generated parameter list for the particular IIV.

[0062] The prediction system 102, in some examples, may output the first and second predicted concentrations 118 and 120 to one or more end-user devices 126. The end-user device(s) 126 may include a mobile device, a medical device (e.g., a monitor, etc.), a computing device, or the like. The end-user device(s) 126 may include a device used by the user 124, a researcher, a clinical trial designer, a clinician, a data scientist, a regulatory specialist. In some examples, theprediction system 102 is configured to output the first and second predicted concentrations 118 and 120 to an application (e.g., a web application, a mobile application, or the like), and the end- user device(s) 126 are configured to run the application. In some cases, the end-user device(s) 126 includes a visual display configured to output an indication of the first and second predicted concentrations 118 and 120. The application may include the visual display.

[0063] In various examples, it may be beneficial to predict the concentration-time profile of the drug in a subject 128. For instance, the subject 128 may have a brain disorder, and the drug may reduce or eliminate the symptoms of the brain disorder. Examples of brain disorders include epilepsy, Parkinson's disease, Huntington's disease, Alzheimer’s disease, schizophrenia, depression, generalized anxiety disorder, panic disorder, eating disorders, bipolar disorder, obsessive-compulsive disorder, post-traumatic stress disorder, borderline personality disorder, essential tremor, multiple sclerosis, traumatic brain injury, migraine, autism spectrum disorder, cerebrovascular disease (e.g., due to a stroke), or another disorder associated with the brain. In some examples, the subject 128 may have a brain cancer, and the drug may treat or reduce the symptoms of the brain cancer. Examples of brain cancer include glioblastoma, glioma, glioblastoma multiforme, astrocytoma, meningioma, medulloblastoma, pituitary adenoma, oligodendroglioma, ependymoma, a germ cell tumor, pinealoma, primary central nervous system lymphoma, neuroblastoma, a congenital tumor, or another a central nervous system cancer. The drug may have the highest efficacy when present within a specific range of concentrations in a region of the brain. In some examples, the drug may be administered to individuals with the brain disorder or the brain cancer as part of a clinical trial. Determining a personalized dosage for each of the individuals (e.g., the subject 128) may improve understanding of the treatment efficacy and safety profile of the drug.

[0064] These issues can be addressed, for example, by inputting patient parameters 130 into the prediction system 102. For instance, patient parameters 130 may be collected from the subject 128 by a researcher, a clinician, the user 124, or the like. These patient parameters 130 may enable prediction of the concentration-time profile of the drug in the subject 128. Accordingly, a dosage of the drug can be determined that reduces side effects and optimizes therapeutic effects in the subject 128. In some implementations, a clinician may input the patient parameters 130 into the prediction system 102 to determine a dosage of the drug to treat the brain disorder of the subject 128. In some examples, a clinical trial designer may determine that the concentration- time profile of the drug in the subject 128 is predicted to be different than other individuals participating in a clinical trial. The clinical trial designer may exclude the subject 128 from the clinical trial or determine a different dosage of the drug for the subject 128.

[0065] The patient parameters 130 may include at least one of the system parameters 110 collected from the subject 128. For instance, the patient parameters 130 may include a volume of a brain region, a cerebral blood flow, or another system parameter derived from the subject 128. In some examples, the subject 128 may be administered an initial dose of the drug, and the plasma concentration-time profile of the drug (e.g., the plasma concentration 114) in the subject 128 may be provided to the prediction system 102. Based on the plasma concentration-profile in the subject 128, the prediction system 102, in some examples, provides a more accurate prediction of the concentration-time profile in the brain of the subject 128. Accordingly, subsequent doses of the drug can be optimized before administration to the subject 128.

[0066] In various examples, at least one of the system parameters 110 and / or at least one of the drug parameters 112 may be generated based on observed data 132 collected from a population of individuals. The observed data 132 may be collected by a researcher or a clinician. The observed data 132 may indicate a variability of at least one of the system parameters 110 and / or at least one of the drug parameters 112. The observed data 132, in some examples, includes an indication of each of the individuals. For instance, the observed data 132 may indicate that a first system parameter and a second system parameter were collected from the same individual. In various cases, the observed data 132 includes a concentration-time profile of the drug in a brain region. For instance, the observed data 132 may include a concentration-time profile of the drug in ventricular CSF. In some examples, some or all of the individuals have a brain tumor, and the observed data 132 includes a concentration-time profile and / or a pharmacokinetic parameter of the drug in the brain tumor. In some implementations, the patient parameters 130 and / or the observed data 132 include at least one concentration, in a particular region, of the drug at a particular time.

[0067] The system parameters 110, in some implementations, are optimized. For instance, results of the prediction system 102 using the system parameters 110 may be compared to a concentration-time profile in a brain region collected from the subject 128. In some examples, the output of the prediction system 102 may include an indication of the observed data 132. For instance, the prediction system 102 may predict a concentration-time profile of the drug in each of the individuals.

[0068] FIG.2 illustrates an example process 200 for predicting the concentration of a drug in one or more brain regions. The process 200 may be performed by an entity, such as at least one of the prediction system 102, the end user device(s) 126, or one or more processors, or a trained user, such as a researcher, a clinician, a data scientist, or the like.

[0069] At 202, the entity identifies input data. The input data (e.g., the input data 108), in variousexamples, includes a plasma concentration-time profile (e.g., the plasma concentration 114) of the drug. In some examples, the input data includes multiple plasma concentration-time profiles from a population of individuals. One or more metrics indicative of the multiple plasma concentration-time profiles (e.g., a mean, a median, a standard deviation, a variability, etc.) may be used as the input data. In various implementations, the input data includes system parameters (e.g., the system parameters 110) and / or drug parameters (e.g., the drug parameters 112).

[0070] At 204, the entity predicts, based on the input data, a concentration of the drug in one or more brain concentrations (e.g., the first and second predicted concentrations 118 and 120). The input data may be applied to a prediction system (e.g., the prediction system 102) that is configured to predict the drug concentration in the one or more brain regions. The prediction system may include one or more models (e.g., the first and second brain region models 104 and 106) that are each configured to predict the drug concentration in a brain region. The concentration of the drug may include a concentration-time profile of the drug and / or one or more pharmacokinetic parameters. In some examples, the entity predicts the drug concentration based on patient parameters (e.g., the patient parameters 130) collected from a patient (e.g., the subject 128). In some examples, the entity predicts the drug concentration based on observed data (e.g., the observed data 132) collected from a population of subjects. In some examples, the entity predicts the drug concentration during a particular time period or in a population of simulated individuals. In some examples, the entity determines the impact of a particular parameter on the drug concentration (e.g., how the drug concentration changes when the parameter is altered). The entity may receive, from a user (e.g., the user 124), an input indicating the particular time period, a number of simulated individuals, or the particular parameter. The user may provide the input to the entity by using an input device (e.g., the input device 122).

[0071] At 206, the entity outputs the concentration of the drug in the one or more brain regions. The entity may output the drug concentration to an end user device (e.g., the end user device(s) 126) or to a user (e.g., the user 124). The entity may output a visual signal of the concentration- time profile of the drug in each of the one or more brain regions. In some examples, the entity outputs one or more pharmacokinetic parameters associated with the concentration-time profile of the drug in each of the one or more brain regions. The entity may output an indication of the user input (e.g., the particular time period, the number of simulated individuals, or the particular parameter). For instance, the entity may output the drug concentration in each of the simulated individuals.

[0072] FIG.3 illustrates an example process 300 for generating one or more input parameters used to predict the concentration of a drug in one or more brain regions. The process 300 maybe performed by an entity, such as at least one of the prediction system 102, the end user device(s) 126, or one or more processors, or a trained user, such as a researcher, a clinician, a data scientist, or the like. The input parameter(s) may include one of the system parameters 110 and / or one of the drug parameters 112 described above with reference to FIG. 1. The input parameter(s) may be provided to a prediction system (e.g., the prediction system 102) that is configured to predict the concentration of the drug in one or more brain regions.

[0073] At 302, the entity identifies subject data indicative of one or more input parameters. The data, in some examples, is collected from a population of individuals. In some examples, the subject data is identified from a database (e.g., clinical trial data, deidentified clinical data, etc.). The data may be analyzed to determine the input parameter(s). The input parameter(s), in various cases, includes one or more system parameters (e.g., the system parameters 110) and / or one or more drug parameters (e.g., the drug parameters 112).

[0074] At 304, the entity generates, based on the subject data, the input parameter(s). The subject data, for instance, may be analyzed to determine the input parameter(s). For instance, the entity may compute the input parameter(s) based on the subject data. In some examples, the entity may determine that the input parameter(s) include a metric associated with the subject data (e.g., a mean, a median, a standard deviation, a variability, or another statistical metric). In some examples, the entity computes one or more drug parameters based on published methods (Li, et al., Clin Pharmacol Ther.2021;109:494-506; Li, et al., Clin Cancer Res.2022;28(15):3329-3341).

[0075] At 306, the entity validates the input parameter(s). The entity may input the input parameter(s) into the prediction system and analyze the output of the prediction system. For instance, the entity may compare an output of the prediction system to data collected from one or more patients (e.g., the subject 128). Based on the comparison, the entity may optimize the input parameter(s). For instance, the entity may alter the input parameter(s) until the difference between the output of the prediction system and the data collected from the patient(s) is below a threshold. In some examples, the entity performs a sensitivity analysis to optimize the input parameter(s). In some examples, the entity generates one or more input parameters and identifies one or more input parameters from published literature, drug information (e.g., provided by a pharmaceutical company, a regulatory agency, or the like), clinical data, or the like. Based on validating the input parameter(s), the entity may use the prediction system to predict the concentration of the drug in one or more brain regions.

[0076] FIG.4 illustrates an example of one or more devices 400 that can be used to implement any of the functionality described herein. In some implementations, some or all of the functionality discussed in connection with other figures described herein can be implemented in the device(s)400. Further, the device(s) 400 can be implemented as one or more server computers 402, a network element on a dedicated hardware, as a software instance running on a dedicated hardware, or as a virtualized function instantiated on an appropriate platform, such as a cloud infrastructure, and the like. It is to be understood in the context of this disclosure that the device(s) 400 can be implemented as a single device or as a plurality of devices with components and data distributed among them.

[0077] As illustrated, the device(s) 400 include a memory 404. In various embodiments, the memory 404 is volatile (such as RAM), non-volatile (such as ROM, flash memory, etc.) or some combination of the two.

[0078] The memory 404 may store, or otherwise include, various components 406. In some cases, the components 406 can include objects, modules, and / or instructions to perform various functions disclosed herein. The components 406 can include methods, threads, processes, applications, or any other sort of executable instructions. The components 406 can include files and databases. The memory 404 may store instructions to perform various functions of the prediction system 102 described herein with reference to FIG.1.

[0079] In some implementations, at least some of the components 406 can be executed by processor(s) 408 to perform operations. In some embodiments, the processor(s) 408 includes a Central Processing Unit (CPU), a Graphics Processing Unit (GPU), or both CPU and GPU, or other processing unit or component known in the art.

[0080] The device(s) 400 can also include additional data storage devices (removable and / or non-removable) such as, for example, magnetic disks, optical disks, or tape. Such additional storage is illustrated in FIG. 4 by removable storage 410 and non-removable storage 412. Tangible computer-readable media can include volatile and nonvolatile, removable and nonremovable media implemented in any method or technology for storage of information, such as computer readable instructions, data structures, program modules, or other data. The memory 404, removable storage 410, and non-removable storage 412 are all examples of computer- readable storage media. Computer-readable storage media include RAM, ROM, EEPROM, flash memory or other memory technology, CD-ROM, Digital Versatile Discs (DVDs), Content Addressable Memory (CAM), or other optical storage, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other medium which can be used to store the desired information and which can be accessed by the device(s) 400. Any such tangible computer-readable media can be part of the device(s) 400.

[0081] The device(s) 400 also can include, or be connected to, input device(s) 414, such as a keypad, a cursor control, a touch-sensitive display, voice input device, etc., and output device(s)416 such as a display, speakers, printers, etc. In some implementations, the input device(s) 414, in some cases, may include a device configured to record or store data collected from individuals (e.g., the patient parameters 130, the observed data 132, or the like). In certain examples, the output device(s) 416 can include a user device (e.g., the end-user device(s) 126) or a display (e.g., a screen, a hologram display, etc.).

[0082] As illustrated in FIG.4, the device(s) 400 can also include one or more wired or wireless transceiver(s) 418. For example, the transceiver(s) 418 can include a Network Interface Card (NIC), a network adapter, a Local Area Network (LAN) adapter, or a physical, virtual, or logical address to connect to the various base stations or networks contemplated herein, for example, or the various user devices and servers. The transceiver(s) 418 can include any sort of wireless transceivers capable of engaging in wireless, Radio Frequency (RF) communication. The transceiver(s) 418 can also include other wireless modems, such as a modem for engaging in Wi- Fi, WiMAX, Bluetooth, or infrared communication. The transceiver(s) 418 may be configured to transmit signals to the output device(s).

[0083] In some instances, one or more components may be referred to herein as “configured to,” “configurable to,” “operable / operative to,” “adapted / adaptable,” “able to,” “conformable / conformed to,” etc. Those skilled in the art will recognize that such terms (e.g., “configured to”) can generally encompass active-state components and / or inactive-state components and / or standby-state components, unless context requires otherwise. EXPERIMENTAL EXAMPLE

[0084] This Experimental Example describes the development of a novel 9-compartment, permeability-limited CNS PBPK model, also referred to herein as a “9-compartment model” or a “9-CNS model,” that allows prediction of spatial pharmacokinetics of small-molecule drugs in the human CNS, including in the brain blood, 2 distinct brain parenchyma compartments (representing brain tissue adjacent to the CSF tract and deep brain parenchyma), 3 CSF compartments (representing ventricular CSF, cranial and spinal subarachnoid CSF), and 3 brain tumor compartments (representing tumor rim, bulk tumor, and tumor core) (FIGs.5A.5B). The 9- CNS model accounts for the general anatomical structure, physiological processes, and pathological changes of the human CNS and brain tumors, while maintaining reasonable computational speed. The drug distribution and fluid transfer into and out of each compartment in the 9-CNS model are described by system of linear nonhomogeneous ordinary differential equations that contain drug-specific and system-specific parameters. As compared to the existing 4-compartment CNS (4-CNS) model (FIG. 5B) (which is implemented in a commercial PBPKmodeling software, Simcyp Simulator, Certara Inc.) that assumes the brain as a homogeneous compartment (Jamei et al., Expert Opin Drug Metab Toxicol), the 9-CNS model accounts for regional physiological and pathological differences in the brain and brain tumors, thus providing a mechanism-based computational tool for prediction of spatial heterogeneity of drug penetration and exposure in different brain tumor regions and in different locations of the brain parenchyma and CSF system.

[0085] The R / Shiny interface enables creation of web application (app) with both front-end (visual design and interactivity) and back-end (calculations and database manipulation) capabilities. The app allows users to take advantage of the robust library of packages for data science and statistical analyses offered by the R language. While several Shiny-based statistical software tools have been developed for pharmacokinetic / pharmacodynamic (PK / PD) analysis (Vaddady and Kandala. CPT Pharmacometrics Syst Pharmacol. 2021;10(11):1323-31; Wojciechowski et al., CPT Pharmacometrics Syst Pharmacol. 2015;4(3); Cho and Lee. Transl Clin Pharmacol. 2019;27(2):73-9; Lu et al., CPT Pharmacometrics Syst Pharmacol.2024;13(3):341-58), none of them are specifically designed for PBPK modeling of spatial pharmacokinetics in the human CNS.

[0086] To enable a broad range of users to easily apply the disclosed 9-CNS model for prediction of spatial CNS pharmacokinetics, the 9-CNS model is packaged, in some implementations, into a user-friendly, web-based platform. In this Experimental Example, the 9-CNS model is packaged into a R / Shiny platform, named SpatialCNS-PBPK app. The app is programmed in R and utilizes Shiny (Chang et al., shiny: Web Application Framework for R. version 1.6.0.2021) as the web application framework, taking advantages of key R packages, such as tidyverse (Wickham et al., J Open Source Softw.2019;4(43):1686), deSolve (Soetaert et al., J Stat Softw. 2010;33:1-25), ggplot2 (Wickham and Wickham. ggplot2. 2016:11-31), and dplyr (Wickham et al., dplyr. A Grammar of Data Manipulation 2020). This Experimental Example describes the development and validation of SpatialCNS-PBPK app, introduces the key app features, and provides a user guide with application examples.

[0087] 9-CNS MODEL

[0088] Model structure and biological rationale. The 9-CNS model structure (FIGs.5A, 5B) was designed to represent the general anatomy and pathophysiology of the human CNS while maintaining reasonable simplicity needed for computational feasibility. The 9 compartments include a brain blood compartment, 2 brain parenchyma compartments (representing brain tissue adjacent to CSF compartments and deep brain parenchymal region with > 2 mm distance from CSF compartments), 3 tumor compartments (representing infiltrative tumor rim, bulk tumor, and tumor core), and 3 CSF compartments (representing ventricular CSF, cranial subarachnoidspace, and spinal subarachnoid space).

[0089] Following systemic administration, drug penetration into the CNS is driven by the plasma pharmacokinetics, which is the input function in the 9-CNS model. Drug transport across the BBB and blood-CSF barrier is governed by passive permeability and transporter-mediated active efflux or uptake. Within the CNS, drug distribution between different brain / tumor regions and between the brain / tumor compartments and CSF compartments is driven by a combination of simple diffusion and paravascular convective bulk flow. Simple diffusion facilitates drug distribution from the ventricular or cranial subarachnoid CSF into the adjacent brain tissue (brain parenchyma 1), while it is inefficient for drug distribution from CSF to the deep brain (brain parenchyma 2) at the distance > 2 mm away from the CSF tract or drug distribution between different brain / tumor regions (Blasberg et al., J Pharmacol Exp Ther.1975;195(1):73-83). By contrary, convective bulk flow along paravascular spaces is the preferential pathway for drug distribution between different brain / tumor regions and between the brain / tumor compartments and CSF compartments (Nedergaard M. Science. 2013;340(6140):1529-30; Iliff et al., Sci Transl Med. 2012;4(147); Mestre et al. Elife.2018;7). Once in the CSF, drug moves along the CSF circulation through the ventricular system to the cranial and spinal subarachnoid spaces and is subsequently absorbed into the systemic circulation through the arachnoid villi and along the olfactory mucosa, cranial and spinal nerve sheaths (Hladky and Barrand. Fluids Barriers CNS.2014;11(1):26). Metabolism in the brain parenchyma is allowed in the 9-CNS model.

[0090] Notably, heterogenous BBB integrity and transporter expression in the normal brain and brain tumors can be considered in the 9-CNS model. For example, it is assumed that the 3 tumor compartments (tumor rim, bulk tumor, and tumor core) present the BBB varying from complete intactness to 10-20 fold disruption of tight junctions; and in addition, BBB transporter expression levels decrease to 50% and 10% of the normal level in tumor rim and bulk tumor while being completely lost in tumor core. Regional differences in brain / tumor interstitial pH, for example ranging from pH 7.2 to 6.0, can be considered from the normal brain parenchyma to tumor core, respectively (Gerweck and Seetharaman. Cancer Res.1996;56(6):1194-8; Tannock and Rotin. Cancer Res.1989;49(16):4373-84; Martin and Jain. Cancer Res.1994;54(21):5670-4). Moreover, pathophysiological changes caused by tumor edema can be considered in the 9-CNS model. For example, as compared to that in the normal brain, the paravascular bulk flow is assumed doubled in tumor rim due to edema-induced expansion of tumor extracellular water volume, while decreasing by 25-50% in bulk tumor and tumor core due to the increased interstitial pressure. Additionally, the change of drug binding in the brain parenchyma and different tumor compartments is considered due to the different tissue compositions and plasma proteinextravasation in tumor edema.

[0091] Differential equations. Drug distribution and fluid flow into and out of each compartment of the 9-CNS model are described by differential equations that contain system-specific and drug- specific parameters, as shown below. In some implementations of the 9-CNS model (referred to as the first version), each brain or tumor compartment is treated as a homogeneous unit, assuming rapid equilibrium between interstitial and intracellular spaces for unbound drug distribution (FIG.5A). Under this assumption, predicted total and unbound drug concentrations (where unbound concentration = total concentration × unbound fraction in tissue) can be directly validated by comparing model outputs to measured concentrations from tissue homogenates. In some implementations of the 9-CNS model (referred to as the second version), the model structure is revised by subdividing each brain and tumor compartment into distinct interstitial and intracellular spaces to account for drugs that do not rapidly equilibrate between extra- and intracellular spaces, particularly those with intracellular targets (FIG. 5B). This feature enables separate prediction of interstitial and intracellular drug concentrations, providing a more accurate mechanistic link between drug exposure and pharmacological effects at the site of action. The differential equations marked with an asterisk (*) are included in the second version of the 9-CNS model and excluded from the first version of the 9-CNS model. The differential equations marked with two asterisks (**) are included in the first version of the 9-CNS model and excluded from the second version of the 9-CNS model.

[0092] The system-specific parameters including a description and their population mean values are summarized in Table 1. The drug-specific parameters are defined in Table 2. Table 1. System-specific parameters for the 9-CNS model.Page 25 of 72Page 26 of 72^. , app, →MDCKII cell monolayer; SA is the human brain microvasculature surface area (mean, 20 m2); and λ is unionization efficiency.b ^^^^^^^^,^^^ = ^^^^^^^^,^^^^^ × ^^ = ^^^^^^^^,^^^^^ × ^!^"#$"%^ ^" ^^^^^" ^^^^^ × ^&'^(^ × ^) (Eq.brain; BW is the average human brain weight; abundance in vivo or in vitro represents the ABCB1 / ABCG2 transporter protein expression level in human brain microvessels or in MDCKII- ABCB1 and –ABCG2 cells, respectively.cUnionization fraction (λ) is the ratio of unionized form to total drug (the sum of unionized and ionized forms), where the unionized-to-ionized ratio is calculated based on Henderson-Hasselbalch equation: ^*+ !$.^ (^^ ^"^^"^0^#),- $%^# (^^"^0^#) = 23 − ^56

[0093] Brain Blood. 78^!!!! 89 = :!^$^" (^$^^– ^!!)+^^^B (=!>B?@!>B^!>B − =!!?@!!^!!)+^^^^^,!!!B?@!>B^!>B−^^^A,!!!B?@!!^!!+^^C, (=C,?@C,^C, − =!!?@!!^!!)+^^^^^,C,?@C,^C,−^^^A,C,?@!!^!!+^^CB (=CB?@CB^CB − =!!?@!!^!!)+^^^^^,CB?@CB^CB−^^^A,CB?@!!^!!+^^CD (=CD?@CD^CD − =!!?@!!^!!)+^^^^^,CD?@CD^CD−^^^A,CD?@!!^!!−^^^A,%%.^?@!!^!!+:H.^"I^%%.^

[0094] Brain parenchyma 1 (brainCSF tract). 8^JK1= −+^^^A,!!!,?@!!^!!F=%%.^?@%%.^^%%.^ −−^^>^^,?@!>,^!>,** +^^N!>,(=^!>,?@^!>,^^!>, − =!>,?@!>,^!>,) *−^^N^A!>,^!>,* * *−^^>^^!>,^^!>,*

[0095] Brain parenchyma 2 (deep brain parenchyma). 8^ 7JK2JK2 = ^^^2 F=JJ?@JJ^JJ − =JK2?@JK2^JK2G+:!^^I,H^B^%%.^−:!^^I,^BH?@!>B^!>B−^^>^^B?@!>B^!>B**+^^N!>B(=^!>B?@^!>B^^!>B − =!>B?@!>B^!>B) *−^^N^A!>B^!>B* +^^N^^^!>B^^!>B* #HOPQV − *−^^>^^!>B^^!>B*

[0096] Tumor mass 1 (tumor rim). 8^ 7T1T1 89 = ^^T1 F=JJ?@JJ^JJ − =T1?@T1^T1G−:!^^I,C,^B?@C,^C,+:!^^I,CBC,?@CB^CB−:!^^I,C,CB?@C,^C,+:!^^I,HC,^%%.^−:!^^I,C,H?@C,^C,+^^NC,(=^C,?@^C,^^C, − =C,?@C,^C,) *−^^N^AC,^C,* +^^N^^^C,^^C,* *−^^N^^^C,^^C,* −^^>^^C,^^C,*

[0097] Tumor mass 2 (bulk tumor). 8^T2= −+^^^A,CB?@!!^!!+^^T1T2 −*−^^N^^^CB^^CB* −^^>^^CB^^CB*

[0098] Tumor mass 3 (tumor core). 8^ 7T3T3 = ^^T3 F=JJ?@JJ^JJ − =T3?@T3^T3G−:!^^I,CDCB?@CD^CD+:!^^I,HCD^%%.^−:!^^I,CDH?@CD^CD+^^NCD(=^CD?@^CD^^CD − =CD?@CD^CD) *−^^N^ACD^CD* +^^N^^^CD^^CD* *−^^N^^^CD^^CD* −^^>^^CD^^CD*

[0099] Ventricular CSF. 8^ 7'Z[?'Z[? 89 = ^^7 \=JJ?@JJ^JJ − ='Z[??@'Z[?^'Z[?]+:^^",^^%%.^

[0100] Cranial subarachnoid CSF. 8^ 7ZZ[?ZZ[? = +^^^1 \=JK1?@JK1^JK1 − =ZZ[??@ZZ[?^ZZ[?]−:!^^I,HC,^%%.^+:!^^I,C,H?@C,^C,−:!^^I,HCB^%%.^+:!^^I,CBH?@CB^CB − :!^^I,HCD^%%.^+:!^^I,CDH?@CD^CD+:^^",^^%.^−:^^",^^%%.^−:H.^"I^%%.^−:_^`,%%.^^%%.^

[0101] Spinal subarachnoid CSF. 8^ 7[Z[?[Z[? 89 = :^ab2^'Z[?−:^.^"I^.%.^−:^^"B^^.%.^−:_^`,.%.^^.%.^

[0102] Methods for solving differential equations. As presented above, the rates of change in the drug amounts (or concentrations) in individual compartments of the 9-CNS model are described by a set of non-homogeneous linear ordinary differential equations (ODEs). Initial value problems for ordinary differential equations are seldom solvable in closed form. Even when such solutions are available, understanding their behavior can still be challenging. To gain deeper insight, solutions are typically approximated numerically through discretization methods. The details of numerical methods for solving differential equations can be found in published papers (Atkinson et al., Numerical solution of ordinary differential equations; 2009; Cheney and Kincaid. Numerical mathematics and computing; 1998; Butcher JC. Numerical methods for ordinary differential equations; 2016; Teschl, supra; Brannan and Boyce, supra).

[0103] Several numerical techniques are available to solve systems of differential equations, including Euler’s method, Runge Kutta methods, and Adam’s method. While each method has its own advantage and disadvantages, the Livermore solver for ordinary differential equations (LSODE) was used to solve systems of the 9-CNS model (Radhakrishnan and Hindmarsh, supra). This solver is a part of the deSolve package, which is a powerful tool for handling differential equations within the R programming environment. The function ODE within the deSolve package returns the values of the state variables (columns) in the 9-CNS model at the requested time points.

[0104] For stiff system of differential equations, LSODE package uses the backward differentiation formula (BDF) method, which is among the most popular currently used for such problems (Gear CW. Numerical initial value problems in ordinary differential equations. 1971; Shampine L. J Comput Phys.1984;54(1):74-86). For example, if x'=((x_n-x_(n-1) ))⁄((t_n-t_(n-1)) ) is used to obtain a numerical approximation to the ordinary differential equation x^'=f(x,t), one obtains the Backward Euler method: x_n=x_(n-1)+(t_n-t_(n-1) )f(x_n,t_n). The LSODE package also includes the implicit Adams method (Lambert, supra), which is well-suited for non-stiff system of ordinary differential equations.

[0105] Application Validation. A 4-compartment permeability-limited CNS (4-CNS) PBPK model has been implemented in the Simcyp Simulator v18. The model structure, differential equations, and system-specific parameters for the 4-CNS model can be found in the published paper (Gaohua et al., Drug Metab Pharmacokinet. 2016;31(3):224-33). To validate the SpatialCNS- PBPK app, the 4-CNS PBPK model was packaged into the SpatialCNS-PBPK app using the same methodology as that for the 9-CNS model, and then compared the simulation results of the 4- CNS model from the Simcyp Simulator v18 and SpatialCNS-PBPK app.

[0106] Ribociclib was used as the model drug for 4-CNS model simulation comparison. First, simulations were performed with the Simcyp 4-CNS model to predict ribociclib concentration – time profiles in the plasma, brain mass, cranial and spinal CSF compartments in 100 Simcyp virtual cancer patients (e.g., 10 trials with 10 cancer patients in each trial) following oral administration of a single dose (600 mg). The drug- and system-specific parameters for ribociclib simulations with the Simcyp whole-body-4-CNS PBPK model have been published (Li et al., Clin Pharmacol Ther. 2021;109(2):494-506). Then, using the Simcyp model-simulated ribociclib plasma concentration – time profiles in individual 100 virtual patients as the input function, simulations were performed with the app 4-CNS PBPK model to predict the drug concentration – time profiles in the brain mass, cranial and spinal CSF compartments in the same 100 Simcyp virtual patients.

[0107] Based on the Simcyp and app simulated ribociclib concentration – time profiles for the 4 CNS compartments in the same 100 simcyp virtual patients, the mean, 5th, and 95th percentiles of concentration profiles in each compartment were generated. As shown in FIGs.6A and 6B, the mean and inter-individual variability (represented by 5th and 95th percentile) of ribociclib concentration profiles in each of 4 brain compartments generated from the app 4-CNS model simulations were well aligned with those generated from the Simcyp 4-CNS model simulations; and further correlation analysis indicated a Pearson’s correlation coefficient (R) of approximate 1 between the Simcyp and app 4-CNS model-simulated mean concentrations for each of 4 brain compartments. Collectively, these data suggest that the methodology such as the method for solving differential equations used in the SaptialCNS PBPK app is fully validated by an existing software Simcyp Simulator.

[0108] SpatialCNS-PBPK app features and user guide. The front page of the graphical userinterface (GUI) of SpatialCNS-PBPK consists of five tabs: About SpatialCNS-PBPK, Upload Data, 4-Compartment Model, 9-CNS Model, and Help. The "About SpatialCNS-PBPK" tab links to the SpatialCNS-PBPK documentation, providing detailed instructions on how to use the interface for running simulations together with a few demonstration videos. This tab also presents the model structure and includes sample input files for model simulations. The “Upload data” tab provides a space to upload the input file and obtain a summary report of the input file. The tabs for compartment models are to conduct simulations. The Help tab primarily allows users to contact the authors to clarify any questions they may have regarding the SpatialCNS-PBPK software and its output. Within the app, users have the opportunity to experience the following features: • Use two input panels for simulations and sensitivity analysis • Obtain concentration-time profiles for an individual and / or a group of individuals • Calculate PK parameters Cmax, Tmax, and AUC • Conduct sensitivity analysis • Simultaneously update outputs as inputs change • View and download plots and data tables through the three layers of the right panel

[0109] Model Simulations. Upload data. To upload data, the user must first prepare the required input file in .csv or .xlsx format, and then upload it from the user's local directory. Once the data file is uploaded, the user can view the uploaded data file and a summary report of the data file. Please refer to the rows of a sample input file prepared for 9-CNS model simulations, as shown in Table 3. Table 3: Example input parameters prepared for 9-CNS model

[0110] The first row (Time) in the input file lists all the time points. The second row (Plasma) contains the mean plasma concentrations corresponding to each time point in the first column. The third row (Parameters) shows the list of parameters in the system of ODEs used in the 9- CNS model. The fourth row (Sim) lists the mean values of these parameters. The fifth row (IIV) shows the inter-individual variability of the parameters. The sixth row (Subject) shows the patient ID. The purpose of this column (Subject) in the input file is to distinguish the observed data by patient. If the user has observed data, it can be included in rows six to twelve. This allows the observed data to be visualized together with the simulated data in plots for comparison purposes. The seventh row lists the observed time points of the tumor concentration in the non-enhanced region of the tumor. The eighth row contains the corresponding tumor concentrations for the time points in the seventh row. The ninth row lists the observed time points of the tumor concentration in the enhanced region of the tumor. The tenth row contains the corresponding tumor concentrations for the time points in the ninth row. The eleventh row lists the observed time points of the CSF concentration, and the twelfth row contains the corresponding CSF tumor concentrations for the time points in the eleventh row.

[0111] It is noted that the user is free to add as many rows as needed to the input file for the Time, Plasma, Sim, and IIV for different simulations. In some examples, the input file may be transposed. However, the row names should follow the sequence of the current row names. For example, if the user wants to add another set of parameters, the new row can be named Sim1.

[0112] Drug Plasma Concentration-Time Profile. The drug plasma concentration-time profile is used as the input function for the 9-CNS model simulations. Users need to provide this information in the columns named “Time” and “Plasma” in the input file. Drug plasma concentration-time profiles can be obtained from individual patients or a patient population. As described previously, population plasma pharmacokinetic analysis was performed to characterize the population mean and inter-individual variability (expressed as the 5thand 95th percentiles) of the plasma concentration-time profiles for the model drugs, which were subsequently applied as the input functions for the 9-CNS model simulations (J. Li, et al., Clin. Pharmacol. Ther.117 (2024): 690– 703). As an example, the input file template includes the population mean plasma concentration- time profile of abemaciclib determined from glioblastoma patients (Li 2024, supra). In addition to using the population mean plasma concentration-time profile as the input function to predict CNS pharmacokinetics in the “average” patient population, the observed plasma concentration-time profile in an individual patient can be used as the input function to predict CNS pharmacokinetics in that particular patient. Of note, observed drug plasma concentration data with either intensive or sparse sampling time can be used as the input function because the app internally convertsthe discrete drug plasma concentration-time profile to a continuous profile via linear interpolation.

[0113] System- and Drug-Specific Parameters. Users need to provide system-and drug-specific parameters in the column “Sim” in the input file (input parameters described elsewhere herein). The typical or reference values of the system-specific parameters for the 9-CNS model (as presented in Table 1 and input file template) were determined or assumed based on literature data (L. Sakka, et al., Eur Ann Otorhinolaryngol Head Neck Dis. 128 (2011): 309–316; K. P. Cosgrove, et al., Biol. Psychiatry.62 (2007): 847–855; C. S. Sinnatamby, Last's Anatomy (2011); H. F. Cserr, et al, Am. J. Physiol. 240 (1981): F319–F328; M. Edsbagge, et al., Am J Physiol Regul Integr Comp Physiol. 287 (2004): R1450–R1455) and further validated using 6 different drugs (Li 2024, supra). Users can use these typical values as the starting point for simulations and modify them if needed.

[0114] The drug-specific parameters are defined in Table 2. As an example, the input file template (input parameters described elsewhere herein) includes the drug-specific parameter values for abemaciclib, as published previously (Li 2024, supra). Users need to provide drug-specific parameter values for their model drugs. The methods for determination of drug-specific parameters were described briefly below, and details can be found in published papers (Li 2024, supra; Li 2022, supra; Li 2021, supra).

[0115] Mechanistic in vitro-in vivo extrapolation (IVIVE) strategy is used to predict in vivo passive clearance and transporter-mediated active efflux clearance at the BBB. Specifically, in vivo passive clearance at the BBB or BBTB, parameterized as the passive permeability-surface area product (PSB), can be estimated by scaling of the apical-to-basolateral apparent permeability (Papp,A−B) determined from in vitro epithelial cell model to the human brain / tumor microvasculature surface area (SA) using the equation: ^^^ = c^^^,^^^ ×^^^ ,where Papp,A−B is corrected by the unionization fraction (λ) of a drug because passive permeability allows only unbound and unionized drug to pass through (L. Gaohua, et al., Drug Metab Pharmacokinet.31 (2016): 224–233; J. Li, et al., Clin Pharmacol Ther.109 (2020): 494–506). The unionization efficiency (λ) is calculated using the Henderson-Hasselbalch equation: ^*+ J6[d (*e @ba*bafd8),- 6Za8 (a*bafd8) = 23 − ^5(Li 2022, supra; Li 2021, supra). The active efflux clearance at the BBB (CLefflux,BBB,) can be estimated based on the intrinsic efflux clearance (CLefflux,vitro) determined from in vitro transporter system using the equation: CLefflux,BBB= CLefflux,vitro× RAF × BMvPGB × BW,where CLefflux,vitrois the in vitro efflux transporter-mediated intrinsic clearance determined from MDCKII cells with stable expression of an efflux transporter (e.g., ABCB1 or ABCG2), RAF is the in vivo-in vitro relative activity factor of the transporter, BMvPGB is the milligrams of brain microvessels per gram brain / tumor, BW is the brain / tumor weight. Drug unbound fraction (Fu) in human plasma and brain / tumor can be experimentally determined from the plasma and brain tumor samples (A. C. Tien, et al., Clin Cancer Res 25 (2019): 5777–5786; S. Mehta, et al., Clin Cancer Res 28 (2022): 289–297; N. C. Y. Sanai, et al., J. Clin. Oncology 39, no.15_suppl (2021): 2005; T. Margaryan, et al., J. Pharm. Anal.12 (2022): 601–609; W. R. Kennedy, et al., Int J Radiat Oncol Biol Phys 117 (2023): e115; K. T. A. Johnson, et al., Neuro-Oncology 25 (2023): v78–v79; X. Bao, et al., J. Pharm. Anal.8 (2018): 20–26; X. Bao, et al., J. Pharm. Biomed. Anal.166 (2019): 197–204).

[0116] Set simulation inputs. The left panel under compartment models is divided into two main input sections as shown in FIGs.7A and 7B. In the top input section, the user can select the time profile, mean plasma concentration profile, a set of model parameter values, and a set of inter- individual variability values from the user-provided input file for the simulation. Additionally, the user has the option to enter the group size to run the simulation for a group of individuals. Moreover, the user can provide a time range to obtain the PK parameters AUC, Cmax, and Tmax. Once all the inputs are entered, the user can submit them by clicking the button at the bottom of the top input section to view and download the simulation results in the right panel.

[0117] Obtain simulation outputs. The right panel of the GUI is designed to display and download simulation output results through three layers. Once the file is uploaded and the inputs are submitted, users can view the simulation results in the main panel. Multiple outputs are generated when the simulation is carried out. The tabs in the second layer of the main panel consist of the following output options: • View mean profile simulation results • View group simulation results • View parameter sensitivity simulation results • Download mean profile simulation results • Download group simulation results • Download parameter sensitivity simulation results

[0118] The third layer is created to view and download the outputs for each component of the second layer. All the downloadable tables and plots for the 9-compartment model are shown in FIG.7C.

[0119] View and download mean profile simulation results. The “View mean profile simulationresults” tab consists of the following options: selected model parameters, concentration table, concentration plots, concentration log plots, and PK parameters. The tab for the selected model parameters shows a list of parameter values chosen for the simulation. The concentration table provides the time and concentration data of each compartment in the model. The concentration plots and the log concentration plots display time-concentration graphs for each compartment. It is noted that all the logarithmic plots displayed in the SpatialCNS-PBPK software are based on a base-10 logarithm. The PK parameters tab presents Cmax, Tmax, and AUC for each compartment of the brain model, which will be discussed in detail in a following section. All the outputs that can be viewed can also be downloaded through the download tabs. The tables can be downloaded as .csv files, while the plots can be downloaded in .pdf format.

[0120] FIGs.8A-8D show the simulated mean concentration-time profiles (in common logarithmic scale) of total abemaciclib in individual compartments of the 9-CNS model. The observed abemaciclib concentrations in the contrast-enhancing (shown with circles, FIGs.8B, 8C) and non- enhancing tumors (shown with triangles, FIGs. 8B, 8C) of glioblastoma patients are overlayed with the simulated mean total drug concentration-time profiles in the deep brain parenchyma compartment (Cbm2) and three tumor compartments including tumor rim (CT1), bulk tumor (CT2), and tumor core (CT3); the observed abemaciclib concentrations in CSF (shown with circles, FIG. 8D) are overlayed with the simulated mean total drug concentration-time profiles in three CSF compartments including ventricular CSF (Cvcsf), cranial subarachnoid CSF (Cccsf), and spinal subacrachnoid CSF (Cscsf, not shown).

[0121] Of note, if observed data are provided in the input file, observed data will be overlayed with the simulated profiles in the plots, thus allowing a direct visualization of how well the model predicts the observed data. As illustrated in FIGs.8A-8D, observed total drug concentrations of abemaciclib in the contrast-enhancing and non-enhancing tumors of glioblastoma patients are overlayed with the simulated mean total drug concentration—time profiles (in common logarithmic scale) for the deep brain parenchyma compartment (Cbm2) and three tumor compartments including tumor rim (CT1), bulk tumor (CT2), and tumor core (CT3); the observed total drug concentrations in CSF are overlayed with the simulated mean total drug concentration—time profiles for three CSF compartments including ventricular CSF (Cvcsf), cranial subarachnoid CSF (Cccsf), and spinal subacrachnoid CSF (Cscsf).

[0122] The PK parameters (i.e., Cmax, Tmax, and AUC) for total or unbound drug can be estimated based on the simulated mean total / unbound drug concentration—time profiles in individual CNS compartments. Users have the flexibility to define the time interval for PK parameter calculation. By clicking “Pharmacokinetic parameters (total / unbound)” tab, users canview or download the PK parameter tables for both total and unbound drug.

[0123] View and download group simulation results. The SpatialCNS-PBPK app has the capability of generating a patient population based on the mean values and interindividual variabilities (IIVs) of system-and drug-specific parameters that are provided in the input file. For example, if users want to generate a virtual population of n patients, the values of a particular system-or drug-specific parameter for these n patients are generated using the equation for Pvec shown below, where P is the mean parameter value provided in the input file, IIV is the interindividual variability for parameter P, Pvec is a vector of size n with list of IIV based parameter values, and Norm generates random numbers from a standard normal distribution. ^'dZ = d(ghijc √,lmmEVnl\oghi(,lmmEV)](^O)); q^~s*eK (0,1), a = 1, … , b

[0124] profile simulationresults" tab in Table 3. Time, Plasma, Sim, and IIV were selected from the input file to the top input section in the left panel. The group size is set to 5 by default. It is recommended to ignore the group size if user only want to run an individual simulation. It is only meaningful if the user wants to run simulation for a group of individuals. The time range to calculate PK parameters is set from 0 to 200 hours for this simulation. However, users have the opportunity to change the time range and observe the changes in the calculated parameters simultaneously. All the simulation output tabs will be displayed after submission, as shown in FIG.9A. Table 4. The concentration table presents concentration-time data of each compartment for the given time points through the input file. Due to its size, the content of the concentration table is not displayed entirely.ach compartment. Additionally, the observed data is incorporated into the concentration and log concentration plots so that users can assess whether the simulation results align with the observed data. Here, the concentrations of tumor-enhanced and tumor-nonenhanced substancesare plotted into compartments named Cbm2, CT1, CT2, and CT3, while tumor cerebrospinal fluid (CSF) concentrations are plotted into compartments named Cvcsf, Cccsf, and Cscsf. For brevity, a few concentration plots are displayed, as shown in FIGs. 9B and 9C with additional concentration data shown in Table 4. Table 5. Calculated pharmacokinetic parameters related to FIG. 9B and 9C. PK_par = pharmacokinetic parameters. etic(PK) parameters (Cmax, Tmax, and AUC) for individual simulations under "View mean profile simulation results" tab. In addition to viewing the estimated parameters through the interface, users can download the estimated parameter values into a data table (.csv file) under the "Download mean profile simulation" tab. Calculated pharmacokinetic parameters can be seen in Table 5 for the selected inputs above.

[0127] Example B. As an example, the disclosed model may generate a table that shows the parameter values of system-and drug-specific parameters for five individual patients, generated by the app based on the mean parameter values (Sim1) and respective interindividual variability (IIV1) provided in the input file (input parameters described elsewhere herein). Users have the flexibility of defining the group size (i.e., number of patients) for a virtual population and perform simulations for individual patients. Users can click “View simulated individual concentration-time profile” tab to view the simulated concentration data tables and profile plots (in either normal scale or normal logarithmic scale) for the total drug; in addition, users can download data tables as .csv files and plots as .pdf files. FIGs.11A-11C illustrate the simulated total drug concentration-time profiles of abemaciclib (in normal logarithmic scale) in individual CNS compartments for five individual patients. The system-and drug-specific parameters for five individuals were generated by the app based on the mean parameter values (Sim1) and respective IIVs (IIV1) provided in the input file. In addition, users can click “percentile plots” to view the mean, 5th and 95th percentiles of the simulated total drug concentration-time profiles (in normal scale or normal logarithmic scale)for a virtual population (FIGs.12A-12C). Of note, if observed data are provided in the input file, observed data will be overlayed with the simulated percentile profiles, thus allowing visualization of the distribution of both observed and simulated concentration profiles.

[0128] FIGs.12A-12C illustrate simulated mean, 5th and 95th percentiles of the concentration- time profiles (in common logarithmic scale) of total abemaciclib in individual compartments of the 9-CNS model from five individuals. The observed abemaciclib concentrations in the contrast- enhancing (shown with circles for Cbm2, CT1, CT2, and CT3) and non-enhancing tumors (shown with triangles for Cbm2, CT1, CT2, and CT3) of glioblastoma patients are overlayed with the simulated percentile concentration-time profiles in the deep brain parenchyma compartment (Cbm2) and three tumor compartments including tumor rim (CT1), bulk tumor (CT2), and tumor core (CT3); the observed abemaciclib concentrations in CSF (shown with circles for Cvcsf and Cccsf) are overlayed with the simulated percentile concentration-time profiles in three CSF compartments including ventricular CSF (Cvcsf), cranial subarachnoid CSF (Cccsf), and spinal subacrachnoid CSF (Cscsf, not shown here due to the space limit. As illustrated in FIGs.12A- 12C, observed total abemaciclib concentrations in the contrast-enhancing and non-enhancing tumors of glioblastoma patients are overlayed with the simulated percentile profiles (50th, 5th, and 95th) of total drug concentrations for the deep brain parenchyma compartment (Cbm2) and three tumor compartments (i.e., tumor rim CT1, bulk tumor CT2, and tumor core CT3); the observed abemaciclib concentrations in CSF are overlayed with the simulated percentile profiles (50th, 5th, and 95th) of drug concentration in the three CSF compartments.

[0129] Sensitivity Analysis. SpatialCNS-PBPK app provides sensitivity analysis function to examine the impact of a particular system-or drug-specific parameter on the concentration-time profiles in individual compartments of the 9-CNS model. This function is useful for parameter optimization to improve the model's predictivity. For example, to enable sensitivity analysis of a drug-specific parameter (e.g., PSB2, passive permeability clearance at the BBB between the blood and deep brain parenchyma compartments), users need to upload the input file (input parameters described elsewhere herein) and select the inputs for the sampling time (e.g., Time1), plasma concentration (e.g., Plasma1), and model parameter (e.g., Sim1); then, select the parameter name (e.g., PSB2), value range (e.g., from 2.5 to 250 L / h), and number of points (e.g., 5), and submit for sensitivity analysis (FIGs.7A, 7B). Of note, users can set the space between parameter points based on the uniform or normal logarithm of the parameter values. For example, when “uniform” is selected for parameter space, drug concentration-time profiles are simulated using the PSB values of 2.5, 64.4, 126.2, 188.1, and 250 L / h. When “log” is selected for parameter space, drug concentration-time profiles are simulated using the PSB values of 2.5, 7.9, 25, 79,and 250 L / h (FIGs.13A-13C).

[0130] View and download parameter sensitivity simulation results. After sensitivity analysis is submitted, users can click “View parameter sensitivity simulation results” or “Download parameter sensitivity simulation results” tab to view or download the simulated concentration data tables and profile plots (in either normal scale or normal logarithmic scale) for total or unbound drug, as well as the calculated PK parameters (i.e., Tmax, Cmax, and AUC) and AUC scatter plot (i.e., the plot of AUC versus tested parameter values). For example, for sensitivity analysis of PSB2 ranging from 2.5 to 250 L / h (at 5 parameter points using log space), FIGs.13A-13C illustrate a sensitivity analysis of the impact of PSB2 (passive permeability clearance at the BBB between the blood and deep brain parenchyma compartments) on the total abemaciclib concentration—time profiles in individual CNS compartments. Sensitivity analysis was performed with the PSB2 values of 2.5, 7.9, 25, 79, and 250 L / h while other parameters remain the same as provided in the input “Sim1”. The total drug concentration-time profiles in individual compartments simulated with the PSB2 values of 2.5, 7.9, 25, 79, and 250 L / h while other parameters remain the same as defined in the input “Sim1”. These data suggest that PSB2 significantly influences abemaciclib pharmacokinetic profile in the deep brain parenchyma compartment, while having negligible impacts on the PK profiles in other compartments.

[0131] Based on the simulated concentration-time profiles, the SpatialCNS-PBPK app is capable of calculating PK parameters (i.e., Tmax, Cmax, and AUC) for any user-defined time interval (e.g., 72–96 h). Users can view or download PK parameter tables for total and unbound drug. In addition, users can view or download the AUC scatter plots, which provide a direct visualization of the impact of the tested parameter (e.g., PSB2) on drug exposure (AUC) in individual CNS compartments. FIGs. 14A-14C illustrate a sensitivity analysis of the impact of PSB2 (passive permeability clearance at the BBB between the blood and deep brain parenchyma compartments) on the total abemaciclib drug exposure (i.e., AUC) in individual CNS compartments. Sensitivity analysis was performed with the PSB2 values of 2.5, 7.9, 25, 79, and 250 L / h while other parameters remain the same as provided in the input “Sim1”. As illustrated in FIGs. 14A-14C, PSB2 has a significant impact on the total drug exposure (AUC) of abemaciclib in the deep brain parenchyma, but not in the other CNS compartments.

[0132] Example B. In this Example, several output results from a sensitivity analysis are presented. The parameter PSB1B2 is selected for the sensitivity analysis. Three parameter points are entered within the range from 0.01 to 100. This means that three equally spaced parameter values within the range from 0.01 to 100 are generated for the parameter PSB1B. The time range for the PK parameters is set from 0 to 200 and the outputs will be discussed in the next section.Output tabs of the sensitivity analysis results will be displayed after submitting the input and selecting the view tab of the sensitivity analysis, as shown in FIG.10A.

[0133] The concentration table provides concentration data for all compartments. For example, if the number of parameter points entered is 3, then five concentration columns will be generated for each compartment. The concentration table is lengthy and thus is not displayed in FIGs.10A and 10B. The concentration profiles of six compartments are shown in FIG. 10B for simplicity. From FIG.10B, it is concluded that concentrations in the compartments Cbm1, Cbm2, Cvcsf, and Cccsf are sensitive to changes in the parameter PBB1B2. Additionally, users can observe changes in sensitivity plots while simultaneously changing the inputs. All features available for sensitivity analysis can also be downloaded as .csv files for tables and .pdf files for plots.

[0134] While performing a sensitivity analysis, the user can calculate the PK parameters by simultaneously changing the following inputs: • The parameter of interest in the sensitivity analysis • The minimum value of the selected parameter • The maximum value of the selected parameter • The number of parameter points within the selected range • The minimum time point to obtain PK parameters • The maximum time point to obtain PK parameters

[0135] Example C. This Example demonstrates how to calculate PK parameters and AUC scatter plots via sensitivity analysis. For this purpose, the parameter PSB1B2 was selected, the range of the parameter values was set to 0.01 to 10, the number of parameters to generate within the given range was set to 10, and the time range for the PK parameters was set to 0 to 200 hours. The PK parameters and the scatter plots of AUC can be viewed tabs under “View parameter sensitivity simulation results” tab. A data table (.csv file) of PK parameters will be created for every change made and can be downloaded through the "Download parameter sensitivity simulation" tab. The complete list of estimated parameter table is lengthy and thus is not displayed. However, a part of the table is displayed as shown in Table 6.

[0136] Scatter plots of parameter values versus AUC for all the compartments can be generated under the "AUC scatter plots" tab. For brevity the first four scatter plots in the model are presented, as shown in FIG. 15B. The user can observe the changes in the AUC scatter plots for every change of the input stated above.Table 6. Estimated parameters associated with FIGs.15A and 15B. The rows, from top to bottom, correspond to: Parameter_values, Cbb_C_max, Cbb_T_max, Cbb_AUC, NA, Cbm1_C_max, Cbm1_T_max, Cbm1_AUC, NA, Cbm2_C_max, Cbm2_T_max, Cbm2_AUC, NA, CT1_C_max, CT1_T_max, and CT1_AUC.of abemaciclib, ribociclib, pamiparib, olaparib, temuterkib, and ceritinib. The circle symbols, cross symbols, and chevron symbols mark the mean, 5thand 95thpercentiles of the drug plasma concentration – time profiles, respectively, simulated by 1000 bootstraps using the population pharmacokinetic models. The corresponding dashed lines represent respective 95% confident intervals. The triangle symbols represent observed drug plasma concentrations in glioblastoma patients following the clinical standard dosing regimens.

[0138] Spatial pharmacokinetics in the human CNS. The nine-CNS PBPK model allows prediction of spatial pharmacokinetics in two distinct brain parenchyma compartments that represent the brain tissue adjacent to the CSF tract and deep brain parenchyma (at a distance > 2 mm away from the CSF tract). This assumption is based on the experimental evidence of different mechanisms governing drug distribution between the CSF and brain parenchyma.Generally, size-dependent simple diffusion efficiently facilitates drug distribution between the ventricular or cranial subarachnoid CSF and the adjacent brain tissue,14 thus leading to a rapid equilibrium and thereby similar unbound drug exposure in the CSF tract and adjacent brain tissue. This is demonstrated by 5 of 6 drugs (i.e., abemaciclib, ribociclib, pamiparib, olaparib, and temuterkib) (FIGs. 17A-17C, 18A-18C, 19A-19C, 21A, 21B). In FIGs. 18A-18C, solid lines represent model-predicted drug concentration – time profiles in the ventricular, cranial and spinal subarachnoid CSF, using the population mean drug plasma concentration – time profiles as the input function. Different dashed lines represent respective drug CSF concentration – time profiles using the 5thand 95thpercentiles of drug plasma concentration – time profiles as the input function. Circle symbols represent observed drug concentrations in CSF samples (most of which were collected from cranial ventricles) in glioblastoma patients. In FIGs.19A-19C, solid lines represent model-predicted drug concentration – time profiles using the population mean drug plasma concentration – time profiles as the input function. Different dashed lines represent respective drug concentration – time profiles using the 5thand 95thpercentiles of drug plasma concentration – time profiles as the input function. Open circles and open triangles represent observed drug concentrations in the non-enhancing and enhancing tumors of glioblastoma patients. Of note, the non-enhancing and enhancing tumor samples were collected at the same time in patients, but the sampling times are shown at 24 h interval for easy visualization. FIGs.21A, 21B illustrate the 9- CNS model-predicted and observed unbound drug steady-state concentrations in the brain, tumor, and CSF for abemaciclib, ribociclib, pamiparib, olaparib, temuterkib, and ceritinib. The model-predicted unbound drug steady-state concentrations are shown as the median values with the 5th and 95th percentiles predicted using the mean, 5th and 95th percentiles of the population plasma concentration–time profiles as the input function, respectively. Observed unbound drug concentrations are shown as the median values with the 5th and 95th percentiles from 39 patients for abemaciclib, 20 patients for ribociclib, 40 patients for pamiparib, 6 patients for olaparib, 39 patients for temuterkib, and 9 patients for ceritinib. Cbm1, brain mass 1 (adjacent brain parenchyma); Cbm2, brain mass 2 (deep brain parenchyma); Cccsf, cranial subarachnoid CSF; Cscsf, spinal subarachnoid CSF; CT1, tumor rim; CT2, bulk tumor; CT3, tumor core; Cvcsf, ventricular CSF; Obs_CSF, observed data in CSF; Obs_ENT, observed data in contrast- enhancing tumor region Obs_NET, observed data in non-enhancing tumor region.

[0139] However, ceritinib is an exception, for which unbound drug exposure in the adjacent brain tissue is 10-fold lower than that in the CSF. This could be explained by the extremely slow equilibrium between the CSF and adjacent brain tissue because the extremely high binding of ceritinib to brain / tumor tissue (with the median unbound fraction of 0.0005 in glioblastomapatients), instead of simple drug diffusion from the CSF to adjacent tissue, becomes the rate- limiting determinant of the equilibrium.

[0140] Simple diffusion is inefficient for drug distribution between the CSF and the deep brain parenchyma (at the distance > 2 mm away from the CSF tract) (Blasberg, R.G., et al. J. Pharmacol. Exp. Ther. 195, 73–83 (1975)). Instead, convective bulk flow along paravascular spaces (i.e., glymphatic pathway) is the preferential pathway for CSF-brain interstitial fluid exchange and interstitial solute clearance (Iliff, J.J. et al. Sci. Transl. Med. 4, 147ra11 (2012); Abbott, N.J. Neurochem. Int.45, 545–552 (2004)). Since the paravascular bulk flow is relatively slow (with an estimated average bulk flow rate of 0.15 μL / min / g or 0.0126 L / h given an average human brain weight of 1,400 g) (Abbott, supra; Cserr, H.F., et al. Am. J. Physiol.240, F319–F328 (1981)), the unbound drug exposure in the deep brain parenchyma is mainly driven by the extent of drug penetration across the BBB (as assessed by Kp,uu). The Kp,uu is determined by the relative contribution of passive clearance and transporter-mediated active clearance at the BBB. When the BBB transport of a drug is dominated by passive permeability, the Kp,uu would be close to 1; whereas when a drug is actively transported by efflux transporters at the BBB, the Kp,uu would be significantly smaller than 1.0. Consistent with this rationale, the model-predicted mean Kp,uu in the deep brain parenchyma is > 0.3 for weak substrates of ABCB1 and ABCG2 (abemaciclib and pamiparib), while ranging from 0.003 to 0.06 for strong ABCB1 / ABCG2 substrates (ribociclib, olaparib, temuterkib, and ceritinib) (FIGs.20A, 20B, Tables 7 and 8).

[0141] FIGs. 20A, 20B illustrate the 9-CNS model-predicted and observed unbound drug brain / tumor / CSF-to-plasma partition ratio (Kp,uu) for abemaciclib, ribociclib, pamiparib, olaparib, temuterkib, and ceritinib. The model-predicted Kp,uu are shown as the median values predicted using the population mean plasma concentration—time profile as the input function. Observed Kp,uu are shown as the median with the 5thand 95th percentiles of the data from 39 patients for abemaciclib, 20 patients for ribociclib, 40 patients for pamiparib, 6 patients for olaparib, 39 patients for temuterkib, and 9 patients for ceritinib. Cbm1, brain mass 1 (adjacent brain parenchyma); Cbm2, brain mass 2 (deep brain parenchyma); CT1, tumor rim; CT2, bulk tumor; CT3, tumor core; Cvcsf, ventricular CSF; Cccsf, cranial subarachnoid CSF; Cscsf, spinal subarachnoid CSF; Obs_NET, observed data in non-enhancing tumor region; Obs_ENT, observed data in contrast-enhancing tumor region; Obs_CSF, observed data in CSF.

[0142] FIGs.21A, 21B illustrate the 9-CNS model-predicted and observed unbound drug steady- state concentrations in the brain, tumor, and CSF for (a) abemaciclib, (b) ribociclib, (c) pamiparib, (d) olaparib, (e) temuterkib, and (f) ceritinib. The model-predicted unbound drug steady-state concentrations are shown as the median values with the 5th and 95th percentiles predicted usingthe mean, 5th and 95th percentiles of the population plasma concentration–time profiles as the input function, respectively. Observed unbound drug concentrations are shown as the median values with the 5th and 95th percentiles from 39 patients for abemaciclib, 20 patients for ribociclib, 40 patients for pamiparib, 6 patients for olaparib, 39 patients for temuterkib, and 9 patients for ceritinib. Cbm1, brain mass 1 (adjacent brain parenchyma); Cbm2, brain mass 2 (deep brain parenchyma); Cccsf, cranial subarachnoid CSF; Cscsf, spinal subarachnoid CSF; CT1, tumor rim; CT2, bulk tumor; CT3, tumor core; Cvcsf, ventricular CSF; Obs_CSF, observed data in CSF; Obs_ENT, observed data in contrast-enhancing tumor region Obs_NET, observed data in non- enhancing tumor region. Table 7. 9-CNS model-predicted pharmacokinetic parameters for pharmacologically active (unbound) drugs. Css, steady-state unbound drug concentration; Kp,uu, brain / tumor / CSF-to-plasma unbound drug concentration ratio.aData are shown as the model-predicted median steady-state concentration with the 5th and 95th percentiles in the parenthesis, using the mean, 5th and 95th percentiles of the population plasma concentration–time profiles as the input function, respectively.bData are shown as the model-predicted median Kp,uu, using the population mean plasma concentration—time profile as the input function.tive(unbound) drugs in glioblastoma patients. Observed data are shown as the median with the 5thand 95thpercentiles in the parenthesis. Observed data are obtained from 39 patients for abemaciclib, 20 patients for ribociclib, 40 patients for pamiparib, 6 patients for 50laparib, 39 patients for temuterkib, and 9 patients for ceritinib. Css, steady-state unbound drug concentration; Kp,uu, brain / tumor / CSF-to-plasma unbound drug concentration ratio.atedrugs, ABCB1 may facilitate the drug transport from the circulation blood to ventricular CSF given its location at the apical, CSF-facing side of the choroid plexus epithelial cells (which form the blood–CSF barrier) (Rao, V.V. et al. Proc. Natl. Acad. Sci. USA 96, 3900–3905 (1999)). It is therefore not surprising that the model-predicted mean Kp,uu, and unbound drug Cssin the ventricular or cranial subarachnoid CSF are > 10-fold (ranging from 13-to 133-fold) of those achieved in the deep brain parenchyma for strong ABCB1 / ABCG2 substrates (ribociclib, olaparib, temuterkib, and ceritinib) (FIGs.20A, 20B, 21A, and 21B; Tables 7 and 8). These data further support the notion that CSF concentrations over-estimate unbound drug brain concentrations for drugs undergoing dominant active transport at the BBB (Pardridge, W.M. Fluids Barriers CNS 8, 7 (2011)). On the contrary, for weak substrates of ABCB1 and ABCG2 (abemaciclib and pamiparib), the model-predicted mean Kp,uuand unbound drug Cssin the ventricular or cranial subarachnoid CSF are similar to those achieved in the deep brain parenchyma, suggesting that CSF concentrations could be a surrogate of unbound drug brain concentrations for drugs transporting across the BBB by passive permeability.

[0144] Within the CSF system, drugs move along with the CSF circulation through the ventricle and cranial / spinal subarachnoid spaces and are subsequently absorbed into the blood circulation via the CSF bulk flow (Hladky & Barrand. Fluids Barriers CNS 11, 26 (2014)). The 9-CNS PBPK model allows prediction of spatial pharmacokinetics in the 3 CSF compartments representing the ventricular CSF, cranial subarachnoid CSF, and spinal subarachnoid CSF. For all six drugs, the ventricular and cranial subarachnoid CSF share similar drug concentration–time profiles, while the spinal subarachnoid CSF presents lower drug exposure (FIGs.17A-17C, 18A-18C, 19A-19C, 21A, and 21B). The different pharmacokinetic profiles in the ventricular / cranial CSF and spinal CSF could be explained by the anatomical structure and dynamics of the CSF circulation system, whereby drugs quickly distribute and equilibrate between the ventricular and cranial subarachnoid CSF due to anatomical adjacency while drug concentrations may be diluted in the spinal subarachnoid CSF because of its larger volume (80 mL) as compared with the ventricular CSF (25 mL) or cranial subarachnoid CSF (45 mL) (Sakka, L., et al. Eur. Ann. Otorhinolaryngol. Head Neck Dis.128, 309–316 (2011)). While lumbar punction is often used to collect CSF samples for drug measurement, it should be cautious to use lumbar or spinal CSF drug concentrations as the surrogate of ventricular or cranial CSF drug concentrations.

[0145] Notably, the CSF concentrations of all six drugs exhibit large inter-individual variability in glioblastoma patients. This variability is likely attributable, in large part, to the inter-individual plasma pharmacokinetic variability. As demonstrated by model simulations, when using the 5th and 95th percentiles of population plasma concentration–time profiles as the input function, the model-predicted drug concentration–time profiles in the ventricular / cranial CSF capture the majority of the clinically observed CSF drug concentrations (FIGs.18A-18C and 19A-19C). The remaining inter-individual variability of CSF drug concentrations could be further explained by the heterogeneity of blood–CSF barrier integrity and CSF circulation dynamics. When using the population mean plasma concentration–time profile of each drug following the standard clinical dosing regimen as the input function, the model-predicted unbound drug Css in the ventricular / cranial subarachnoid CSF is within twofold of the observed median ventricular CSF drug concentration in glioblastoma patients (FIGs.21A and 21B; Tables 7 and 8). Collectively, these data indicate that the 9-CNS PBPK model well predicts the CSF pharmacokinetics and its inter-individual variability for all six drugs as observed in glioblastoma patients.

[0146] Spatial pharmacokinetics in brain tumors. Large inter-individual and intra-tumoral variabilities were observed in the extent of drug tumor penetration (as assessed by Kp,uu) and drug exposure (as assessed by unbound drug Css) for all six drugs in glioblastoma patients (FIGs.18A- 18C, 19A-19C, 20A, 20B, 21A, and 21B; Tables 7 and 8). The variability in drug tumor penetration (Kp,uu) is mainly attributable to the pathophysiological heterogeneity of tumors, in terms of the BBTB integrity, efflux transporter expression levels, tumor interstitial pH (influencing drug ionization), tissue composition (influencing drug tissue binding), and paravascular bulk flow rates. The variability in drug tumor exposure (Css) is driven by both tumor heterogeneity and plasma pharmacokinetic variability.

[0147] The 9-CNS model incorporates regional heterogeneity in the normal brain parenchyma and three-tumor regions, thus enabling the prediction of spatial heterogeneity of drug brain / tumor penetration. Compared with the normal brain parenchyma (represented by the deep brain parenchyma), the 3 tumor compartments (from tumor rim, bulk tumor, to tumor core) are characterized by the increased BBTB disruption, decreased loss of efflux transporter expression at the BBTB, increased acidity of tumor interstitial pH, and change of paravascular bulk flow. As demonstrated by the 6 study drugs, the extent of drug penetration (Kp,uu) is generally enhanced from the normal brain parenchyma to tumor rim and to the bulk tumor and tumor core (FIGs.20A and 20B; Tables 7 and 8). The model-predicted median Kp,uufrom the deep brain parenchyma to tumor rim, bulk tumor, and tumor core is increased 2.6-, 7.4-, and 22-folds, respectively (Kp,uuranging from 0.90 to 19.5) for abemaciclib; 16-, 82-, and 256-folds, respectively (Kp,uurangingfrom 0.06 to 15.3) for ribociclib; 1.6-, 3.0-, and 3.5-folds, respectively (Kp,uuranging from 0.33 to 1.17) for pamiparib; 2.0-, 12-, and 22-folds, respectively (Kp,uuranging from 0.02 to 0.44) for olaparib; 4.0-, 22-, and 44-folds (Kp,uuranging from 0.04 to 1.63) for temuterkib; 14-, 170-, and 757-folds (Kp,uuranging from 0.003 to 2.50) for ceritinib. Notably, for all six drugs, the clinically observed drug penetration (Kp,uu) into the non-enhancing and enhancing tumors of glioblastoma patients are largely overlapped while falling within the predicted Kp,uu ranges across the normal brain parenchyma and three-tumor compartments (FIGs.20A and 20B; Tables 7 and 8), indicating that the 9-CNS PBPK model well predicts the large intra-tumoral and inter-individual variability in the extent of drug tumor penetration as observed in glioblastoma patients.

[0148] When considering the inter-individual plasma pharmacokinetic variability together with brain / tumor heterogeneity, the 9-CNS model well predicts the inter-individual and intra-tumoral variability of drug tumor exposure (Css) for all six drugs. As shown in FIGs. 21A and 21B and Tables 7 and 8, using the 5th and 95th percentiles of population plasma concentration–time profiles as the input function, the model-predicted unbound drug steady-state concentrations (Css) across the deep brain parenchyma and 3 tumor compartments range from 3.5 to 406 nmol / L for abemaciclib, 5.0 to 4,577 nmol / L for ribociclib, 30 to 944 nmol / L for pamiparib, 0.3 to 141 nmol / L for olaparib, 0.3 to 367 nmol / L for temuterkib, and 0.05 to 86 nmol / L for ceritinib. The predicted unbound drug Css ranges well capture the clinically observed unbound drug concentrations in the non-enhancing and contrast-enhancing tumors of glioblastoma patients for all six drugs (FIGs. 21A and 21B; Tables 7 and 8).

[0149] As illustrated by the six drugs, when using the population mean plasma concentration– time profiles as the input function, the model-predicted mean unbound drug Css in the deep brain parenchyma and 3 tumor compartments range from 8.3 to 179 nmol / L for abemaciclib, 9.4 to 2,307 nmol / L for ribociclib, 90 to 317 nmol / L for pamiparib, 2.4 to 53 nmol / L for olaparib, 2.1 to 91 nmol / L for temuterkib, and 0.1 to 71 nmol / L for ceritinib (FIGs.21A and 21B; Tables 7 and 8). Because adequate target engagement is required for intracranial activity, target engagement ratio, defined as the ratio of unbound drug Css to in vitro IC50 for target inhibition (determined from cell-free assays), can be used as a crude indicator of potential efficacy. Given the determined in vitro IC50for target inhibition, the mean target engagement ratios achieved in the deep brain parenchyma and three-tumor compartments are predicted to be 4.2– 90 for abemaciclib inhibition of CDK4 (IC50, 2 nmol / L), 0.9–231 for ribociclib inhibition of CDK4 (IC50, 10 nmol / L), 100–352 for pamiparib inhibition of PARP1 / 2 (IC50, 0.9 nmol / L), 0.5–11 for olaparib inhibition of PARP1 / 2 (IC50, 5 nmol / L), 0.4–18 for temuterkib inhibition of ERK1 / 2 (IC50, 5 nmol / L), and 0.5–355 for ceritinib inhibition of ALK (IC50, 0.2 nmol / L). Notably, while the drug penetration and exposure areenhanced in tumor regions for ribociclib, olaparib, temuterkib, and ceritinib, the target engagement ratios of these drugs in the deep brain parenchyma (< 1) are probably insufficient (< 50% target inhibition) for elimination of infiltrating tumor cells or micrometastases. By contrary, abemaciclib and pamiparib are predicted to achieve adequate target inhibition in not only tumor regions with disrupting BBB but also infiltrating tumor cells behind an intact BBB. These data suggest that abemaciclib and pamiparib would be better drug candidates than the other four drugs (i.e., ribociclib, olaparib, temuterkib, and ceritinib) for further clinical development to treat parenchyma brain tumors (e.g., glioblastoma) especially as adjuvant therapy. In fact, abemaciclib has demonstrated clinical efficacy in a phase I / II clinical trial where three glioblastoma patients achieved stable disease on single-agent abemaciclib treatment, and two of them continued the treatment without progression for nearly 2 years (Patnaik, A. et al. Cancer Discov. 6, 740–753 (2016)).

[0150] Notably, the 9-CNS PBPK model allows prediction of spatial pharmacokinetics in two distinct brain parenchyma compartments that represent the brain tissue adjacent to the CSF tract and deep brain parenchyma at a distance > 2 mm away from the CSF tract. For all six drugs, the model-predicted drug exposure in the brain tissue adjacent to the CSF tract is similar to that in the CSF (FIGs.17A-17C, 18A-18C, 19A-19C, 21A, and 21B). Accordingly, the predicted mean target engagement ratio in the adjacent brain tissue is 4.8 for abemaciclib inhibition of CDK4, 8.5 for ribociclib inhibition of CDK4, 276 for pamiparib inhibition of PARP1 / 2, 14 for olaparib inhibition of PARP1 / 2, 7 for temuterkib inhibition of ERK1 / 2, and 5 for ceritinib inhibition of ALK, indicating potentially adequate target inhibition is likely achieved in brain tissue adjacent to the CSF tract.

[0151] Conclusion. This Experimental Example describes the development of a novel 9-CNS PBPK model that enables prediction of spatial pharmacokinetic profiles of systemically administered small-molecule drugs in the 9 CNS compartments, including the brain blood, 2 distinct brain parenchyma compartments (representing brain tissue adjacent to the CSF tract and deep brain parenchyma), 3 CSF compartments (representing ventricular CSF, cranial and spinal subarachnoid CSF), and 3 brain tumor compartments (representing tumor rim, bulk tumor, and tumor core). This Experimental Example describes the development of a user-friendly, web-based R / Shiny platform, SpatialCNS-PBPK app, which allows a broad range of users to easily apply the developed 9-CNS model. The methodology and simulation functions of the SpatialCNS-PBPK app is fully validated by comparison with a commercial PBPK software (Simcyp Simulator), whereby the simulated pharmacokinetic profiles of a model drug (ribociclib) in an existing 4-CNS PBPK model from the app are in line with those from the Simcyp Simulator. The SpatialCNS-PBPK app has functions for model simulation, sensitivity analysis, and PKparameter calculation. This tutorial provides a user guide with examples to demonstrate how to use these functions as well as view and download the results. In addition, the tutorial provides theoretical context and practical demonstrations of executing certain R functions, ensuring that users have a thorough understanding of the SpatialCNS-PBPK app functionality rather than treating it as a black box, though using the app does not demand advanced statistical or programming skills. The SpatialCNS-PBPK is launched as an open-source initiative and can be accessed at: pbpkcharuka.shinyapps.io / SpatialCNS_PBPK_2024_V1 / . The 9-CNS PBPK model offers a unique advantage by enabling the prediction of spatiotemporal drug penetration and exposure in the human CNS and brain tumors based on plasma concentration–time profiles, irrespective of the route of systemic drug administration. Since drug plasma concentrations can be readily measured in individual patients or a population, this model serves as a powerful computational tool for prospectively and reliably predicting spatial pharmacokinetics in the human CNS and brain tumors across various clinical settings and patient populations. The quantitative insights gained from this model are invaluable for guiding efficient clinical trial designs, selecting optimal drug candidates, and refining dosing regimens. Notably, a significant challenge in treating brain tumors is the substantial inter-individual variability and spatial heterogeneity in drug penetration and exposure, making one-size-fits-all treatment strategies often ineffective. The 9- CNS PBPK model addresses this challenge by enabling individualized dosing regimens. By leveraging observed plasma concentration–time profiles and patient-specific brain or tumor characteristics, the model can predict drug exposure in the CNS and tumors in an individual patient. If the predicted drug exposure is suboptimal, alternative dosing regimens can be simulated to determine the optimal strategy for achieving therapeutic drug concentrations in the brain and tumor tissue.

[0152] The disclosed model enhances the ability to predict the spatial pharmacokinetics of anticancer drugs in the human CNS and brain tumors with greater accuracy and efficiency. This invaluable computational tool supports the development of more effective therapies and the optimized use of existing drugs, thereby improving treatment outcomes for brain cancer patients. EXEMPLARY EMBODIMENTS 1. A method including: identifying input data including plasma concentration of a drug over time; determining, by one or more processors, a metric associated with a concentration of the drug in at least two brain regions including: at least two regions of a brain mass; orat least one region of the brain mass and at least one region of a brain tumor; generating, by the one or more processors, an output indicative of the metric. 2. The method of embodiment 1, wherein regions of the brain mass include: cerebrospinal fluid (CSF) adjacent brain tissue or deep brain tissue. 3. The method of embodiment 1 or 2, wherein regions of the brain tumor include: tumor rim, bulk tumor, or tumor core. 4. The method of any of embodiments 1-3, wherein the at least two brain regions further include a brain blood region. 5. The method of any of embodiments 1-4, wherein the at least two brain regions further include at least one CSF region. 6. The method of embodiment 5, wherein the at least one CSF region includes: ventricular CSF, cranial CSF, or spinal CSF. 7. The method of any of embodiments 1-6, wherein the at least two brain regions include 2, 3, 4, 5, 6, 7, 8, 9, or more than 9 brain regions. 8. The method of any of embodiments 1-7, wherein the input data further includes drug- specific parameters and system-specific parameters. 9. The method of embodiment 8, wherein the system-specific parameters include at least one of a region volume, a cerebral blood flow, a CSF absorption rate, a CSF flow rate, a CSF back flow rate, a paravascular bulk flow rate, or a convective bulk flow rate. 10. The method of embodiment 9, wherein the region volume includes at least one of a volume of brain blood, a volume of adjacent brain tissue, a volume of deep brain tissue, a volume of tumor rim region, a volume of tumor bulk region, a volume of tumor core region, a volume of ventricular CSF, a volume of cranial CSF, a volume of spinal CSF., 11. The method of embodiment 9 or 10, wherein the CSF absorption rate includes at least one of an absorption rate of cranial CSF into blood circulation through arachnoid villi, an absorption rate of spinal CSF into blood circulation through arachnoid villi, an absorption rate of cranial CSF via olfactory mucosa and cranial nerve sheaths, or an absorption rate of spinal CSF via spinal nerve sheaths. 12. The method of any of embodiments 9-11, wherein the CSF flow rate includes at least one of a CSF flow rate from a ventricular space to a cranial space, a CSF flow rate from the ventricular space to a spinal space, a CSF flow rate from the spinal space to the cranial space, or a CSF flow rate from the cranial space to the spinal space.13. The method of any of embodiments 9-12, wherein the CSF back flow rate includes a CSF back flow rate from a cranial space to a ventricular space and / or a CSF back flow rate from a spinal space to a ventricular space. 14. The method of any of embodiments 9-13, wherein the paravascular bulk flow rate includes at least one of a paravascular bulk flow rate from cranial CSF to CSF adjacent brain tissue, a paravascular bulk flow rate from CSF adjacent brain tissue to cranial CSF, a paravascular bulk flow rate from ventricular CSF to CSF adjacent brain tissue, a paravascular bulk flow rate from CSF adjacent brain tissue to ventricular CSF, a paravascular bulk flow rate from cranial CSF to deep brain tissue, a paravascular bulk flow rate from deep brain tissue to cranial CSF, a paravascular bulk flow rate from cranial CSF to tumor rim, a paravascular bulk flow rate from tumor rim to cranial CSF, a paravascular bulk flow rate from cranial CSF to tumor bulk, a paravascular bulk flow rate from tumor bulk to cranial CSF, a paravascular bulk flow rate from cranial CSF to tumor core, or a paravascular bulk flow rate from tumor core to cranial CSF. 15. The method of any of embodiments 9-14, wherein the convective bulk flow rate includes at least one of a convective bulk flow rate from CSF adjacent brain tissue to deep brain tissue, a convective bulk flow rate from deep brain tissue to CSF adjacent brain tissue, a convective bulk flow rate from deep brain tissue to tumor rim, a convective bulk flow rate from tumor rim to deep brain tissue, convective bulk flow rate from tumor rim to tumor bulk, a convective bulk flow rate from tumor bulk to tumor rim, a convective bulk flow rate from tumor bulk to tumor core, or a convective bulk flow rate from tumor core to tumor bulk. 16. The method of any of embodiments 8-15, wherein the drug-specific parameters include at least one of: a passive permeability clearance, a simple diffusion rate, a transporter-mediated clearance, a metabolic clearance in a region of the brain mass, an unbound fraction in a region, or a unionized drug fraction in a region. 17. The method of embodiment 16, wherein the passive permeability clearance includes at least one of a passive permeability clearance at a blood-brain barrier (BBB) between brain blood and CSF adjacent brain tissue, a passive permeability clearance at the BBB between brain blood and deep brain tissue, a passive permeability clearance at a blood-brain tumor barrier (BBTB) between brain blood and tumor rim, a passive permeability clearance at the BBTB between brain blood and bulk tumor, a passive permeability clearance at the BBTB between brain blood and tumor core, a passive permeability clearance at a blood-CSF barrier between the brain blood and ventricular CSF, or a passive permeability clearance at the blood-CSF barrier between the brain blood and cranial CSF.18. The method of embodiment 16 or 17, wherein the simple diffusion rate includes at least one of a simple diffusion rate between cranial CSF and CSF adjacent brain tissue, a simple diffusion rate between ventricular CSF and CSF adjacent brain tissue, a simple diffusion rate between CSF adjacent brain tissue and deep brain tissue, a simple diffusion rate between deep brain tissue and tumor rim, a simple diffusion rate between tumor rim and bulk tumor, or a simple diffusion rate between bulk tumor and tumor core. 19. The method of any of embodiments 16-18, wherein the transporter-mediated clearance includes at least one of a transporter-mediated clearance at a BBB, a transporter-mediated clearance at a BBTB, or a transporter-mediated clearance at a blood-CSF barrier. 20. The method of embodiment 19, wherein the transporter-mediated clearance at the BBB includes at least one of an efflux transporter-mediated efflux clearance at the BBB between brain blood and CSF adjacent brain tissue, an uptake transporter-mediated uptake clearance at the BBB between brain blood and CSF adjacent brain tissue, an efflux transporter-mediated efflux clearance at the BBB between the brain blood and deep brain tissue, or an uptake transporter- mediated uptake clearance at the BBB between the brain blood and deep brain tissue. 21. The method of embodiment 19 or 20, wherein the transporter-mediated clearance at the BBTB includes at least one of an efflux transporter-mediated efflux clearance at the BBTB between brain blood and tumor rim, an uptake transporter-mediated uptake clearance at the BBTB between brain blood and tumor rim, an efflux transporter-mediated efflux clearance at the BBTB between brain blood and bulk tumor, an uptake transporter-mediated uptake clearance at the BBTB between the brain blood and bulk tumor, an efflux transporter-mediated efflux clearance at the BBTB between brain blood and tumor core, or an uptake transporter-mediated uptake clearance at the BBTB between the brain blood and tumor core. 22. The method of any of embodiments 19-21, wherein the transporter-mediated clearance at the blood-CSF barrier includes at least one of an efflux transporter-mediated efflux clearance at the blood-CSF barrier between brain blood and ventricular CSF, an uptake transporter-mediated uptake clearance at the blood-CSF barrier between the brain blood and ventricular CSF, an efflux transporter-mediated efflux clearance at the blood-CSF barrier between the brain blood and cranial CSF, or an uptake transporter-mediated uptake clearance at the blood-CSF barrier between the brain blood and cranial CSF. 23. The method of any of embodiments 16-22, wherein the metabolic clearance in a region of the brain mass includes a metabolic clearance in CSF adjacent brain tissue and / or metabolic clearance in deep brain tissue.24. The method of any of embodiments 16-23, wherein the unbound fraction in a region includes at least one of an unbound fraction in CSF adjacent brain tissue, an unbound fraction in deep brain tissue, an unbound fraction in tumor rim, an unbound fraction in bulk tumor, an unbound fraction in tumor core, an unbound fraction in ventricular CSF, an unbound fraction in cranial CSF, or an unbound fraction in spinal CSF. 25. The method of any of embodiments 16-24, wherein the unionized drug fraction in a region includes at least one of a unionized drug fraction in brain blood, a unionized efficiency in CSF adjacent brain tissue, a unionized efficiency in deep brain tissue, a unionized efficiency in tumor rim, a unionized efficiency in bulk tumor, a unionized efficiency in tumor core, a unionized efficiency in ventricular CSF, a unionized efficiency in cranial CSF, or a unionized efficiency in spinal CSF. 26. The method of any of embodiments 8-25, further including: determining at least one drug-specific parameter and / or at least one system-specific parameter. 27. The method of embodiment 26, wherein determining at least one system-specific parameter includes: identifying, from a subject or from a population of subjects, data indicative of the at least one system-specific parameter. 28. The method of any of embodiments 1-27, wherein the input data further includes observed data from one or more subjects. 29. The method of embodiment 28, wherein the observed data includes a variability of at least one input parameter between the one or more subjects. 30. The method of embodiment 28 or 29, wherein the observed data includes an indication of each of the one or more subjects. 31. The method of any of embodiments 28-30, wherein the observed data includes a concentration of the drug in a tumor over time. 32. The method of any of embodiments 28-31, wherein the observed data includes a concentration of the drug in CSF over time. 33. The method of any of embodiments 28-32, wherein the output is indicative of the observed data. 34. The method of any of embodiments 1-33, wherein determining the metric associated with the concentration of the drug includes analyzing, by the one or more processors, a system of ordinary differential equations (ODEs).35. The method of embodiment 34, wherein analyzing the system of ODEs includes applying Euler’s method, Runge Kutta methods, Adam’s method, or a Livermore solver for ordinary differential equations (LSODE) to the system of ODEs. 36. The method of any of embodiments 1-35, wherein the metric includes a pharmacokinetic parameter of the drug in the at least two brain regions and / or a concentration of the drug in the at least two brain regions over time. 37. The method of embodiment 36, wherein the pharmacokinetic parameter includes an AUC, a maximum concentration (Cmax), or a time to Cmax (Tmax). 38. The method of embodiment 36 or 37, further including: receiving, from an input device, a user input indicative of a time period, wherein the metric includes the pharmacokinetic parameter during the time period and / or the concentration of the drug in the at least two brain regions during the time period. 39. The method of any of embodiments 1-38, wherein the generating the output indicative of the metric includes outputting, to a visual display, a visual signal indicative of the concentration of the drug in the at least two brain regions. 40. The method of embodiment 39, wherein the visual display includes a web application or a mobile application. 41. The method of embodiment 39 or 40, wherein the visual signal includes a pharmacokinetic parameter associated with the drug. 42. The method of any of embodiments 1-41, wherein the output includes a mean profile simulation result, a group simulation result, or a parameter sensitivity simulation result. 43. The method of embodiment 42, wherein the mean profile simulation result includes at least one of: a concentration table, a concentration plot, a concentration log plot, or a pharmacokinetic parameter. 44. The method of embodiment 43, wherein pharmacokinetic parameter includes an AUC, a Cmax, or a Tmax, for each of the two or more brain regions. 45. The method of any of embodiments 42-44, wherein the group simulation result includes at least one of: a generated parameter list for a given inter-individual variability (IIV), a concentration table, a concentration plot, a concentration log plot, a percentile data table, a percentile plot, or a percentile log plot. 46. The method of any of embodiments 42-45, wherein generating the output including the group simulation result includes: receiving, from an input device, a user input indicative of a number of simulated individuals in a group, andwherein the group simulation result is indicative of the metric of each simulated individual in the group. 47. The method of any of embodiments 42-46, wherein the parameter sensitivity simulation result is indicative of an impact of at least one parameter on the output. 48. The method of any of embodiments 42-47, wherein the parameter sensitivity simulation result includes a concentration table, a concentration plot, a concentration log plot, a pharmacokinetic parameter, or an AUC scatter plot. 49. The method of any of embodiments 42-48, wherein generating the output including the parameter sensitivity simulation result includes: receiving, from a user device, a user input indicative at least one of: a minimum value for one or more parameters, a maximum value for one or more parameters, a number of points to generate within a range of one or more parameters; a minimum time point for one or more parameters, or a maximum time point for one or more parameters; determining, based on the user input, an impact of the one or more parameters. 50. The method of any of embodiments 1-49, further including transmitting the output to an external device or to a user. 51. The method of embodiment 50, wherein the user is a researcher or a clinician. 52. The method of embodiment 50 or 51, further including determining, based on the output, a dose of the drug to be administered to one or more subjects. 53. A system, including: at least one processor; and memory storing instructions that, when executed by the at least one processor, cause the at least one processor to perform operations including: identifying input data including plasma concentration of a drug over time; determining, by the at least processors, a metric associated with a concentration of the drug in at least two brain regions including: at least two regions of a brain mass; or at least one region of the brain mass and at least one region of a brain tumor; generating, by the at least processors, an output indicative of the metric. 54. The system of embodiment 53, further including: a transceiver configured to transmit data indicating the metric associated with the concentration of the drug in two or more brain regions. 55. The system of embodiment 53 or 54, further including:an output device configured to output an indication of the metric associated with the concentration of the drug in two or more brain regions. 56. A non-transitory computer-readable medium storing instructions for performing operations including: identifying input data including plasma concentration of a drug over time; determining a metric associated with a concentration of the drug in at least two brain regions including: at least two regions of a brain mass; or at least one region of the brain mass and at least one region of a brain tumor; generating an output indicative of the metric. CLOSING PARAGRAPHS

[0153] As will be understood by one of ordinary skill in the art, each embodiment disclosed herein can comprise, consist essentially of or consist of its particular stated element, step, ingredient or component. Thus, the terms “include” or “including” should be interpreted to recite: “comprise, consist of, or consist essentially of.” The transition term “comprise” or “comprises” means has, but is not limited to, and allows for the inclusion of unspecified elements, steps, ingredients, or components, even in major amounts. The transitional phrase “consisting of” excludes any element, step, ingredient or component not specified. The transitional phrase “consisting essentially of” limits the scope of the embodiment to the specified elements, steps, ingredients or components and to those that do not materially affect the embodiment.

[0154] Unless otherwise indicated, all numbers expressing quantities of ingredients, properties such as molecular weight, reaction conditions, and so forth used in the specification and claims are to be understood as being modified in all instances by the term “about.” Accordingly, unless indicated to the contrary, the numerical parameters set forth in the specification and attached claims are approximations that may vary depending upon the desired properties sought to be obtained by the present invention. At the very least, and not as an attempt to limit the application of the doctrine of equivalents to the scope of the claims, each numerical parameter should at least be construed in light of the number of reported significant digits and by applying ordinary rounding techniques. When further clarity is required, the term “about” has the meaning reasonably ascribed to it by a person skilled in the art when used in conjunction with a stated numerical value or range, i.e. denoting somewhat more or somewhat less than the stated value or range, to within a range of ±20% of the stated value; ±19% of the stated value; ±18% of the stated value; ±17% of the stated value; ±16% of the stated value; ±15% of the stated value; ±14% of the stated value;±13% of the stated value; ±12% of the stated value; ±11% of the stated value; ±10% of the stated value; ±9% of the stated value; ±8% of the stated value; ±7% of the stated value; ±6% of the stated value; ±5% of the stated value; ±4% of the stated value; ±3% of the stated value; ±2% of the stated value; or ±1% of the stated value.

[0155] Notwithstanding that the numerical ranges and parameters setting forth the broad scope of the invention are approximations, the numerical values set forth in the specific examples are reported as precisely as possible. Any numerical value, however, inherently contains certain errors necessarily resulting from the standard deviation found in their respective testing measurements.

[0156] The terms “a,” “an,” “the” and similar referents used in the context of describing the invention (especially in the context of the following claims) are to be construed to cover both the singular and the plural, unless otherwise indicated herein or clearly contradicted by context. Recitation of ranges of values herein is merely intended to serve as a shorthand method of referring individually to each separate value falling within the range. Unless otherwise indicated herein, each individual value is incorporated into the specification as if it were individually recited herein. All methods described herein can be performed in any suitable order unless otherwise indicated herein or otherwise clearly contradicted by context. The use of any and all examples, or exemplary language (e.g., “such as”) provided herein is intended merely to better illuminate the invention and does not pose a limitation on the scope of the invention otherwise claimed. No language in the specification should be construed as indicating any non-claimed element essential to the practice of the invention.

[0157] Groupings of alternative elements or embodiments of the invention disclosed herein are not to be construed as limitations. Each group member may be referred to and claimed individually or in any combination with other members of the group or other elements found herein. It is anticipated that one or more members of a group may be included in, or deleted from, a group for reasons of convenience and / or patentability. When any such inclusion or deletion occurs, the specification is deemed to contain the group as modified thus fulfilling the written description of all Markush groups used in the appended claims.

[0158] Certain embodiments of this invention are described herein, including the best mode known to the inventors for carrying out the invention. Of course, variations on these described embodiments will become apparent to those of ordinary skill in the art upon reading the foregoing description. The inventor expects skilled artisans to employ such variations as appropriate, and the inventors intend for the invention to be practiced otherwise than specifically described herein. Accordingly, this invention includes all modifications and equivalents of the subject matter recitedin the claims appended hereto as permitted by applicable law. Moreover, any combination of the above-described elements in all possible variations thereof is encompassed by the invention unless otherwise indicated herein or otherwise clearly contradicted by context.

[0159] Furthermore, numerous references have been made to patents, printed publications, journal articles and other written text throughout this specification (referenced materials herein). Each of the referenced materials are individually incorporated herein by reference in their entirety for their referenced teaching.

[0160] It is to be understood that the embodiments of the invention disclosed herein are illustrative of the principles of the present invention. Other modifications that may be employed are within the scope of the invention. Thus, by way of example, but not of limitation, alternative configurations of the present invention may be utilized in accordance with the teachings herein. Accordingly, the present invention is not limited to that precisely as shown and described.

[0161] The particulars shown herein are by way of example and for purposes of illustrative discussion of the preferred embodiments of the present invention only and are presented in the cause of providing what is believed to be the most useful and readily understood description of the principles and conceptual aspects of various embodiments of the invention. In this regard, no attempt is made to show structural details of the invention in more detail than is necessary for the fundamental understanding of the invention, the description taken with the drawings and / or examples making apparent to those skilled in the art how the several forms of the invention may be embodied in practice.

[0162] Definitions and explanations used in the present disclosure are meant and intended to be controlling in any future construction unless clearly and unambiguously modified in the example(s) or when application of the meaning renders any construction meaningless or essentially meaningless. In cases where the construction of the term would render it meaningless or essentially meaningless, the definition should be taken from Webster's Dictionary, 11th Edition or a dictionary or reference well-known to and used by those of ordinary skill in the art.

Claims

LISTING OF CLAIMS What is claimed is:

1. A method comprising: identifying input data comprising plasma concentration of a drug over time; determining, by one or more processors, a metric associated with a concentration of the drug in at least two brain regions comprising: at least two regions of a brain mass; or at least one region of the brain mass and at least one region of a brain tumor; generating, by the one or more processors, an output indicative of the metric.

2. The method of claim 1, wherein regions of the brain mass comprise: cerebrospinal fluid (CSF) adjacent brain tissue or deep brain tissue.

3. The method of claim 1, wherein regions of the brain tumor comprise: tumor rim, bulk tumor, or tumor core.

4. The method of claim 1, wherein the at least two brain regions further comprise a brain blood region.

5. The method of claim 1, wherein the at least two brain regions further comprise at least one CSF region.

6. The method of claim 5, wherein the at least one CSF region comprises: ventricular CSF, cranial CSF, or spinal CSF.

7. The method of claim 1, wherein the at least two brain regions comprise 2, 3, 4, 5, 6, 7, 8, 9, or more than 9 brain regions.

8. The method of claim 1, wherein the input data further comprises drug-specific parameters and system-specific parameters.

9. The method of claim 8, wherein the system-specific parameters comprise at least one of a region volume, a cerebral blood flow, a CSF absorption rate, a CSF flow rate, a CSF back flow rate, a paravascular bulk flow rate, or a convective bulk flow rate.

10. The method of claim 9, wherein the region volume comprises at least one of a volume of brain blood, a volume of adjacent brain tissue, a volume of deep brain tissue, a volume of tumor rim region, a volume of tumor bulk region, a volume of tumor core region, a volume of ventricular CSF, a volume of cranial CSF, a volume of spinal CSF., 11. The method of claim 9, wherein the CSF absorption rate comprises at least one of an absorption rate of cranial CSF into blood circulation through arachnoid villi, an absorption rate of spinal CSF into blood circulation through arachnoid villi, an absorption rate of cranial CSF viaolfactory mucosa and cranial nerve sheaths, or an absorption rate of spinal CSF via spinal nerve sheaths.

12. The method of claim 9, wherein the CSF flow rate comprises at least one of a CSF flow rate from a ventricular space to a cranial space, a CSF flow rate from the ventricular space to a spinal space, a CSF flow rate from the spinal space to the cranial space, or a CSF flow rate from the cranial space to the spinal space.

13. The method of claim 9, wherein the CSF back flow rate comprises a CSF back flow rate from a cranial space to a ventricular space and / or a CSF back flow rate from a spinal space to a ventricular space.

14. The method of claim 9, wherein the paravascular bulk flow rate comprises at least one of a paravascular bulk flow rate from cranial CSF to CSF adjacent brain tissue, a paravascular bulk flow rate from CSF adjacent brain tissue to cranial CSF, a paravascular bulk flow rate from ventricular CSF to CSF adjacent brain tissue, a paravascular bulk flow rate from CSF adjacent brain tissue to ventricular CSF, a paravascular bulk flow rate from cranial CSF to deep brain tissue, a paravascular bulk flow rate from deep brain tissue to cranial CSF, a paravascular bulk flow rate from cranial CSF to tumor rim, a paravascular bulk flow rate from tumor rim to cranial CSF, a paravascular bulk flow rate from cranial CSF to tumor bulk, a paravascular bulk flow rate from tumor bulk to cranial CSF, a paravascular bulk flow rate from cranial CSF to tumor core, or a paravascular bulk flow rate from tumor core to cranial CSF.

15. The method of claim 9, wherein the convective bulk flow rate comprises at least one of a convective bulk flow rate from CSF adjacent brain tissue to deep brain tissue, a convective bulk flow rate from deep brain tissue to CSF adjacent brain tissue, a convective bulk flow rate from deep brain tissue to tumor rim, a convective bulk flow rate from tumor rim to deep brain tissue, convective bulk flow rate from tumor rim to tumor bulk, a convective bulk flow rate from tumor bulk to tumor rim, a convective bulk flow rate from tumor bulk to tumor core, or a convective bulk flow rate from tumor core to tumor bulk.

16. The method of claim 8, wherein the drug-specific parameters comprise at least one of: a passive permeability clearance, a simple diffusion rate, a transporter-mediated clearance, a metabolic clearance in a region of the brain mass, an unbound fraction in a region, or a unionized drug fraction in a region.

17. The method of claim 16, wherein the passive permeability clearance comprises at least one of a passive permeability clearance at a blood-brain barrier (BBB) between brain blood and CSF adjacent brain tissue, a passive permeability clearance at the BBB between brain blood and deep brain tissue, a passive permeability clearance at a blood-brain tumor barrier (BBTB)between brain blood and tumor rim, a passive permeability clearance at the BBTB between brain blood and bulk tumor, a passive permeability clearance at the BBTB between brain blood and tumor core, a passive permeability clearance at a blood-CSF barrier between the brain blood and ventricular CSF, or a passive permeability clearance at the blood-CSF barrier between the brain blood and cranial CSF.

18. The method of claim 16, wherein the simple diffusion rate comprises at least one of a simple diffusion rate between cranial CSF and CSF adjacent brain tissue, a simple diffusion rate between ventricular CSF and CSF adjacent brain tissue, a simple diffusion rate between CSF adjacent brain tissue and deep brain tissue, a simple diffusion rate between deep brain tissue and tumor rim, a simple diffusion rate between tumor rim and bulk tumor, or a simple diffusion rate between bulk tumor and tumor core.

19. The method of claim 16, wherein the transporter-mediated clearance comprises at least one of a transporter-mediated clearance at a BBB, a transporter-mediated clearance at a BBTB, or a transporter-mediated clearance at a blood-CSF barrier.

20. The method of claim 19, wherein the transporter-mediated clearance at the BBB comprises at least one of an efflux transporter-mediated efflux clearance at the BBB between brain blood and CSF adjacent brain tissue, an uptake transporter-mediated uptake clearance at the BBB between brain blood and CSF adjacent brain tissue, an efflux transporter-mediated efflux clearance at the BBB between the brain blood and deep brain tissue, or an uptake transporter- mediated uptake clearance at the BBB between the brain blood and deep brain tissue.

21. The method of claim 19, wherein the transporter-mediated clearance at the BBTB comprises at least one of an efflux transporter-mediated efflux clearance at the BBTB between brain blood and tumor rim, an uptake transporter-mediated uptake clearance at the BBTB between brain blood and tumor rim, an efflux transporter-mediated efflux clearance at the BBTB between brain blood and bulk tumor, an uptake transporter-mediated uptake clearance at the BBTB between the brain blood and bulk tumor, an efflux transporter-mediated efflux clearance at the BBTB between brain blood and tumor core, or an uptake transporter-mediated uptake clearance at the BBTB between the brain blood and tumor core.

22. The method of claim 19, wherein the transporter-mediated clearance at the blood-CSF barrier comprises at least one of an efflux transporter-mediated efflux clearance at the blood-CSF barrier between brain blood and ventricular CSF, an uptake transporter-mediated uptake clearance at the blood-CSF barrier between the brain blood and ventricular CSF, an efflux transporter-mediated efflux clearance at the blood-CSF barrier between the brain blood andcranial CSF, or an uptake transporter-mediated uptake clearance at the blood-CSF barrier between the brain blood and cranial CSF.

23. The method of claim 16, wherein the metabolic clearance in a region of the brain mass comprises a metabolic clearance in CSF adjacent brain tissue and / or metabolic clearance in deep brain tissue.

24. The method of claim 16, wherein the unbound fraction in a region comprises at least one of an unbound fraction in CSF adjacent brain tissue, an unbound fraction in deep brain tissue, an unbound fraction in tumor rim, an unbound fraction in bulk tumor, an unbound fraction in tumor core, an unbound fraction in ventricular CSF, an unbound fraction in cranial CSF, or an unbound fraction in spinal CSF.

25. The method of claim 16, wherein the unionized drug fraction in a region comprises at least one of a unionized drug fraction in brain blood, a unionized efficiency in CSF adjacent brain tissue, a unionized efficiency in deep brain tissue, a unionized efficiency in tumor rim, a unionized efficiency in bulk tumor, a unionized efficiency in tumor core, a unionized efficiency in ventricular CSF, a unionized efficiency in cranial CSF, or a unionized efficiency in spinal CSF.

26. The method of claim 8, further comprising: determining at least one drug-specific parameter and / or at least one system-specific parameter.

27. The method of claim 26, wherein determining at least one system-specific parameter comprises: identifying, from a subject or from a population of subjects, data indicative of the at least one system-specific parameter.

28. The method of claim 1, wherein the input data further comprises observed data from one or more subjects.

29. The method of claim 28, wherein the observed data comprises a variability of at least one input parameter between the one or more subjects.

30. The method of claim 28, wherein the observed data comprises an indication of each of the one or more subjects.

31. The method of claim 28, wherein the observed data comprises a concentration of the drug in a tumor over time.

32. The method of claim 28, wherein the observed data comprises a concentration of the drug in CSF over time.

33. The method of claim 28, wherein the output is indicative of the observed data.

34. The method of claim 1, wherein determining the metric associated with the concentration of the drug comprises analyzing, by the one or more processors, a system of ordinary differential equations (ODEs).

35. The method of claim 34, wherein analyzing the system of ODEs comprises applying Euler’s method, Runge Kutta methods, Adam’s method, or a Livermore solver for ordinary differential equations (LSODE) to the system of ODEs.

36. The method of claim 1, wherein the metric comprises a pharmacokinetic parameter of the drug in the at least two brain regions and / or a concentration of the drug in the at least two brain regions over time.

37. The method of claim 36, wherein the pharmacokinetic parameter comprises an AUC, a maximum concentration (Cmax), or a time to Cmax (Tmax).

38. The method of claim 36, further comprising: receiving, from an input device, a user input indicative of a time period, wherein the metric comprises the pharmacokinetic parameter during the time period and / or the concentration of the drug in the at least two brain regions during the time period.

39. The method of claim 1, wherein the generating the output indicative of the metric comprises outputting, to a visual display, a visual signal indicative of the concentration of the drug in the at least two brain regions.

40. The method of claim 39, wherein the visual display comprises a web application or a mobile application.

41. The method of claim 39, wherein the visual signal comprises a pharmacokinetic parameter associated with the drug.

42. The method of claim 1, wherein the output comprises a mean profile simulation result, a group simulation result, or a parameter sensitivity simulation result.

43. The method of claim 42, wherein the mean profile simulation result comprises at least one of: a concentration table, a concentration plot, a concentration log plot, or a pharmacokinetic parameter.

44. The method of claim 43, wherein pharmacokinetic parameter comprises an AUC, a Cmax, or a Tmax, for each of the two or more brain regions.

45. The method of claim 42, wherein the group simulation result comprises at least one of: a generated parameter list for a given inter-individual variability (IIV), a concentration table, a concentration plot, a concentration log plot, a percentile data table, a percentile plot, or a percentile log plot.

46. The method of claim 42, wherein generating the output comprising the group simulation result comprises: receiving, from an input device, a user input indicative of a number of simulated individuals in a group, and wherein the group simulation result is indicative of the metric of each simulated individual in the group.

47. The method of claim 42, wherein the parameter sensitivity simulation result is indicative of an impact of at least one parameter on the output.

48. The method of claim 42, wherein the parameter sensitivity simulation result comprises a concentration table, a concentration plot, a concentration log plot, a pharmacokinetic parameter, or an AUC scatter plot.

49. The method of claim 42, wherein generating the output comprising the parameter sensitivity simulation result comprises: receiving, from a user device, a user input indicative at least one of: a minimum value for one or more parameters, a maximum value for one or more parameters, a number of points to generate within a range of one or more parameters; a minimum time point for one or more parameters, or a maximum time point for one or more parameters; determining, based on the user input, an impact of the one or more parameters.

50. The method of claim 1, further comprising transmitting the output to an external device or to a user.

51. The method of claim 50, wherein the user is a researcher or a clinician.

52. The method of claim 50, further comprising determining, based on the output, a dose of the drug to be administered to one or more subjects.

53. A system, comprising: at least one processor; and memory storing instructions that, when executed by the at least one processor, cause the at least one processor to perform operations comprising: identifying input data comprising plasma concentration of a drug over time; determining, by the at least processors, a metric associated with a concentration of the drug in at least two brain regions comprising: at least two regions of a brain mass; or at least one region of the brain mass and at least one region of a brain tumor; generating, by the at least processors, an output indicative of the metric.

54. The system of claim 53, further comprising: a transceiver configured to transmit data indicating the metric associated with the concentration of the drug in two or more brain regions.

55. The system of claim 53, further comprising: an output device configured to output an indication of the metric associated with the concentration of the drug in two or more brain regions.

56. A non-transitory computer-readable medium storing instructions for performing operations comprising: identifying input data comprising plasma concentration of a drug over time; determining a metric associated with a concentration of the drug in at least two brain regions comprising: at least two regions of a brain mass; or at least one region of the brain mass and at least one region of a brain tumor; generating an output indicative of the metric.

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