Pharmacokinetic model based on nasal-brain physiology

Abstract

The present disclosure relates to the establishment and use of physiology-based pharmacokinetic models for predicting the absorption / distribution of nasal administered compounds of interest.

Description

Cross Reference to Related Applications

[0001] This application claims the benefit of priority to U.S. Application No. 63 / 461,111, filed April 21, 2023, the contents of which are incorporated herein by reference. TECHNICAL FIELD

[0002] The present invention relates to a computer-implemented nose-to-brain pharmacokinetic simulation model. BACKGROUND

[0003] Pharmacodynamics refers to the study of the fundamental and / or molecular interactions between a drug and the body’s constituents, leading to a pharmacological response through a subsequent series of events. For most drugs, the magnitude of the pharmacological effect depends on the time-dependent concentration of the drug at the site of action (e.g., target receptor-ligand / drug interaction). Factors that affect the rate of delivery and disappearance of the drug to or from the site of action over time include absorption, distribution, metabolism, and elimination. The study of factors that affect drug concentration as a function of time is the subject of pharmacokinetics.

[0004] Each step of drug absorption, distribution, metabolism, and elimination can be mathematically described as a rate process. Many of these biochemical processes involve first- or pseudo-first-order rate processes. In other words, the rate of the reaction is proportional to the concentration of the drug. For example, pharmacokinetic data analysis is based on empirical observations following the administration of a known dose of a drug and the simulation of events through descriptive equations or mathematical (compartmental) models. This allows for the summarization of experimental measurements (plasma / blood level-time curves) and predictions under certain experimental conditions.

[0005] Simulations (i.e., computer-implemented models) have been used in pharmacokinetics to provide solutions to complex pharmacokinetic equations and modeling of pharmacokinetic processes. While tools exist to develop and implement pharmacokinetic models, the pharmacokinetic models and computer systems developed to date have not been able to adequately predict the pharmacokinetic fate of nasally administered drugs to brain tissue in mammals. Therefore, there is a need to develop a comprehensive, physiology-based pharmacokinetic model that is capable of predicting the pharmacokinetics of nasally inhaled drugs. SUMMARY

[0006] The present disclosure relates to the generation and establishment of a physiologically-based pharmacokinetic (PBPK) model based on whole body physiology. The PBPK model is a multi-compartment mathematical model that includes operatively connected components: (i) differential equations for one or more of fluid transport, fluid absorption, mass transport, mass dissolution, mass solubility, and mass absorption for one or more compartments of a mammalian system of interest; and (ii) initial parameter values for the differential equations corresponding to physiological parameters and compound-specific parameters for one or more compartments of the mammalian system of interest. Initially, the PBPK model is established based on known compounds that have known information related to their pharmacokinetics. Also provided herein are methods of using the PBPK model to predict pharmacokinetic data for a new compound and / or a candidate compound in a mammalian (e.g., human) system of interest. The PBPK model and methods of use rely on a computer-implemented system and / or simulation engine having the ability to solve differential equations.

[0007] Accordingly, in a first aspect, the present disclosure provides a method, e.g., a computer- implemented method, for generating a trained nose-brain physiologically-based pharmacokinetic (PBPK) model for delivery of a drug to brain tissue via nasal inhalation, the method comprising: (a) generating a multi-compartment PBPK model, the multi-compartment PBPK model comprising a plurality of independent body compartments; (b) adding a brain compartment and a nasal compartment to the multi-compartment PBPK model, thereby generating an initial nose-brain PBPK model, wherein the nasal compartment comprises one or more independent nose compartments; (c) parameterizing the initial nose-brain PBPK model to include data for a plurality of physiological parameters for one or more or all of the plurality of independent body compartments and / or independent nose compartments; (d) parameterizing the initial nose-brain PBPK model to include compound-specific parameters for a drug having known pharmacokinetic data for each body compartment and each nose compartment, to generate a parameterized nose-brain PBPK model; (e) running the parameterized nose-brain model and generating a report comprising drug concentration data for one or more body compartments and / or one or more independent nose compartments at one or more time points; and (f) analyzing and comparing the drug concentration data in the report to the known pharmacokinetic data for the drug and updating the parameterized nose-brain model to obtain a trained nose-brain model.

[0008] In some embodiments, the plurality of compartments of the multi-compartment physiologically-based pharmacokinetic model represent one or more or all of arterial blood, lung, fat, bone, brain, heart, kidney, nose, muscle, skin, intestine, spleen, liver, remaining body compartments, and / or venous blood.

[0009] In some embodiments, the one or more independent nose compartments represent one or more or all of the nasal region, the nasal floor, the turbinates, the olfactory region, or the nasopharyngeal region.

[0010] In some embodiments, the brain compartments include independent subcompartments representing one or more or all of brain blood outside the blood brain barrier, brain parenchyma representing brain tissue, cranial cerebrospinal fluid (CSF), and / or spinal CSF.

[0011] In some embodiments, at least one of the nose compartments further represents a mucus layer, an epithelial layer, and a subepithelial layer, wherein the mucus layer is where the drug is assumed to deposit, the epithelial layer allows penetration to deeper tissue, and the subepithelial layer is perfused by vessels capable of transporting the drug into the systemic circulation.

[0012] In certain embodiments, the physiological parameters of the at least one compartment and subcompartment are selected from the parameters recited in Table 1.

[0013] In some embodiments, the compound-specific parameters of the at least one compartment and subcompartment are selected from the parameters recited in Table 2.

[0014] In some embodiments, the compound-specific parameters of the drug include: P permeability of the nasal epithelium), Log P (log of the octanol / water partition coefficient), pK a (negative log of the acid dissociation constant), fu fraction of drug in solution in plasma that is unbound to plasma proteins, R blood / plasma ratio, Cl h hepatic clearance, and mass deposited in at least one region of the nose.

[0015] In some embodiments, the body compartments of the multi-compartment PBPK model are represented by differential equations, wherein the differential equations represent one or more or all of: (i) concentrations of the drug in one or more of the lung, fat, bone, heart, kidney, muscle, skin, or the remainder of the body, and (ii) plasma concentrations of the drug in one or more or all of the spleen, liver, intestine, arterial plasma, and / or veins as a function of time as a function of lung tissue volume, and wherein the differential equations are a function of one or more or all of the following parameters: blood flow to the lung; concentration of the drug in venous plasma; blood; plasma ratio; tissue:plasma partition coefficient of the drug in each tissue type; fraction of the drug that is unbound in tissue; tissue clearance of the drug; volume of each tissue or plasma type; concentration of the drug in each tissue or plasma type; blood flow rate to each tissue type; hepatic clearance; and / or blood clearance of the drug. In some embodiments, the differential equations are one or more or all of:

[0016]

[0017]

[0018]

[0019]

[0020] and

[0021] wherein, Vp is the volume of lung tissue; Cp is the concentration of drug in lung tissue; Qp is the blood flow to the lung; Cv is the concentration of drug in venous plasma; Bp is the blood:plasma ratio; Kp is the tissue:plasma distribution coefficient of drug in the lung; fu is the fraction unbound in tissue of drug; CLt is the tissue clearance of drug; is fat, bone, heart, kidney, muscle, skin, and the rest of the body; Vs is the volume of spleen tissue; Cs is the concentration of drug in spleen tissue; Qs is the blood flow to the spleen; Ks is the tissue:plasma distribution coefficient of drug in the spleen; Vg is the volume of gut tissue; Cg is the concentration of drug in gut tissue; Qg is the blood flow to the gut; Kg is the tissue:plasma distribution coefficient of drug in the gut; Vh is the volume of liver tissue; Ch is the concentration of drug in liver tissue; Qh is the blood flow to the liver; Kh is the tissue:plasma distribution coefficient of drug in the liver; Cav is the concentration of drug in arterial plasma; CLh is the hepatic clearance; CLb is the blood clearance.

[0022] In some embodiments, the nasal compartments are represented by differential equations representing one or more or all of: (i) the concentration of drug in nasal mucus, (ii) the concentration of drug in nasal epithelium, and (iii) the concentration of drug under the nasal epithelium, and wherein the differential equations are functions of one or more of the following parameters: permeability of the nasal epithelium; area of each region in the nasal cavity; tissue:plasma partition coefficient of the drug; mucus-ciliary clearance rate of each region of the nasal cavity; rate of transport from olfactory tissue to cerebrospinal fluid via intracellular and extracellular pathways through the olfactory region and / or trigeminal nerve; rate of transport from cerebrospinal fluid to olfactory tissue via intracellular and extracellular pathways through the olfactory region and / or trigeminal nerve; and / or fraction of unbound drug in the cranial CSF and / or concentration in the cranial CSF.

[0023] In some embodiments, the differential equations are one or more of:

[0024]

[0025]

[0026] wherein , , , , and are the volume and drug concentration of the nasal mucus, epithelium, and under the epithelium of the ith nasal region (referring to the nasal valve, the nasal floor, the middle turbinate, the superior turbinate, the olfactory region, and the nasopharynx); is the permeability in the nasal epithelium; is the area of the ith nasal region; is the tissue:plasma partition coefficient of the drug in the nose; is the mucus-ciliary clearance rate of the substance into the ith region (equal to 0 for all regions except the nasopharynx, which is equal to ); is the mucus-ciliary clearance rate of the substance out of the ith region (equal to for the nasal floor, middle turbinate, and olfactory region, and equal to for the nasopharynx); is the rate of transport from olfactory tissue to cerebrospinal fluid via intracellular and extracellular pathways; is the rate of transport from cerebrospinal fluid to olfactory tissue via intracellular and extracellular pathways (both parameters are zero for non-olfactory regions); is the fraction of unbound drug in the cranial CSF; and is the concentration in the cranial CSF.

[0027] In some embodiments, the brain compartment is represented by a differential equation representing one or more of the following: (i) the concentration of the drug in the cerebral blood, (ii) the concentration of the drug in the brain parenchyma, (iii) the concentration of the drug in the cerebrospinal fluid, and (iv) the concentration of the drug in the spinal cerebrospinal fluid; and wherein the differential equation is a function of one or more of the following parameters: the concentration of drug molecules in the cerebral blood; the blood flow to the brain; the concentration of the compound in arterial plasma; the fraction of unbound compounds in tissue; the tissue clearance rate of the compound; the concentration of the cerebral blood... The product of permeability and surface area between the brain parenchyma and the brain parenchyma; the fraction of unbound drug in the brain parenchyma; the blood concentration in the brain parenchyma; the fraction of unbound drug in the cerebral blood; the product of permeability and surface area between the cerebral blood and cranial CSF; the fraction of unbound drug in the cranial CSF; the concentration of drug in the cranial CSF; the flow rate from the cranial CSF and spinal CSF to the cerebral blood; the concentration of drug in the spinal CSF; the volume of the brain parenchyma; the product of permeability and surface area between the brain parenchyma and cranial CSF; the bulk flow from the brain parenchyma to the cranial CSF; the CSF shuttle flow between the cranial CSF and spinal CSF; the rate of transport from olfactory tissue to cerebrospinal fluid along the olfactory region and / or trigeminal nerve via intracellular and extracellular pathways; the tissue:plasma partition coefficient of the drug in the nose; the drug concentration in the epithelium of each region of the nasal cavity; the rate of transport from cerebrospinal fluid to olfactory tissue along the olfactory region and / or trigeminal nerve via intracellular and extracellular pathways; and / or The drug concentration in the subepithelial space of each region of the nasal cavity and / or the volume of spinal cord CSF. In some implementations, the differential equation is:

[0028]

[0029]

[0030]

[0031] in It is the volume of blood in the brain; It refers to the concentration of drug molecules in the bloodstream of the brain; It is the blood flow to the brain; It is the concentration of compounds in arterial plasma; It is the fraction of unbound compounds in the tissue; It is the tissue clearance rate of the compound; It is the product of the permeability and surface area between the blood and brain parenchyma; It represents the fraction of unbound drugs in the brain parenchyma; It refers to the blood concentration in the brain parenchyma; It is the fraction of unbound drugs in the brain blood; It is the product of the permeability and surface area between cerebral blood and cranial CSF; It is the fraction of unbound drug in the cranial CSF; It is the concentration of the drug in the cranial CSF; and These refer to the blood flow from the cranial CSF and spinal CSF to the brain, respectively. It refers to the concentration of the drug in the spinal cord CSF; It refers to the volume of the brain parenchyma; It is the product of the permeability and surface area between the brain parenchyma and the cranial CSF; It is the overall flow from the brain parenchyma to the cranial CSF; and It is the CSF shuttle flow between cranial CSF and spinal CSF; It is the rate at which substances are transported from the olfactory tissue to the cerebrospinal fluid via intracellular and extracellular pathways; It is the tissue-plasma partition coefficient of the drug in the nose; The concentration of the drug in the epithelium of the i-th nasal region (referring to the nasal flap, nasal floor, nasal turbinates, olfactory region, and nasopharynx); It is the rate at which cerebrospinal fluid is transported to the olfactory tissue via intracellular and extracellular pathways; This refers to the drug concentration in the subepithelial region of the i-th nasal region (referring to the nasal flap, nasal floor, nasal turbinates, olfactory region, and nasopharynx); and It refers to the volume of the spinal cord CSF.

[0032] In some implementations, the compound-specific parameters of step (c) are based on preclinical studies of a known drug. In some cases, preclinical studies include in vitro cell assays, in vitro protein assays (e.g., binding data), and / or in vivo studies.

[0033] In some implementations, physiologically specific parameters are obtained from literature and / or database searches.

[0034] In some implementations, step (e) includes solving the differential equations representing the compartments of the PBPK model. In some cases, the solution is performed using a differential equation solver.

[0035] In some implementations, the pharmacokinetic data in step (f) are based on clinical data of a known drug. In some cases, the model is trained by adjusting one or more physiological parameters or compound-specific parameters.

[0036] In some implementations, the PBPK model is species-specific. In some cases, the species is human. In some cases, the species is a non-human primate.

[0037] In some implementations, the known drug is sumatriptan.

[0038] On the other hand, this disclosure provides a method for predicting the outcome of a novel drug transport to brain tissue via nasal inhalation, such as a computer-implemented method. The method includes: (a) accessing a trained nasal-brain PBPK model generated using any of the methods described above, and parameterizing the nasal-brain PBPK model with compound-specific parameters known about the drug; (b) receiving nasal cast deposition data of the drug and inputting it into the trained nasal-brain PBPK model of step (a); (c) solving the equations of the trained nasal-brain PBPK model using a differential equation solver; (d) obtaining a report including drug concentration data from the trained nasal-brain model at one or more time points for one or more or all of the compartments and one or more or all of the sub-compartments; and (e) based on the report, providing a prediction of the outcome of drug transport to brain tissue via nasal inhalation, based on pharmacokinetic data for the brain compartments.

[0039] In some embodiments, the compound-specific parameters of step (a) are based on preclinical studies. In some embodiments, preclinical studies include in vitro cell assays, in vitro protein assays (e.g., binding data), and / or in vivo studies.

[0040] In some implementations, the nasal mold deposition data includes the mass of the drug deposited in each region of the nasal mold.

[0041] In some implementations, step (a) further includes updating the naso-brain PBPK model using clinical data known about the drug.

[0042] In some implementations, the clinical data are intravenous data, intranasal data, or both.

[0043] In another aspect, this disclosure also provides a system comprising: a memory for storing executable instructions; and one or more processing devices connected to the memory, wherein the one or more processing devices are configured to execute the instructions to perform operations including: (a) generating a multi-compartment PBPK model comprising a plurality of independent body compartments; (b) adding a brain compartment and a nasal compartment to the multi-compartment PBPK model to generate an initial naso-brain PBPK model, wherein the nasal compartment comprises one or more independent nasal compartments; and (c) parameterizing the initial naso-brain PBPK model to include options for the plurality of independent body compartments and / or independent nasal compartments. (d) Parameterizing the initial nas-brain PBPK model to include compound-specific parameters for a drug with known pharmacokinetic data for each body compartment and each nasal compartment, to generate a parameterized nas-brain PBPK model; (e) Running the parameterized nas-brain model and generating a report including drug concentration data for one or more body compartments and / or one or more independent nasal compartments at one or more time points; and (f) Analyzing and comparing the drug concentration data in the report with the known pharmacokinetic data of the drug, and updating the parameterized nas-brain model to obtain a trained nas-brain model.

[0044] In some implementations, the multiple compartments based on a physiological pharmacokinetic model represent one or more or all of the following: arterial blood, lung, fat, bone, brain, heart, kidney, nose, muscle, skin, intestine, spleen, liver, other body compartments, and / or venous blood.

[0045] In some embodiments, the brain compartment includes separate subcompartments that represent one or more of the following: brain blood outside the blood-brain barrier, brain parenchyma representing brain tissue, cerebrospinal fluid (CSF), and / or spinal CSF.

[0046] In some embodiments, a nasal compartment represents one or more or all of the nasal region, nasal floor, nasal turbinate, olfactory region, and / or nasopharyngeal region, and at least one of the nasal compartments is further represented as including a mucus layer, an epithelial layer, and a subepithelial layer, wherein the mucus layer is the assumed site for drug deposition, the epithelial layer allows penetration into deeper tissues, and the subepithelial layer is perfused with blood vessels capable of transporting the drug to the systemic circulation.

[0047] In some embodiments, the physiological parameters of at least one compartment and subcompartment are selected from those listed in Table 1. In some embodiments, the compound-specific parameters of at least one compartment and subcompartment are selected from those listed in Table 2.

[0048] In some implementations, the compound-specific parameters of the drug include: P (Nasal epithelial permeability), Log P (Logarithm of octanol / water partition coefficient) pK a (negative logarithm of the acid dissociation constant) fu (The fraction of drug dissolved in plasma that is not bound to plasma proteins) R (Blood / Plasma Ratio) Cl h (Liver clearance rate) and the mass of deposits in at least one region of the nose.

[0049] In another aspect, this disclosure provides one or more non-transient machine-readable storage media storing instructions that are executed to perform operations including: (a) generating a multi-compartment PBPK model comprising a plurality of independent body compartments; (b) adding a brain compartment and a nasal compartment to the multi-compartment PBPK model to generate an initial nose-brain PBPK model, wherein the nasal compartment comprises one or more independent nasal compartments; and (c) parameterizing the initial nose-brain PBPK model to include data for one or more or all of the plurality of physiological parameters for the plurality of independent body compartments and / or the independent nasal compartments. (d) Parameterize the initial nas-brain PBPK model to include compound-specific parameters for drugs with known pharmacokinetic data for each body compartment and each nasal compartment to generate a parameterized nas-brain PBPK model; (e) Run the parameterized nas-brain model and generate a report including drug concentration data for one or more body compartments and / or one or more individual nasal compartments at one or more time points; and (f) Analyze and compare the drug concentration data in the report with the known pharmacokinetic data of the drug, and update the parameterized nas-brain model to obtain a trained nas-brain model.

[0050] In some implementations, the multiple compartments based on a physiological pharmacokinetic model represent one or more or all of the following: arterial blood, lung, fat, bone, brain, heart, kidney, nose, muscle, skin, intestine, spleen, liver, other body compartments, and / or venous blood.

[0051] In some embodiments, the brain compartment includes separate subcompartments that represent one or more of the following: brain blood outside the blood-brain barrier, brain parenchyma representing brain tissue, cerebrospinal fluid (CSF), and / or spinal CSF.

[0052] In some embodiments, a nasal compartment represents one or more or all of the nasal region, nasal floor, nasal turbinate, olfactory region, and / or nasopharyngeal region, and at least one of the nasal compartments is further represented as including a mucus layer, an epithelial layer, and a subepithelial layer, wherein the mucus layer is the assumed site for drug deposition, the epithelial layer allows penetration into deeper tissues, and the subepithelial layer is perfused with blood vessels capable of transporting the drug to the systemic circulation.

[0053] In some embodiments, the physiological parameters of at least one compartment and subcompartment are selected from those listed in Table 1. In some embodiments, the compound-specific parameters of at least one compartment and subcompartment are selected from those listed in Table 2.

[0054] In some implementations, the compound-specific parameters of the drug include: P (Nasal epithelial permeability), Log P (Logarithm of octanol / water partition coefficient) pK a (negative logarithm of the acid dissociation constant) fu (The fraction of drug dissolved in plasma that is not bound to plasma proteins) R (Blood / Plasma Ratio) Cl h (Liver clearance rate) and the mass of deposits in at least one region of the nose.

[0055] On the other hand, this disclosure also provides a trained naso-brain physiology-based pharmacokinetic (PBPK) model for drug delivery to brain tissue via nasal inhalation, wherein the trained naso-brain PBPK model is (1) encoded on one or more non-transient machine-readable storage media and (2) generated by operations including: (a) generating a multi-compartment PBPK model comprising a plurality of independent body compartments; (b) adding brain compartments and nasal compartments to the multi-compartment PBPK model to generate an initial naso-brain PBPK model, wherein the nasal compartments comprise one or more independent nasal compartments; and (c) parameterizing the initial naso-brain PBPK model to include options for the plurality of independent body compartments. (d) Parameterizing the initial nas-brain PBPK model to include compound-specific parameters for the drug with known pharmacokinetic data for each body compartment and each nasal compartment, to generate a parameterized nas-brain PBPK model; (e) Running the parameterized nas-brain model and generating a report including drug concentration data for one or more body compartments and / or one or more independent nasal compartments at one or more time points; and (f) Analyzing and comparing the drug concentration data in the report with the known pharmacokinetic data of the drug, and updating the parameterized nas-brain model to obtain a trained nas-brain model.

[0056] In some implementations, the trained nasal-to-brain PBPK model is configured to: (a) receive one or more compound-specific parameters known about the drug; (b) solve differential equations; and (c) generate a report including drug concentration data from the trained nasal-to-brain model for one or more of the compartments and one or more of the sub-compartments at one or more time points; and (e) based on the report, provide a prediction of the outcome of drug transport to brain tissue via nasal inhalation, based on pharmacokinetic data for the brain compartments.

[0057] In some implementations, the multiple compartments based on a physiological pharmacokinetic model represent one or more of arterial blood, lung, fat, bone, brain, heart, kidney, nose, muscle, skin, intestine, spleen, liver, other body compartments, and / or venous blood.

[0058] In some embodiments, the brain compartment includes separate subcompartments that represent one or more of the following: brain blood outside the blood-brain barrier, brain parenchyma representing brain tissue, cerebrospinal fluid (CSF), and / or spinal CSF.

[0059] In some embodiments, the nasal compartment represents one or more or all of the nasal region, nasal floor, nasal turbinate, olfactory region, and / or nasopharyngeal region, and at least one further represents comprising a mucus layer, an epithelial layer, and a subepithelial layer, wherein the mucus layer is the assumed site for drug deposition, the epithelial layer allows penetration into deeper tissues, and the subepithelial layer is perfused with blood vessels capable of transporting the drug to the systemic circulation.

[0060] In some embodiments, the physiological parameters of at least one compartment and subcompartment are selected from those listed in Table 1. In some embodiments, the compound-specific parameters of at least one compartment and subcompartment are selected from those listed in Table 2.

[0061] In some implementations, the compound-specific parameters of the drug include: P (Nasal epithelial permeability), Log P (Logarithm of octanol / water partition coefficient) pK a (negative logarithm of the acid dissociation constant) fu (The fraction of drug dissolved in plasma that is not bound to plasma proteins) R (Blood / Plasma Ratio) Cl h (Liver clearance rate) and the mass of deposits in at least one region of the nose.

[0062] On the other hand, this disclosure provides a system comprising: a memory for storing executable instructions; and One or more processing devices connected to the memory, the one or more processing devices being configured to execute the instructions to perform operations including: (a) accessing a trained nasal-brain PBPK model generated using any of the methods described above, and parameterizing the nasal-brain PBPK model with compound-specific parameters known about the drug; (b) receiving nasal model deposition data of the drug and inputting it into the trained nasal-brain PBPK model of step (a); (c) solving the equations of the trained nasal-brain PBPK model using a differential equation solver; (d) obtaining a report including drug concentration data from the trained nasal-brain model for one or more time points in one or more compartments and one or more sub-compartments; and (e) based on the report, providing a prediction of the transport outcome of the drug to brain tissue via nasal inhalation, based on pharmacokinetic data for the brain compartments.

[0063] In some implementations, the multiple compartments based on a physiological pharmacokinetic model represent one or more or all of the following: arterial blood, lung, fat, bone, brain, heart, kidney, nose, muscle, skin, intestine, spleen, liver, other body compartments, and / or venous blood.

[0064] In some embodiments, the brain compartment includes separate subcompartments that represent one or more of the following: brain blood outside the blood-brain barrier, brain parenchyma representing brain tissue, cerebrospinal fluid (CSF), and / or spinal CSF.

[0065] In some embodiments, the nasal compartment represents one or more or all of the nasal region, nasal floor, turbinate, olfactory region, and / or nasopharyngeal region, and at least one is further indicated to include a mucus layer, an epithelial layer, and a subepithelial layer, wherein the mucus layer is the assumed site for drug deposition, the epithelial layer allows penetration into deeper tissues, and the subepithelial layer is perfused with blood vessels capable of transporting the drug to the systemic circulation.

[0066] In some embodiments, the physiological parameters of at least one compartment and subcompartment are selected from those listed in Table 1. In some embodiments, the compound-specific parameters of at least one compartment and subcompartment are selected from those listed in Table 2.

[0067] In some implementations, the compound-specific parameters of the drug include: P (Nasal epithelial permeability), Log P (Logarithm of octanol / water partition coefficient) pK a (negative logarithm of the acid dissociation constant) fu (The fraction of drug dissolved in plasma that is not bound to plasma proteins) R (Blood / Plasma Ratio) Cl h (Liver clearance rate) and the mass of deposits in at least one region of the nose.

[0068] This document also provides one or more non-transient machine-readable storage media storing instructions that are executed to perform operations including: (a) accessing a generated, trained nas-brain PBPK model produced using any of the methods described above, and parameterizing the nas-brain PBPK model with compound-specific parameters known about the drug; (b) receiving nasal model deposition data of the drug and inputting it into the trained nas-brain PBPK model of step (a); (c) solving the equations of the trained nas-brain PBPK model using a differential equation solver; (d) obtaining a report including drug concentration data from the trained nas-brain model for one or more of the compartments and one or more of the sub-compartments at one or more time points; and (e) based on the report, providing a prediction of the transport outcome of the drug to brain tissue via nasal inhalation, based on pharmacokinetic data for the brain compartments.

[0069] In some implementations, the multiple compartments based on a physiological pharmacokinetic model represent one or more or all of the following: arterial blood, lung, fat, bone, brain, heart, kidney, nose, muscle, skin, intestine, spleen, liver, other body compartments, and / or venous blood.

[0070] In some embodiments, the brain compartment includes separate subcompartments that represent one or more of the following: brain blood outside the blood-brain barrier, brain parenchyma representing brain tissue, cerebrospinal fluid (CSF), and / or spinal CSF.

[0071] In some embodiments, the nasal compartment represents one or more or all of the nasal region, nasal floor, turbinate, olfactory region, and / or nasopharyngeal region, and at least one is further indicated to include a mucus layer, an epithelial layer, and a subepithelial layer, wherein the mucus layer is the assumed site for drug deposition, the epithelial layer allows penetration into deeper tissues, and the subepithelial layer is perfused with blood vessels capable of transporting the drug to the systemic circulation.

[0072] In some embodiments, the physiological parameters of at least one compartment and subcompartment are selected from those listed in Table 1. In some embodiments, the compound-specific parameters of at least one compartment and subcompartment are selected from those listed in Table 2.

[0073] In some implementation schemes, the compound-specific parameters of the drug include: P (Nasal epithelial permeability), Log P (Logarithm of octanol / water partition coefficient) pK a (negative logarithm of the acid dissociation constant) fu (The fraction of drug dissolved in plasma that is not bound to plasma proteins) R (Blood / Plasma Ratio) Cl h (Liver clearance rate) and the mass of deposits in at least one region of the nose.

[0074] definition Absorption: The transfer of a compound across a physiological barrier, which is a function of time and initial concentration. The amount or concentration of the compound outside and / or inside the barrier is a function of the rate and extent of transfer.

[0075] Bioavailability: The fraction of the administered dose of a compound that reaches the sampling site and / or site of action. It can range from zero to one. It can be assessed as a function of time.

[0076] Compartment: Represents a tissue or organ, or a sub-part of a given tissue or organ. Multiple compartments can be assembled to generate a model, such as a multi-compartment model or a whole-body model.

[0077] Compound: A compound is a chemical entity. As used herein, the term "compound" may be used interchangeably with "drug."

[0078] Computer-readable media: Media used to store, retrieve, and / or manipulate information using a computer. This includes optical, digital, and magnetic media; examples include portable computer disks, CD-ROMs, and hard drives on a computer. It also includes remote access media; examples include the Internet or intranet systems. It allows for temporary or permanent data storage, access, and manipulation.

[0079] Data: Variables collected and / or predicted in the experiment. This may include dependent and independent variables.

[0080] Dissolution: The process by which a compound dissolves in a solvent.

[0081] Permeability: The ability of a physiological barrier to allow substances to pass through. It involves the rate (flux) of transport, whether concentration-dependent or not, and reflects the overall properties of a compound, such as the influence of molecular size, charge, partition coefficient, and stability on transport. Permeability is specific to both the substance and the barrier.

[0082] Simulation engine: A computer-implemented instrument that uses an approximate mathematical model of a system to simulate its behavior. It combines a mathematical model with user-input variables to simulate or predict the system's behavior. It may include system control components, such as control components (e.g., logic components and discrete objects).

[0083] Solubility: the property of being able to dissolve; relative solubility.

[0084] Transport mechanisms: The mechanisms by which compounds cross the physiological barriers of tissues or cells. These include four basic transport modes: passive paracellular transport, passive transcellular transport, carrier-mediated influx, and carrier-mediated efflux.

[0085] Parameterization / Parameterizing: Updating a model to include data for specific parameters. For example, data on specific physiological parameters of one or more compartments (and / or subcompartments) and / or parameters of specific compounds (e.g., drugs) included in the model.

[0086] Training: Updating and calibrating the model using ground truth data. For example, updating the model with known pharmacokinetic data of a specific compound (e.g., a drug) from one or more compartments (and / or subcompartments) included in the model.

[0087] The PBPK models described in this article simulate drug delivery via two pathways: direct translocation and absorption into the bloodstream along the olfactory region and trigeminal nerve, and subsequent translocation across the blood-brain barrier, representing naso-brain administration / deposition into the brain. These models are parameterized using non-clinical data, thus enabling the prediction of concentrations of new drugs or drug candidates in nasal and brain tissues without the need for costly clinical studies. These models also provide organ-specific targeting information, including that for the brain, which can inform the development of nasal spray products. They can be used to predict safe and effective dosages to mitigate risks prior to clinical trials and can be continuously improved through product development to increase their credibility commensurate with the decision-making risks predicted.

[0088] The PBPK model of this application improves upon existing techniques by explicitly simulating two simultaneous pathways of absorption into the brain: transport across the blood-brain barrier and transport through the olfactory cortex and trigeminal nerve. This improves the accuracy of predicting brain exposure after nasal administration compared to other models that assume transport not through the olfactory cortex and trigeminal nerve.

[0089] The PBPK model of this application supports the development of nasal drug delivery products in the early stages by predicting the impact of changes in drug delivery devices or formulations on drug concentrations in plasma or the brain. Without the nas-brain PBPK model disclosed herein, this information would not be available until clinical studies, at which point substantial changes to the drug product would typically be too late. Therefore, obtaining predictive clinical information early in development reduces the risk of altering formulations and devices during early development and provides assurance of clinical performance before clinical studies, avoiding unnecessary human and animal clinical trials.

[0090] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. This document describes the methods and materials used in this invention; however, other suitable methods and materials known in the art may also be used. Materials, methods, and examples are illustrative only and are not intended to be limiting. All publications, patent applications, patents, sequences, database entries, and other references mentioned herein are incorporated herein by reference in their entirety. In case of conflict, this specification (including definitions) shall prevail.

[0091] Other features and advantages of the invention will become apparent from the following detailed description, drawings, and claims. Attached Figure Description

[0092] Figure 1 This is a schematic diagram of a part of a multi-compartment physiological pharmacokinetic (PBPK) model, as described in this article, which includes compartments representing the nose and brain.

[0093] Figure 2This is a schematic diagram showing the sub-compartment structure of the nasal septum added to the PBPK model.

[0094] Figure 3 This is a schematic diagram illustrating the subcompartmental structure of a brain septum as added to a PBPK model, wherein the subcompartments of the brain septum include cerebrospinal fluid (CSF), brain tissue parenchyma, and the blood-brain barrier.

[0095] Figure 4 This is a schematic diagram showing the structure of the nasal region, olfactory region, and nasopharyngeal subcompartment region of the nasal septum in the PBPK model.

[0096] Figure 5A This is a flowchart of an example system used to generate PBPK models.

[0097] Figure 5B This is a flowchart and schematic diagram of an example of a computer system based on the PBPK model for predicting delivery and / or pharmacokinetic data.

[0098] Figure 6 This is a schematic diagram of system components that can be used to implement the models, systems, and methods described in this paper.

[0099] Figure 7 This is a graph showing the clinical (points) and predicted (lines, each line representing a row in Table 6) pharmacokinetics using the initial parameters (Table 4) in the PBPK model.

[0100] Figure 8 This is a graph showing the clinical (dots) and predicted (lines, each line representing a row in Table 6) pharmacokinetics using model parameters from the PBPK model (see Table 5).

[0101] Figure 9 The graph shows the predicted nasal and venous plasma concentrations relative to time, which was used to calculate the predicted nasal bioavailability of sumatriptan delivered using the UDS-L nasal spray device, a single-dose (unidose) nasal spray from Aptar.

[0102] Figures 10A to 10B This is a PCA biplot showing the pharmacokinetic data from nasal model deposition and prediction. Figure 10A ) and factor weighting vector ( Figure 10B A series of diagrams.

[0103] Figures 11A to 11B It shows C max ( Figure 11A ) and AUC 0-t ( Figure 11B A series of graphs showing the relationship between the deposition fraction in the nasal turbinate compartment and the nasal septum.

[0104] Figures 12A to 12B It shows C max ( Figure 12A ) and AUC 0-t ( Figure 12B A series of graphs showing the relationship between the deposition fractions in the nasal turbinates and nasal basal compartments of the nasal septum.

[0105] Figures 13A to 13B It shows C max ( Figure 13A ) and AUC 0-t ( Figure 13B A series of graphs showing the relationship between the deposition fraction in the nasal basal compartment and the deposition fraction in the nasal basal compartment.

[0106] Figures 14A to 14B It shows C max ( Figure 14A ) and AUC 0-t ( Figure 14B A series of graphs showing the relationship between the deposition fraction in the nasal basal compartment and the deposition fraction in the nasal basal compartment.

[0107] Figure 15 This shows the nasal turbinate deposition fraction versus predicted C for different 100 μL devices and orientations. max A graph showing the relationship between the data points. The lines are guides to the eye and represent the closest approximations of the data points.

[0108] Figure 16 This shows the nasal turbinate deposition fraction versus predicted C for different 50 μL devices and orientations. max A graph showing the relationship between the data points. The lines are guides to the eye and represent the closest approximations of the data points.

[0109] Figure 17 The figures show the graphs of the model simulations. Simulation 1 shows a model with no input mass, which, as expected, produces a plasma concentration of zero. Simulation 2 shows a model assuming the hypothetical drug decays from an initial plasma concentration of 1 ng / mL to zero. Simulation 3 shows a model assuming the olfactory mucus concentration decays from an initial concentration of 1 ng / mL to zero.

[0110] Figures 18A to 18B This demonstrates the use of high-odor zone deposition ( Figure 18A ) and low-odor zone deposition ( Figure 18B The model is a series of graphs predicting systemic plasma concentrations obtained from a single dose of 0.5 mg dihydroergotamine (DHE).

[0111] Figures 19A to 19B This demonstrates the use of high-odor zone deposition ( Figure 19A ) and low-odor zone deposition ( Figure 19B ( ) pattern, a series of graphs predicting brain compartment concentrations obtained from a single 0.5 mg dose of DHE. Detailed Implementation

[0112] Intranasal administration has been around for decades and is a common route of administration for localized therapies for conditions such as allergic rhinitis, sinusitis, and congestion. It is also increasingly being used and explored for systemic administration, such as for migraines and pain management.

[0113] The naso-brain physiology-based pharmacokinetic (PBPK) model disclosed in this paper can help assess the distribution of a specific drug or drug candidate in the brain of subjects (e.g., mammalian subjects, such as humans). The novel PBPK model offers advantages over existing PBPK models because it explicitly simulates transmission across the blood-brain barrier and along the olfactory cortex and trigeminal nerve. Current techniques do not explicitly simulate transmission along the olfactory cortex and trigeminal nerve, thus underestimating brain exposure. Therefore, the novel naso-brain PBPK model described in this paper provides a more accurate predictive model of brain exposure after intranasal administration.

[0114] A. Establishing a nose-brain PBPK a. Compartment A multi-compartment PBPK model is a mathematical model of a multi-compartment physiological model of a mammalian system (e.g., tissues / organs of a mammalian system). Depending on the intended end use of the model, compartments representing specific anatomical parts or regions of the body (e.g., tissues, organs, or vascular systems) may be added or removed, for example, when examining individual parts, or when parameters affecting the bioavailability of additional sampling points need to be considered.

[0115] Figure 1 The diagram schematically illustrates a multi-compartment PBPK model, showing an example of a multi-compartment model divided into the following compartments: arterial blood, lungs, fat, bone, brain, heart, kidneys, nose, muscles, skin, intestines, spleen, liver, the remaining body compartments, and venous blood.

[0116] like Figure 2 As shown, the nasal septum is further compartmentalized. Specifically, the nasal septum is divided into subcompartments of the nasal region, nasal floor, turbinates, olfactory region, and nasopharynx. Nasal septum subdivided in this way has never been seen before in this PBPK model.

[0117] Based on the physiological systems studied, compartments and subcompartments can be modified by factors influencing absorption, such as mass, volume, surface area, concentration, permeability, solubility, fluid secretion / absorption, fluid transport, and mass transport. More specifically, as presented herein, the PBPK model is represented by a series of differential equations describing the rate-process interactions between the multi-compartment anatomical parts when a specific drug is administered nasally (i.e., inhaled). Individual compartments are mathematically represented as integrated compartmental dynamic systems. In other words, the compartments are connected in a stepwise manner to form an integrated physiological model describing the absorption of a compound relative to its anatomical parts.

[0118] As presented in this paper, the PBPK model is defined by the following system of differential equations:

[0119]

[0120] in It refers to the volume of lung tissue. It refers to the concentration of the compound in lung tissue. It is the blood flow to the lungs. It refers to the concentration of compounds in venous plasma. It is the blood:plasma ratio. It is the tissue:plasma partition coefficient of the compound in the lung. It is the fraction of compounds that are not bound in the tissue. It is the tissue clearance rate of the compound.

[0121] The symbols in the second equation have the same meaning, where T Representing different tissues and organs: fat, bone, brain, heart, kidneys, muscles, skin, or the rest of the body, and This represents the concentration of compounds in arterial plasma. Different tissue and organ compartments are represented by the following equation.

[0122]

[0123]

[0124]

[0125]

[0126]

[0127] The symbols are as indicated by the subscripts above, referring to compartments. It is the liver clearance rate. It refers to blood clearance rate.

[0128]

[0129]

[0130]

[0131] in , , , , and It is the pair of nasal mucus, epithelium, and subepithelial volume and compound concentration in the i-th nasal region (referring to the nasal flap, nasal floor, turbinate, olfactory region, and nasopharyngeal subcompartment). It is the permeability of the nasal epithelium. It is the area of ​​the i-th nasal region. It is the mucociliary clearance rate of the substance transported to the i-th region (which is equal to 0 for all regions except the nasopharynx, while the nasopharynx is equal to...). ),and It is the mucociliary clearance rate of the substance transported out of the i-th region (equal to) It represents the mucociliary clearance rate that propels substances from the nasal floor, turbinates, and olfactory region to the nasopharynx, and is equal to... It represents the mucociliary clearance rate, which propels substances from the nasopharynx to the pharynx and ultimately into the gastrointestinal tract.

[0132] In some cases, if the assessment is of substance transport from brain blood to cerebrospinal fluid (CSF), then in situations such as Figure 3 The brain compartments are modeled in the subcompartmental system shown. Specifically, the regions outside the blood-brain barrier (BBB) ​​and blood-CSF barrier (BCSFB) are divided into brain parenchyma, cranial CSF, and spinal CSF regions. Furthermore, as... Figure 4 As shown, transport from the olfactory region of the nasal epithelium to the brain (beyond the BBB and BCSFB) is compartmentalized by illustrating transport between the subcompartments of the nasal region, olfactory region, and nasopharynx. Since olfactory neurons penetrate the entire depth of the epithelium, the model includes transport between the epithelial and subepithelial subcompartments of the olfactory region. Figure 3 and Figure 4 As shown, the transport of substances from brain blood to CSF ​​is defined by the following equation:

[0133]

[0134]

[0135] in , , , , and It is the ratio of nasal mucus, epithelium, and subepithelial volume to drug concentration in the i-th nasal region (referring to the nasal flap, nasal floor, turbinate, olfactory region, and nasopharyngeal compartment). It is the permeability of the nasal epithelium. It is the area of ​​the i-th nasal region. It is the mucociliary clearance rate of the substance transported to the i-th region (which is equal to 0 for all regions except the nasopharynx, while the nasopharynx is equal to...). ), It is the mucociliary clearance rate of the i-th region (for the nasal floor, turbinates, and olfactory region, it is equal to...). For the nasopharynx, it equals ). It is the rate at which substances are transported from the olfactory tissue to the cerebrospinal fluid via intracellular and extracellular pathways. It is the rate at which cerebrospinal fluid is transported to olfactory tissues via intracellular and extracellular pathways (for non-olfactory tissues, these two parameters are zero). It is the fraction of unbound drug in the cranial CSF. It refers to the concentration of cranial CSF.

[0136]

[0137]

[0138]

[0139]

[0140] in It is the volume of blood in the brain. It refers to the concentration of drug molecules in the bloodstream of the brain. It is the blood flow to the brain. It is the product of the permeability and surface area between the brain blood and brain parenchyma. It represents the fraction of unbound drugs in the brain parenchyma. It refers to the concentration of blood in the brain parenchyma. It represents the fraction of unbound drugs in the brain's bloodstream. It is the product of the permeability and surface area between cerebral blood and cranial CSF. It is the fraction of unbound drug in the cranial CSF. It refers to the concentration of the drug in the cranial CSF. and These refer to the flow rates of cerebrospinal fluid and spinal CSF to the brain, respectively. It refers to the concentration of the drug in the spinal cord CSF. It refers to the volume of the brain parenchyma. It is the product of the permeability and surface area between the brain parenchyma and cranial CSF. It refers to the overall flow from the brain parenchyma to the cranial CSF. and It is the CSF shuttle flow between cranial CSF and spinal CSF.

[0141] b. Parameterization of the PBPK model PBPK models are useful in part because they utilize two key components: compound-specific parameters (e.g., partition coefficients and metabolic rates) and species-specific physiological or anatomical parameters (e.g., cardiac output, organ weight, blood flow rate, relevant concentrations, etc.). Once a PBPK model updated with brain and nasal compartments and subcompartments, as discussed herein, has been prepared, various physiologically specific and compound-specific parameters must be filled in. In this step, all parameters describing the compartments and subcompartments involved in any differential equation in the PBPK model must be provided for the model to function.

[0142] i. Physiological specific parameters In the development, validation, extrapolation, and application of PBPK models, the use of accurate species-specific physiological parameters is crucial. These parameters are well-known for many species and can be retrieved from literature and databases. Table 1 below lists examples of physiological parameters (and their values) that can be implemented in this PBPK model. The specific physiological parameters included in the model depend on the compartments (i.e., organs / tissues) included in the model.

[0143] Table 1: Physiological Specific Parameters

[0144] ii. Compound-specific parameters Compound-specific parameters are characteristics of a specific compound (i.e., a drug, a chemical entity) obtained from any type of preclinical study. For example, this may include in vitro cell assays, in vitro protein assays (e.g., binding data), and / or in vivo studies conducted in mice, rats, or any other laboratory animals.

[0145] When building a PBPK model, known drugs with known compound-specific parameters (preclinical and clinical) are used to test and train the model.

[0146] Examples of compound-specific parameters that can be implemented in the PBPK model of this application include: Table 2: Compound-specific parameters iii. Required parameters of the PBPK model In order for the PBPK model to be correctly used for the analysis and modeling of new compounds, the following compound-specific parameters are required as input: ● P - Nasal epithelial permeability, o Use RPMI 2650, Calu-3, or other cell line models for approximation; ●Log P - Logarithm of octanol / water partition coefficient (used to calculate blood:tissue partition coefficient using common methods); ● pKa - The negative logarithm of the acid dissociation constant (used to calculate the blood:tissue partition coefficient); ● fu - The fraction of drug dissolved in plasma that is not bound to plasma proteins. o Measured using a protein binding assay; ● R - Blood / plasma ratio, the ratio of drug dissolved in whole blood to drug dissolved in plasma. o Measurement is performed by dissolving the drug in a blood sample and separating the plasma; ● Cl h-liver clearance rate (liver clearance rate) o Measured using liver or mitochondrial clearance assays. o Adjustments are typically made to improve the consistency between the model and clinical pharmacokinetic data (once they become available). ●The quality of compounds deposited in each area of ​​the nose, o Measurements were taken using a nose mold.

[0148] B. Application of the nose-brain PBPK model This paper also provides a method for predicting the delivery and pharmacokinetics of new or previously unknown candidate nasally administered (i.e., inhaled) drugs to brain tissue using PBPK models as described herein.

[0149] Preclinical data The nose-brain PBPK model is updated with known preclinical data on the compounds, as discussed in detail in the "Compound-Specific Parameters" section above. Specifically, compound-specific parameters are characteristics of the compounds obtained from preclinical studies. For example, this may include in vitro cell-based assays, in vitro protein assays (e.g., binding data), and / or in vivo studies in mice, rats, or any other laboratory animals.

[0150] Nasal deposition data The nasal-brain model was then updated using nasal cast deposition data. Nasal cast deposition data can be obtained from any known in vitro nasal cast device or physical model. In short, nasal casts help facilitate formulation and product development. Nasal deposition has been shown to correlate with pharmacokinetic results. Nasal casts are replicas of the human nasal cavity and have evolved from cadaver-based models to sophisticated 3D-printed replicas. They can be segmented into regions of interest for quantitative deposition, and various techniques have been utilized for quantitative deposition.

[0151] In some instances of the methods described in this application, Aeronose from AptarGroup, Inc. (Crystal Lake, IL) is used. ® Nasal molds. Nasal molds can be tested with various drug delivery devices in the form of nasal spray devices and nasal inhalation devices, including, for example, Adella N2B (D03 / 106), CPS, pre-loaded nozzles, UDSl Adella N2B, UDSl std, UDSpLiquide, VP7+232N2B, and VP7+CB18.

[0152] The medication (via a nasal spray device) is sprayed onto the nasal mold, and the amount of medication deposited in each area of ​​the nasal mold is fed into the model.

[0153] Running model Once the necessary inputs (physiological parameters, compound parameters, nasal deposition data, and the time points to be solved) are entered into the model, the mathematical equations describing the model (see the "Compartment" section) can be solved numerically using any suitable programming software (e.g., SciPy, MATLAB, Differential Equations.jl).

[0154] Prediction Once the model is run, a report is generated that includes information relating to drug concentrations in each compartment at one or more time points. This information can then be further analyzed (i.e., to obtain pharmacokinetic data) to provide predictions of delivery outcomes to brain tissue via nasal inhalation.

[0155] Model refinement To determine appropriate values ​​for the model parameters, available clinical data (i.e., intravenous and / or nasal data) describing the potential evolution of the model are used. This data is used to further refine the model. Model predictions of concentrations in one or more model compartments representing body regions (i.e., venous or arterial plasma, cerebrospinal fluid, nasal tissue, or brain tissue) at clinical time points are compared with clinical concentrations. The model parameters are then optimized using any suitable method. For example, this can be achieved by minimizing the objective function (i.e., least squares or average folding error) using a suitable algorithm (e.g., Levenberg-Marquardt or sequential least squares programming). A subset of parameters with known values ​​(e.g., subject weight) can be kept fixed, and other parameters can be allowed to vary within the range known from best practices or prior knowledge (i.e., the known range of the molecular categories being modeled or variability in preclinical data). Ideally, clinical data from intravenous and nasal administration are used, with the first step using intravenous data to optimize parameters related to systemic distribution (i.e., those related to tissue:plasma partition coefficient, blood-brain barrier permeability, and / or clearance rate), then these parameters are fixed, and a second step is performed to optimize parameters related to transport from the nasal cavity (i.e., epithelial permeability and / or transport rate along the olfactory region or trigeminal nerve).

[0156] In some implementations, if pharmacokinetic data following intravenous administration are available, this can be used to refine systemic treatment parameters (tissue:plasma partition coefficient, hepatic clearance, and blood clearance). If the initial elimination phase (just after maximum concentration) is too slow, hepatic clearance is increased (and vice versa). If the terminal elimination phase is too slow, the tissue:plasma partition coefficient can be scaled down proportionally (these coefficients are typically scaled down by the same amount), and vice versa. If the overall curve is too low, blood clearance can be introduced to increase blood clearance and lower the predicted concentration, and vice versa. Adjustments are typically made one parameter at a time, in increments of ~10% to find the correct region, and then adjusted in smaller increments to refine the parameter. Once all parameters have been optimized visually, parameters such as R... 2 The parameters can be further fine-tuned using goodness-of-fit indices such as chi-square or sum of squares.

[0157] Similarly, if pharmacokinetic data after nasal administration are available, they can be used to refine nasal penetration. This is adjusted in the same manner as the intravenous data described above.

[0158] C.PBPK Model System PBPK models can be generated, trained, and used to simulate the results of novel drug compounds on various computers and / or hardware or hybrid systems. An example of a computer and / or hardware system for generating such a physiologically based pharmacokinetic model is disclosed here. Figure 5AA flowchart illustrating the steps for generating, training, and using the PBPK model described in this application is provided. This is achieved by defining, as follows: Figures 1 to 4 The compartments outlined in the diagram are used to generate an initial PBPK model (10a). Furthermore, differential equations describing the relationships between the compartments are defined (10b). Species-specific physiological parameters for each compartment and subcompartment are defined (10c). Compound-specific parameters for known compounds (with known pharmacokinetic data) in one or more of the compartments and one or more of the subcompartments are also defined (10d).

[0159] The model is then parameterized by including parameters in the initial nas-brain PBPK model to include data for multiple physiological parameters for one or more or all of the compartments and one or more or all of the subcompartments (20a). The initial nas-brain PBPK model is also parameterized to include compound-specific parameters for drugs with known pharmacokinetic data for one or more or all of the compartments and one or more or all of the subcompartments, to generate a parameterized nas-brain PBPK model (20a). The compound-specific parameters may be derived from preclinical studies. The parameterized nas-brain model is then run by solving the equations using an engine with a differential equation solver (20b).

[0160] Next, a report is generated by running a parameterized nose-brain model, which includes drug concentration data for one or more compartments and / or one or more subcompartments at one or more time points (30). Finally, the drug concentration data in the report are analyzed and compared with known pharmacokinetic data of the compound (40). The parameterized nose-brain model is then updated to obtain a trained nose-to-brain model (40). Once the trained nose-brain model is established, it can be used to simulate predictions for new compounds with unknown pharmacokinetic data (50).

[0161] Figure 5B This is a block diagram of an example system 100 for generating and using PBPK models to predict delivery of transnasal administration to the brain. System 100 includes an input device 140, a network 120, and one or more computers 130 (e.g., one or more local processors or cloud-based processors).

[0162] Input device 140 is configured to input physiologically specific parameters 102a, nasal deposition data 102b, and compound-specific parameters 102c, and to provide these parameters to another device via network 120. Physiologically specific parameters 102a include, for example, the parameters listed in Table 1. They are species-specific and obtained through literature and data retrieval. Nasal deposition data 102b includes deposition data obtained after the drug is sprayed onto the nasal mold. The amount (e.g., mass) of the compound in each region of the nasal mold is nasal deposition data 102c. Compound-specific parameters 102c include preclinical data (and sometimes clinical data). This may include, for example, assays based on in vitro cells, in vitro protein assays (e.g., binding data), and / or in vivo studies performed in mice, rats, or any other laboratory animals.

[0163] In some embodiments, input device 140 may include server 140a configured to obtain physiologically specific parameters 102a and compound-specific parameters 102c from literature retrieval or relevant pharmacology-related databases. In some embodiments, one or more other input devices may access and receive nasal deposition data 102b and transmit the nasal deposition data 102b to computer 130 via network 120. Network 120 represents a computer network and may include wired Ethernet, wired optical network, wireless WiFi network, LAN, WAN, Bluetooth network, cellular network, Internet or other suitable network, or one or more of any combination thereof.

[0164] Computer 130 is configured to acquire and store physiologically specific parameters 102a, nasal deposition data 102b, and compound-specific parameters 102c, and to generate a PBPK model. Computer 130 may include necessary engines for writing and / or accessing necessary software for generating differential equations defining the PBPK model, as well as solvers for solving these differential equations. In some embodiments, computer 130 is a server. For the purposes of this disclosure, an "engine" may include one or more software modules, one or more hardware modules, or a combination of one or more software modules and one or more hardware modules. In some embodiments, one or more computers are dedicated to a particular engine. In some embodiments, multiple engines may be installed and run on the same or multiple computers.

[0165] Model generation engine 104 is configured to define independent compartments and sub-compartments for PBPK models (see example...) Figures 1 to 4 Once the model generation engine 104 generates the model, simulations are run using known compounds with known pharmacokinetic data. The model is updated and trained by comparing the simulations with known clinical data of the compounds.

[0166] To obtain pharmacokinetic data for a new compound, nasal deposition data 105 and preclinical compound-specific parameters 106 of the new compound are obtained and input into an updated / trained PBPK model 107. The simulation engine 108 can then provide delivery / pharmacokinetic predictions 110 for the specific new compound. The computer 130 can generate rendering data when rendered by a device with a display, such as a user device 150 (e.g., a computer with a monitor 150a, a mobile computing device such as a smartphone 150b, or another suitable user device).

[0167] D. Systems used for building and using PBPK models Figure 6 An example of a block diagram of system components that can be used to implement the systems, models, and methods described herein is shown. Figure 6 Computing device 500 is illustrated, representing any one or more of various forms of digital computers, such as laptops, desktop computers, workstations, personal digital assistants, servers, blade servers, mainframes, and other suitable computers. Computing device 550 is intended to represent various forms of mobile devices, such as personal digital assistants, cellular phones, smartphones, and other similar computing devices. Furthermore, computing devices 500 or 550 may include a Universal Serial Bus (USB) flash drive. The USB flash drive may store an operating system and other applications. The USB flash drive may include input / output components, such as a wireless transmitter or USB connector that can be plugged into a USB port of another computing device. The components shown herein, their connections and relationships, and their functions are merely exemplary and are not intended to limit the implementation of the invention described and / or claimed herein.

[0168] The computing device 500 includes a processor 502, a memory 504, a storage device 506, a high-speed controller 508 connected to the memory 504 and a high-speed expansion port 510, and a low-speed controller 512 connected to a low-speed bus 514 and the storage device 506. Each of the components 502, 504, 508, 508, 510, and 512 is interconnected using various buses and can be mounted on a common motherboard or otherwise suitably mounted. The processor 502 can process instructions for execution within the computing device 500, including instructions stored in the memory 504 or on the storage device 506 to display graphical information for a GUI on an external input / output device, such as a display 516 connected to the high-speed controller 508. In other embodiments, multiple processors and / or multiple buses, as well as various types of memory, can be suitably used. Furthermore, multiple computing devices 500 can be connected, with each device providing a portion of the necessary operation, for example, as a server group, a set of blade servers, or a multiprocessor system.

[0169] Memory 504 stores information within computing device 500. In one embodiment, memory 504 is a volatile memory cell or multiple volatile memory cells. In another embodiment, memory 504 is a non-volatile memory cell or multiple non-volatile memory cells. Memory 504 may also be another form of computer-readable medium, such as a magnetic disk or optical disk.

[0170] Storage device 506 provides mass storage for computing device 500. In one embodiment, storage device 506 may be or include computer-readable media, such as floppy disk devices, hard disk devices, optical disk devices, magnetic tape devices, flash memory or other similar solid-state storage devices, or device arrays, including devices or other configurations in a storage area network. The computer program product may be tangibly embodied in an information carrier. The computer program product may also contain instructions that, when executed, perform one or more methods, such as those described above. The information carrier is a computer-readable or machine-readable medium, such as memory 504, storage device 506, or memory on processor 502.

[0171] High-speed controller 508 manages bandwidth-intensive operations of computing device 500, while low-speed controller 512 manages lower bandwidth-intensive operations. This functional allocation is merely exemplary. In one embodiment, high-speed controller 508 is connected to memory 504, display 516 (e.g., via a graphics processor or accelerator), and high-speed expansion port 510, which can accept various expansion cards (not shown). In another embodiment, low-speed controller 512 is connected to storage device 506 and low-speed bus 514. The low-speed expansion port may include various communication ports such as USB, Bluetooth, Ethernet, wireless Ethernet, and may be connected to one or more input / output devices, such as keyboards, pointing devices, microphone / speaker pairs, scanners, or network devices (e.g., switches or routers), for example via a network adapter.

[0172] As shown, computing device 500 can be implemented in a variety of different forms. For example, it can be implemented as a standard server 520, or multiple times in a group of such servers. It can also be implemented as part of a rack-mount server system 524. Furthermore, it can be implemented in a personal computer, such as a laptop computer 522. Alternatively, components from computing device 500 can be combined with other components in a mobile device (not shown), such as device 550. Each such device may include one or more of computing devices 500, 550, and the entire system may consist of multiple computing devices 500, 550 communicating with each other.

[0173] As shown in the figure, computing device 500 can be implemented in a variety of different forms. For example, it can be implemented as a standard server 520, or multiple times in a group of such servers. It can also be implemented as part of a rack server system 524. Furthermore, it can be implemented in a personal computer such as a laptop computer 522. Alternatively, components from computing device 500 can be combined with other components in a mobile device (not shown), such as device 550. Each such device may include one or more of computing devices 500, 550, and the entire system may consist of multiple computing devices 500, 550 communicating with each other.

[0174] The computing device 550 includes a processor 552, a memory 564, and input / output devices such as a display 554, a communication interface 566 and a transceiver 568, as well as other components. The device 550 may also be equipped with storage devices, such as microdrives or other devices, to provide additional storage. Each of components 550, 552, 564, 554, 566, and 568 is interconnected using various buses, and several components may be mounted on a common motherboard or otherwise suitably mounted.

[0175] Processor 552 can execute instructions within computing device 550, including instructions stored in memory 564. The processor can be implemented as a chipset comprising individual and multiple analog and digital processors. Furthermore, the processor can be implemented using any of a variety of architectures. For example, the processor can be a CISC (Complex Instruction Set Computer) processor, a RISC (Reduced Instruction Set Computer) processor, or a MISC (Minimum Instruction Set Computer) processor. The processor can provide, for example, coordination of other components of device 550, such as control of the user interface, applications running on device 550, and wireless communication of device 550.

[0176] Processor 552 can communicate with the user via control interface 558 and display interface 556 connected to display 554. Display 554 can be, for example, a TFT (Thin Film Transistor Liquid Crystal Display) or OLED (Organic Light Emitting Diode) display or other suitable display technology. Display interface 556 may include suitable circuitry for driving display 554 to present graphics and other information to the user. Control interface 558 can accept commands from the user and translate them for submission to processor 552. Additionally, an external interface 562 can be provided to communicate with processor 552, enabling device 550 to communicate with other devices in close proximity. In some embodiments, external interface 562 may provide, for example, wired communication, or in other embodiments, wireless communication, and multiple interfaces may also be used.

[0177] Memory 564 stores information in computing device 550. Memory 564 may be implemented as one or more of computer-readable media, volatile memory cells, or non-volatile memory cells. Extended memory 574 may also be provided and connected to device 550 via extended interface 572, which may include, for example, a SIMM (Single In-line Memory Module) card interface. Extended memory 574 may provide additional storage space for device 550, or it may store applications or other information for device 550. Specifically, extended memory 574 may include instructions for performing or supplementing the above processes, and may also include security information. Thus, for example, extended memory 574 may be provided as a security module of device 550 and can be programmed with instructions that allow secure use of device 550. Furthermore, secure applications and additional information, such as identification information placed on the SIMM card in an unbreakable manner, may be provided via a SIMM card.

[0178] The memory may include, for example, flash memory and / or NVRAM memory, as described below. In one embodiment, the computer program product is tangibly embodied in an information carrier. The computer program product contains instructions that, when executed, perform one or more methods, such as those described above. The information carrier is a computer-readable or machine-readable medium that can be received, for example, by a transceiver 568 or an external interface 562, such as memory 564, extended memory 574, or memory on processor 552.

[0179] Device 550 can communicate wirelessly via communication interface 566, which may include digital signal processing circuitry if necessary. Communication interface 566 can provide communication under various modes or protocols, such as GSM voice calls, SMS, EMS or MMS messages, CDMA, TDMA, PDC, WCDMA, CDMA2000, or GPRS. This communication can be performed, for example, via (RF) transceiver 568. Furthermore, short-range communication can be performed, such as using Bluetooth, Wi-Fi, or other such transceivers (not shown). Additionally, GPS (Global Positioning System) receiver module 570 can provide device 550 with additional navigation and location-related wireless data, which can be appropriately used by applications running on device 550.

[0180] Device 550 can also use audio codec 560 for audible communication, which can receive voice information from a user and convert it into usable digital information. Audio codec 560 can also generate audible sounds for the user, for example, through a speaker, such as in the handheld device of device 550. Such sounds may include sounds from voice telephone calls, recorded sounds such as voice messages, music files, etc., and may also include sounds generated by applications running on device 550.

[0181] As shown in the figure, the computing device 550 can be implemented in a variety of different forms. For example, it can be implemented as a cellular phone 780. It can also be implemented as part of a smartphone 782, a personal digital assistant, or other similar mobile device.

[0182] Various implementations of the systems and methods described herein can be implemented in digital electronic circuits, integrated circuits, specially designed ASICs (Application-Specific Integrated Circuits), computer hardware, firmware, software, and / or combinations of such implementations. These various implementations may include implementations in one or more computer programs executable and / or interpretable on a programmable system, wherein the programmable system includes at least one programmable processor, which may be dedicated or general-purpose, configured to receive data and instructions from a storage system, at least one input device, and at least one output device, and to transmit data and instructions to the storage system, at least one input device, and at least one output device.

[0183] These computer programs (also known as programs, software, software applications, or code) include machine instructions for a programmable processor and can be implemented using high-level procedural and / or object-oriented programming languages, and / or assembly / machine languages. As used herein, the terms "machine-readable medium" and "computer-readable medium" refer to any computer program product, device, and / or apparatus for providing machine instructions and / or data to a programmable processor, such as a disk, optical disk, memory, or programmable logic device (PLD), including machine-readable media that receive machine instructions as machine-readable signals. The term "machine-readable signal" refers to any signal used to provide machine instructions and / or data to a programmable processor.

[0184] To provide interaction with the user, the systems and techniques described herein can be implemented on a computer having a display device, such as a CRT (cathode ray tube) or LCD (liquid crystal display) monitor for displaying information to the user, and a keyboard and pointing device, such as a mouse or trackball through which the user can provide input to the computer. Other types of devices for user interaction can also be provided; for example, feedback provided to the user can be any form of sensory feedback, such as visual feedback, auditory feedback, or tactile feedback; and input from the user can be received in any form, including sound, speech, or tactile input.

[0185] The systems and technologies described herein can be implemented in computing systems that include backend components, such as data servers; or middleware components, such as application servers; or frontend components, such as client computers with graphical user interfaces or web browsers through which users can interact with implementations of the systems and technologies described herein; or any combination of such backend, middleware, or frontend components. The components of the system can be interconnected via digital data communication of any form or medium, such as a communication network. Examples of communication networks include local area networks (“LANs”), wide area networks (“WANs”), and the Internet.

[0186] A computing system may include clients and servers. Clients and servers are typically remote to each other and usually interact via a communication network. The relationship between clients and servers is established through computer programs running on their respective computers, and they have a client-server relationship with each other.

[0187] Example The invention is further described in the following embodiments, which do not limit the scope of the invention as described in the claims.

[0188] Example 1: Pharmacokinetic prediction of sumatriptan via nasal administration using a physiologically based pharmacokinetic model from four different devices. The objective of this embodiment is to develop a PBPK model to predict the systemic pharmacokinetics of sumatriptan from in vitro nasal deposition data. In this embodiment, systemic PK is predicted based on deposition data from various devices, formulation viscosity, and orientation to cover a broad but relevant range of deposition profiles. This allows for the assessment of the impact of device variability and subject behavior on systemic pharmacokinetics.

[0189] The purpose of this embodiment is: 1. Develop a PBPK model that takes in vitro nasal model deposition data as input and outputs a curve of plasma concentration versus time.

[0190] 2. Parameterize the model using in vitro, in vivo, and clinical data from the literature.

[0191] 3. Compare the model predictions with clinical pharmacokinetic data from the literature.

[0192] 4. Predict pharmacokinetics.

[0193] 5. Perform statistical analysis to assess the effects of device, angle, insertion depth, dose, and viscosity on the pharmacokinetic overview parameters and any interactions between these factors.

[0194] In this embodiment, the following nasal deposition profiles for transnasal delivery devices were used: Adella N2B (D03 / 106), CPS, Preloaded Nozzle, UDS1 Adella N2B, UDS1 std, UDSp Liquide, VP7+232N2B, and VP7+CB18. The profiles for each of these devices are shown below. In Table 3, in the formulation column, the unit cP is centipoise, a measure of dynamic viscosity. In the orientation column, the first value represents the vertical angle, the second the horizontal angle, and the last the depth to which the device is inserted into the nostril of the nasal mold. The angle and depth are fixed using a guide inserted into the nasal spray device, thereby fixing its orientation relative to the nasal mold.

[0195] Table 3. Device Configuration Files

[0196] PBPK model Using the multi-compartment PBPK model as described herein, it is assumed that well-mixed tissue and blood compartments (i.e., each compartment is uniformly distributed) represent arterial blood, lungs, fat, bone, brain, heart, kidneys, nose, muscles, skin, intestines, spleen, liver, the remaining body compartments, and venous blood. It is assumed that clearance occurs in the liver and blood compartments. The nose is modeled by five compartments representing five different parts of the nose.

[0197] Based on the model structure reported by MS Bogdanffy, SRDR Plowchalk, A. Jarabek and ME Andersen, “A biologically-based risk assessment for vinyl acetate-induced cancer and non-cancer inhalation toxicity,” Toxicological Sciences, vol. 51, pp. 19-35, 1999, the nasal septum is divided into three subcompartments representing nasal mucus, epithelium, and subepithelial compartment. Following Bogdanffy et al., mass transport between the mucus, epithelium, and subepithelial compartments is modeled as osmotic limitation, and mass transport between the subepithelial and blood compartments is modeled as perfusion limitation. Sumatriptan is modeled as being delivered via an aqueous solution, thus assuming that deposited droplets are uniformly distributed in the mucus at the deposition point and that dose-volume does not significantly affect mucus volume. Figure 1 A schematic diagram of the system components of the model is shown. The nose is further compartmentalized. Figure 2 A schematic diagram of the nose portion of the model is shown.

[0198] The blood flow to the nasal floor, turbinates, olfactory cortex, and nasopharynx is assumed to constitute the total blood flow to the nose. It is known that blood flows to the nasal vestibule and atrium (which constitute...) Figure 2 The blood flow in the nasal region is so small as to be negligible that the blood flow rate in this region was set to 0 (A. Pires, A. Fortuna, G. Alves and A. Falcão, “Intranasal drug delivery: How, why and what for?,” Journal of Pharmacy and PharmaceuticalSciences, vol. 12, pp. 288-311, 2009).

[0199] The mucociliary clearance was modeled as a first-order mass transport process, pushing substances from the nasal floor, turbinates, and olfactory region into the nasopharynx at a fixed pre-mucociliary clearance rate (I. Gonda and E. Gipps, “Model of Disposition of Drugs Administered into the Human Nasal Cavity,” Pharm Res, vol. 7, pp. 69-75, 1990). It is noteworthy that the olfactory region is known to include few or no motile cilia (S. Gänger and K. Schindowski, “Tailoring Formulations for Intranasal Nose-to-Brain Delivery: A Review on Architecture, Physico-Chemical Characteristics and Mucociliary Clearance of the Nasal Olfactory Mucosa,” Pharmaceutics, vol. 10, p. 116, 2018). However, mass transport by gravity or centrifugal sliding and the continuous production of mucus from Bowman's glands are thought to facilitate mass transport away from this region (TT Solbu and T. Holen, “Aquaporin Pathways and MucinSecretion of Bowman's Glands Might Protect the Olfactory Mucosa,” ChemicalSenses, vol. 37, pp. 35-46, 2012). Therefore, the pre-mucociliary clearance rate is also applied to the olfactory region, but in this case, it represents a different mass transport mechanism.

[0200] The transport from the nasopharynx to the gastrointestinal tract is described by Gonda and Gipps (I. Gonda and E. Gipps, “Model of Disposition of Drugs Administered into the Human Nasal Cavity”). Pharm Res,The post-transfer coefficient is represented by the value reported in vol. 7, pp. 69-75, 1990. Due to the low oral bioavailability of sumatriptan (LF Lacey, HEK and PA Fowler, “Single dose pharmacokinetics of sumatriptan in healthy volunteers,” European Journal of Clinical Pharmacology, vol. 47, pp. 543-548, 1995) and the low proportion of the dose likely to enter the gastrointestinal tract, oral bioavailability was set to 0%. The following table summarizes the physiological and compound-specific parameters of the PBPK model used in this embodiment.

[0201] Table 4: Sources and values ​​of initial model parameters

[0202] The final model parameters are shown in Table 5. Any parameters not included here are equal to the values ​​in Table 4.

[0203] Table 5: Sources and values ​​of the final model parameters

[0204] The mathematical equations describing the model are solved using Python version 3.10.4 and SciPy version 1.8.1.

[0205] PBPK model validation and modification Comparing model predictions with C. Duquesnoy, JP Mamet, D. Sumner and E. Fuseau, “Comparative clinical pharmacokinetics of single doses of sumatriptan following subcutaneous, oral, rectal and intranasal administration,” European Journal of Pharmaceutical Sciences,The model was compared with clinical data reported in vol. 6, pp. 99-104, 199. For this purpose, the model input was in vitro nasal membrane deposition data from the USD-L standard device at multiple orientations (see Table 6 below) and a 20 mg dose. Nasal epithelial permeability, tissue:plasma partition coefficient scaling, liver clearance, and blood clearance were all modified to improve the consistency between the model and clinical data. The model's consistency with the reported 16% nasal bioavailability was also tested.

[0206] Table 6: In vitro nasal mold deposition fractions of 2cP formulations delivered by USDI standard devices under different orientations

[0207] Model application - prediction of systemic pharmacokinetics After establishing the model and validating it against clinical pharmacokinetic data, systemic pharmacokinetic predictions were made for each orientation outlined in Table 3. A total of 1000 time points were simulated over 0 to 6 hours to obtain maximum plasma concentrations and area under the curve (AUC). Plasma concentrations relative to time were plotted, and Cd values ​​for each configuration were reported. max The area under the curve (AUC) up to the final time point 0-t ).

[0208] Model application - statistical analysis Then, JMP 15.1 was used to plot the predicted pharmacokinetic results for each input factor.

[0209] Results PBPK model validation and modification Initially, the model was used to predict the systemic pharmacokinetics of the input UDSI std data using the initial estimated parameters shown in Table 4 (see the “Model Building” section in the detailed implementation). Figure 7 The initial predicted values ​​are shown in C. Duquesnoy, JP Mamet, D. Sumner and E. Fuseau, “Comparative clinical pharmacokinetics of single doses of sumatriptan following subcutaneous, oral, rectangular and intranasal administration,” European Journal of Pharmaceutical Sciences, The clinical pharmacokinetics of sumatriptan solution administered intranasally, as reported in vol. 6, pp. 99-104, 1998.

[0210] The initially predicted slow absorption suggests that some parameter adjustments are necessary. Parameters with significant uncertainty (or those completely unknown) are: ·Nasal epithelial permeability (N. Sibinovska, S. Žakelj, J. Trontelj and K. Kristan, "Applicability of RPMI 2650 and Calu-3 Cell Models for Evaluation of NasalFormulations," Pharmaceutics, The value reported in vol. 14, pp. 1-19, 2021 is 1.39 × 10⁻⁶. -7 62.7×10 -7 cm / s and 107 × 10 -7 (value of cm / s); • Tissue: Plasma partition coefficient proportionality factor (unknown, typically used to adjust for linearity (SA Peters, "Evaluation of a generic physiologically based pharmacokinetic model for lineshape analysis," Clinical Pharmacokinetics, vol. 47, pp. 261-275, 2008); • Liver clearance rate (unknown); • Removed from the blood (unknown).

[0211] First, the liver clearance rate was adjusted because it is known to saturate at larger values. The system was found to have a saturation value of 30,000 hr. -1 This still does not allow the drug to be cleared from the systemic circulation, such as Figure 7 As observed in the clinical data shown, this value is therefore fixed at the saturation point.

[0212] The permeability was then scaled to increase the rate of release from the nasal epithelium into the systemic circulation. It was found that 12.54 × 10⁻⁶... -7 The value of cm / s brings the curve close to clinical data and is located at N. Sibinovska, S. Žakelj, J. Trontelj and K. Kristan, “Applicability of RPMI 2650 and Calu-3 Cell Models for Evaluation of Nasal Formulations,” Pharmaceutics, The values ​​reported in vol. 14, pp. 1-19, 2021 are between those reported in vol. 14, pp. 1-19, 2021.

[0213] At this point, the tissue:plasma partition coefficient was increased from 1 to 1.8 to reduce the amount of drug that could be partitioned into plasma from all tissues. Finally, the blood clearance rate was increased from 0 to 1000 hr. -1 This was done to further control for the linearity of systemic elimination and to visually align the predictions with clinical pharmacokinetics. The final optimized model predictions are as follows: Figure 8 As shown.

[0214] Subsequently, the nasal bioavailability of the known 16% Imigran nasal spray (GlaxoSmithKline, "Imigran® NASAL SPRAY") [online] accessible at https: / / gskpro.com / content / dam / global / hcpportal / en_NA / PI / Imigran-20-mg-Nasal-Spray-GDS07.pdf was determined by C. Duquesnoy, JP Mamet, D. Sumner and E. Fuseau, "Comparative clinical pharmacokinetics of single doses of sumatriptan following subcutaneous, oral, rectal and intranasal administration," European Journal of Pharmaceutical Sciences, The time points reported in vol.6, pp. 99-104, 1998 simulated a 20 mg intravenous bolus dose and nasal dose (using the nasal deposition pattern in the first row of Table 4) and took the AUC. 0-t The model predictions were validated using the ratio of values. The model predicted a nasal bioavailability of 21.59%, close to the reported clinical value, and the curve of predicted plasma concentration relative to time used to calculate this value is shown in [the figure]. Figure 9 middle.

[0215] Model application - prediction of systemic pharmacokinetics After successfully validating the model, the systemic pharmacokinetics of each nasal deposit curve shown in Table 3, along with a dose of 20 mg sumatriptan, were input into the model. Table 7 shows the nasal deposit results for each configuration.

[0216] Table 7: Nasal mold deposition data input into the model

[0217] The predicted pharmacokinetic parameters are shown in Table 8.

[0218] Table 8: Pharmacokinetic parameters predicted from the nasal mold deposition data shown in Table 7

[0219] Discussion In the initial project plan, linear models were used to evaluate the most influential factors other than device and orientation. However, in a more recent scope, a large number of device parameters were screened, so the relationship between nasal mold deposition data and predicted pharmacokinetics was initially examined to establish an in vitro computer model. in vitro - in silico The simulation relationship. Principal component analysis (PCA) was first used to examine the relationship between the nasal model deposition fraction and the predicted pharmacokinetic parameters. The PCA bipolar plot is shown in... Figures 10A to 10B .

[0220] PCA of factor-weighted vectors indicates the correlation between parameters. Parallel vectors in the same direction indicate a positive correlation. Parallel vectors in opposite directions indicate a negative correlation. Orthogonal vectors indicate no correlation. Figure 10B The vectors in the figure indicate the relationship between nasal turbinate deposition and predicted AUC and C. max The strong correlation between them, and the limited correlation with other individual nasal regions. To further investigate this, the deposition fraction of each nasal region and C were examined. max and AUC 0-t The image shows nasal turbinate deposition and C. max and AUC 0-t The relationship between them is shown in Figures 11A to 11B .

[0221] These data indicate a strong positive correlation between deposition in the nasal turbinates and predicted systemic exposure. max The correlation is stronger than that of AUC. 0-t However, in cases of low nasal turbinate deposition, C max An outlier was observed on the graph. Upon examination, this was identified as the CPS pump (ID 3 in Tables 3, 7, and 8), which exhibited significantly higher deposition in the nasal floor region than other devices (66%, compared to a maximum of 20% for all other data). This indicates that combined deposition in the nasal floor and turbinates is significant for systemic exposure. The combination was plotted against predicted systemic exposure, showing the effect in... Figures 12A to 12B middle.

[0222] Comparison between turbinate and nasal floor deposition fractions and predicted C max The correlation is stronger, but it seems to increase with AUC. 0-t The dispersion of the relationship. This indicates that both parameters are important in the driving system. At this stage, due to the input of a more limited range of nasal base deposition values ​​into the model, stronger conclusions regarding nasal base dependence cannot be drawn, such as... Figures 13A to 3As shown in Figure B, it illustrates the relationship between the deposition fraction at the nasal base and the predicted whole-body exposure.

[0223] PCA showed limited correlation between predicted systemic exposure and deposits in the olfactory region, nasopharynx, and filter / lungs; therefore, these were not plotted. Despite showing limited correlation in PCA, the nasal region was investigated because the influence of areas that do not allow absorption into the systemic circulation is noteworthy. Figures 14A to 14B C is shown in max (Left) and AUC 0-t (Right) Relationship with the fraction of deposits in the nose.

[0224] These data suggest a certain degree of negative correlation between nasal deposition and systemic pharmacokinetics. This could be explained by the lack of absorption pathways in this region of the nose; however, some points in the lower nasal region show low and high C2O2. max and AUC 0-t This indicates that sedimentation in other regions will also affect the predicted whole-body PK.

[0225] The conclusion drawn in this section is that the predicted systemic exposure largely depends on deposition in the nasal turbinates. This is due to the fact that this region exhibits a high surface area (9057 mm²) compared to other regions except the olfactory zone. 2 In contrast, the nasal base is 4019mm. 2 The nasopharynx is 2919 mm. 2 The olfactory region is 9743 mm. 2 ) and thin mucus (25 μm, compared to 80 μm in the olfactory region (CB Frederick, ML Bush, LG Lomax, KA Black, L. Finch, JSKimbell, KT Morgan, RP Subramaniam, JB Morris and JS Ultman, “Application of a hybrid computational fluid dynamics and physiologically based inhalation model for interspecies dosimetry extrapolation of acidic vapors in the upper airways,” Toxicology and Applied Pharmacology,vol. 152, pp. 211-231, 1998)) and the epithelial layer (10 μm, compared to the olfactory region of 10 μm) (CB Frederick, ML Bush, LG Lomax, KA Black, L. Finch, JS Kimbell, KT Morgan, RP Subramaniam, JB Morris and JS Ultman, “Application of a hybrid computational fluid dynamics and physiologically based inhalation model for interspecies dosimetry extrapolation of acidic vapors in the upper airways,” Toxicology and Applied Pharmacology, (vol. 152, pp. 211-231, 1998). Therefore, drugs targeting the central nasal cavity have a high probability of landing in the turbinates and do not need to penetrate far through the mucus and epithelial layer to reach the perfused subepithelial tissue, where they can penetrate into the capillaries and be transported into the systemic circulation. Drugs landing in the olfactory region must penetrate through a larger space before reaching the perfused tissue, and therefore do not have a strong effect on the system's exposure.

[0226] Using the insights developed in the previous section, we analyzed the differences in predicted systemic exposure across different device types and orientations. To ensure valuable comparisons, 100µL dosing devices (CPS, UDS1 Adella N2B (D03 / L06), UDS1 std, and VP7 CB18) were compared with 50µL devices (Adella N2B, pre-loaded nozzle, UDSp Liquide, and VP7 232 N2B). Results for the 100µL devices are shown in... Figure 15 middle.

[0227] These data indicate that with increasing nasal turbinate deposition, the predicted C max Generally increasing (as described above), for all devices except CPS, with decreasing insertion angle, nasal turbinate deposition and predicted C max All increase, with 55° producing the lowest predicted C. max 35° produces the highest predicted C max During high nasal turbinate deposition, UDSl Adella N2B, UDSl std, and VP7CB18 all produced similar predicted C values. max Nasal turbinate deposition and predicted Cmax The dependence between them diverged at low nasal turbinate deposition sites. VP7 CB18 showed a higher predictive C at nasal turbinate deposition fractions of 0.5 to 0.6. max Furthermore, the dependence on increased deposition is relatively weak. This appears to be due to the increased nasal floor deposition in VP7 CB18, which weakens the effect of turbinate deposition on variation. This suggests that VP7 CB18 may have reduced variability due to angular differences compared to the other two devices. This relationship also explains why, despite lower turbinate deposition in the CPS device, its predicted C... max The nasal base deposition fraction is higher because this device exhibits a significantly larger fraction than other devices. The relationship between the nasal turbinate deposition fraction and predicted Cmax for different 50µL devices and orientations is shown in... Figure 16 middle.

[0228] For the 50µL device, the relationship was more direct than for the 100µL device, because all 50µL devices showed nasal turbinate deposition in relation to predicted C. max Similar dependencies exist between them. This is likely because the nasal floor deposition of these devices is low and does not affect the predicted systemic exposure. The nasal turbinate deposition of the 50µL device (and therefore the predicted C...) max The value of Cmax also increases as the insertion angle decreases. Therefore, the difference in predicted Cmax between devices depends on the ability of each device to deliver to the nasal turbinates, with the Adella N2B (D03 / 106) showing the highest value, while other devices cover a similar range.

[0229] In summary, a PBPK model for systemic absorption of sumatriptan via nasal delivery was successfully developed and validated using clinical pharmacokinetic data.

[0230] Example 2: Construction of a pharmacokinetic model based on nasal-brain physiology The aim of this study was to develop a PBPK model that could facilitate the prediction of systemic and local neuropharmacokinetics of a given molecule from in vitro human nasal model deposition data (which could then be retrained to simulate non-human primates (NHP)). In this preliminary study, the model was designed, built, and parameterized using literature data or estimated parameters.

[0231] The purpose of this study is: 1. Develop a PBPK model that takes in vitro nasal model deposition data as input and outputs curves of plasma concentration relative to time, CSF concentration relative to time, and brain tissue concentration relative to time.

[0232] 2. Parameterize the model using in vitro, in vivo, and clinical data from the literature, as well as estimated parameters.

[0233] 3. It was confirmed that the model can produce predictions using the estimated input parameters.

[0234] PBPK model Using the multi-compartment PBPK model as described herein, it is assumed that well-mixed tissue and blood compartments (i.e., each compartment is uniformly distributed) represent arterial blood, lung, fat, bone, brain, heart, kidney, nose, muscle, skin, intestine, spleen, liver, the remaining body compartments, and venous blood. Clearance is assumed to occur in the liver and blood compartments. The nose is represented as a stack of epithelial cells consisting of the nasal region, nasal floor, turbinates, olfactory region, and nasopharynx. Each region consists of a mucus layer, an epithelial layer, and a subepithelial layer, where the mucus layer is assumed to be the site of drug deposition, the epithelial layer allows penetration into deeper tissues, and the subepithelial layer is perfused with blood vessels capable of transporting drugs to the systemic circulation. See, for example, some descriptions in Example 1 and... Figure 1 and Figure 2 The brain is represented by cerebral blood outside the blood-brain barrier, brain parenchyma representing most of the brain tissue, cranial CSF, and spinal CSF. There are material transport processes from the olfactory epithelium and subepithelial layer to the cranial CSF, representing a combination of intracellular and extracellular transport. The transport of materials from cerebral blood to CSF ​​and brain parenchyma is modeled according to LF Verscheijden, JB Koenderink, SN de Wildt and FG Russel, “Development of a physiologically-based pharmacokinetic pediatric brain model for prediction of cerebrospinal fluid drug concentrations and the influence of meningitis,” PLoS Computational Biology, vol. 15, p. e1007117, 2019, where the region outside the blood-brain barrier (BBB) ​​and blood-CSF barrier (BCSFB) is divided into brain parenchyma, cranial CSF, and spinal CSF regions. A schematic diagram of the nasal portion of the model is shown below. Figure 3As shown. Finally, transport from the olfactory region of the nasal epithelium to the brain (beyond the BBB and BCSFB) was modeled as a single primary transport process determined by ingress and egress coefficients. Intracellular (endocytosis and transport through the olfactory region and trigeminal nerve) and extracellular (diffusion into the perineural space via tight junctions) were considered; however, due to the difficulty in separating these mechanisms, they were considered as a single process transporting substances from the olfactory region to the cranial CSF (TP Crowe, MHW Greenlee, AG Kanthasamy and WH Hsu, “Mechanism of intranasal drug delivery directly to the brain,” Life Sciences, vol. 195, pp. 44-52, 2018). Since olfactory neurons penetrate the entire depth of the epithelium, transport from the epithelial and subepithelial compartments of the olfactory region was considered. Figure 4 A schematic diagram of the olfactory region of the nose and its transport pathway to the brain is shown.

[0235] The model was parameterized using physiological values ​​from the literature and compound-specific parameters of DHE (see Table 1 above for a list of physiological parameters and values, and Table 9 below for a list of compound-specific parameters of DHE). Since the purpose of this study was solely to construct an effective PBPK model, any unknown parameters were estimated at this stage. A schematic diagram of the multi-compartment model is shown in [the table below]. Figure 1 The model is described in detail below. The equations defining the model are outlined in the subsection titled "Compartment" under the section titled "Model Building" above the specific implementation. The mathematical equations describing the model are solved using Python version 3.10.4 and SciPy 1.8.1.

[0236] Table 9: Sources and values ​​of specific parameters for the initial model compounds

[0237] Note that many parameters are estimated at this stage, so the numerical predictions from the model have no credibility and are only used to explore possible model outputs. The estimated model parameters are summarized in Table 10.

[0238] Table 10: Showing the estimated parameters for the model

[0239] To ensure the correct implementation of the model, three simulations were conducted. One simulation set the initial mass of all areas of the body to zero; the second simulation set the initial intravenous bolus dose to a plasma concentration of 1 ng / mL; and the third simulation set the initial dose to a concentration of 1 ng / mL in the olfactory mucus.

[0240] If the model is implemented correctly, the first case should produce zero concentrations in all compartments (including whole-body plasma), the second case should show a multi-exponential decay of plasma concentrations from 1 ng / mL, and the third case should show a multi-exponential decay of olfactory mucus compartments to zero. The results of these three simulations are shown in... Figure 17 middle.

[0241] These simulations demonstrate that the model correctly reproduces the three expected behaviors: a predicted concentration of zero when no mass input is fed into the model; a plasma concentration that decays to zero as DHE is metabolized and cleared; and a concentration in olfactory mucus that decays to zero as DHE diffuses and permeates into the nasal epithelium. The model's reproduction of all three expected behaviors proves its effectiveness.

[0242] Following the successful establishment and validation of the model behavior (see above), numerous exemplary simulations were performed to confirm the predictions that could be made using the model. Simulations were conducted using two different deposition patterns—high-olfactory zone deposition pattern and low-olfactory zone deposition pattern—to represent a single spray dose of 0.5 mg from Migranal (DHE Nasal Spray) (FDA, “Migranal Product Label”, [online]. Accessible online: accessdata.fda.gov / drugsatfda_docs / label / 2019 / 020148orig1s025lbl.pdf). These data are taken from Example 1, based on in vitro nasal model deposition data, and are summarized in Table 11.

[0243] Table 11: Nasal deposition patterns input into the model

[0244] The whole-body plasma concentrations predicted by the two deposition patterns are shown in Figure 18.

[0245] Predicted maximum body concentration (C) in high-odor zone sedimentation max The concentration was 11.91 pg / mL, lower than the 21.95 pg / mL obtained from low-odor deposition. For both high-odor and low-odor deposition modes, the area under the concentration-time curve (AUC) was similar, at 180.24 pg h / mL and 180.29 pg h / mL, respectively. This is consistent with the predicted C... max Compared to a time of 1.83 h, the prediction of sedimentation simulation in the high-odor area reached C. max Time (T) maxThe duration was longer at 3.53 h. These trends are consistent with the expected trend that higher deposition in the nasal turbinates results in higher systemic drug exposure (see Example 1 above). Furthermore, the same total systemic dose (similar AUC) was obtained, but release occurred at different time ranges for different levels of olfactory deposition. It should be noted that these findings are specific to this case and may differ when the uncertain parameters are refined, and may vary for different molecules.

[0246] To determine the impact of olfactory deposition on predicted brain exposure, predicted concentrations of DHE in brain blood, brain parenchyma, cranial CSF, and spinal CSF were also plotted and are shown in Figure 19.

[0247] For deposition in the high and low olfactory regions, the material transport pathway between the olfactory region and cranial CSF (by...) and Represents a combination of intracellular and extracellular transport mechanisms and (Parameter capture) caused significant concentrations of DHE in all brain regions. Predicted brain region C max The values ​​are shown in Table 12.

[0248] Table 12: Predicted Brain C max value

[0249] Although the predicted C in brain blood max Only minor differences were observed, but in cases of deposition in the high olfactory region, C in the brain parenchyma and both CSF compartments... max This is an order of magnitude larger than in the case of hypoolfactory deposition. This suggests that, within the highly uncertain parameters presented by the initial model, increased olfactory deposition could significantly improve brain targeting due to direct penetration of the blood-brain barrier through the olfactory region of the nose. This contrasts with hypoolfactory deposition, which relies on systemic exposure via the nasal turbinates, delivery to the cerebral bloodstream, and penetration across the blood-brain barrier for brain exposure. As confirmed by Figure 19 and Table 12, the latter pathway appears to be much less efficient within the highly uncertain parameters of the current form of the model.

[0250] A PBPK model was successfully designed and implemented, which includes cerebral blood, brain parenchyma, and two CSF ​​compartments, in addition to the mass transport pathway from the olfactory cortex epithelium and subepithelial region to the brain. A series of simple theoretical cases were tested to ensure that the model produces the expected behavior.

[0251] Example 3: Non-human PBPK model Validating the PBPK model for predicting CSF and brain parenchyma concentration in humans is either impossible or considered unethical. However, the model can be validated in animal models, such as rats, dogs, cats, rabbits, non-human primates, pigs, sheep, goats, cattle, or horses, where CSF is sampled or used in terminal studies and brain parenchyma concentration is measured.

[0252] Therefore, the model is parameterized for animals. Specifically, physiological differences are adjusted for tissue quality and blood flow, as these are known for many species (such as those mentioned above, i.e., rats, dogs, and non-human primates). Furthermore, this will be achieved by obtaining... The model is parameterized for drug-specific differences by using different values ​​of other potential parameters.

[0253] The parameters are refined to ensure the model reproduces the observed plasma, cerebrospinal fluid, and / or brain parenchyma concentrations. This will include identifying any unknown brain transport parameters. , and (These are the product of different surface areas within the brain and the permeability of drugs across various membranes), and parameters and (These are the transport coefficients from nose to brain and from brain to nose, respectively).

[0254] Assuming that the brain transport parameters are the same for animal species and humans (unless the surface area ratio is known, in which case the parameters can be scaled), the remaining physiological and drug-specific parameters will be changed to those used for humans. The model can then predict changes in CSF and brain tissue concentrations over time after nasal administration. The model can also predict what percentage of the dose reaching the brain is transported directly from the nose through the olfactory cortex and trigeminal nerve, and what percentage is first absorbed into the bloodstream and then crosses the blood-brain barrier.

[0255] Other implementation methods It should be understood that although the invention has been described in conjunction with its detailed description, the foregoing description is intended to illustrate and not limit the scope of the invention, which is defined by the scope of the appended claims. Other aspects, advantages, and modifications are within the scope of the appended claims.

Claims

1. A computer-implemented method for generating a trained naso-brain physiology-based pharmacokinetic (PBPK) model for the delivery of a drug to brain tissue via nasal inhalation, the method comprising: (a) Generate a multi-compartment PBPK model, wherein the multi-compartment PBPK model includes multiple independent body compartments; (b) Adding a brain compartment and a nasal compartment to the multi-compartment PBPK model to generate an initial nose-brain PBPK model, wherein the nasal compartment comprises one or more independent nasal compartments; (c) Parameterize the initial nose-brain PBPK model to include data for one or more or all of the multiple physiological parameters for the multiple independent body compartments and / or the multiple independent nasal compartments; (d) The initial nas-brain PBPK model is parameterized to include compound-specific parameters for drugs with known pharmacokinetic data for each body compartment and each nasal compartment to generate a parameterized nas-brain PBPK model. (e) Run the parameterized nose-brain model and generate a report that includes drug concentration data for one or more body compartments and / or one or more independent nasal compartments at one or more time points; as well as (f) Analyze and compare the drug concentration data in the report with the known pharmacokinetic data of the drug, and update the parameterized nose-brain model to obtain a trained nose-brain model.

2. The method according to claim 1, wherein, Multicompartmental pharmacokinetic models based on physiology represent one or more or all of the following: arterial blood, lungs, fat, bone, brain, heart, kidneys, nose, muscles, skin, intestines, spleen, liver, other body compartments, and / or venous blood.

3. The method according to claim 1 or 2, wherein, The one or more separate nasal compartments represent one or more or all of the nasal region, nasal floor, turbinate, olfactory region, or nasopharyngeal region.

4. The method according to any one of claims 1 to 3, wherein, The brain compartment includes independent subcompartments, which represent one or more of the following: brain blood outside the blood-brain barrier, brain parenchyma representing brain tissue, cerebrospinal fluid (CSF), and / or spinal CSF.

5. The method according to any one of claims 1 to 4, wherein, At least one of the nasal compartments further represents a mucus layer, an epithelial layer, and a subepithelial layer, wherein the mucus layer is the assumed site for drug deposition, the epithelial layer allows penetration into deeper tissues, and the subepithelial layer is perfused with blood vessels capable of transporting the drug into the systemic circulation.

6. The method according to any one of claims 1 to 5, wherein, The physiological parameters of at least one compartment and at least one subcompartment are selected from those described in Table 1.

7. The method according to any one of claims 1 to 5, wherein, The compound-specific parameters of at least one compartment and at least one subcompartment are selected from those described in Table 2.

8. The method according to any one of claims 1 to 6, wherein, The specific parameters of the compound in the drug include: P (Nasal epithelial permeability), Log P (Logarithm of octanol / water partition coefficient) pK a (negative logarithm of the acid dissociation constant) fu (The fraction of drug dissolved in plasma that is not bound to plasma proteins) R (Blood / Plasma Ratio) Cl h (Liver clearance rate) and the mass of deposits in at least one region of the nose.

9. The method according to any one of claims 1 to 8, wherein, The body compartments of the multi-compartment PBPK model are represented by differential equations, which represent one or more of the following: (i) the concentration of the drug in one or more of the lungs, fat, bone, heart, kidneys, muscles, skin, or the rest of the body, and (ii) The plasma concentration of the drug in one or more of the spleen, liver, intestines, arterial plasma and / or veins is a function of lung tissue volume with respect to time, and wherein... The differential equation is a function of one or more of the following parameters: Blood flow to the lungs; The concentration of the drug in venous plasma; Blood:Plasma ratio; The tissue:plasma partition coefficient of the drug in each tissue type; The fraction of the drug that is not bound in the tissue; The tissue clearance rate of the drug; Volume of each tissue or plasma type; The concentration of the drug in each tissue or plasma type; Blood flow rate to each tissue type; Liver clearance rate; and / or The blood clearance rate of the drug.

10. The method according to claim 9, wherein, The differential equation is one or more of the following: ,as well as in, It is the volume of lung tissue; This refers to the concentration of the drug in the lung tissue; It is the blood flow to the lungs; It refers to the concentration of the drug in venous plasma; It is the blood:plasma ratio; It is the tissue-to-plasma partition coefficient of the drug in the lungs; It represents the fraction of drug that is not bound in the tissue; It is the tissue clearance rate of the drug; It includes fat, bones, heart, kidneys, muscles, skin, and the rest of the body; It refers to the volume of the spleen tissue; It refers to the concentration of the drug in the spleen tissue; It is the blood flow to the spleen; It is the tissue-to-plasma partition coefficient of the drug in the spleen; It is the volume of the intestinal tissue; It refers to the concentration of the drug in the intestinal tissue; It refers to the blood flow to the intestines; It is the tissue-plasma partition coefficient of the drug in the intestine; It refers to the volume of liver tissue; It refers to the concentration of the drug in liver tissue; It refers to the blood flow to the liver; It is the tissue:plasma partition coefficient of the drug in the liver; It refers to the concentration of the drug in arterial plasma; It is the liver clearance rate; It refers to blood clearance rate.

11. The method according to any one of claims 1 to 10, wherein, The nasal compartment is represented by a differential equation, which represents one or more of the following: (i) The concentration of the drug in the nasal mucus, (ii) The concentration of the drug in the nasal epithelium, and (iii) The concentration of the drug in the subepithelial space of the nose, and among which The differential equation is a function of one or more of the following parameters: The permeability of the nasal epithelium; The area of ​​each region in the nasal cavity; Drug distribution in nasal tissues; plasma partition coefficient; Mucociliary clearance rate in each region of the nasal cavity; The rate at which the olfactory tissue is transported to the cerebrospinal fluid via intracellular and extracellular pathways through the olfactory region and / or the trigeminal nerve; The rate at which cerebrospinal fluid transports tissues from the olfactory region and / or the trigeminal nerve via intracellular and extracellular pathways to the olfactory region tissues; and / or The fraction of unbound drug in cranial CSF and / or the concentration in cranial CSF.

12. The method according to claim 11, wherein, The differential equation is one or more of the following: in , , , , and It is the ratio of nasal mucus, epithelium, and subepithelial volume to drug concentration in the i-th nasal region (referring to the nasal flap, nasal floor, nasal turbinates, olfactory region, and nasopharynx); It is the permeability of the nasal epithelium; It is the area of ​​the i-th nasal region; It is the tissue-plasma partition coefficient of the drug in the nose; It is the mucociliary clearance rate of the substance transported to the i-th region (which is equal to 0 for all regions except the nasopharynx, while the nasopharynx is equal to...). ); It is the mucociliary clearance rate of the i-th region (for the nasal floor, turbinates, and olfactory region, it is equal to...). The nasopharynx is equal to ); It is the rate at which substances are transported from the olfactory tissue to the cerebrospinal fluid via intracellular and extracellular pathways; It is the rate at which cerebrospinal fluid is transported to olfactory tissues via intracellular and extracellular pathways (for non-olfactory areas, these two parameters are zero). It is the fraction of unbound drug in the cranial CSF; and It refers to the concentration of cranial CSF.

13. The method according to any one of claims 1 to 12, wherein, The brain septum is represented by a differential equation, which represents one or more of the following: (i) The concentration of the drug in the cerebral blood, (ii) The concentration of the drug in the brain parenchyma, (iii) The concentration of the drug in the cerebrospinal fluid, and (iv) The concentration of the drug in the spinal cord and cerebrospinal fluid; and among which The differential equation is a function of one or more of the following parameters: The concentration of drug molecules in the brain blood; Blood flow to the brain; Concentration of compounds in arterial plasma; The fraction of unbound compounds in the tissue; Tissue clearance rate of the compound; The product of the permeability and surface area between cerebral blood and brain parenchyma; The fraction of unbound drug in the brain parenchyma; Blood concentration in brain parenchyma; The fraction of unbound drugs in the brain blood; The product of the permeability and surface area between cerebral blood and cranial CSF; The fraction of unbound drug in cranial CSF; The concentration of the drug in the cranial CSF, and the flow rate from the cranial CSF and spinal CSF to the cerebral blood; Drug concentration in spinal CSF; The volume of brain parenchyma; The product of permeability and surface area between brain parenchyma and cranial CSF; Overall flow from brain parenchyma to cranial CSF; CSF shuttle flow between cranial CSF and spinal CSF; The rate at which substances are transported from olfactory tissues to cerebrospinal fluid via intracellular and extracellular pathways along the olfactory region and / or the trigeminal nerve; Drug partition coefficient in nasal tissue: plasma partition coefficient; Drug concentration in the epithelium of each region of the nasal cavity; The rate at which cerebrospinal fluid transports substances along the olfactory region and / or the trigeminal nerve from cerebrospinal fluid to the olfactory tissue via intracellular and extracellular pathways; and / or Drug concentration in the subepithelial space of each region of the nasal cavity and / or volume of spinal CSF.

14. The method according to claim 13, wherein, The differential equation is: in It is the volume of blood in the brain; It refers to the concentration of drug molecules in the bloodstream of the brain; It is the blood flow to the brain; It is the concentration of compounds in arterial plasma; It is the fraction of unbound compounds in the tissue; It is the tissue clearance rate of the compound; It is the product of the permeability and surface area between the blood and brain parenchyma; It represents the fraction of unbound drugs in the brain parenchyma; It refers to the blood concentration in the brain parenchyma; It is the fraction of unbound drugs in the brain blood; It is the product of the permeability and surface area between cerebral blood and cranial CSF; It is the fraction of unbound drug in the cranial CSF; It is the concentration of the drug in the cranial CSF; and These refer to the blood flow from the cranial CSF and spinal CSF to the brain, respectively. It refers to the concentration of the drug in the spinal cord CSF; It refers to the volume of the brain parenchyma; It is the product of the permeability and surface area between the brain parenchyma and the cranial CSF; It is the overall flow from the brain parenchyma to the cranial CSF; and It is the CSF shuttle flow between cranial CSF and spinal CSF; It is the rate at which substances are transported from the olfactory tissue to the cerebrospinal fluid via intracellular and extracellular pathways; It is the tissue-plasma partition coefficient of the drug in the nose; The concentration of the drug in the epithelium of the i-th nasal region (referring to the nasal flap, nasal floor, nasal turbinates, olfactory region, and nasopharynx); It is the rate at which cerebrospinal fluid is transported to the olfactory tissue via intracellular and extracellular pathways; This refers to the drug concentration in the subepithelial region of the i-th nasal region (referring to the nasal flap, nasal floor, nasal turbinates, olfactory region, and nasopharynx); and It refers to the volume of the spinal cord CSF.

15. The method according to any one of claims 1 to 14, wherein, The compound-specific parameters in step (c) are based on preclinical studies of known drugs.

16. The method according to claim 15, wherein, The preclinical studies include in vitro cell assays, in vitro protein assays (e.g., combined data), and / or in vivo studies.

17. The method according to any one of claims 1 to 16, wherein, The specific physiological parameters were obtained from literature and / or database searches.

18. The method according to any one of claims 1 to 17, wherein, Step (e) involves solving the differential equations representing the compartments of the PBPK model.

19. The method according to claim 18, wherein, The solution is obtained using a differential equation solver.

20. The method according to any one of claims 1 to 19, wherein, The pharmacokinetic data in step (f) are based on clinical data of known drugs.

21. The method of claim 20, further comprising adjusting one or more of physiological parameters or compound-specific parameters to train the model.

22. The method according to any one of claims 1 to 21, wherein, The PBPK model is species-specific.

23. The method according to claim 22, wherein, The species mentioned is human.

24. The method according to claim 22, wherein, The species in question is a non-human primate.

25. The method according to any one of claims 1 to 24, wherein, The known drug is sumatriptan.

26. A computer-implemented method for predicting the delivery of a new drug to brain tissue via nasal inhalation, the method comprising: (a) Access a trained nas-brain PBPK model generated using the method of any one of claims 1 to 25, and parameterize the nas-brain PBPK model with compound-specific parameters known about the drug; (b) Receive the nasal model deposition data of the drug and input it into the trained nas-brain PBPK model of step (a); (c) Solve the equations of the trained nose-brain PBPK model using a differential equation solver; (d) Obtaining a report comprising drug concentration data from the trained nose-brain model for one or more of the compartments and one or more of the sub-compartments at one or more time points; and (e) Based on the report, and based on pharmacokinetic data for the brain compartment, provide a prediction of the transport outcome of the drug to brain tissue via nasal inhalation.

27. The method according to claim 26, wherein, The compound-specific parameters in step (a) are based on preclinical studies.

28. The method according to claim 27, wherein, The preclinical studies include in vitro cell assays, in vitro protein assays (e.g., combined data), and / or in vivo studies.

29. The method according to any one of claims 26 to 28, wherein, Nasal mold deposition data includes the mass of the drug deposited in each region of the nasal mold.

30. The method according to any one of claims 26 to 29, wherein, Step (a) also includes updating the naso-brain PBPK model using known clinical data about the drug.

31. The method according to claim 30, wherein, The clinical data refers to intravenous data, nasal data, or both.

32. A system comprising: A memory for storing executable instructions; and One or more processing devices connected to the memory, wherein the one or more processing devices are configured to execute the instructions to perform operations including: (a) Generate a multi-compartment PBPK model, wherein the multi-compartment PBPK model includes multiple independent body compartments; (b) Adding a brain compartment and a nasal compartment to the multi-compartment PBPK model to generate an initial nose-brain PBPK model, wherein the nasal compartment comprises one or more independent nasal compartments; (c) Parameterize the initial nose-brain PBPK model to include data for one or more or all of the multiple physiological parameters for the multiple independent body compartments and / or the multiple independent nasal compartments; (d) The initial nas-brain PBPK model is parameterized to include compound-specific parameters for drugs with known pharmacokinetic data for each body compartment and each nasal compartment to generate a parameterized nas-brain PBPK model. (e) Run the parameterized nose-brain model and generate a report that includes drug concentration data for one or more body compartments and / or one or more individual nasal compartments at one or more time points; as well as (f) Analyze and compare the drug concentration data in the report with the known pharmacokinetic data of the drug, and update the parameterized nose-brain model to obtain a trained nose-brain model.

33. The system according to claim 32, wherein, The multiple compartments, based on a physiological pharmacokinetic model, represent one or more or all of the following: arterial blood, lungs, fat, bone, brain, heart, kidneys, nose, muscles, skin, intestines, spleen, liver, other body compartments, and / or venous blood.

34. The system according to claim 32 or 33, wherein, The brain compartment includes independent subcompartments, which represent one or more of the following: brain blood outside the blood-brain barrier, brain parenchyma representing brain tissue, cerebrospinal fluid (CSF), and / or spinal CSF.

35. The system according to any one of claims 32 to 34, wherein, The nasal compartment represents one or more of the nasal region, nasal floor, turbinate, olfactory region, and / or nasopharyngeal region, and at least one of the nasal compartments is further represented as including a mucus layer, an epithelial layer, and a subepithelial layer, wherein the mucus layer is the assumed site for drug deposition, the epithelial layer allows penetration into deeper tissues, and the subepithelial layer is perfused with blood vessels capable of transporting the drug to the systemic circulation.

36. The system according to any one of claims 32 to 35, wherein, The physiological parameters of at least one compartment and at least one subcompartment are selected from those described in Table 1.

37. The system according to any one of claims 32 to 35, wherein, The compound-specific parameters of at least one compartment and at least one subcompartment are selected from those described in Table 2.

38. The system according to any one of claims 32 to 37, wherein, Compound-specific parameters of a drug include: P (Nasal epithelial permeability), Log P (Logarithm of octanol / water partition coefficient) pK a (negative logarithm of the acid dissociation constant) fu (The fraction of drug dissolved in plasma that is not bound to plasma proteins) R (Blood / Plasma Ratio) Cl h (Liver clearance rate) and the mass of deposits in at least one region of the nose.

39. One or more non-transient machine-readable storage media storing instructions that are executed to perform operations including: (a) Generate a multi-compartment PBPK model, wherein the multi-compartment PBPK model includes multiple independent body compartments; (b) Adding a brain compartment and a nasal compartment to the multi-compartment PBPK model to generate an initial nose-brain PBPK model, wherein the nasal compartment comprises one or more independent nasal compartments; (c) Parameterize the initial nose-brain PBPK model to include data for one or more or all of the multiple physiological parameters for the multiple independent body compartments and / or the multiple independent nasal compartments; (d) The initial nas-brain PBPK model is parameterized to include compound-specific parameters for drugs with known pharmacokinetic data for each body compartment and each nasal compartment to generate a parameterized nas-brain PBPK model. (e) Run the parameterized nose-brain model and generate a report that includes drug concentration data for one or more body compartments and / or one or more individual nasal compartments at one or more time points; as well as (f) Analyze and compare the drug concentration data in the report with the known pharmacokinetic data of the drug, and update the parameterized nose-brain model to obtain a trained nose-brain model.

40. One or more non-transient machine-readable storage media storing instructions according to claim 39, wherein, The multiple compartments, based on a physiological pharmacokinetic model, represent one or more or all of the following: arterial blood, lungs, fat, bone, brain, heart, kidneys, nose, muscles, skin, intestines, spleen, liver, other body compartments, and / or venous blood.

41. One or more non-transient machine-readable storage media storing instructions according to claim 39 or 40, wherein, The brain compartment includes independent subcompartments, which represent one or more of the following: brain blood outside the blood-brain barrier, brain parenchyma representing brain tissue, cerebrospinal fluid (CSF), and / or spinal CSF.

42. One or more non-transient machine-readable storage media storing instructions according to any one of claims 39 to 41, wherein, The nasal compartment represents one or more of the nasal region, nasal floor, turbinate, olfactory region, and / or nasopharyngeal region, and at least one of the nasal compartments is further represented as including a mucus layer, an epithelial layer, and a subepithelial layer, wherein the mucus layer is the assumed site for drug deposition, the epithelial layer allows penetration into deeper tissues, and the subepithelial layer is perfused with blood vessels capable of transporting the drug to the systemic circulation.

43. One or more non-transient machine-readable storage media storing instructions according to any one of claims 39 to 42, wherein, The physiological parameters of at least one compartment and at least one subcompartment are selected from those described in Table 1.

44. One or more non-transient machine-readable storage media storing instructions according to any one of claims 39 to 42, wherein, The compound-specific parameters of at least one compartment and at least one subcompartment are selected from those described in Table 2.

45. One or more non-transient machine-readable storage media storing instructions according to any one of claims 39 to 42, wherein, Compound-specific parameters of a drug include: P (Nasal epithelial permeability), Log P (Logarithm of octanol / water partition coefficient) pK a (negative logarithm of the acid dissociation constant) fu (The fraction of drug dissolved in plasma that is not bound to plasma proteins) R (Blood / Plasma Ratio) Cl h (Liver clearance rate) and the mass of deposits in at least one region of the nose.

46. ​​A trained naso-brain physiology-based pharmacokinetic (PBPK) model for drug delivery to brain tissue via nasal inhalation, wherein, The trained nose-brain PBPK model is (1) encoded on one or more non-transient machine-readable storage media and (2) generated by operations including the following: (a) Generate a multi-compartment PBPK model, wherein the multi-compartment PBPK model includes multiple independent body compartments; (b) Adding a brain compartment and a nasal compartment to the multi-compartment PBPK model to generate an initial nose-brain PBPK model, wherein the nasal compartment comprises one or more independent nasal compartments; (c) Parameterize the initial nose-brain PBPK model to include data for one or more or all of the multiple physiological parameters for the multiple independent body compartments and / or the multiple independent nasal compartments; (d) The initial nas-brain PBPK model is parameterized to include compound-specific parameters for drugs with known pharmacokinetic data for each body compartment and each nasal compartment to generate a parameterized nas-brain PBPK model. (e) Run the parameterized nose-brain model and generate a report that includes drug concentration data for one or more body compartments and / or one or more independent nasal compartments at one or more time points; as well as (f) Analyze and compare the drug concentration data in the report with the known pharmacokinetic data of the drug, and update the parameterized nose-brain model to obtain a trained nose-brain model.

47. The trained naso-brain physiology-based pharmacokinetic (PBPK) model according to claim 46, wherein, The trained nose-to-brain PBPK model is configured as follows: (a) Receive one or more compound-specific parameters known about the drug; (b) Solve using differential equations; and (c) Generate a report comprising drug concentration data from the trained nose-brain model for one or more of the compartments and one or more of the sub-compartments at one or more time points; and (e) Based on the report, and based on pharmacokinetic data for the brain compartment, provide a prediction of the transport outcome of the drug to brain tissue via nasal inhalation.

48. The trained naso-brain physiology-based pharmacokinetic model according to claim 47, wherein, The multiple compartments, based on a physiological pharmacokinetic model, represent one or more or all of the following: arterial blood, lungs, fat, bone, brain, heart, kidneys, nose, muscles, skin, intestines, spleen, liver, other body compartments, and / or venous blood.

49. The trained naso-brain physiology-based pharmacokinetic model according to claim 47 or 48, wherein, The brain compartment includes independent subcompartments, which represent one or more of the following: brain blood outside the blood-brain barrier, brain parenchyma representing brain tissue, cerebrospinal fluid (CSF), and / or spinal CSF.

50. The trained nas-brain physiology-based pharmacokinetic model according to any one of claims 47 to 49, wherein, The nasal compartment represents one or more or all of the nasal region, nasal floor, turbinate, olfactory region and / or nasopharyngeal region, and at least one of them further represents a mucous layer, an epithelial layer and a subepithelial layer, wherein the mucous layer is the assumed site for drug deposition, the epithelial layer allows penetration into deeper tissues, and the subepithelial layer is perfused with blood vessels capable of transporting the drug to the systemic circulation.

51. The trained nas-brain physiology-based pharmacokinetic model according to any one of claims 47 to 50, wherein, The physiological parameters of at least one compartment and at least one subcompartment are selected from those described in Table 1.

52. The trained nas-brain physiology-based pharmacokinetic model according to any one of claims 47 to 50, wherein, The compound-specific parameters of at least one compartment and at least one subcompartment are selected from those described in Table 2.

53. The trained nas-brain physiology-based pharmacokinetic model according to any one of claims 47 to 52, wherein, The specific parameters of the compound in the drug include: P (Nasal epithelial permeability), Log P (Logarithm of octanol / water partition coefficient) pK a (negative logarithm of the acid dissociation constant) fu (The fraction of drug dissolved in plasma that is not bound to plasma proteins) R (Blood / Plasma Ratio) Cl h (Liver clearance rate) and the mass of deposits in at least one region of the nose.

54. A system comprising: A memory for storing executable instructions; and One or more processing devices connected to the memory, the one or more processing devices being configured to execute the instructions to perform operations including: (a) Access a trained nas-brain PBPK model generated using the method of any one of claims 1 to 25, and parameterize the nas-brain PBPK model with compound-specific parameters known about the drug; (b) Receive the nasal model deposition data of the drug and input it into the trained nas-brain PBPK model of step (a); (c) Solve the equations of the trained nose-brain PBPK model using a differential equation solver; (d) Obtaining a report comprising drug concentration data from the trained nose-brain model for one or more of the compartments and one or more of the sub-compartments at one or more time points; and (e) Based on the report, and based on pharmacokinetic data for the brain compartment, provide a prediction of the transport outcome of the drug to brain tissue via nasal inhalation.

55. The system according to claim 54, wherein, Multicompartmental pharmacokinetic models based on physiology represent one or more or all of the following: arterial blood, lungs, fat, bone, brain, heart, kidneys, nose, muscles, skin, intestines, spleen, liver, other body compartments, and / or venous blood.

56. The system according to claim 54 or 55, wherein, The brain compartment includes independent subcompartments, which represent one or more of the following: brain blood outside the blood-brain barrier, brain parenchyma representing brain tissue, cerebrospinal fluid (CSF), and / or spinal CSF.

57. The system according to any one of claims 54 to 56, wherein, The nasal compartment represents one or more or all of the nasal region, nasal floor, turbinate, olfactory region and / or nasopharyngeal region, and at least one is further indicated to include a mucus layer, an epithelial layer and a subepithelial layer, wherein the mucus layer is the assumed site for drug deposition, the epithelial layer allows penetration into deeper tissues, and the subepithelial layer is perfused with blood vessels capable of transporting the drug to the systemic circulation.

58. The system according to any one of claims 54 to 57, wherein, The physiological parameters of at least one compartment and at least one subcompartment are selected from those described in Table 1.

59. The system according to any one of claims 54 to 57, wherein, The compound-specific parameters of at least one compartment and at least one subcompartment are selected from those described in Table 2.

60. The system according to any one of claims 54 to 59, wherein, The specific parameters of the compound in the drug include: P (Nasal epithelial permeability), Log P (Logarithm of octanol / water partition coefficient) pK a (negative logarithm of the acid dissociation constant) fu (The fraction of drug dissolved in plasma that is not bound to plasma proteins) R (Blood / Plasma Ratio) Cl h (Liver clearance rate) and the mass of deposits in at least one region of the nose.

61. One or more non-transient machine-readable storage media storing instructions that are executed to perform operations including: (a) Access a trained nas-brain PBPK model generated using the method of any one of claims 1 to 25, and parameterize the nas-brain PBPK model with compound-specific parameters known about the drug; (b) Receive the nasal model deposition data of the drug and input it into the trained nas-brain PBPK model of step (a); (c) Solve the equations of the trained nose-brain PBPK model using a differential equation solver; (d) Obtaining a report comprising drug concentration data from the trained nose-brain model for one or more of the compartments and one or more of the sub-compartments at one or more time points; and (e) Based on the report, and based on pharmacokinetic data for the brain compartment, provide a prediction of the transport outcome of the drug to brain tissue via nasal inhalation.

62. The one or more non-transient machine-readable storage media storing instructions according to claim 61, wherein, Multicompartmental pharmacokinetic models based on physiology represent one or more or all of the following: arterial blood, lungs, fat, bone, brain, heart, kidneys, nose, muscles, skin, intestines, spleen, liver, other body compartments, and / or venous blood.

63. One or more non-transient machine-readable storage media storing instructions according to claim 61 or 62, wherein, The brain compartment includes independent subcompartments, which represent one or more of the following: brain blood outside the blood-brain barrier, brain parenchyma representing brain tissue, cerebrospinal fluid (CSF), and / or spinal CSF.

64. One or more non-transient machine-readable storage media storing instructions according to any one of claims 61 to 63, wherein, The nasal compartment represents one or more or all of the nasal region, nasal floor, turbinate, olfactory region and / or nasopharyngeal region, and at least one is further indicated to include a mucus layer, an epithelial layer and a subepithelial layer, wherein the mucus layer is the assumed site for drug deposition, the epithelial layer allows penetration into deeper tissues, and the subepithelial layer is perfused with blood vessels capable of transporting the drug to the systemic circulation.

65. One or more non-transient machine-readable storage media storing instructions according to any one of claims 61 to 64, wherein, The physiological parameters of at least one compartment and at least one subcompartment are selected from those described in Table 1.

66. One or more non-transient machine-readable storage media storing instructions according to any one of claims 61 to 64, wherein, The compound-specific parameters of at least one compartment and at least one subcompartment are selected from those described in Table 2.

67. One or more non-transient machine-readable storage media storing instructions according to any one of claims 61 to 66, wherein, The specific parameters of the compound in the drug include: P (Nasal epithelial permeability), Log P (Logarithm of octanol / water partition coefficient) pK a (negative logarithm of the acid dissociation constant) fu (The fraction of drug dissolved in plasma that is not bound to plasma proteins) R (Blood / Plasma Ratio) Cl h (Liver clearance rate) and the mass of deposits in at least one region of the nose.

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