Optimal Tumor Microenvironment Normalization Therapy

Abstract

An individualized method for treating a cancer patient having a tumor using a computing system having a processing system and a memory system storing instructions executed by the processing system, the method comprising: the computing system performing parameter estimation to determine a physiological parameter π of the tumor, including a vascular permeability coefficient and an interstitial permeability coefficient; and determining whether a selected tumor transport model is valid or invalid by solving the physiological parameter π, and if it is determined that the selected tumor transport model is valid, the method including determining a treatment, and the treatment being applied to the cancer patient according to the method.

Description

Technical Field

[0001] (Cross - Reference to Related Applications) This application claims priority to U.S. Provisional Application No. 63 / 337,334, filed May 2, 2022, the entire disclosure of which is incorporated herein by reference.

[0002] (Statement Regarding Federally Sponsored Research and Development) This invention was made with government support under Grant No. 1932723 awarded by the National Science Foundation. The government has certain rights in this invention.

[0003] (Field of the Invention) This disclosure relates to tumor therapies, and more specifically to optimizing tumor microenvironment normalization therapies.

Background Art

[0004] Solid tumors are characterized by pathophysiological abnormalities that are biophysical barriers to the transport of anticancer agents. These barriers impede the effectiveness of such therapies by restricting their accumulation and spatial distribution. Improving pathophysiology such that tumor microenvironment (TME) components have a more "normalized" phenotype increases the delivery and effectiveness of small - molecule and nanocarrier - based therapies in cancer patients. However, TME normalization in combination with anticancer therapies has not led to cures across the cancer patient population. Therefore, it is necessary to better understand how TME normalization affects the transport of therapies within tumors in order to completely avoid these spatially and temporally heterogeneous biophysical barriers.

[0005] Described herein is a modeling method that can be used to construct a robust framework for determining how a normalized TME regulates the biophysical barriers to transport phenomena in tumors, thereby enabling the discovery of deeper insights into effective TME normalization.

Prior Art Documents

Patent Documents

[0006]

Patent Document 1

Patent Document 2

Summary of the Invention

[0007] In one aspect, an individualized method of treating a cancer patient having a tumor is provided using a computing system having a processing system and a memory system storing instructions executed by the processing system. The method includes the steps of the computing system performing parameter estimation to determine the physiological parameters π of the tumor, including the vascular permeability coefficient and the interstitial permeability coefficient, and determining whether a selected tumor transport model is valid or invalid by solving the physiological parameters π. When it is determined that the selected tumor transport model is valid, the method includes determining a treatment, and according to the method, the treatment is applied to the cancer patient.

[0008] Another aspect is a computerized system comprising a processing system and a memory system storing instructions executed by the processing system, whereby the system performs parameter estimation to determine a physiological parameter π of a tumor, including a vascular permeability coefficient and an interstitial permeability coefficient, and determines whether a selected tumor transport model is valid or invalid by solving the physiological parameter π, and when it is determined that the selected tumor transport model is valid, the method includes determining a treatment and further includes applying the treatment to a cancer patient.

[0009] Another aspect is a computer program product comprising a memory device storing computer-executable instructions that, when executed by one or more processors, cause the one or more processors to perform parameter estimation to determine a physiological parameter π of a tumor, including a vascular permeability coefficient and an interstitial permeability coefficient, and determine whether a selected tumor transport model is valid or invalid by solving the physiological parameter π, and when it is determined that the selected tumor transport model is valid, the method includes determining a treatment and further includes applying the treatment to a cancer patient. BRIEF DESCRIPTION OF THE DRAWINGS

[0010]

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[0011] The above and other features will be recognized and understood by those skilled in the art from the following forms of implementing the invention, drawings, and appended claims.

Forms of Implementing the Invention

[0012] Nanoscale anticancer therapies on the order of tens of nanometers, including polymer micelles and macromolecules such as antibodies, benefit from longer circulation in the body due to slower clearance, selective accumulation in tumors due to leaky tumor blood vessels, and long-term retention in tumor tissue due to high-density fibrosis and non-functional lymphatic vessels in the TME. In fact, currently, nanoscale therapies are being used in cancer patients. Nevertheless, leaky blood vessels, high-density fibrosis, and non-functional lymphatic vessels together construct a biophysical barrier that reduces the effectiveness of cancer treatment. Nanoscale therapies are affected in a size-dependent manner. In tumors, plasma from the circulation overflows excessively from leaky blood vessels into the interstitial (i.e., extravascular) space and still moves slowly because high-density fibrosis restricts fluid movement. Eventually, because tumor lymphatic vessels are non-functional, fluid cannot be removed. Thus, one prominent feature of tumors is an increase in interstitial fluid pressure (IFP), which eliminates transvascular convective transport of drugs within tumors by reducing the transvascular pressure gradient to zero.

[0013] Vascular normalization involves strengthening leaky tumor blood vessels by blocking angiogenesis. ECM normalization involves reversing high-density fibrosis by reprogramming cancer-associated fibroblasts to a quiescent phenotype so that fibroblasts stop producing and maintaining excessive levels of extracellular matrix (ECM). As a result, high-density fibrosis that slows interstitial fluid movement and compresses lymphatic tumor blood vessels within tumors so that they do not function is reduced. Already, vascular normalization has been used in patients with nanomedicine, while ECM normalization has recently been successful in clinical trials using small molecule chemotherapy. "TME normalization" is an umbrella term for either or both of ECM normalization and vascular normalization.

[0014] Dexamethasone, a glucocorticoid steroid often used to manage chemotherapy-related toxicities, can simultaneously induce vascular and ECM normalization when used at appropriate doses and schedules. However, how dexamethasone affects vascular leakage, fibrosis, and lymphatic function towards reducing IFP and restoring the transvascular pressure gradient is multifactorial. Each factor depends diversely on the dose of dexamethasone. Furthermore, how the size of nanocarrier-based anticancer agents interacts with these factors is unknown. Therefore, enhancing the delivery of nanocarriers is a multifaceted engineering problem, and thus, a model-based systems engineering approach provides an understanding of the physical phenomena and complex relationships underlying biological systems. Throughout this disclosure, the term "nanocarrier" generally includes nanoscale (nm) biomolecules and polymeric therapies. It should be understood that this disclosure is not limited to dexamethasone. There are many drugs or combinations of drugs that achieve vascular normalization or ECM normalization or both.

[0015] The transport of nanocarriers from the systemic circulation to cancer cells involves three steps: flow via blood vessels to different regions of the tumor, transvascular transport, and transport through the tumor interstitial space. Specifically, the capillary system is a very dynamic region for the transvascular transport of drugs, nutrients, and waste products exchanged between blood vessels and the interstitial space. There are two important transvascular transport mechanisms: diffusion and convection. Generally, smaller nanocarriers result from diffusion that uses a concentration gradient as an additional driving force for transvascular transport, while larger nanocarriers must rely on convective transport that uses a pressure gradient due to steric hindrance that makes diffusion very slow. Previous studies have shown that diffusion is the main mechanism for the transport of substances across the blood vessel wall in tumors due to the lack of a transvascular pressure gradient. However, dexamethasone can restore the transvascular pressure gradient because it affects vascular leakage, fibrosis, and lymphatic function. It is unclear how diffusion and convection are affected for variously sized nanocarriers. The main properties that relate diffusion and convection to the nanocarrier concentration in tumors are S / V, K, and Lp. TME normalization refers to any drug or combination of drugs that affects any one or a combination of these properties. To investigate, a first-principles-based modeling approach can quantify the important physiological parameters that govern transport in tumors.

[0016] Vascular and interstitial transport phenomena in tumors have been widely modeled. In addition to first-principles mechanistic models, artificial intelligence (AI) is increasingly becoming a common model-based approach in pharmacokinetics / pharmacodynamics (PKPD) research. Efficient machine learning models simplify computationally intensive simulations by creating mathematically simple regression models that capture input-output relationships with high accuracy. Specifically, artificial neural networks (ANNs) are powerful computational models that can approximate and predict the behavior of such complex systems with high accuracy and efficiency for optimal therapy design within the context of the TME normalization process. First, deterministic global optimization is proposed to solve the parameter estimation problem and provide a rigorous quantitative basis for in silico model discrimination. Using this basis, the relative contributions of convection and diffusion are quantified for solute transport across the vessel wall. Moreover, an optimized TME normalization therapy design approach is developed for dose selection to demonstrate the relationship between dexamethasone dose and interstitial concentration of the anticancer agent in the pharmacokinetic system. Finally, this tumor transport model is utilized to determine the optimal nanomedicine size for maximum accumulation in the tumor interstitial space. To reduce the computational cost of solving challenging deterministic global optimization problems for model validation, dexamethasone dose selection, and anticancer nanocarrier size selection, an ANN surrogate modeling approach is proposed. Details of establishing and using such machine learning models within an optimization-based decision-making framework are presented in this study.

[0017] The methods described herein enhance the practicality and predictive ability of tumor transport models using mechanistic and data-driven model validation approaches and rigorous methods in global optimization for a more powerful model-based systems engineering approach for optimal therapy design in cancer research. The information obtained through this approach helps in the development of better models and provides deeper insights into the physical behavior of molecular transport during TME normalization for drug development and delivery.

[0018] The present invention is further illustrated by the following non-limiting examples.

[0019] (Examples) Figures 1A - 1F, discussed below, illustrate the overall systematic framework proposed for model-based TME normalization therapy and drug size design. Formal methods were used to estimate and quantify important parameters for model validation to enhance the predictive ability of the models and provide evidence of their usefulness for model-based approaches for drug and therapy development. This approach involves solving a nonconvex nonlinear program (NLP) constrained by a mechanistic tumor transport model as an unsteady partial differential equation (PDE). A simulation-based executable path approach is proposed and the PDE-constrained optimization problem is reformulated as an NLP with box constraints. Additionally, ANN machine learning is proposed to construct a surrogate model to reduce the time cost of solving the global optimization problem. Moreover, well-established mechanistic models and ANN models are also used in TME normalization design for optimal neoadjuvant dose selection and drug size design for anti-cancer nanocarriers.

[0020] Figure 1A is flowchart 10 demonstrating a systematic framework for optimal therapy design within the context of tumor microenvironment (TME) normalization. Based on experimental data, parameter estimation is utilized to validate / invalidate a proposed mechanistic or data-driven model of the tumor. The validated model is then applied to TME normalization therapy design for dose selection and anti-cancer agent sizing. Note that the TME normalization therapy design and drug sizing within the dashed box can be implemented separately, sequentially, or simultaneously. The various blocks of Figure 1A are considered in more detail below and addressed in Figures 1B - 1F, but the TME block represents the physical tumor with a microenvironment consisting of blood vessels, cancer cells, fibroblasts, collagen, hyaluronan, and other components of the tissue, and the disclosed process includes (i) measuring and collecting data, (ii) determining an appropriate therapy, and (iii) modifying and normalizing as part of the therapy.

[0021] Figure 1B is another flowchart showing an overview of the flowchart of Figure 1A. As shown in step 1, the method includes a step in which a computing system (or generally, a system), such as those illustrated in Figures 11 and 12, performs parameter estimation to determine the physiological parameters π of the tumor, including the vascular permeability coefficient and the interstitial permeability coefficient. As shown in step 2, the method includes determining whether a selected tumor transport model is valid or invalid by solving the physiological parameters π. If the determination is "valid", as shown in step 3, the method includes the system determining a treatment. As shown in step 4, the method includes a physician (or other actor) applying the treatment to a cancer patient. If the parameters are invalid in step 2, the process continues to Figure 1D, which is considered below.

[0022] Figure 1C is a flowchart showing additional aspects related to parameter estimation identified in Figures 1A and 1B. As shown in step 1A, the method is a step of measuring Peff and using a parameter estimation problem to predict / determine K and L, where Peff is the effective permeability quantified as the velocity of the fluorescence signal passing through the tumor vessel wall, Lp is the water permeability coefficient of the microvessel wall (cm / mm Hg-second), K is the water permeability coefficient of the tumor stroma (cm2 / mmHg-second), or directly measuring K and using experimental data when solving the parameter estimation problem. As shown in step 1B, the vascular density S / V is measured when measuring Peff and is measured as the vascular surface area per unit volume (cm-1). As shown in step 1C, the method includes determining a time-dependent spatially averaged drug concentration profile,

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[0023] As shown in step 1E, the method includes a step of determining a physiological parameter π through a first parameter estimation problem,

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[0024] Figure 1D is another flowchart showing additional aspects related to the steps performed when it is determined that the physiological parameter π determined during the disclosed process is considered invalid. As shown in step 2A, the method includes the system acquiring more data and solving the parameter estimation problem again. As shown in step 2B, the method includes the system selecting a different tumor transport model or modifying the tumor transport model and solving the parameter estimation problem. As shown in step 2C, the method includes the system making a determination based on the type of tumor transport model being utilized. Specifically, a determination is made based on whether a mechanistic tumor transport model is directly utilized or not utilized in order to generate simulation data for training a machine learning model (e.g., an ANN model). If the mechanistic tumor transport model is directly utilized in step 2D, the method includes a system that utilizes a first parameter estimation problem when determining the physiological parameter π using the mechanistic tumor transport model. Otherwise, as shown in step 2E, the method includes a system that utilizes a second parameter estimation problem when determining the physiological parameter π using a data-driven tumor transport model, which has a lower computational burden compared to the mechanistic tumor transport model. The second parameter estimation problem is as follows:

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[0025] Figure 1E is another flowchart showing additional aspects related to determining a dosage selection or drug size, as identified in Figure 1A. As shown in step 3A, a determination is made as to whether there is a previously applied and quantified treatment. If not, as shown in step 3B, the method is for the system to determine a dosage selection when the patient has not yet received adjuvant therapy, the dosage selection including determining that it refers to a TME normalization agent that is an adjuvant. As shown in step 3C, the method includes the system determining the vascular permeability coefficient Lp and the interstitial permeability coefficient K from an empirical correlation between the causal relationship between the tumor normalization dosage K and Lp. As shown in step 3D, the method includes the system determining an optimal dosage that maximizes drug accumulation in the tumor,

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[0026] Figure 1F is another flowchart showing additional aspects related to simultaneously determining a dosage selection or drug size, as identified in Figure 1A. Figure 1F is an alternative process compared to Figure 1F. As shown in step 4A, the method includes the system simultaneously performing determining a dosage selection module and a drug size. As shown in step 4B, the method includes the system applying an empirical correlation that associates tumor physiology with an adjuvant dosage. As shown in step 4C, the method includes the system making the same determination as in step 2C. When a mechanistic tumor transport model is directly used, as shown in step 4D, the method includes determining the vascular permeability coefficient L p and the interstitial permeability coefficient K from an empirical correlation between the causal relationship between the tumor normalization dosage K and L p and. In step 4E, the method includes the system

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[0027] In summary, the disclosed process includes: 1.) performing in vivo imaging to determine Peff and optionally S / V, and directly measuring K; 2.) executing the processes of steps 1 - 4; 3.) determining the dosage of the TME normalization regimen and administering it; 4.) executing the processes of steps 1 - 4; 5.) determining the anti-cancer agent nanocarrier size and administering it. Alternatively, instead of step 3, the process includes simultaneously determining the dosage of the TME normalization regimen and the anti-cancer agent nanocarrier size, and administering the TME normalization regimen and the anti-cancer nanocarrier. Alternatively, instead of step 5, the process may include repeating step 3 to determine a second dosage of the TME normalization regimen and administering it, followed by performing steps 4 and 5.

[0028] In short, the present disclosure provides the following high-level procedures (and their substitutions) conveyed by a flowchart diagram. Option 1: Image, then determine the adjuvant dosage, then administer the dosage, then image, then determine the anti-cancer agent size, and then administer the anti-cancer agent. Option 2: Image, then determine the anti-cancer agent size, and then administer the anti-cancer agent. Option 3: Image, then determine the adjuvant dosage and the anti-cancer agent size, and then perform the treatment.

[0029] Parameter Estimation and Model Validation by Deterministic Global Optimization: Glucocorticoid steroid DEX is a drug mainly used to reduce the side effects of chemotherapy and has been identified as a pretreatment adjuvant for normalizing metastatic tumor blood vessels and an ECM for enhanced efficacy of drug delivery. To verify the effect of DEX on nanoparticle delivery by the blood vessel and ECM normalization processes, the optimal solution of the parameter estimation problem introduced in the art by deterministic global optimization is determined. This approach is important because only the global optimal solution can guarantee the most accurate fit to the obtained experimental data. The mechanistic tumor transport model used in this study is introduced in Supplementary Example 1.

[0030] Previously, a series of experiments were conducted in vivo to investigate the efficacy of DEX. In these experiments, immunocompetent mice with orthotopic 4T1 breast cancer were treated daily with 3 and 30 mg / kg of DEX for 4 days. Subsequently, two fluorescent dyes (70 kDa rhodamine-conjugated dextran and 500 kDa FITC-conjugated dextran) were injected as tracers. In vivo confocal laser scanning microscopy was used to characterize the spatiotemporal distribution of dextran in mouse tumors treated with different doses of DEX. Based on the in vivo microscopy images, the effective permeability P eff was quantified as the rate of the nanoparticle fluorescence signal passing through the blood vessel wall and normalized with respect to the blood vessel surface area and the transvascular concentration difference. The effective permeability includes both convective and diffusive components. However, it may significantly overestimate the diffusive part and not match the actual transcapillary transport. Next, the spatially averaged concentration in the interstitial space (dc ata av / dt) was calculated from the conservation equation. That is,

Equation

[0031] In this study, a similar approach is taken, by which the dimensionless spatially averaged concentration of solute c data avg (determined from the overall conservation equation) serves as the experimental concentration profile for each P eff measured experimentally and is used for parameter estimation of the target mechanistic model. The deterministic global optimization method is used to validate the mechanistic model by finding the parameter values that result in a proposed model that best fits the experimental data as closely as possible, and subsequently verifying the TME normalization process. The objective function is formulated as the sum-of-squared error (SSE) between the mean concentration profile predicted by the model and the measurement data at discrete time points over the entire time range of the experiment (from the overall conservation equation using experimentally measured P eff ). The inequality constraints are formulated for the IFP parameters based on experimentally determined values. The parameter estimation problem is formulated as follows,

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[0032] where the dimensionless spatially averaged concentration of the solute

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[0033] In Table 1, the physical boundaries for the upper surface (peripheral) tumor IFP for the control, 3 mg / kg, and 30 mg / kg DEX treatment cases are reported here. These values are used in the parameter estimation problem formulated as (1) to ensure that physically meaningful solutions are identified.

Table 1

[0034] Boundary methods for tumor transport models: Deterministic global optimization can prevent the incorrect invalidation of mechanistic models when the quasi-optimal solutions obtained by local optimization algorithms lead to incompatibilities. The method for solving the global optimization problem in this study relies on a branch-and-bound (BnB) framework for deterministic search. Specifically, the flexible and open-source BnB-based solver EAGO is utilized. The BnB algorithm iteratively and continuously divides the search space into smaller subdomains and solves a sequence of lower-upper bound subproblems on each subdomain. The algorithm converges to the optimal global solution in a finite number of iterations or terminates with a proof of infeasibility by comparing the bounds obtained over the nodes. The upper bound problem typically determines the achievable local solutions (if any) on each subdomain. The lower bound problem depends on the ability to compute tight global bounds for all variables and functions involved in the optimization formulation. Computing an effective lower bound for the global optimization problem is the most difficult step. This is particularly true for the PDE systems encountered in this work, as this task corresponds to constructing tight bounds on the spatio-temporal state solutions over the entire domain of the optimization variables (i.e., the reachable set).

[0035] A method is disclosed for constructing a global boundary surrounding the reachable set of a tumor transport model. In this study, several different boundary - setting methods are presented and analyzed to determine the most effective method for use with the tumor transport model. The basic approach is to use the method of lines with finite differences for spatial discretization and then use differential inequality (DI) to construct the state boundaries of the discretized large - scale ODE - IVP system. Apart from implementing interval arithmetic (IA) to construct the boundary, a mixed interval arithmetic / affine arithmetic (IA / AA) approach is also implemented. In addition to standard DI, a modified DI approach with an interval - correction operator is implemented for problems with a priori known prescribed boundary - setting information. An overview of these set - valued mapping approaches is presented in Supplementary Example 2. In summary, four boundary - setting methods are considered for comparison: IA and DI, IA and DI with interval correction, IA / AA and DI, and IA / AA and DI with interval correction.

[0036] The significant non - linearity of the model poses a major challenge in finally constructing the exact boundary. In the tumor transport model, the problematic term that requires special consideration is the solute source term that describes the transvascular mass transport of nanocarriers:

Equation

[0037] The solute source term stems from the IA-dependency problem (i.e., overestimation of interval arithmetic due to independent processing of the same variable). The non-linearity caused by the exponential term significantly amplifies this overestimation. The dependency problem is overcome using the following strategy. Pe appears in both the numerator and denominator of the term

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[0038] The boundaries for the state variables of the tumor transport model were constructed based on four approaches. The spatial domain was discretized into N = 100 nodes, and the discrete time DI scheme was used to construct the boundaries over a simulation time (5 minutes) with 21 time steps. Two physiological parameters were considered as decision variables, and the interval region π=(L p ,K) ∈ π = [7.5×10 -7 ,7.6×10 -7 ×[1.15×10 -6 ,1.2×10 -6is bounded by. The numerical solutions and the bounding results are illustrated in FIGS. 2A and 2B for the four bounding methods considered.

[0039] To compare the effectiveness of the different bounding procedures, the volume between the upper and lower bounds of the dimensionless concentration over the entire spatial and temporal domains is quantified, along with the corresponding time cost for constructing these boundaries, and listed in Table 2. It is observed that the time costs of the pure IA method and the hybrid IA / AA method are almost the same, but the hybrid IA / AA method can provide much narrower boundaries. The prescribed physical boundaries

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[0040] Table 2 reports the achieved amounts and time costs for the different bounding methods considered herein. The IA / AA boundary is significantly narrower than the pure IA boundary (91% volume reduction) without additional computational time. The IA / AA boundary is also almost as narrow as the IA / AA(DI with G) boundary (38% volume increase), but with almost two orders of magnitude less computational time.

Table 2

[0041] Machine learning model: Figures 2A and 2B show the numerical solutions and boundary conditions plotted for the tumor transport model. In Figure 2A, the dimensionless concentration within the tumor at t = 150 s [Number] of is plotted for several values of π together with the state boundaries derived from pure IA, IA with modified DI, mixed IA / AA, and mixed IA / AA with modified DI. In Figure 2B, the solute concentration within the tumor at the position r^ = 0.5 [Number] of is plotted for several values of π together with the state boundaries derived from pure IA, IA with modified DI, mixed IA / AA, and mixed IA / AA with modified DI. [Number] is approximated by the corresponding numerical solution calculated by the explicit Euler method, and the state boundary is calculated by the discrete-time DI method.

[0042] Machine learning regression is proposed to establish a computationally equivalent artificial neural network (ANN) as a surrogate for the mechanistic tumor transport model. The established ANN model is then used to solve the model validation parameter estimation problem as formulated in Equation (1). This approach is proposed to analyze the relative performance and accuracy of the ANN models, and to evaluate their applicability within the proposed framework for drug and therapy design, as well as the broader context of scientific machine learning in cancer research and therapy. This was implemented by Julia version 1.6.1 running on an Intel Xeon W-2195 (18 cores / 32 threads) 2.3 GHz / 4.3 GHz (base / turbo) CPU with 64 GB RAM running on Windows 10 Pro. The inputs to the ANN considered are the two physiological parameters L p and K. Since DEX treatment normalizes the TME and then affects the transport phenomena in the tumor, different ANN surrogate models were constructed to represent the control and DEX-treated tumors for higher accuracy. Furthermore, since the experimental data varied slightly across the 70 kDa nanocarrier and 500 kDa nanocarrier experimental groups, separate ANN surrogate models were also constructed for higher accuracy within these mouse groups. Thus, four different ANN surrogates are considered: 70 kDa nanocarrier control cases, 70 kDa nanocarrier 3 mg / kg and 30 mg / kg DEX-treated cases, 500 kDa nanocarrier control cases, and 500 kDa nanocarrier 3 mg / kg and 30 mg / kg DEX-treated cases. For each case, the tumor transport model was parameterized by L p and K. The discretized fluid and solute transport models were solved for data collection using the method of lines via the stiff QNDF solver in DifferentialEquations.jl. The spatially averaged concentration over a discrete time range of 5 minutes was then obtained as the output.

[0043] Using the Sobol array sampling protocol in Surrogates.jl, 10 within the bounds described in Table 3 6A dataset of points was generated. Then, the data was scaled using min-max normalization and randomly split into a training set (70%) and a test set (30%). The ANN model was trained and constructed using Flux.jl. Architectures with 2 - 4 hidden layers, 16 - 32 nodes per hidden layer, and several different activation functions (sigmoid, tanh, gelu, and swish) were considered. Through tuning and comparison, a two - hidden - layer model with 24 neurons each having the swish activation function was selected for use in this study. This ANN model is depicted in Figure 3.

[0044] Figure 3 shows a fully - connected feed - forward multilayer perceptron surrogate model 300 and represents the model architecture used for the simplified parameter - estimation problem considered herein. The 2 - node input layer (layer 1) receives the physiological parameters L p and K as inputs. These inputs are fed into two hidden layers (layers 2 and 3) using 24 nodes and the swish activation function. Then, the output of the second hidden layer (layer 3) is passed to an output layer (layer 4) consisting of 21 nodes that represent the temporally discretized cumulative profile.

[0045] In Table 3, the bounds for the input variables L p and K are used for surrogate model construction to create the ANN in formulation (3).

Table 3

[0046] Since the size of the ANN was relatively small, the model was trained using a combination of batch and mini - batch gradient descent with a mini - batch size of 10% of the training dataset. The Adam optimizer was used for training with the mean - squared - error (MSE) loss function. The model was run for 10 -7With an MSE tolerance of, it was trained over 50 epochs using an early stopping criterion. The learning rate was kept constant at 10 -3 Subsequent to training, the MSE and mean relative percent error were evaluated on the test set. This training protocol was found to be effective as shown by the time and performance metrics listed in Table 4.

[0047] Table 4 shows the benchmark metrics of development time and performance of an artificial neural network surrogate model for the control case (70 kDa - control). 70 kDa - treatment, 500 kDa - control, 500 kDa - treatment are reported. "70 kDa" and "500 kDa" indicate the molecular weights of the nanocarriers. "Treatment" indicates both 3 mg / kg and 30 mg / kg dexamethasone (DEX) treatments.

Table 4

[0048] In previous studies, recurrent neural network model architectures have been used as a typical method for simulating dynamic systems by directly approximating the numerical integration function as opposed to the entire numerical integration procedure. This method was not used herein because it requires an iterative loop in the objective function to create the concentration function for each function evaluation (with feedback of information from earlier time states), and such a process would introduce additional complexity that would adversely affect the solution time when included in the deterministic global optimization routines used in this work.

[0049] Simplified parameter estimation problem: The simplified parameter estimation problem is proposed using the ANN surrogate model introduced in the above disclosure for machine learning models. Similar to (1), the SSE is minimized between the average concentration predicted by the ANN surrogate model and the experimental data over the entire time range, with the following inequality constraints for the upper surface IFP:

Equation

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[0050] The optimization formulation (3) can then be reformulated as follows:

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[0051] In Table 5, the components for the constraints on the upper surface (peripheral) IFP are calculated for the control, 3 mg / kg, and 30 mg / kg DEX-treated cases in formulation (3) based on the previously reported IFP boundaries. These values are used to ensure that physically meaningful solutions are identified.

Table 5

[0052] TME Normalization Therapy Design for Dose Selection: A method for optimal TME normalization therapy design for dose selection is disclosed, which has the overall objective of improving the transport and accumulation of anti-cancer agents within the tumor stroma. To do so, the experimental results of different doses of pretreatment DEX are investigated, and empirical correlations are utilized for optimal decision-making. The empirical correlation is required to construct the mathematical relationship (vascular permeability coefficient L p and interstitial permeability coefficient K) between the DEX dose and two important physiological parameters. A systematic mathematical methodology for TME normalization therapy design is disclosed.

[0053] Based on the obtained preclinical data, non-linear regression is utilized with a rational model to establish the following relationship,

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[0054] Since the obtained data is limited to three pretreatment DEX doses, different dose-dependent relationships may exist with other data sets. This is demonstrated using virtual experimental data presenting a complex dose-dependent treatment relationship for the pretreatment DEX dose between the actual data at dosages set at 3 mg / kg and 30 mg / kg at dosages of 10 mg / kg, 15 mg / kg, 20 mg / kg, and 25 mg / kg to demonstrate the applicability of the disclosed method.

[0055] In FIGS. 4A and 4B, the original data, virtual data, and corresponding polynomial regression models are plotted. The regression equation is given by the following formula,

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[0056] Figure 4A shows the experimental data and the regression model corresponding to Equation (7) plotted as the relationship of (4A) L with respect to dosage, and Figure 4B shows the experimental data and the regression model corresponding to Equation (8) plotted as the relationship of (4B) K with respect to the dosage of dexamethasone. To demonstrate the applicability of the proposed approach to the naturally occurring complex dose-dependent relationships, auxiliary virtual data are considered. p

[0057] The TME normalization therapy design problem is formulated as the following NLP:

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[0058] ​​Drug Size Design: Address the practicality of the tumor transport model for the drug size design problem. After determining the optimal dose of pretreatment DEX and quantifying the patient's response to the treatment, an anticancer nanocarrier that provides optimal delivery to the tumor stroma is designed. For example, the nanoparticle size can be adjusted for patient-specific tumor pathophysiology.

[0059] After DEX pretreatment, it is desirable to determine the optimal nanocarrier size that can maximize the drug concentration in the interstitial space of the tumor. Changes in pharmacokinetics such as distribution and excretion can have a substantial impact on achieving the desired therapeutic concentration of a specific nanocarrier. Very high concentrations can lead to side effects or toxicity. At very low concentrations, there will be no effect. In this situation, the optimal therapy requires strict assurance of several safety / performance specificities. The drug size design problem is formulated as a PDE-constrained NLP to account for these potential requirements.

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[0060] Furthermore, a therapeutic design strategy is proposed that simultaneously determines the optimal dose of DEX and the optimal nanocarrier size to maximize the accumulation of nanocarrier concentration in the tumor stromal space:

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[0061] An ANN surrogate model is also proposed for the simultaneous design problem (11) to reduce the computational load for the PDE-constrained problem. To achieve this, two ANNs are established, each having \(L\), \(K\), and \(d\) as inputs. Each ANN has a single output p , \(K\), and \(d\) m . These ANN models are different from those in the above disclosure for machine learning models. To train these new ANNs, the Sobol sequence sampling method is used again to create a dataset of 10 points on the domain \((L_p, K, d)\in[5\times10^{-5},5\times10^{-3}]\times[5\times10^{-3},5\times10^{-1}]\times[10,60]\). Consistent with the parameter estimation of the ANN model, the dataset is scaled using min-max normalization and randomly split into a training set (70%) and a validation set (30%). Training is performed using Flux.jl with the Adam optimizer with a learning rate of \(10^{-4}\).

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[0062] In Table 6, the table provides benchmark metrics for the time and performance (data generation time, training time, mean squared error, and mean percent error) for the ANN surrogate model development in (12) below.

Table 6

[0063] The formulation using the ANN model for the co - design approach can be expressed as follows:

Equation

[0064] Settings for Solving Optimization Problems: The settings used for numerical methods and software packages to solve optimization problems are discussed herein. For parameter estimation, TME normalization therapy design, and drug sizing design problems, the spatial domains of both the fluid transport model and the solute transport model are discretized into N = 100 nodes. The simulation time range includes 21 time nodes (5 minutes). Based on the upper surface region (about 0.07 mm from the surface) and the average tumor diameter (0.6 - 1.1 cm) in the DEX treatment study, the relationship n = 99 is selected to describe the upper surface region of the tumor. The physiological parameters used in the tumor transport model are provided in Table 7. All of the parameter estimation, drug sizing design, and TME normalization therapy design problems are solved for global optimality using the EAGO v0.6.1 solver via JuMP v0.21.4 in the Julia programming language. To solve the parameter estimation and drug sizing design problems, a custom bounding routine with a hybrid IA / AA method and standard DI is utilized in the BnB algorithm. For the parameter estimation problem, the absolute global convergence tolerance is set to 10 -6 and the relative global convergence tolerance is set to 10 -1 for each case. For the drug sizing design and TME normalization therapy design problems, the absolute convergence tolerance is set to 10 -6 and the relative convergence tolerance is set to 10 -2 . Each problem was run on a personal workstation equipped with an Intel Xeon E3-1270v5 (4 cores / 8 threads) CPU operating at 3.60 GHz / 4.00 GHz (base / turbo) frequency and 32 GB ECC RAM running on Windows 10 Version 2004.

[0065] In Table 7, the physiological parameter values are reported to construct the tumor transport model, which is discussed below in the part of the present disclosure directed to the tumor transport model. "70 kDa" and "500 kDa" indicate the molecular weights of the nanocarriers.

Table 7

[0066] Example 1: Global Optimization Results for Model Verification The results of the global optimization are considered for the parameter estimation problem. The global optimal solutions obtained from the parameter estimation problems for different doses of DEX-treated cases are listed in Table 8 for each formulation using the original mechanistic tumor transport model (1) as well as the ANN surrogate model (4). The dose selection for the experiment was based on previous studies that identified 3 mg / kg of DEX as the minimum dose for reducing IFP. Additionally, this dose is similar to the dose used in the clinical trial of CDDP / m (NCT02043288). The global solutions found for both the mechanistic model and the ANN model are very close to each other, with the relative error within 2.5% for each case. This demonstrates the accuracy of the ANN surrogate model and the validity of the simplification of the inequality constraints. Prior to this, local optimal conditions were obtained for the parameter estimation problem. In that study, the estimated L p values showed a decreasing trend from the control cases but were found to have an increasing trend. This does not represent a contradiction since the parameter estimation problem varies significantly in terms of considering different simulation time ranges. Furthermore, in the prior art, the inequality constraints on IFP were not considered.

[0067] Table 8 shows the global optimal conditions of the parameter estimation problem using the mechanistic model (1) and the ANN model (4). The solutions obtained for the ANN surrogate model are very close to those obtained for the mechanistic model. This is expected since high accuracy of the ANN was obtained during training. L * p The unit of is cm / mmHg-second, and the unit of K * The unit of is cm 2 / mmHg-second. [Table 8]

[0068] The time costs of each model are reported in Table 9. For DEX treatment cases, the parameter estimation problems for the mechanistic model and the proposed customized bounding routines are computationally very expensive. Despite using the most efficient global bounding method considered, these problems still required hours or days to solve. In contrast, the parameter estimation problem for DEX treatment using the ANN surrogate model can be solved within one minute. Even considering the time costs of data generation and training, the ANN surrogate model significantly reduces the burden of solving the parameter estimation problem on global optimality. Interestingly, it takes approximately an order of magnitude longer to solve the parameter estimation problem for the control cases using the ANN model compared to the mechanistic model. In these cases, it is observed that the lower bound problems solved for the ANN problems provide weaker bounds than the mechanistic modeling cases, leading to slower convergence of the BnB algorithm.

[0069] Table 9 shows the computational time costs of the parameter estimation problems using the mechanistic model (1) and the ANN model (4). Except for the control cases, solving the PDE-constrained optimization problem (1) requires significantly more time than the problem using ANN (4) without considering the ANN training time.

Table 9

[0070] Example 2: Pressure and Velocity Profiles of Interstitial Fluid Previous studies have shown that an important barrier to drug delivery in the TME is the elevated IFP that results in a decrease in the pressure gradient across the vessel wall. This is due to the leaky blood vessels and the lack of functional lymphatic vessels to drain excess fluid from the tumor tissue, which causes the phenomenon of interstitial hypertension. TME normalization therapy can repair the abnormal vasculature and reduce the IFP, resulting in a higher pressure gradient for higher transvascular and interstitial fluid flow. Therefore, the IFP was quantified (i29uantifyied) with different doses of DEX treatment to characterize the TME normalization process. The dimensionless IFP profile as a function of the dimensionless radial position for the optimal solution (i.e., from Table 8) is shown in Figure 5A. The IFP profile tends to reach a steady-state pressure p ss at the center of the tumor, where the IFP is equal to the vascular pressure p v . However, at the periphery, the IFP rapidly decreases as the distance from the tumor center increases. This finding is consistent with previous mathematical models and experimental findings. Therefore, the IFP profile indicates that the extravasation of fluid from the blood vessels is very slow near the center but highest at the periphery due to the lower IFP, resulting in an increase in the transvascular pressure gradient. In addition, this model confirms that DEX reduces the spatially averaged IFP and thus establishes a more favorable transvascular pressure gradient that contributes to enhanced transvascular fluid flow, which further affects interstitial fluid transport.

[0071] Figures 5A and 5B show the radial dose-dependent interstitial fluid pressure and velocity profiles. Figure 5A shows the dimensionless interstitial fluid pressure (IFP) p^ = (p - p ∞ ) / (p ss - p ∞) shows the mathematical model generation profile with the dimensionless tumor radial position \(r^{\wedge}\). This is presented for control tumors and tumors in mice treated with 3 mg / kg and 30 mg / kg of dexamethasone (DEX) per day for 4 days, based on vascular permeability data collected using fluorescently labeled 500 kDa dextran. The spatially averaged IFP decreases with DEX treatment. The inner bar graph illustrates the fraction of tumor volume with a favorable transvascular pressure gradient (i.e., \(\hat{p}\leq0.9933\)). This IFP threshold is determined by the region with \(r^{\wedge}\geq0.6\) for the 3 mg / kg DEX treatment cases, which is taken as the volume with a favorable transvascular pressure gradient. Figure 5B shows that the normalized interstitial fluid velocity (\(\hat{u}=uR / (K(p ss -p ∞ )) is plotted against the dimensionless tumor radial position \(r^{\wedge}\). A larger IFV is achieved deeper in the tumor stroma after DEX treatment, with a decrease in velocity closest to the tumor periphery. This increases the interstitial transport of nanocarriers.

[0072] The interstitial fluid velocity (IFV) is generated from the inner IFP gradient by Darcy's law (introduced in Supplementary Example 1.1). To investigate the effect of TME normalization on interstitial fluid transport, the normalized IFV (\(\hat{u}=uR / (K(p ss -p ∞ ))) profile is quantified for different doses of DEX. Positive values of IFV indicate that the interstitial fluid flow is from the center to the periphery of the tumor. As shown in Figure 5(b), the normalized IFV is very low near the center and increases towards the periphery where the highest flow velocity exists. The dimensionless parameter

Number

[0073] Example 3: Solute Concentration Profile Drug distribution is determined within the tumor by obtaining the solute concentration profile from the IFP and IFV profiles. The IFP gradient induces transvascular convective transport, the IFV profile induces interstitial convective transport, and the solute concentration gradient induces interstitial diffusive transport. Figure 6 shows the model-predicted solute concentration profile for the dimensionless tumor radius direction position r^ for the 500 kDa dextran experimental data, together with the vascular concentration after exponential decay following administration.

[0074] Figures 6A - 6D show the radial and time - dependent solute concentration profiles. The interstitial concentration of 500 kDa dextran

Number

Number

[0075] As shown in Figure 6A, the interstitial concentration 1 hour after dextran administration is equal to the normal tissue concentration at the periphery (equal to 0 in dimensionless form), rapidly increases to a peak in the peripheral region where there is a higher transvascular pressure gradient, which significantly enhances convective transcapillary solute transport. The fraction of the tumor volume with a higher transvascular pressure gradient is graphed for each treatment group in the inset of Figure 5A. At the same time, the higher IFV in the peripheral region causes a higher interstitial fluid flux that transports solute outward to the periphery. As a result, the solute accumulates and reaches a peak concentration near the periphery, then decreases to 0 near r^ = 0.8 for the control case and near r^ = 0.6 for the 3 mg / kg and 30 mg / kg DEX treatment cases. In fact, the region with the favorable transvascular pressure gradient in the DEX - treated cases is larger than that in the control case (Figure 5A). This pressure gradient leads to enhanced convective transvascular transport that carries solute to a larger fraction of the interstitial space of the tumor. In other words, the region with higher solute accumulation occurs over a longer fraction of the tumor radius for the DEX - treated cases compared to the control.

[0076] As presented in FIG. 6A, the interstitial concentration profiles for all treatment cases have higher peaks at 24 hours than at 1 hour. The concentration peaks at 72 hours for all cases (FIG. 6C) are lower than at 24 hours but higher than at 1 hour. This is because the vascular concentration decays at 72 hours compared to 24 hours, so there are fewer nanocarriers transported to the interstitial space by transvascular flow. In addition, the interstitial concentration profile at 72 hours is flatter than at 24 hours, and higher concentrations are retained towards the center of the tumor, such as r^ = 0.5. This is generated by a concentration gradient that gradually moves the nanocarriers from the concentration peak at the periphery towards the tumor center where the concentration of the nanocarriers is nearly zero, caused by slower interstitial diffusion. Transvascular flow is limited at 72 hours due to the systemic clearance of circulating nanocarriers, but diffusion caused by the concentration gradient becomes more evident in the flatter concentration profile.

[0077] As shown in FIG. 6D, the spatially averaged interstitial concentration rises to a peak and then stabilizes. The vascular concentration of the nanocarriers decays exponentially, but the spatially averaged interstitial concentration decreases slowly after reaching the peak. The concentration profile at the time of the highest spatially averaged concentration accumulation is shown in FIG. 6E, which is discussed below. The highest spatially averaged concentrations occur at 38.8 hours, 34.2 hours, and 53.9 hours for the control, 3 mg / kg, and 30 mg / kg DEX treatment cases, respectively. Generally, the nanocarriers accumulate to peak concentrations in the first few tens of hours and then decrease at a slow rate.

[0078] FIG. 6E shows the radial interstitial concentration profiles at the time corresponding to the highest spatially averaged concentration for the control (38.8 hours), 3 mg / kg dexamethasone treatment (34.2 hours), and 30 mg / kg DEX treatment (53.9 hours) cases.

[0079] The spatially averaged concentrations at 72 hours are 84%, 92%, and 99% of their respective maximum concentrations for the control, 3 mg / kg, and 30 mg / kg DEX-treated cases (shown in Fig. 6f and discussed below). The spatially averaged concentration of 500 kDa dextran in the control tumor decreased by only 16% at 33.2 hours after reaching the maximum concentration, indicating a retention effect. Both 3 mg / kg and 30 mg / kg DEX treatments enhanced this retention effect (92% and 99% are higher than the control case). The 3 mg / kg DEX treatment did not result in the highest retention rate (92% < 99%) at 72 hours but had the highest spatially averaged concentration over the entire time range. In contrast, the control case had the lowest percentage and the lowest spatially averaged concentration. Therefore, these findings demonstrate that DEX treatment not only increases permeability but also increases retention towards promoting the EPR effect.

[0080] Fig. 6F shows the percentage of the spatially averaged concentration at 72 hours relative to the respective highest spatially averaged concentration for the control, 3 mg / kg, and 30 mg / kg dexamethasone (DEX)-treated cases. DEX treatment enhanced the retention effect.

[0081] Determine the relationship between the solute concentration profile over time and the dose of DEX treatment. The concentration profile of the 30 mg / kg DEX-treated case was closer to the control case at 1 hour after administration but closer to the 3 mg / kg DEX-treated case at 72 hours after administration. At 1 hour after administration, there were many nanocarriers in the perfused blood vessels, and they were carried into the tumor tissue by transvascular flow. A larger vascular permeability coefficient L p indicates a higher transvascular flow rate. However, the L pis closer to the control case (Table 8). The blood vessels are normalized after 30 mg / kg DEX treatment, but there is an excessive pericyte coverage, which reduces the pore size of the vessel wall, thereby limiting nanocarrier extravasation at 1 hour post-administration. In contrast, nanocarrier extravasation is negligible at 72 hours due to the attenuation of its concentration in the vasculature, and the interstitial concentration profile has already reached its peak and is decreasing. Thus, interstitial diffusion transport becomes more prominent. Both 3 mg / kg and 30 mg / kg DEX treatments similarly reduce hyaluronan levels and tissue stiffness, resulting in an interstitial permeability coefficient K that is much larger than that of the control case (Table 8), so enhanced interstitial diffusion transport results in the observed profile. Additionally, the 3 mg / kg DEX-treated case results in a much higher accumulation of the overall nanocarrier concentration in tumor tissue at all time nodes (1 hour, 24 hours, and 72 hours) compared to the control and 30 mg / kg cases, which, as previously demonstrated, indicates that increased delivery of anticancer nanocarriers results in improved efficacy. Considering that the 3 mg / kg DEX treatment results in the highest nanocarrier accumulation, convective and diffusive transvascular fluxes are determined separately to understand how DEX increased the accumulation.

[0082] Example 4: Dexamethasone increases convective transvascular flux in tumors Figures 7A - 7D show the dose - dependent transvascular convection and diffusion flux profiles. The transvascular flux profile of 500 kDa dextran with respect to the dimensionless tumor radial position r^ at 1 hour post - administration is plotted in Figure 7a for control, in Figure 7b for the 3 mg / kg dexamethasone (DEX) - treated case, and in Figure 7c for the 30 mg / kg DEX - treated case. In Figure 7d, the spatially averaged convective flux 7d1 and diffusive flux 7d2 at 1 hour post - administration for different doses of DEX are presented in this bar graph. The general trend shows the maximum convective flux at the tumor periphery and the maximum diffusive flux deeper within the tumor center. After DEX treatment, convection accounts for a larger proportion of the spatially averaged transvascular flux, demonstrating how TME normalization induces a larger transvascular pressure gradient that is favorable for improving nanocarrier delivery in tumors. Treatment with 3 mg / kg of DEX induces the highest convective transport, indicating that a moderate amount of DEX is more favorable for enhancing convective transport.

[0083] After finding the interstitial concentration profiles indicating enhanced nanocarrier distribution and accumulation due to DEX treatment, the difference in concentration between the control and DEX - treated cases depends on the relative contributions of convective and diffusive transvascular fluxes. Previous studies have shown that the main mechanism of transvascular transport is diffusion because the elevated IFP in the TME invalidates the transvascular pressure gradient. Since DEX reduces the IFP, it can enhance the convective flux, which results in a faster transport than the diffusive flux. However, the relative contributions from convection and diffusion over the entire tumor volume have not been studied previously.

[0084] Based on the optimal permeability coefficient value determined by global optimization, the model-predicted transvascular convection and diffusion fluxes are quantified. As explained in (2), the convective flux is calculated by L_p S / V(p_v - p)(1 - σ)c_v, and the diffusive flux is calculated by P S / V(c_v - c)Pe / (e^Pe - 1). The relative contributions from the convective and diffusive fluxes to the spatially averaged concentration profile over time are illustrated in FIGS. 7E and 7F (discussed below). The contribution of the convective flux in the DEX-treated cases is dominant throughout the entire time range compared to the control cases. This indicates that the normalized TME after DEX treatment is favorable for convective transport.

[0085] FIGS. 7E and 7F show, for the control in FIG. 7E, the contributions from the convective flux 7e1 and the diffusive flux 7e2 to the spatially averaged concentration over time. FIG. 7F shows the case of a 3 mg / kg dexamethasone (DEX) treatment. Since the diffusive flux then becomes extremely small, the profile is plotted in the range of 12 hours. The contribution from the convective flux becomes more dominant after DEX treatment.

[0086] To better understand the effect of TME normalization on transvascular transport, the spatial dependence of the model-predicted diffusion and convective fluxes in tumors was determined. Previously, continuous intravital microscopy was performed on mice 1 hour after administration to investigate the fine distribution of nanocarriers. Here, the spatial convective and diffusion fluxes were quantified at 1 hour after administration to determine their distribution in tumors. As shown in Figure 7A, in regions with r^<0.8, the convective flux is close to 0, while diffusion is the main mode of transport. This is because the IFP is close to the microvascular pressure (Figure 5A), indicating that there is no driving force for convection. The tumor is dominant but small, so there is little transvascular flux at the tumor center. In contrast, in regions with r^>0.8, there is more convective flux than diffusive flux, and the diffusive flux is close to 0. This convective flux at the periphery is 22 times larger than the convective flux at the center. The reason for this is that the IFP in the convection-dominated region is low (Figure 5A), which induces a high transvascular convective flux driven by a large pressure gradient. Thus, convective transport increases the interstitial concentration, thereby reducing the concentration gradient and the driving force for diffusion. In addition, the Pe number, which represents the ratio between the transvascular convection and diffusion rates, is very large at the periphery, reflecting the extremely small diffusion flux as observed in Figure 7A. As a result, there are convection-dominated and diffusion-dominated regions, and the maximum velocity of the convective flux is one order of magnitude larger than the maximum diffusion flux.

[0087] Next, the effect of TME normalization on the spatial distribution of these fluxes is determined. As shown in Fig. 7B, the maximum convective flux in the periphery for 3 mg / kg of DEX is 48 times larger than the maximum diffusive flux occurring at the tumor center. Since the maximum diffusive flux is close to that of the control cases, this indicates that convection is highly enhanced and is responsible for a larger proportion of the total transvascular transport in the normalized TME after treatment with 3 mg / kg of DEX. In contrast, in Fig. 7C, the maximum convective flux for 30 mg / kg of DEX is 22 times larger than the maximum diffusive flux, which is comparable to that of the control cases. Indeed, by comparing the values of the maximum convective flux in the periphery, the flux for 30 mg / kg of DEX is 14.3% lower than that of the control cases. The reason is that the vascular permeability coefficient L p is 13% lower than that of the control cases (Table 8). This is because DEX normalizes the blood vessels, increases vascular maturation, and thereby reduces vascular leakage. As a result, the vascular permeability coefficient decreases, leading to a lower maximum convective flux at the tumor periphery. However, these findings do not show that the convective flux for 30 mg / kg of DEX decreases across the whole tumor compared to the control. This is because the volume of the convection-dominated region is much larger in the DEX-treated cases.

[0088] As shown in FIGS. 7B and 7C, the convective fluxes in both the 3 mg / kg and 30 mg / kg DEX-treated cases begin to increase around r^ = 0.6 as compared to r^ = 0.8 in the control case, indicating a larger convective-dominated region. These findings are illustrated in FIG. 8 (see below), which shows schematic diagrams of tumor cross-sections for the control case and the 3 mg / kg DEX-treated case. The 30 mg / kg DEX-treated case has approximately the same proportion of the convective-to-diffusive dominated region as the 3 mg / kg case. Therefore, 3 mg / kg of DEX was selected to explain the treated cases in FIG. 8. The tumor volume fraction of the convective-dominated region for the control case is only 49%, but this jumps sharply to 78% for tumors treated with DEX. This represents a 61% increase in the volume fraction of tumors dominated by convective transport as a result of TME normalization by DEX treatment. The transvascular fluxes in FIG. 8 are scaled according to 70 kDa dextran, and the corresponding convective and diffusive fluxes are presented in FIGS. 7G - 7J, which are discussed below. The findings for determining the convective and diffusive dominated regions using 70 kDa dextran are consistent with those using 500 kDa dextran. Both doses increase the volume of the convective-dominated region approximately equally, but 3 mg / kg of DEX is superior as it also significantly increases the maximum convective flux.

[0089] FIGS. 7G - 7J show the transvascular flux profiles on the dimensionless radius r^ for the control in FIG. 7G, for the 3 mg / kg dexamethasone (DEX) treatment in FIG. 7H, and for the 30 mg / kg DEX-treated case with 70 kDa dextran 1 hour after administration in FIG. 7I. FIG. 7J shows that the spatially averaged convective flux 7j1 and diffusive flux 7j2 at 1 hour after administration for different doses of DEX are presented in this bar graph.

[0090] To quantify the contributions of convection and diffusion across the whole tumor, spatially averaged transvascular convection and diffusion fluxes were determined and presented as bar graphs as shown in Fig. 7D. Compared to the control cases, the convection flux increased by 360% with 3 mg / kg of DEX and by 80% with 30 mg / kg of DEX. This indicates that the DEX dosage has a significant impact on convective transport. It can be seen that moderate amounts of DEX greatly enhance convection. Excessive DEX still enhances convective transport, but the effect is much lower. The reason is that the vascular permeability coefficient L p for 30 mg / kg of DEX is much smaller than that for 3 mg / kg of DEX (Table 7). In addition, higher doses of DEX treatment result in lower spatially averaged doses (a 20% decrease with 3 mg / kg of DEX and a 65% decrease with 30 mg / kg of DEX compared to the control). One reason is that the increased convection flux due to DEX treatment results in much higher interstitial concentrations. Therefore, the driving force from the transvascular concentration gradient decreases, resulting in a lower diffusion gradient. In addition, with 30 mg / kg of DEX treatment, the vessel wall pore size is smaller because vascular normalization reduces vascular leakage by contracting the vessel wall pores. Therefore, the diffusion barrier (introduced in Supplementary Example 1.3) is also smaller. A smaller diffusion barrier represents a higher barrier to diffusion. Therefore, 30 mg / kg of DEX treatment results in a lower dose. In conclusion, these results demonstrate that DEX increases the accumulation of nanocarriers in tumors by increasing the convective transvascular flux, but the dosage of the TME normalization treatment should be titrated to avoid a decrease in vessel wall pore size that limits the benefit of enhanced convection.

[0091] Figure 8 shows that the cross-section of the spherical tumor 800 is illustrated in this schematic diagram for the control case 805 (left) and the 3 mg / kg DEX-treated case 810 (right). The perfused blood vessels 815 are more abundant and have a larger average diameter after DEX treatment compared to the control case. As a result of normalizing the tumor microenvironment. The outer shaded compartment (or outer region) 820 represents the convection-dominated region, which has a significant pressure gradient, resulting in a dominant convective transvascular flux (arrow 835). The inner compartment (or inner region) 825 represents the diffusion-dominated region, which has little pressure gradient (the highest interstitial fluid pressure (IFP)), resulting in a dominant diffusive transvascular flux (arrow 845). The inner region 825 is much larger for the control case with the boundary 830 (dashed curve) between the regions occurring at r^ = 0.8, while the boundary 830 for the DEX-treated case is at r^ = 0.6. The arrows illustrate the convective transvascular flux 835 (arrow pointing outward from the perfused blood vessels in the outer region), the convective interstitial flux 840 (a single large arrow pointing radially outward away from the perfused blood vessels in each case), the diffusive transvascular flux 845 (arrow pointing outward from the perfused blood vessels in the inner region), and the diffusive interstitial flux 850 (a single large arrow pointing radially inward away from the perfused blood vessels in each case). After DEX treatment, the convective transvascular flux is significantly enhanced. The large arrow pointing in the radially outward direction 840 and the large arrow pointing in the radially inward direction 850 represent the convective and diffusive fluxes of the nanocarriers in the tumor stroma, respectively. The direction of the interstitial convective transport of the nanocarriers is outward toward the periphery caused by the IFP gradient, while the direction of the interstitial convective transport of the nanocarriers is inward toward the center caused by the concentration gradient. The overall interstitial flux is significantly larger after DEX treatment. Based on the results of the global optimization for the 13 nm nanocarrier experiment, the interstitial flux and the transvascular flux are illustrated. The lengths of the arrows for the interstitial and transvascular fluxes are each normalized to their own relevant reference for ease of explanation and should not be compared to each other. Since the interstitial flux is spatially dependent, the arrows represent the spatially averaged flux.

[0092] Example 5: Global optimization reveals the dose of dexamethasone that maximizes nanocarrier accumulation Considering that a moderate amount of DEX is superior to no DEX and high-dose DEX in enhancing transvascular transport, there exists an optimal dose of DEX that can maximize nanocarrier or antibody concentration accumulation. DEX as a drug for TME normalization is both (1) an anti-angiogenic agent that can normalize tumor blood vessels and (2) a cancer-associated fibroblast reprogramming agent that reduces the ECM level and brings about decompression of tumor blood vessels. The functions of (1) and (2) are related to the vascular permeability coefficient L p and the interstitial permeability coefficient K, respectively. Both L p and K are favored by drug delivery using a moderate amount of DEX treatment, but the relative contributions of (1) and (2) cannot be directly controlled using drugs such as DEX that affect both. In addition, as shown by Table 7, excessive doses of DEX decrease L p thereby limiting the transvascular flux for drug delivery. Therefore, it is not clear which dose of DEX should be used to maximize the treatment effect of the subsequently administered nanocarrier or antibody. The global optimization method and the TME normalization therapy design formulation (introduced above along with the disclosure directed to TME normalization therapy design for dose selection) enable the ability to determine the optimal dose of DEX that maximizes nanocarrier accumulation.

[0093] As described above, the disclosure regarding TME normalization therapy design for dose selection discloses two cases of the TME normalization therapy design problem. (Case 1) The relationship between the DEX dose and L p and K is established based on previously published original data and is represented as equations (5) and (6). (Case 2) The DEX dose and L pThe relationship between and K is established based on the original data combined with auxiliary data points and is represented as (7) and (8). Both TME normalization therapy design problems were solved for global optimality. It took 2.5 hours to solve Case 1 and 3.6 hours to solve Case 2. The more complex relationship between the DEX dosage and the water permeability coefficient in Case 2 resulted in higher complexity and a longer solution time to reach global optimality. Nevertheless, the proposed methodology using a mixed IA / AA approach for the bounding routine was able to find the optimal solution in time units. Thus, this short computation time demonstrates that the proposed TME normalization therapy design methodology is practical for real-world clinical studies. The optimal solution for Case 1 was found at x * = 5.30 mg / kg, and the optimal solution for Case 2 was found at x * = 4.41 mg / kg. The optimal dosage found in Case 1 results in a 3% higher concentration accumulation than the 3 mg / kg DEX treatment and a 74% higher concentration accumulation than the 30 mg / kg DEX treatment. As a result, the TME normalization therapy design method in this study demonstrates that global optimization can be used in a reasonable time window to determine the optimal dosage of DEX, which is predicted to be implemented 3% better than the best dosage determined experimentally.

[0094] Example 6: Dexamethasone dosage A affects the transvascular convective transport size dependence (Dependentl) Figures 9A to 9D show that the interstitial concentrations of nanocarriers of different sizes (500 kDa nanocarrier - 32 nm, 70 kDa nanocarrier - 13 nm, case 1 - 16.40 nm) 1 hour after administration are plotted against the dimensionless tumor radius position r^ in Figure 9A, for control in Figure 1, for 3 mg / kg DEX treatment in Figure 9B, and for 30 mg / kg DEX treatment in Figure 9C. In Figure 9D, the spatially averaged transvascular convective fluxes for dextran 9c1, 9c2 of 32 nm and 13 nm at 1 hour after administration are plotted, and the diffusion fluxes for dextran 9c3, 9c4 of 32 nm and 13 nm at 1 hour after administration are plotted. The interstitial concentration due to 30 mg / kg DEX treatment for 32 nm dextran is lower than that for 13 nm dextran, mainly due to its lower convective flux.

[0095] After finding the optimal dose of DEX treatment to maximize concentration accumulation, the size of the nanocarriers also affects the interstitial concentration. Since unrelated previous studies have demonstrated that vascular permeability depends on nanocarrier size, compare the vascular permeability experimental data (with previously published data) of two nanocarriers with different hydrodynamic diameters. The smaller nanocarrier is 13 nm, which is similar to the size of circulating nanoparticle albumin-bound paclitaxel, and the larger nanocarrier is similar to the size of NC-6004, a clinical-stage polymeric micelle containing cisplatin. Using this experimental data and the disclosed mathematical model, the model-predicted interstitial concentration regarding the tumor radial position for these nanocarriers is determined. As shown in Figure 9A, the interstitial concentration of the control cases is almost the same for dextrans of 32 nm and 13 nm. For the 3 mg / kg DEX treatment case shown in Figure 9B, the peak of the 13 nm dextran is slightly higher, but the overall concentration distribution is still very close for these dextrans. However, for the 30 mg / kg DEX treatment case shown in Figure 9C, the concentration profile of the 13 nm dextran is higher than that of 32 nm. The possible reason is that the pore size of the blood vessel wall decreases with 30 mg / kg DEX treatment. Therefore, steric hindrance is greater, especially for larger nanocarriers. As a result, fewer larger nanocarriers are transported to the tumor tissue, resulting in a lower concentration profile. To better understand this phenomenon, determine the effects of convective transport and diffusive transport.

[0096] To demonstrate their effects on accumulation, the spatial averaged convection and diffusion fluxes are quantified for 13 nm and 32 nm dextrans. As shown in Figure 9D, a 3 mg / kg DEX treatment enhances convection to a similar extent for each dextran (360% increase for both 13 nm dextran and 32 nm dextran compared to the control case). However, a 30 mg / kg DEX treatment results in an 80% increase in convection for 32 nm dextran and a 180% increase for 13 nm dextran. Thus, the relatively low convection flux with 30 mg / kg DEX for 32 nm dextran results in less accumulation in tumor tissue. In addition, DEX decreases diffusion for both nanocarriers. The higher interstitial concentration and smaller pore size at 30 mg / kg DEX result in a lower diffusion flux. Since diffusion is inversely proportional to the hydrodynamic diameter of the nanocarrier, the decrease in diffusion after DEX is more significant for smaller nanocarriers that rely on diffusion. In conclusion, 3 mg / kg DEX enhances transvascular transport size-independently, which is consistent with the findings using the ECM normalizer tranilast in the art. However, considering the anti-angiogenic properties of DEX, excessive doses of DEX are less effective in enhancing convection, especially for larger nanocarriers.

[0097] Example 7: Global optimization determines the dexamethasone dose and nanocarrier size that maximize accumulation DEX enhances convection but reduces diffusion, and thus, the optimal hydrodynamic diameter of the nanocarriers that achieve the maximum accumulation with safety / performance specificity is determined by leveraging the balance of these two effects. Three cases of drug size design problems are disclosed. These correspond to 3 mg / kg DEX treatment, the optimal dose of DEX for case 1 (5.30 mg / kg), and the optimal dose of DEX for case 2 (4.41 mg / kg), respectively. The 3 mg / kg dose induced the highest transvascular flux in the experiment, while cases 1 and 2 were determined from the corresponding TME normalization therapy design problems. These drug size design problems formulated as (10) were solved for global optimality. The optimal solutions and time costs found for each case are summarized in Table 10. The optimal nanocarrier sizes in these designs strictly meet the safety / performance requirements to avoid potential side effects and ensure effectiveness, which restricts the nanocarrier concentration at the periphery of tumor normal tissues, as demonstrated in (10). Smaller nanocarriers diffuse and accumulate more rapidly within the tumor interstitial space but may violate the safety specificity in these designs. Therefore, these optimal solutions explain the drug size design results along with the requirements. Additionally, these problems can be solved within minutes, demonstrating their practicality for real-world applications.

[0098] Table 10 shows the optimal solutions and time costs of the drug size design problems for the case studies of 3 mg / kg DEX treatment, case 1, and case 2 of the therapy design problem.

Table 10

[0099] (12) The simultaneous therapy design approach using the ANN model formulated as was also implemented using case 1 and case 2 studies. The optimal solution for case 1 was found to be (x * ,d m * ) = (5.32, 16.40), and the optimal solution for case 2 was (x * ,d m *)=(4.38, 12.41) was found. The time cost was 42 seconds for Case 1 and 350 seconds for Case 2. However, the global optimum of (11) using the mechanistic model could not be obtained within a reasonable time limit. Continued research on global bounding methods may accelerate convergence and make it possible to address this problem in the future. Alternatively, a multi-start local optimization procedure is implemented for the problem formulated as (11), and the result with the lowest objective function value is selected. For Case 1

Number

Number

[0100] The therapy design method in this study provides the ability to identify the optimal dosage and drug size to maximize the improvement in nanocarrier delivery induced by TME normalization therapy.

[0101] A rigorous method for model validation and the development of optimal TME normalization dosage and nanocarrier size therapy design were developed. This study was motivated by the need for a more rigorous method for in-silico model-based decision-making in cancer research. The use of a comprehensive theoretical framework for model-based applications in preclinical PKPD research and development. The dynamic optimization problem was formulated as an NLP with PDE constraints and solved for global optimality, providing a rigorous solution for cancer drug delivery research. To improve the performance of the global optimization algorithm, an efficient bounding routine using the IA / AA approach and the DI approach, as well as a special bounding rule for the Peclet number in the solute source term, were proposed. In addition, a machine learning approach was utilized to establish a data-driven model via an ANN as a surrogate model for the original PDE system. The ANN was utilized in place of the mechanistic model to solve the parameter estimation problem using a simplified formulation. In particular, based on the values of the global solutions obtained for the permeability coefficient, transvascular transport was quantified with respect to convective and diffusive fluxes to elucidate their contributions to the accumulation of anticancer nanocarriers in tumors after TME normalization with DEX. In addition, a methodology for optimal TME normalization therapy design was proposed to optimize the dosage of DEX for enhancing the accumulation of anticancer nanocarriers in tumors. The nanocarrier size design method was also proposed to determine the optimal size of patient-specific TME with safety / performance specificity. Finally, a simultaneous design formulation was considered to determine the optimal dosage of DEX and the optimal nanocarrier size that result in maximized accumulation in the tumor stroma.

[0102] Supplementary Example 1: Tumor Transport Model Previously proposed one-dimensional (1D) tumor transport models have been used as a mechanistic basis for determining transvascular exchange and extravascular transport in tumors. The actual vasculature of tumors is complex, and cells between regions have significant differences. There is a necrotic region at the center of the tumor (i.e., most / all cells are dead). In contrast, the outer regions of the tumor contain rapidly dividing cells that require a large blood supply by abundant active blood vessels. Thus, actual solid tumors are spatially heterogeneous, and some physiological parameters in this model may be space-dependent. The tumor microenvironment (TME) is simplified to be spatially homogeneous without lymphatic vessels or extravascular connections, which is useful for demonstrating and evaluating the overall role of interstitial fluid pressure (IFP) on the fluid transport and penetration of nanocarriers within the tumor. Blood vessels, cells, extracellular matrix (ECM), and other microscopic structures (discussed below) as illustrated in FIG. 10 are also not explicitly considered in the model as this level of granularity is not important at the relevant length scales. Additionally, one focus is to determine the overall macromolecular solute concentration in the tumor over a defined time range. Thus, spatial averaging is utilized in the data and simulation results, which essentially homogenizes the macroscopic structure. Additionally, it is also assumed that the vasculature is continuously distributed over a spatial region rather than at discrete or local positions.

[0103] FIG. 10 shows FIG. 1000 of the tumor microenvironment illustrating fluid and solute transport from blood vessels with high transvascular permeability to the interstitial space.

[0104] Supplementary Example 1.1: Fluid Transport Fluid transport in the tumor interstitium follows Darcy's law:

Equation

Equation

[0105] The continuity equation for a steady-state incompressible fluid in spherical coordinates is given by the following equation:

Equation

Equation

Equation

[0106] The boundary conditions consist of the no-flux symmetry condition at the center of the spherical tumor and the Dirichlet condition at the periphery, respectively, as follows

Equation

[0107] Supplementary Example 1.2: Solute Transport To explain and characterize the transport mechanism of nanocarriers in tumors, the polymeric solute transport model is governed by the following convection-diffusion equation:

Number

Number

[0108] It is assumed that the polymeric solute does not exist in the tumor before injection, and thus the initial condition is c(0, r) = 0. The boundary conditions are defined as follows,

Number

[0109] Supplementary Example 1.3: Pore Theory In the technical field, applying the pore theory, it is assumed that the pores of blood vessels are cylindrical. In this case, the permeability coefficient is determined by the pore theory for tumor blood vessels L p , the vascular permeability P, and the reflection coefficient σ,

Equation

Equation

Equation

[0110] The corresponding coefficient ak and b k are listed in Table 11. As shown by (S9), the vascular permeability P depends on the particle size and the vascular wall properties such as pore size, thickness, charge, and arrangement. Larger particles result in lower P, and when the particle size is larger than the pore cut-off size, P becomes 0. The vascular water permeability coefficient L p depends on the wall morphology and the fraction of the wall surface occupied by the active pores.

[0111] Table 11 shows the hydrodynamic coefficients used in the cylindrical pore model.

Table 11

[0112] Supplementary Example 1.4 The fluid and solute transport models were numerically solved. First, the dimensionless forms of the tumor radius, IFP, and solute concentration were defined as follows.

Number

[0113] After reformulating the tumor transport model into a dimensionless form, the spatial domain was discretized using the central finite difference method. The IFP profile was obtained by solving the fluid transport model (S4). For the solute transport model, a backward difference scheme was used for the discretization of the first-order partial derivative ∂c / ∂r. Then, the explicit Euler method was used to integrate the transient convection-diffusion equation with a step size set as h = 15 s to obtain the drug concentration profile across the tumor radius.

[0114] Supplementary Example 2: Set-Valued Mapping Approach Supplementary Example 2.1: Interval Arithmetic and Affine Arithmetic Interval arithmetic (IA) is an operation performed on intervals according to basic interval calculation rules. The main purpose of IA is to calculate the upper and lower bounds of the range of a function in one or more variables. IA is plagued by dependency problems because different intervals in an equation are treated as completely independent variables. When some of the intervals are dependent on each other (for example, a variable occurs several times within an equation), the combination of IA operations for a function can significantly overestimate the inclusion of the function.

[0115] Affine arithmetic (AA) can overcome the overestimation caused by the dependency problems of conventional IA. AA tracks the dependencies between interval variables throughout the calculation and, in most cases, results in a better interval approximation. Additionally, the associated properties regarding the combined range of interval variables can be represented as a geometry by AA that reduces overestimation. When implementing non-affine operations, an extra noise term is required to estimate the affine approximation of the non-affine part for each operation. Generally speaking, as a result, the basic operations of AA are more computationally costly than standard IA. The non-affine operations and the additional complexity they introduce are ignored and do not result in an extra time cost beyond standard IA.

[0116] Supplementary Example 2.2 Differential inequalities (DI) is an approach that uses IA to construct component-wise lower and upper bounds for the solution set of a system of ordinary differential equations (ODEs). The DI method can be classified into two types: continuous-time DI and discrete-time DI. In continuous-time DI, an auxiliary system of ODE-IVP is formulated and sent directly to a numerical integrator to construct the bounds. In contrast, discrete-time DI reformulates the system of ODEs into a discrete-time form. Then, the bounding rules are applied at each discrete time point. In this study, the discrete-time DI method was utilized. Additionally, in a system where additional bounding information is known a priori, an interval correction operator can be applied to standard DI to further reduce the overestimation of the bounding results.

[0117] Supplementary Example 3: Simplification of Inequality Constraints The inequality constraints for the upper surface IFP can be expressed as linear constraints for the optimization variables L p and K, whereby,

Number

Number

[0118] Next, the IFP in the upper surface region can be expressed as follows,

Number

Number

[0119] If (S15) is active, the following equation holds:

Number

[0120] L p Differentiating (S17) with respect to gives the following equation:

Number

Number

[0121] Therefore, when the constraint is active, it is as follows.

Number

[0122] For this equation to hold, this means that α must be constant with respect to L p Since all parameters in α other than L and K are constants, K must necessarily be a scalar multiple of L p p .

[0123] This gives the following result Some

Number

[0124] By the same procedure, if (S16) is active, K must be a scalar multiple of L p Therefore, (S15) and (S16) can be simplified as follows, respectively: K ≦ ζ max L p , (S21) K ≧ ζ min L p .(S22)

[0125] ζ min and ζ max values are listed in Table 5. The value of ζ min is calculated according to the following procedure. 1. Select two different values of L within the interval boundary p . 2. For the corresponding K values of L p ​Solve the non-linear equation (S17) using each value of 3.L p Calculate ζ as the slope of the secant line connecting two points on the K plot min Calculate. 4.ζ max The calculation of the ζ value continues in the same way.

[0126] Supplementary Example 4: Relationship between nanocarrier size and physiological parameters The nanocarrier size d m There are two physiological parameters directly related to it, the diffusion coefficient D and the half-life circulation time k d exist. The previous experimental results regarding their correlation are listed in Table 12.

[0127] In Table 12, data on the diffusion coefficient and blood half-life circulation time with respect to the nanocarrier size are reported.

Table 12

[0128] For these quantities below, a non-linear regression model is established (power model for D vs. d m ; k d vs. d m for the Gaussian model):

Equation

Equation

[0129] According to one or more embodiments, as shown above, an individualized method of treating a cancer patient is disclosed, the method comprising administering to the cancer patient a first dose of an adjuvant (dexamethasone) for chemotherapy, performing in vivo imaging to determine the effective permeability (Peff) of the first dose of dexamethasone in the tumor of the cancer patient, executing the process disclosed herein, determining a second dose of an adjuvant for chemotherapy and the nanoparticle carrier size for a chemotherapeutic drug for the cancer patient, and optionally, administering the second dose of an adjuvant for chemotherapy and the chemotherapeutic drug in the sized nanoparticle carrier.

[0130] Dexamethasone is an adjuvant for chemotherapy used to reduce inflammation and suppress the body's immune response. Dexamethasone can typically be administered as an oral formulation before, during, or after chemotherapy.

[0131] Typical doses of dexamethasone are 0.3 - 1.7 mg / kg / day.

[0132] Examples of in vivo imaging for determining the effective permeability (Peff) of a first dose of dexamethasone in the tumor of a cancer patient include computed tomography (CT), magnetic resonance imaging (MRI), ultrasound (US), positron emission tomography (PET), single-photon emission computed tomography (SPECT), fluorescence reflectance imaging (FRI), fluorescence-mediated tomography (FMT), bioluminescence imaging (BLI), microscopy methods such as laser-scanning confocal microscopy (LSCM), and multiphoton microscopy (MPM).

[0133] Exemplary nanocarriers have diameters of 5 to 500 kDa.

[0134] The type of nanocarrier is not limited and includes polymer nanoparticles, protein-based carriers such as cell surface proteins, micelles, dendrimers, lipid nanoparticles including liposomes, inorganic nanoparticles, magnetic nanoparticles, etc. Polymer nanoparticles include natural polymers such as albumin, heparin, and chitosan, as well as biodegradable polymers such as PLA, PLC, and PLGA. Examples of inorganic nanoparticles include mesoporous silica NC (MSNCs), gold NC (AuNC)

[21] , magnetic NC (MNC), carbon nanotube NC (CNT-NC), graphene oxide, and quantum dots (QD).

[0135] The type of chemotherapy depends on the type of tumor being treated. Exemplary chemotherapies include ashibicin, aclarubicin, acodazole, acronine, adozelesin, aldosterone, alitretinoin, allopurinol, altretamine, amphomycin, ametantrone, amifostine, aminoglutethimide, amsacrine, anastrozole, anthramycin, arsenic trioxide, asparaginase, asperlin, azacitidine, azetepa, azotomycin, batimastat, benzodepa, bicalutamide, bisantrene, bisnafide dimesiate, bizelesin, bleomycin, brequinar, broxuridine, busulfan, calicheamicin, calusterone, capecitabine, caracemide, carbetimer, carboplatin, carmustine, carboquone, carzelesin, cedefingol, celecoxib, chlorambucil, cirolemycin, cisplatin, cladribine, crisnatol mesylate, cyclophosphamide, cytarabine, dacarbazine, dactinomycin, daunorubicin, decitabine, dexormaplatin, dezaguanine, dezaguanine mesylate, diaziquone, docetaxel, doxorubicin, droloxifene, drostanolone, duazomycin, edatrexate, eflornithine, elsamitrucin, enoplatin, enpromate, epipropidine, epirubicin, exemestane, esorubicin, estramustine, etanidazole, etoposide, etoprine, fadrozole, fazarabine, fenretinide, floxuridine, fludarabine, fluorouracil, flurocitabine, fosquidone, fostriecin, fulvestrant, gemcitabine, hydroxyurea, idarubicin, ifosfamide, ilmofosine, interleukin II (including IL-2, recombinant interleukin II or rIL2), interferon alpha-2a, interferon alpha-2b, interferon alpha-n1, interferon alpha-n3, interferon beta-Ia, interferon gamma-Ib, iplatin, irinotecan, lanreotide, letrozole, leuprolide, liarozole, lometrexol, lomustine, losoxantrone, masoprocol, maytansine, mechlorethamine hydrochloride, megestrol,Meringue roll acetate, melphalan, menogaril, mercaptopurine, methotrexate, methoprin, methuredepa, mitindomide, mitocarcin, mitochromin, mitogirin, mitomarcin, mitomycin, mitosper, mitotan, mitoxantrone, mycophenolic acid, nelarabine, nocodazole, nogalamycin, olaparib, ormnaplatine, oxaliplatin, oxisuran, paclitaxel, pegaspargase, perimycin, pentostatin, peplomycin, perfosfamide, pipobroman, piposulfan, pyroxantrone hydrochloride, plicamycin, promestane, porfimer, porfiromycin, prednimustine, procarbazine, puomycin, pyrazofurin, riboprin, logretimide, rucaparib, safingol, semustine, simtrazene, sparfosate, sparsomycin, spiroglumaniam, spirothromycin, spiroplatin, streptozocin, streptozocin, slophenur, talisomycin, tamoxifen, tecogalan, tegafur, teloxantrone, temoporfin, teniposide, teloxiron, testolactone, thiamiprine, thioguanine, thiotepa, thiazofurin, tirapazamine, topotecan, tremiphene, tretolone, triciribine, trimethoprim, tripterine, tubrolzol, uracil mustard, uredepa, bapreotide, veliparib, verteporfin, vinblastine, vincristine sulfate, vindesine, vinepidine, vinglycinate, vinleurosine, vinorelbine, vinrosidine, vinzolizine, borozole, zeniplatin, dinostatin, zoledronic acid, zorubicin

[0136] Accordingly, according to one aspect of the present disclosure, disclosed herein is an individualized method of treating a cancer patient having a tumor using a computing system comprising a processing system and a memory system storing instructions executed by the processing system. The method includes the computing system performing parameter estimation to determine physiological parameters π of the tumor, including vascular permeability and interstitial permeability; and determining whether a selected tumor transport model is valid or invalid by solving the physiological parameters π. When it is determined that the selected tumor transport model is valid, the method includes determining a treatment and further includes applying the treatment to the cancer patient.

[0137] According to an additional aspect of the present disclosure directed to the present method, the step of performing parameter estimation to determine physiological parameters π is a step of measuring Peff and predicting / determining K and L using a parameter estimation problem, where Peff is the effective permeability quantified as the velocity of a fluorescence signal passing through the tumor vessel wall, Lp is the permeability of the microvessel wall (cm / mmHg-second), K is the permeability of the tumor stroma (cm2 / mmHg-second), or directly measuring K and using experimental data when solving the parameter estimation problem.

[0138] According to an additional aspect of the present disclosure directed to the present method, the vascular density S / V is measured when measuring Peff, where S / V is measured as the vascular surface area per unit volume (cm-1).

[0139] According to an additional aspect of the present disclosure directed to the present method, the step of performing parameter estimation includes determining a time-dependent spatially averaged drug concentration profile representing the state of the tumor, including the ability of the tumor to accumulate drugs and nutrients.

Number

[0140] According to an additional aspect of the present disclosure directed to this method, the step of performing parameter estimation is by utilizing the following to determine a time-dependent spatially averaged drug concentration profile

Number

Number

[0141] According to an additional aspect of the present disclosure directed to this method, the step of performing parameter estimation includes the step of determining a physiological parameter π via a first parameter estimation problem,

Number

Number

Number

Number

[0142] According to an additional aspect of the disclosure directed to this method, if the model is determined to be invalid for this dataset, the method includes a computing system, obtaining more data, solving the parameter estimation problem again, or selecting a different tumor transport model, or modifying the tumor transport model and solving the parameter estimation problem.

[0143] According to an additional aspect of the disclosure directed to this method, modeling spatial-temporal transport in a tumor using experimental data includes a computing system directly utilizing a mechanistic tumor transport model, or generating simulation data for training a machine learning model using a mechanistic tumor transport model.

[0144] According to an additional aspect of the disclosure directed to this method, when repeating the step of performing parameter estimation, the computing system utilizes a first parameter estimation problem when determining the physiological parameter π using a mechanistic tumor transport model, or utilizes a second parameter estimation problem when determining the physiological parameter π using a data-driven tumor transport model, where the second parameter estimation problem is as follows,

Number

Number

[0145] According to an additional aspect of the present disclosure directed to this method, applying the treatment includes the computing system determining a dosing selection when the patient has not yet received adjuvant therapy, the dosing selection being a determination of a TME normalization agent that is an adjuvant, or when the patient has received adjuvant therapy, the computing system determining a drug size selection, the drug size selection being a determination of an anti-cancer agent that is distinct from the adjuvant that is the TME normalization agent.

[0146] According to an additional aspect of the present disclosure directed to this method, determining the dosing selection includes the computing system determining the vascular permeability coefficient L p and the interstitial permeability coefficient K from an empirical correlation between the causal relationship between the tumor normalization dose K and Lp, and determining the optimal dose that maximizes drug accumulation in the tumor,

Number

[0147] According to an additional aspect of the present disclosure directed to this method, implementing the drug size includes the computing system determining the optimal size d of the anti-cancer nanocarrier by determining the following m including determining,

Number

[0148] According to an additional aspect of the present disclosure directed to this method, determining a treatment includes the computing system performing a step of simultaneously determining a dosage selection and a drug size.

[0149] According to an additional aspect of the present disclosure directed to this method, determining a treatment includes the computing system performing a step of applying an empirical correlation associating tumor physiology with an adjuvant dosage.

[0150] According to an additional aspect of the present disclosure directed to this method, a machine learning model is utilized, and determining a treatment includes the computing system determining the vascular permeability coefficient L p and the interstitial permeability coefficient K from an empirical correlation between the causal relationships between the tumor normalization dosage K and Lp, and a step of determining, for j ∈ {r, p}, where t

Number

[0151] According to an additional aspect of the present disclosure directed to this method, an ANN surrogate model is utilized, and determining a treatment includes the computing system determining the vascular permeability coefficient L p and the interstitial permeability coefficient K from an empirical correlation between the causal relationships between the tumor normalization dosage K and L p and a step of determining, for j ∈ {r, p}, where t

Number

[0152] According to an additional aspect of the present disclosure, disclosed herein is a computerized system comprising a processing system and a memory system storing instructions executed by the processing system, whereby the system performs parameter estimation to determine the physiological parameters π of a tumor, including the vascular permeability coefficient and the interstitial permeability coefficient, and determines whether the selected tumor transport model is valid or invalid by solving the physiological parameters π. When it is determined that the selected tumor transport model is valid, the method includes determining a treatment and further includes applying the treatment to a cancer patient.

[0153] According to an additional aspect of the present disclosure, disclosed herein is a computer program product comprising a memory device storing computer-executable instructions, which, when executed by one or more processors, cause the one or more processors to perform parameter estimation to determine the physiological parameters π of a tumor, including the vascular permeability coefficient and the interstitial permeability coefficient, and determine whether the selected tumor transport model is valid or invalid by solving the physiological parameters π. When it is determined that the selected tumor transport model is valid, the method includes determining a treatment and further includes applying the treatment to a cancer patient.

[0154] Next, referring to FIG. 11, the figure shows a medical system for the training and / or application of a machine-learned classifier for tumor information. The medical system includes a medical imaging system 111111, a processor 1113, a memory 1115, and a display 1116. The processor 1113 and the memory 1115 are shown separately from the medical imaging system 1111, and such is associated with a computer or workstation remote from the medical imaging system 1111. In other embodiments, the processor 1113 and / or the memory 1115 are part of the medical imaging system 1111. In alternative embodiments, the medical system is a workstation, a computer, or a server. For example, the medical imaging system 1111 is not provided or is provided to acquire data representing volumes, and a separate database, server, workstation, and / or computer are provided to extract features and apply a classifier to predict one or more results. Additional, different, or fewer components may be used.

[0155] The system is used for the application of a machine learning model (e.g., one or more machine learning classifiers). In alternative embodiments, the system is used for machine learning-based training and / or the generation of examples within a database. If only synthetic samples generated from a computational model of a tumor are used, the medical imaging system 1111 may not be provided. If samples from a library, even if from actual patients (e.g., scan data representing an actual scan), are stored in the memory 1115, the medical imaging system 1111 may not be provided.

[0156] Computing components, devices, or machines of a medical system, such as medical imaging system 1111 and / or processor 1113, are configured by hardware, software, and / or firmware to perform calculations or other actions. The computing components operate independently or in cooperation with each other to perform any given action, such as any of the actions of the methods described above. This action is performed by one of the computer components, another of the computing components, or a combination of the computing components. Other components may be used or controlled by the computing components to perform other functions, such as scanning or performing other actions.

[0157] Medical imaging system 1111 is any currently known or later developed modality for scanning a patient. Medical imaging system 1111 scans a patient. For example, a C-arm x-ray system (e.g., DynaCT from Siemens), a CT-like system, or a CT system is used. Other modalities include MR, x-ray, angiography, fluoroscopy, PET, SPECT, or ultrasound. Medical imaging system 1111 is configured to acquire medical imaging data representative of the patient. The scan data is acquired by scanning the patient using transmission by a scanner and / or by receiving signals from the patient.

[0158] Memory 1115 is a buffer, cache, RAM, removable media, hard drive, solid state drive, magnetic, optical, database, or other memory currently known or later developed. Memory 1115 is a single device or a group of two or more devices. Memory 1115 is within system 1111, part of a computer having processor 1113, external to or remote from other components.

[0159] Memory 1115 is configured to store medical scan data, other data, extracted features, examples (such as training data or data from other patients), and / or other information. Output results, information derived from the results, or calculations used to determine the results are stored in memory 1115. Memory 1115 stores one or more matrices for a machine learning regression model. The memory can store a learned / trained regression model as well as a structural model.

[0160] Memory 1115 is additionally or alternatively a non-transitory computer-readable storage medium having processing instructions. Memory 1115 stores data representing instructions executable by a programmed processor 1113. Instructions for implementing the processes, methods, and / or techniques discussed herein are provided on a computer-readable storage medium or memory such as a cache, buffer, RAM, removable media, hard drive, or other computer-readable storage medium. The computer-readable storage medium includes various types of volatile and non-volatile storage media. The functions, operations, or tasks described herein are executed in response to one or more sets of instructions stored within or on the computer-readable storage medium. The functions, acts, or tasks are independent of a particular type of instruction set, storage medium, processor, or processing strategy and can be implemented by software, hardware, integrated circuits, firmware, microcode, etc., operating alone or in combination. Similarly, the processing strategy can include multiprocessing, multitasking, parallel processing, etc. In one embodiment, the instructions are stored on a removable media device for reading by a local system or a remote system. In other embodiments, the instructions are stored at a remote location for transfer through a computer network or via a telephone line. In still other embodiments, the instructions are stored within a given computer, CPU, GPU, or system.

[0161] Processor 1113 is a general-purpose processor, a digital signal processor, a three-dimensional data processor, a graphics processing unit, an application-specific integrated circuit, a field-programmable gate array, a digital circuit, an analog circuit, a combination thereof, or other currently known or later developed device for processing data. Processor 1113 is a single device, multiple devices, or a network. For two or more devices, parallel or sequential partitioning of processing may be used. Different devices constituting Processor 1113 can perform different functions, such as extracting the value of a feature part by one device and applying a machine learning regression and a mechanical model by another device. In one embodiment, Processor 1113 is a control processor or other processor of the medical imaging system 1111. Processor 1113 operates according to stored instructions to perform various operations described herein.

[0162] Processor 1113 is configured to extract the value of a feature part, input a value, output a result, and / or derive information from the output result. Processor 1113 applies a machine-learned model to the data of one or more patients. A diagnosis, prognosis, therapy response, and / or other information is determined by Processor 1113 for one or more tumors of a patient.

[0163] Display 1116 is a CRT, LCD, plasma, projector, printer, or other output device for displaying an image. Display 1116 displays the result or information derived from the result. A probability associated with any prediction, support data (e.g., the value of an input feature part), an image from medical scan data, and / or other information is output to assist a physician.

[0164] Next, referring to FIG. 12, a computer system 1200 according to one aspect is generally shown. The computer system 1200 can be an electronic computer framework that includes and / or employs any number and combination of computing devices and networks that utilize various communication technologies, as described herein. The computer system 1200 can be easily scalable, extensible, and modular, with the ability to change to different services or reconfigure some features independently of others. The computer system 1200 can be, for example, a server, a desktop computer, a laptop computer, a tablet computer, or a smartphone. In some examples, the computer system 1200 can be a cloud computing node. The computer system 1200 can be described in the general context of computer-executable instructions, such as program modules executed by a computer system. Generally, program modules can include routines, programs, objects, components, logic, data structures, etc., that perform specific tasks or implement specific abstract data types. The computer system 1200 can be practiced in a distributed cloud computing environment where tasks are performed by remote processing devices linked via a communication network. In a distributed cloud computing environment, program modules can be located on both local and remote computer system storage media, including memory storage devices.

[0165] As shown in FIG. 12, computer system 1200 has one or more central processing units (CPUs) 1201a, 1201b, 1201c, etc. (collectively or generically referred to as processor 1201). Processor 1201 can be a single-core processor, a multi-core processor, a computing cluster, or any number of other configurations. Processor 1201 can be any type of circuitry capable of executing instructions. Processor 1201, also referred to as a processing circuit, is coupled to system memory 1203 and various other components via system bus 1202. System memory 1203 can include one or more memory devices such as read-only memory (ROM) 1204 and random-access memory (RAM) 1205. ROM 1204 is coupled to system bus 1202 and can include a basic input / output system (BIOS) that controls certain basic functions of computer system 1200. RAM is a read / write memory coupled to system bus 1202 for use by processor 1201. System memory 1203 provides a temporary memory space for the operation of the above instructions during operation. System memory 1203 can include random-access memory (RAM), read-only memory, flash memory, or any other suitable memory system.

[0166] Computer system 1200 includes an input / output (I / O) adapter 1206 and a communication adapter 1207 coupled to system bus 1202. I / O adapter 1206 can be a small computer system interface (SCSI) adapter that communicates with hard disk 1208 and / or any other similar components. I / O adapter 1206 and hard disk 1208 are collectively referred to herein as mass storage device 1210.

[0167] Software 1211 for execution on computer system 1200 can be stored in mass storage device 1210. Mass storage device 1210 is an example of a tangible storage medium readable by processor 1201, and software 1211 is stored as instructions to be executed by processor 1201 to operate computer system 1200, as will be described below with respect to various figures. Examples of computer program products and execution of such instructions are considered in more detail herein. Communication adapter 1207 interconnects system bus 1202 with network 1212, which may be an external network, to enable computer system 1200 to communicate with other such systems. In one aspect, system memory 1203 and a portion of mass storage device 1210 collectively store an operating system, which can be any suitable operating system for coordinating the functions of the various components shown in FIG. 12.

[0168] An additional input / output device is shown as being connected to the system bus 1202 via a display adapter 1215 and an interface adapter 1216. In one aspect, adapters 1206, 1207, 1215, and 1216 can be connected to one or more I / O buses connected to the system bus 1202 via an intermediate bus bridge (not shown). A display 1219 (e.g., a screen or display monitor) is connected to the system bus 1202 by the display adapter 1215, and the display adapter can include a graphics controller and a video controller for improving the performance of graphics-intensive applications. A keyboard, mouse, touch screen, one or more buttons, speakers, etc. can be interconnected to the system bus 1202 via the interface adapter 1216, and the interface adapter can include, for example, a super I / O chip that integrates multiple device adapters into a single integrated circuit. An I / O bus suitable for connecting peripheral devices such as a hard disk controller, network adapter, and graphics adapter typically includes a common protocol such as Peripheral Component Interconnect (PCI). Thus, as configured in FIG. 12, the computer system 1200 includes processing capabilities in the form of a processor 1201, storage capabilities including a system memory 1203 and a mass storage device 1210, input means such as buttons and touch screens, and output capabilities including a speaker 1223 and a display 1219.

[0169] In some embodiments, communication adapter 1207 can transmit data using any suitable interface or protocol, such as, among other things, an Internet small computer system interface. Network 1212 can be, among other things, a cellular network, a wireless network, a wide area network (WAN), a local area network (LAN), or the Internet. An external computing device can be connected to computer system 1200 via network 1212. In some examples, the external computing device can be an external web server or a cloud computing node.

[0170] It should be understood that the block diagram of FIG. 12 is not intended to show that computer system 1200 includes all of the components shown in FIG. 12. Rather, computer system 1200 can include any suitable fewer or additional components not shown in FIG. 12 (e.g., additional memory components, embedded controllers, modules, additional network interfaces, etc.). Further, the embodiments described herein with respect to computer system 1200 can be implemented with any suitable logic, and the logic referred to herein can, in various embodiments, include any suitable combination of hardware (e.g., among other things, a processor, an embedded controller, or an application specific integrated circuit), software (e.g., among other things, an application), firmware, or hardware, software, and firmware. The various embodiments can be combined to include two or more of the embodiments described herein.

[0171] The embodiments disclosed herein can be a system, method, and / or computer program product at any possible technical detail level of integration. The computer program product can include a computer-readable storage medium having computer-readable program instructions for causing a processor to implement various embodiments.

[0172] A computer-readable storage medium can be a tangible device that can hold and store instructions for use by an instruction execution device. The computer-readable storage medium can be, for example, an electronic storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any suitable combination of the foregoing, but is not limited thereto. A non-exhaustive list of more specific examples of computer-readable storage media includes the following: portable computer diskettes, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), static random access memory (SRAM), portable compact disc read-only memory (CD-ROM), digital versatile disk (DVD), memory stick, floppy disk, punch cards, or mechanically encoded devices such as raised structures within grooves in which instructions are recorded, and any suitable combination of the foregoing. A computer-readable storage medium, as used herein, should not be construed to be a signal per se, such as radio waves or other freely propagating electromagnetic waves, electromagnetic waves propagating through a waveguide or other transmission medium (e.g., optical pulses passing through an optical fiber cable), or electrical signals transmitted through a wire that are transient signals.

[0173] The computer-readable program instructions described herein can be downloaded from a computer-readable storage medium to respective computing / processing devices or to an external computer or external storage device via a network, such as, for example, the Internet, a local area network, a wide area network, and / or a wireless network. The network can include copper transmission cables, optical transmission fibers, wireless transmission, routers, firewalls, switches, gateway computers, and / or edge servers. A network adapter card or network interface in each computing / processing device receives the computer-readable program instructions from the network and transfers the computer-readable program instructions for storage in a computer-readable storage medium within each respective computing / processing device.

[0174] Computer-readable program instructions for carrying out operations of this disclosure may be any combination of source code or object code written in assembly instructions, instruction set architecture (ISA) instructions, machine instructions, machine-dependent instructions, microcode, firmware instructions, state-setting data, configuration data for integrated circuit fabrics, or one or more programming languages (including object-oriented programming languages such as Smalltalk, C++, etc., high-level languages such as Python, and procedural programming languages such as the "C" programming language or similar programming languages). The computer-readable program instructions may execute entirely on the user's computer, partly on the user's computer, as a stand-alone software package, partly on the user's computer and partly on a remote computer, or entirely on the remote computer or server. In the latter scenario, the remote computer may be connected to the user's computer via any type of network, including a local area network (LAN) or a wide area network (WAN), or the connection to an external computer may be made (e.g., via the Internet using an Internet service provider). In some aspects, for example, an electronic circuit, including a programmable logic circuit, a field-programmable gate array (FPGA), or a programmable logic array (PLA), may execute the computer-readable program instructions by utilizing the state information of the computer-readable program instructions to customize the electronic circuit for implementing aspects of this disclosure.

[0175] Aspects are described herein with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to aspects of the disclosure. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer-readable program instructions.

[0176] These computer-readable program instructions, when executed via the processor of a computer or other programmable data processing apparatus, create means for implementing the functions / acts specified in one or more blocks of the flowchart and / or block diagram, and are provided to the processor of the computer system or other programmable data processing apparatus to generate a machine. These computer-readable program instructions may also be stored in a computer-readable storage medium that can direct a computer, programmable data processing apparatus, and / or other devices to function in a particular manner, such that the computer-readable storage medium storing the instructions contains an article of manufacture including instructions for implementing the aspects of the functions / operations specified in one or more blocks of the flowchart and / or block diagram.

[0177] The computer-readable program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other device to cause a series of operational steps to be performed on the computer, other programmable apparatus, or other device to generate a computer-implemented process, whereby the instructions executed on the computer, other programmable apparatus, or other device implement the functions / acts specified in one or more blocks of the flowchart and / or block diagram.

[0178] The flowcharts and block diagrams in the figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products in various manners. In this regard, each block in the flowchart or block diagram may represent a module, segment, or portion of instructions, including one or more executable instructions for implementing the specified logical function. In some alternative implementations, the functions described in the blocks may be performed in an order different from that shown in the figures. For example, two blocks shown in succession may, in fact, be executed substantially simultaneously, or the blocks may sometimes be executed in the reverse order, depending on the functionality involved. Each block of the block diagrams and / or flowchart diagrams, as well as combinations of blocks in the block diagrams and / or flowchart diagrams, can be implemented by a dedicated hardware-based system that performs the specified functions or acts, or by a combination of dedicated hardware and computer instructions.

[0179] The use of the terms "a", "an", and "the" and similar referents (in particular, in the context of the following claims) should be construed to include both the singular and the plural unless otherwise indicated herein or clearly contradicted by the context. The terms "first", "second", etc. used herein are not intended to indicate any particular ordering, but are merely used for convenience to refer to multiple, e.g., layers. The terms "comprising", "having", "including", and "containing" should be construed as open-ended terms (i.e., meaning "including but not limited to") unless otherwise stated. The recitation of a range of values is merely intended to serve as a shorthand for referring individually to each separate value falling within the range, and each separate value is incorporated herein as if it were individually recited herein. All endpoints of ranges are included within the range and are combinable independently. All methods described herein can be performed in a suitable order unless otherwise indicated herein or clearly contradicted by the context. The use of any and all examples, or exemplary language (e.g., "such as") is merely intended to better illustrate the invention and does not limit the scope of the invention unless otherwise claimed. No language in this specification should be construed as indicating any non-claimed element essential to the practice of the invention as used herein.

[0180] Although the present invention has been described with reference to exemplary embodiments, those skilled in the art will understand that various changes can be made without departing from the scope of the present invention and that its elements can be replaced with equivalents. Additionally, many modifications can be made to adapt a particular situation or material to the teachings of the present invention without departing from the essential scope thereof. Accordingly, the present invention is not limited to the particular embodiments disclosed as the best mode contemplated for carrying out the present invention, and the present invention is intended to cover all embodiments that fall within the scope of the appended claims. Any combination of the above-described elements in all possible variations is encompassed by the present invention unless otherwise indicated herein or clearly contradicted by context.

Claims

1. A personalized method for treating a cancer patient with a tumor, comprising a computing system comprising a processing system and a memory system for storing instructions executed by the processing system, The above method is achieved when the computing system The process involves performing parameter estimation to determine the physiological parameters π of the tumor, including the vascular permeability coefficient and the interstitial permeability coefficient. This includes the step of determining whether the selected tumor transport model is effective or ineffective by solving for the physiological parameter π, If it is determined that the selected tumor transport model is effective, the method includes determining a course of action. The method described above is The treatment further includes applying the aforementioned procedure to cancer patients. A method characterized by the following:

2. The step of performing parameter estimation to determine the physiological parameter π is, A step of measuring Peff and predicting / determining K and L using a parameter estimation problem, wherein Peff is effective permeability quantified as the velocity of the fluorescence signal passing through the tumor blood vessel wall, Lp is the permeability coefficient of the microvascular wall (cm / mmHg-sec), and K is the permeability coefficient of the tumor stroma (cm² / mmHg-sec), or This includes the step of directly measuring K and using experimental data when solving the parameter estimation problem, The method according to feature 1.

3. Vascular density S / V is measured when Peff is measured, and S / V is measured as the vascular surface area per unit volume (cm⁻¹). The method according to feature 2.

4. The step of performing the parameter estimation is, A time-dependent, spatially averaged drug concentration profile that represents the state of the tumor, including the ability of drugs and nutrients to accumulate in the tumor. [Math 1] Including determining The method according to feature 3.

5. The step of performing the parameter estimation is, By using the following, the time-dependent spatially averaged drug concentration profile [Math 2] Including determining, [Math 3] In the formula, c ｖ However, this is the solute concentration (g / mL) in the blood vessels of the tumor, and S / V is the blood vessel surface area (cm²) per unit volume. －１ ) The method according to feature 4.

6. The step of performing the parameter estimation is, This includes determining the physiological parameter π through a first parameter estimation problem, 【Number 4】 During the ceremony, [Math 5] However, for all spatial nodes from the mechanistic solute transport model used as the parameter model output, the dimensionless concentration [Math 6] This is the dimensionless spatially averaged concentration of the solute, determined by averaging the following: [Number 7] This is a vector of physiological parameters for the spatially averaged solute transport model, and Lp is the permeability coefficient of the microvascular wall (cm / mmHg-sec). K is the permeability coefficient of the tumor stroma (cm² / mmHg-sec), dm is the diameter of a biomolecule or polymer drug on the nanoscale (nm). The method according to specification 5.

7. If the method determines that the model is invalid for this dataset, the computing system Obtaining more data and solving the parameter estimation problem again, or This includes selecting a different tumor transport model or modifying the tumor transport model and solving the parameter estimation problem. The method according to feature 6.

8. Using experimental data to model spatial-temporal transport in tumors, the computing system can... A process that directly utilizes a mechanistic tumor transport model, or This includes a step of generating simulation data for training a machine learning model using the aforementioned mechanistic tumor transport model. The method according to feature 7.

9. When the process of performing the parameter estimation described above is repeated, the computing system When determining the physiological parameter π using the aforementioned mechanistic tumor transport model, the process involves utilizing the first parameter estimation problem, or When determining the physiological parameter π using a data-driven tumor transport model, a second parameter estimation problem is used, wherein the second parameter estimation problem is as follows: [Number 8] During the ceremony, [Number 9] However, this involves a step that utilizes a second parameter estimation problem that represents the dimensionless spatially averaged nanocarrier concentration at discrete-time node i calculated from the ANN surrogate model, When solving the aforementioned parameter estimation problem, the process of using experimental data is carried out. The method according to feature 8.

10. Applying the above measures means that the computing system A step in determining the dosage when the patient has not yet received adjuvant therapy, wherein the dosage selection refers to an adjuvant TME normalizing agent, or A step of determining the drug size selection when the patient receives adjuvant therapy, the step of determining the drug size selection refers to an anticancer drug that is distinct from the adjuvant, which is the TME normalizing agent. The method according to feature 9.

11. Determining the dose selection is done by the computing system, Vascular permeability coefficient L ｐ And the interstitial permeability coefficient K, tumor normalization dose K and L ｐ A process of determining from the empirical correlation between the causal relationship between and The process includes initiating and determining the optimal dose that maximizes drug accumulation in the tumor, and carrying out the following steps: [Number 10] j ∈ {r, p}, where tf is the final time, x is the TME normalization regimen dose, and f Ｌｐ and f ｋ ｊ However, L after treatment with the regimen doses obtained from experimental data ｐ and K, The method according to the present invention, characterized by the present invention.

12. Performing the drug size is performed by the computing system, Determining the optimal size d of the anti-cancer nanocarrier by the following ｍ including performing a step of determining [Math 11] In the formula, λ １ However, this is the threshold of the safety constraint, λ ２ However, this is a performance constraint. The method according to 11, characterized by the features described above.

13. Determining the treatment includes at least one of the following steps: the computing system performs a step of simultaneously determining the dose selection and the drug size; or the computing system performs a step of applying an empirical correlation relating tumor physiology to the adjuvant dose. The method according to the present invention, characterized by the present invention.

14. The machine learning model or ANN surrogate model is used, and the decision on the action is made by the computing system, Vascular permeability coefficient L ｐ And the interstitial permeability coefficient K, tumor normalization dose K and L ｐ This includes a step of determining from the empirical correlation between the causal relationship between and , and a step of determining the following: [Math 12] j ∈ {r, p}, and in the formula, t ｆ x is the final time, x is the TME normalization regimen dose, and f Ｌｐ ｊ and f ｋ ｊ However, L after treatment at the aforementioned doses obtained from experimental data ｐ and K, λ １ However, this is the threshold of the safety constraint, λ ２ However, this is a performance constraint. The method according to the present invention, characterized by the present invention.

15. A computerized system, The system comprises a processing system and a memory system that stores instructions executed by the processing system, thereby the system The process involves performing parameter estimation to determine the physiological parameters π of the tumor, including the vascular permeability coefficient and the interstitial permeability coefficient. The system is configured to perform the following steps: determine whether the selected tumor transport model is effective or ineffective by solving for the physiological parameter π. If it is determined that the selected tumor transport model is effective, the method includes determining a course of action. The method described above is The treatment further includes applying the aforementioned procedure to cancer patients. A computerized system characterized by the following features.

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