Integrated PK-PD and agent-based modeling in oncology

A comprehensive review of computational cell cycle models in guiding cancer treatment strategies

This article reviews the current knowledge and recent advancements in computational modeling of the cell cycle. It offers a comparative analysis of various modeling paradigms, highlighting their unique strengths, limitations, and applications. Specifically, the article compares deterministic and stochastic models, single-cell versus population models, and mechanistic versus abstract models. This detailed analysis helps determine the most suitable modeling framework for various research needs. Additionally, the discussion extends to the utilization of these computational models to illuminate cell cycle dynamics, with a particular focus on cell cycle viability, crosstalk with signaling pathways, tumor microenvironment, DNA replication, and repair mechanisms, underscoring their critical roles in tumor progression and the optimization of cancer therapies. By applying these models to crucial aspects of cancer therapy planning for better outcomes, including drug efficacy quantification, drug discovery, drug resistance analysis, and dose optimization, the review highlights the significant potential of computational insights in enhancing the precision and effectiveness of cancer treatments. This emphasis on the intricate relationship between computational modeling and therapeutic strategy development underscores the pivotal role of advanced modeling techniques in navigating the complexities of cell cycle dynamics and their implications for cancer therapy.

ABCD of IA: A multi-scale agent-based model of T cell activation in inflammatory arthritis

Biomaterial-based agents have been demonstrated to regulate the function of immune cells in models of autoimmunity. However, the complexity of the kinetics of immune cell activation can present a challenge in optimizing the dose and frequency of administration. Here, we report a model of autoreactive T cell activation, which are key drivers in autoimmune inflammatory joint disease. The model is termed a multi-scale Agent-Based, Cell-Driven model of Inflammatory Arthritis (ABCD of IA). Using kinetic rate equations and statistical theory, ABCD of IA simulated the activation and presentation of autoantigens by dendritic cells, interactions with cognate T cells and subsequent T cell proliferation in the lymph node and IA-affected joints. The results, validated with in vivo data from the T cell driven SKG mouse model, showed that T cell proliferation strongly correlated with the T cell receptor (TCR) affinity distribution (TCR-ad), with a clear transition state from homeostasis to an inflammatory state. T cell proliferation was strongly dependent on the amount of antigen in antigenic stimulus event (ASE) at low concentrations. On the other hand, inflammation driven by Th17-inducing cytokine mediated T cell phenotype commitment was influenced by the initial level of Th17-inducing cytokines independent of the amount of arthritogenic antigen. The introduction of inhibitory artificial antigen presenting cells (iaAPCs), which locally suppress T cell activation, reduced T cell proliferation in a dose-dependent manner. The findings in this work set up a framework based on theory and modeling to simulate personalized therapeutic strategies in IA.

Immune-checkpoint inhibitor therapy response evaluation using oncophysics-based mathematical models

The field of oncology has transformed with the advent of immunotherapies. The standard of care for multiple cancers now includes novel drugs that target key checkpoints that function to modulate immune responses, enabling the patient's immune system to elicit an effective anti-tumor response. While these immune-based approaches can have dramatic effects in terms of significantly reducing tumor burden and prolonging survival for patients, the therapeutic approach remains active only in a minority of patients and is often not durable. Multiple biological investigations have identified key markers that predict response to the most common form of immunotherapy-immune checkpoint inhibitors (ICI). These biomarkers help enrich patients for ICI but are not 100% predictive. Understanding the complex interactions of these biomarkers with other pathways and factors that lead to ICI resistance remains a major goal. Principles of oncophysics-the idea that cancer can be described as a multiscale physical aberration-have shown promise in recent years in terms of capturing the essence of the complexities of ICI interactions. Here, we review the biological knowledge of mechanisms of ICI action and how these are incorporated into modern oncophysics-based mathematical models. Building on the success of oncophysics-based mathematical models may help to discover new, rational methods to engineer immunotherapy for patients in the future. This article is categorized under: Therapeutic Approaches and Drug Discovery > Nanomedicine for Oncologic Disease.

Examining the efficacy of localised gemcitabine therapy for the treatment of pancreatic cancer using a hybrid agent-based model

The prognosis for pancreatic ductal adenocarcinoma (PDAC) patients has not significantly improved in the past 3 decades, highlighting the need for more effective treatment approaches. Poor patient outcomes and lack of response to therapy can be attributed, in part, to a lack of uptake of perfusion of systemically administered chemotherapeutic drugs into the tumour. Wet-spun alginate fibres loaded with the chemotherapeutic agent gemcitabine have been developed as a potential tool for overcoming the barriers in delivery of systemically administrated drugs to the PDAC tumour microenvironment by delivering high concentrations of drug to the tumour directly over an extended period. While exciting, the practicality, safety, and effectiveness of these devices in a clinical setting requires further investigation. Furthermore, an in-depth assessment of the drug-release rate from these devices needs to be undertaken to determine whether an optimal release profile exists. Using a hybrid computational model (agent-based model and partial differential equation system), we developed a simulation of pancreatic tumour growth and response to treatment with gemcitabine loaded alginate fibres. The model was calibrated using in vitro and in vivo data and simulated using a finite volume method discretisation. We then used the model to compare different intratumoural implantation protocols and gemcitabine-release rates. In our model, the primary driver of pancreatic tumour growth was the rate of tumour cell division. We were able to demonstrate that intratumoural placement of gemcitabine loaded fibres was more effective than peritumoural placement. Additionally, we quantified the efficacy of different release profiles from the implanted fibres that have not yet been tested experimentally. Altogether, the model developed here is a tool that can be used to investigate other drug delivery devices to improve the arsenal of treatments available for PDAC and other difficult-to-treat cancers in the future.

Mathematical modeling of cancer immunotherapy for personalized clinical translation

Encouraging advances are being made in cancer immunotherapy modeling, especially in the key areas of developing personalized treatment strategies based on individual patient parameters, predicting treatment outcomes and optimizing immunotherapy synergy when used in combination with other treatment approaches. Here we present a focused review of the most recent mathematical modeling work on cancer immunotherapy with a focus on clinical translatability. It can be seen that this field is transitioning from pure basic science to applications that can make impactful differences in patients' lives. We discuss how researchers are integrating experimental and clinical data to fully inform models so that they can be applied for clinical predictions, and present the challenges that remain to be overcome if widespread clinical adaptation is to be realized. Lastly, we discuss the most promising future applications and areas that are expected to be the focus of extensive upcoming modeling studies.

Investigating Two Modes of Cancer-Associated Antigen Heterogeneity in an Agent-Based Model of Chimeric Antigen Receptor T-Cell Therapy

Simple Summary

Chimeric antigen receptor (CAR) T-cell therapy has shown much promise in liquid tumors but often fails in solid tumors. This work uses a computational model to examine under what conditions this therapy might fail or be successful. The model includes interactions between cancer cells, CAR T-cells (treatment), and vascular cells (that feed and support tumor growth). From our results, we determined specific tumor conditions in which CAR T-cell therapy is predicted to fail and suggest a combination treatment that might improve the efficacy of the treatment.

Abstract

Chimeric antigen receptor (CAR) T-cell therapy has been successful in treating liquid tumors but has had limited success in solid tumors. This work examines unanswered questions regarding CAR T-cell therapy using computational modeling, such as, what percentage of the tumor must express cancer-associated antigens for treatment to be successful? The model includes cancer cell and vascular and CAR T-cell modules that interact with each other. We compare two different models of antigen expression on tumor cells, binary (in which cancer cells are either susceptible or are immune to CAR T-cell therapy) and gradated (where each cancer cell has a probability of being killed by a CAR T-cell). We vary the antigen expression levels within the tumor and determine how effective each treatment is for the two models. The simulations show that the gradated antigen model eliminates the tumor under more parameter values than the binary model. Under both models, shielding, in which the low/non-antigen-expressing cells protect high antigen-expressing cells, reduced the efficacy of CAR T-cell therapy. One prediction is that a combination of CAR T-cell therapies that targets the general population of cells as well as one that specifically targets cancer stem cells should increase its efficacy.

Translational Modeling Identifies Synergy between Nanoparticle-Delivered miRNA-22 and Standard-of-Care Drugs in Triple-Negative Breast Cancer

Purpose

Downregulation of miRNA-22 in triple-negative breast cancer (TNBC) is associated with upregulation of eukaryotic elongation 2 factor kinase (eEF2K) protein, which regulates tumor growth, chemoresistance, and tumor immunosurveillance. Moreover, exogenous administration of miRNA-22, loaded in nanoparticles to prevent degradation and improve tumor delivery (termed miRNA-22 nanotherapy), to suppress eEF2K production has shown potential as an investigational therapeutic agent in vivo.

Methods

To evaluate the translational potential of miRNA-22 nanotherapy, we developed a multiscale mechanistic model, calibrated to published in vivo data and extrapolated to the human scale, to describe and quantify the pharmacokinetics and pharmacodynamics of miRNA-22 in virtual patient populations.

Results

Our analysis revealed the dose-response relationship, suggested optimal treatment frequency for miRNA-22 nanotherapy, and highlighted key determinants of therapy response, from which combination with immune checkpoint inhibitors was identified as a candidate strategy for improving treatment outcomes. More importantly, drug synergy was identified between miRNA-22 and standard-of-care drugs against TNBC, providing a basis for rational therapeutic combinations for improved response

Conclusions

The present study highlights the translational potential of miRNA-22 nanotherapy for TNBC in combination with standard-of-care drugs. 

Supplementary Information

The online version contains supplementary material available at 10.1007/s11095-022-03176-3.

A graph model of combination therapies

The simultaneous use of multiple medications causes drug-drug interactions (DDI) that impact therapeutic efficacy. Here, we argue that graph theory, in conjunction with game theory and ecosystem theory, can address this issue. We treat the coexistence of multiple drugs as a system in which DDI is modeled by game theory. We develop an ordinary differential equation model to characterize how the concentration of a drug changes as a result of its independent capacity and the dependent influence of other drugs through the metabolic response of the host. We coalesce all drugs into personalized and context-specific networks, which can reveal key DDI determinants of therapeutical efficacy. Our model can quantify drug synergy and antagonism and test the translational success of combination therapies to the clinic.

Step-by-step comparison of ordinary differential equation and agent-based approaches to pharmacokinetic-pharmacodynamic models

Mathematical models in oncology aid in the design of drugs and understanding of their mechanisms of action by simulation of drug biodistribution, drug effects, and interaction between tumor and healthy cells. The traditional approach in pharmacometrics is to develop and validate ordinary differential equation models to quantify trends at the population level. In this approach, time‐course of biological measurements is modeled continuously, assuming a homogenous population. Another approach, agent‐based models, focuses on the behavior and fate of biological entities at the individual level, which subsequently could be summarized to reflect the population level. Heterogeneous cell populations and discrete events are simulated, and spatial distribution can be incorporated. In this tutorial, an agent‐based model is presented and compared to an ordinary differential equation model for a tumor efficacy model inhibiting the pERK pathway. We highlight strengths, weaknesses, and opportunities of each approach.

Modeling Pharmacokinetics and Pharmacodynamics of Therapeutic Antibodies: Progress, Challenges, and Future Directions

With more than 90 approved drugs by 2020, therapeutic antibodies have played a central role in shifting the treatment landscape of many diseases, including autoimmune disorders and cancers. While showing many therapeutic advantages such as long half-life and highly selective actions, therapeutic antibodies still face many outstanding issues associated with their pharmacokinetics (PK) and pharmacodynamics (PD), including high variabilities, low tissue distributions, poorly-defined PK/PD characteristics for novel antibody formats, and high rates of treatment resistance. We have witnessed many successful cases applying PK/PD modeling to answer critical questions in therapeutic antibodies’ development and regulations. These models have yielded substantial insights into antibody PK/PD properties. This review summarized the progress, challenges, and future directions in modeling antibody PK/PD and highlighted the potential of applying mechanistic models addressing the development questions.

Amphibian regeneration and mammalian cancer: Similarities and contrasts from an evolutionary biology perspective: Comparing the regenerative potential of mammalian embryos and urodeles to develop effective strategies against human cancer

Here we review and discuss the link between regeneration capacity and tumor suppression comparing mammals (embryos versus adults) with highly regenerative vertebrates. Similar to mammal embryo morphogenesis, in amphibians (essentially newts and salamanders) the reparative process relies on a precise molecular and cellular machinery capable of sensing abnormal signals and actively reprograming or eliminating them. As the embryo's evil twin, tumor also retains common functional attributes. The immune system plays a pivotal role in maintaining a physiological balance to provide surveillance against tumor initiation or to support its initiation and progression. We speculate that susceptibility to cancer development in adult mammals may be determined by the loss of an advanced regenerative capability during evolution and believe that gaining mechanistic insights into how regenerative capacity linked to tumor suppression is postnatally lost in mammals might illuminate an as yet unrecognized route to cancer treatment.

Plasma and intracerebral pharmacokinetics and pharmacodynamics modeling for the acetylcholine releasing effect of ginsenoside Rg1 in mPFC of Aβ model rats

Ginsenoside Rg1 is a major bioactive component of ginseng. Limited information is available regarding Rg1 concentrations in the central neural system and the corresponding relationship of plasma/intracerebral concentrations, and intracerebral effects of Rg1. Awake Aβ model rats received a single subcutaneous administration of Rg1. Concentrations of unbound Rg1 and acetylcholine in the brain extracellular fluid and Rg1 in plasma were then determined. An E_max-two compartment pharmacokinetic/pharmacodynamics (PK/PD) model without effect compartment was finally obtained by evaluating three mechanism-based models. The corresponding relationship between the plasma PK and PD of Rg1 can be described as E = 119.05•C/(73.42 + C).[Formula: see text].

A mathematical model for the quantification of a patient's sensitivity to checkpoint inhibitors and long-term tumour burden

A large proportion of patients with cancer are unresponsive to treatment with immune checkpoint blockade and other immunotherapies. Here, we report a mathematical model of the time-course of tumour responses to immune-checkpoint inhibitors. The model takes into account intrinsic tumour-growth rates, the rates of immune activation and of tumour–immune-cell interactions, and the efficacy of immune-mediated tumour killing. For 124 patients, four cancer types and two immunotherapy agents, the model reliably described the immune responses and final tumour burden across all different cancers and drug combinations examined. In validation cohorts from four clinical trials of checkpoint inhibitors (with a total of 177 patients), the model accurately stratified the patients according to reduced or increased long-term tumour burden. We also provide model-derived quantitative measures of treatment sensitivity for specific drug–cancer combinations. The model can be used to predict responses to therapy and to quantify specific drug–cancer sensitivities in individual patients.

Tumor ablation due to inhomogeneous anisotropic diffusion in generic three-dimensional topologies

In recent decades computer-aided technologies have become prevalent in medicine, however, cancer drugs are often only tested on in vitro cell lines from biopsies. We derive a full three-dimensional model of inhomogeneous -anisotropic diffusion in a tumor region coupled to a binary population model, which simulates in vivo scenarios faster than traditional cell-line tests. The diffusion tensors are acquired using diffusion tensor magnetic resonance imaging from a patient diagnosed with glioblastoma multiform. Then we numerically simulate the full model with finite element methods and produce drug concentration heat maps, apoptosis hotspots, and dose-response curves. Finally, predictions are made about optimal injection locations and volumes, which are presented in a form that can be employed by doctors and oncologists.

Investigating the Effect of Aging on the Pharmacokinetics and Tumor Delivery of Nanomaterials using Mathematical Modeling

The application of nanomedicine for diagnosis and treatment of cancer has immense potential, but has witnessed only limited clinical success, in part due to insufficient understanding of the role of nanomaterial properties and physiological variables in governing nanoparticle (NP) pharmacology. Here, we present a multiscale mathematical model to examine the effects of physiological changes associated with patient age on the pharmacokinetics and tumor delivery efficiency of NPs. We show that physiological changes due to aging prolong the residence of NPs in the systemic circulation, thereby improving passive accumulation of NPs in tumors.Clinical Relevance - Understanding the effect of inter-individual variability on the pharmacological behavior of nanomaterials will improve their clinical translatability.

Modeling of Nanotherapy Response as a Function of the Tumor Microenvironment: Focus on Liver Metastasis

The tumor microenvironment (TME) presents a challenging barrier for effective nanotherapy-mediated drug delivery to solid tumors. In particular for tumors less vascularized than the surrounding normal tissue, as in liver metastases, the structure of the organ itself conjures with cancer-specific behavior to impair drug transport and uptake by cancer cells. Cells and elements in the TME of hypovascularized tumors play a key role in the process of delivery and retention of anti-cancer therapeutics by nanocarriers. This brief review describes the drug transport challenges and how they are being addressed with advanced in vitro 3D tissue models as well as with in silico mathematical modeling. This modeling complements network-oriented techniques, which seek to interpret intra-cellular relevant pathways and signal transduction within cells and with their surrounding microenvironment. With a concerted effort integrating experimental observations with computational analyses spanning from the molecular- to the tissue-scale, the goal of effective nanotherapy customized to patient tumor-specific conditions may be finally realized.

A Multiscale Agent-Based Model of Ductal Carcinoma In Situ

OBJECTIVE

we present a multiscale agent-based model of Ductal Carcinoma in Situ (DCIS) in order to gain a detailed understanding of the cell-scale population dynamics, phenotypic distributions, and the associated interplay of important molecular signaling pathways that are involved in DCIS ductal invasion into the duct cavity (a process we refer to as duct advance rate here).

METHODS

DCIS is modeled mathematically through a hybridized discrete cell-scale model and a continuum molecular scale model, which are explicitly linked through a bidirectional feedback mechanism.

RESULTS

we find that duct advance rates occur in two distinct phases, characterized by an early exponential population expansion, followed by a long-term steady linear phase of population expansion, a result that is consistent with other modeling work. We further found that the rates were influenced most strongly by endocrine and paracrine signaling intensity, as well as by the effects of cell density induced quiescence within the DCIS population.

CONCLUSION

our model analysis identified a complex interplay between phenotypic diversity that may provide a tumor adaptation mechanism to overcome proliferation limiting conditions, allowing for dynamic shifts in phenotypic populations in response to variation in molecular signaling intensity. Further, sensitivity analysis determined DCIS axial advance rates and calcification rates were most sensitive to cell cycle time variation.

SIGNIFICANCE

this model may serve as a useful tool to study the cell-scale dynamics involved in DCIS initiation and intraductal invasion, and may provide insights into promising areas of future experimental research.

Image-guided mathematical modeling for pharmacological evaluation of nanomaterials and monoclonal antibodies

While plasma concentration kinetics has traditionally been the predictor of drug pharmacological effects, it can occasionally fail to represent kinetics at the site of action, particularly for solid tumors. This is especially true in the case of delivery of therapeutic macromolecules (drug-loaded nanomaterials or monoclonal antibodies), which can experience challenges to effective delivery due to particle size-dependent diffusion barriers at the target site. As a result, disparity between therapeutic plasma kinetics and kinetics at the site of action may exist, highlighting the importance of target site concentration kinetics in determining the pharmacodynamic effects of macromolecular therapeutic agents. Assessment of concentration kinetics at the target site has been facilitated by non-invasive in vivo imaging modalities. This allows for visualization and quantification of the whole-body disposition behavior of therapeutics that is essential for a comprehensive understanding of their pharmacokinetics and pharmacodynamics. Quantitative non-invasive imaging can also help guide the development and parameterization of mathematical models for descriptive and predictive purposes. Here, we present a review of the application of state-of-the-art imaging modalities for quantitative pharmacological evaluation of therapeutic nanoparticles and monoclonal antibodies, with a focus on their integration with mathematical models, and identify challenges and opportunities. This article is categorized under: Therapeutic Approaches and Drug Discovery > Nanomedicine for Oncologic Disease Diagnostic Tools > in vivo Nanodiagnostics and Imaging Nanotechnology Approaches to Biology > Nanoscale Systems in Biology.

A mathematical model to predict nanomedicine pharmacokinetics and tumor delivery

Towards clinical translation of cancer nanomedicine, it is important to systematically investigate the various parameters related to nanoparticle (NP) physicochemical properties, tumor characteristics, and inter-individual variability that affect the tumor delivery efficiency of therapeutic nanomaterials. Comprehensive investigation of these parameters using traditional experimental approaches is impractical due to the vast parameter space; mathematical models provide a more tractable approach to navigate through such a multidimensional space. To this end, we have developed a predictive mathematical model of whole-body NP pharmacokinetics and their tumor delivery in vivo, and have conducted local and global sensitivity analyses to identify the factors that result in low tumor delivery efficiency and high off-target accumulation of NPs. Our analyses reveal that NP degradation rate, tumor blood viscosity, NP size, tumor vascular fraction, and tumor vascular porosity are the key parameters in governing NP kinetics in the tumor interstitium. The impact of these parameters on tumor delivery efficiency of NPs is discussed, and optimal values for maximizing NP delivery are presented.

Development of a Physiologically-Based Mathematical Model for Quantifying Nanoparticle Distribution in Tumors

Nanomedicine holds promise for the treatment of cancer, as it enables tumor-targeted drug delivery. However, reports on translation of most nanomedicine strategies to the clinic so far have been less than satisfactory, in part due to insufficient understanding of the effects of nanoparticle (NP) physiochemical properties and physiological variables on their pharmacological behavior. In this paper, we present a multiscale mathematical model to examine the efficacy of NP delivery to solid tumors; as a case example, we apply the model to a clinically detectable primary pancreatic ductal adenocarcinoma (PDAC) to assess tissue-scale spatiotemporal distribution profiles of NPs. We integrate NP systemic disposition kinetics with NP-cell interactions in PDAC abstractly described as a two-dimensional structure, which is then parameterized with human physiological data obtained from published literature. Through model analysis of delivery efficiency, we verify the multiscale approach by showing that NP concentration kinetics of interest in various compartments predicted by the whole-body scale model were in agreement with those obtained from the tissue-scale model. We also found that more NPs were trapped in the outer well-perfused tumor region than the inner semi-necrotic domain. Further development of the model may provide a useful tool for optimal NP design and physiological interventions.

Mathematical Modeling to Address Challenges in Pancreatic Cancer

Pancreatic Ductal Adenocarcinoma (PDAC) is regarded as one of the most lethal cancer types for its challenges associated with early diagnosis and resistance to standard chemotherapeutic agents, thereby leading to a poor five-year survival rate. The complexity of the disease calls for a multidisciplinary approach to better manage the disease and improve the status quo in PDAC diagnosis, prognosis, and treatment. To this end, the application of quantitative tools can help improve the understanding of disease mechanisms, develop biomarkers for early diagnosis, and design patient-specific treatment strategies to improve therapeutic outcomes. However, such approaches have only been minimally applied towards the investigation of PDAC, and we review the current status of mathematical modeling works in this field.

A multiscale model to design therapeutic strategies that overcome drug resistance to tyrosine kinase inhibitors in multiple myeloma

Drug resistance (DR) is a phenomenon characterized by the tolerance of a disease to pharmaceutical treatment. In cancer patients, DR is one of the main challenges that limit the therapeutic potential of the existing treatments. Therefore, overcoming DR by restoring the sensitivity of cancer cells would be greatly beneficial. In this context, mathematical modeling can be used to provide novel therapeutic strategies that maximize the efficiency of anti-cancer agents and potentially overcome DR. In this paper, we present a new multiscale model devoted to the interaction of potential treatments with multiple myeloma (MM) development. In this model, MM cells are represented as individual objects that move, divide, and die by apoptosis. The fate of each cell depends on intracellular and extracellular regulation, as well as the administered treatment. The model is used to explore the combined effects of a tyrosine-kinase inhibitor (TKI) with a pentose phosphate pathway (PPP) inhibitor. We use numerical simulations to tailor effective and safe treatment regimens that may eradicate the MM tumors. The model suggests that an interval for the daily dose of the PPP inhibitor can maximize the responsiveness of MM cells to the treatment with TKIs. Then, it demonstrates that the combination of high-dose pulsatile TKI treatment with high-dose daily PPP inhibitor therapy can potentially eradicate the tumor.The predictions of numerical simulations using such a model can be considered as testable hypotheses in future pre-clinical experiments and clinical studies.

Mathematical modeling and computational prediction of cancer drug resistance

Diverse forms of resistance to anticancer drugs can lead to the failure of chemotherapy. Drug resistance is one of the most intractable issues for successfully treating cancer in current clinical practice. Effective clinical approaches that could counter drug resistance by restoring the sensitivity of tumors to the targeted agents are urgently needed. As numerous experimental results on resistance mechanisms have been obtained and a mass of high-throughput data has been accumulated, mathematical modeling and computational predictions using systematic and quantitative approaches have become increasingly important, as they can potentially provide deeper insights into resistance mechanisms, generate novel hypotheses or suggest promising treatment strategies for future testing. In this review, we first briefly summarize the current progress of experimentally revealed resistance mechanisms of targeted therapy, including genetic mechanisms, epigenetic mechanisms, posttranslational mechanisms, cellular mechanisms, microenvironmental mechanisms and pharmacokinetic mechanisms. Subsequently, we list several currently available databases and Web-based tools related to drug sensitivity and resistance. Then, we focus primarily on introducing some state-of-the-art computational methods used in drug resistance studies, including mechanism-based mathematical modeling approaches (e.g. molecular dynamics simulation, kinetic model of molecular networks, ordinary differential equation model of cellular dynamics, stochastic model, partial differential equation model, agent-based model, pharmacokinetic–pharmacodynamic model, etc.) and data-driven prediction methods (e.g. omics data-based conventional screening approach for node biomarkers, static network approach for edge biomarkers and module biomarkers, dynamic network approach for dynamic network biomarkers and dynamic module network biomarkers, etc.). Finally, we discuss several further questions and future directions for the use of computational methods for studying drug resistance, including inferring drug-induced signaling networks, multiscale modeling, drug combinations and precision medicine.

Leveraging Mathematical Modeling to Quantify Pharmacokinetic and Pharmacodynamic Pathways: Equivalent Dose Metric

Treatment response assays are often summarized by sigmoidal functions comparing cell survival at a single timepoint to applied drug concentration. This approach has a limited biophysical basis, thereby reducing the biological insight gained from such analysis. In particular, drug pharmacokinetic and pharmacodynamic (PK/PD) properties are overlooked in developing treatment response assays, and the accompanying summary statistics conflate these processes. Here, we utilize mathematical modeling to decouple and quantify PK/PD pathways. We experimentally modulate specific pathways with small molecule inhibitors and filter the results with mechanistic mathematical models to obtain quantitative measures of those pathways. Specifically, we investigate the response of cells to time-varying doxorubicin treatments, modulating doxorubicin pharmacology with small molecules that inhibit doxorubicin efflux from cells and DNA repair pathways. We highlight the practical utility of this approach through proposal of the “equivalent dose metric.” This metric, derived from a mechanistic PK/PD model, provides a biophysically-based measure of drug effect. We define equivalent dose as the functional concentration of drug that is bound to the nucleus following therapy. This metric can be used to quantify drivers of treatment response and potentially guide dosing of combination therapies. We leverage the equivalent dose metric to quantify the specific intracellular effects of these small molecule inhibitors using population-scale measurements, and to compare treatment response in cell lines differing in expression of drug efflux pumps. More generally, this approach can be leveraged to quantify the effects of various pharmaceutical and biologic perturbations on treatment response.

Multiscale modeling reveals angiogenesis-induced drug resistance in brain tumors and predicts a synergistic drug combination targeting EGFR and VEGFR pathways

BACKGROUND

Experimental studies have demonstrated that both the extracellular vasculature or microenvironment and intracellular molecular network (e.g., epidermal growth factor receptor (EGFR) signaling pathway) are important for brain tumor growth. Additionally, some drugs have been developed to inhibit EGFR signaling pathways. However, how angiogenesis affects the response of tumor cells to drug treatment has rarely been mechanistically studied. Therefore, a multiscale model is required to investigate such complex biological systems that contain interactions and feedback among multiple levels.

RESULTS

In this study, we developed a single cell-based multiscale spatiotemporal model to simulate vascular tumor growth and the drug response based on the vascular endothelial growth factor receptor (VEGFR) signaling pathway, the EGFR signaling pathway and the cell cycle as well as several microenvironmental factors that determine cell fate switches in a temporal and spatial context. By incorporating the EGFRI treatment effect, the model showed an interesting phenomenon in which the survival rate of tumor cells decreased in the early stage but rebounded in a later stage, revealing the emergence of drug resistance. Moreover, we revealed the critical role of angiogenesis in acquired drug resistance, since inhibiting blood vessel growth using a VEGFR inhibitor prevented the recovery of the survival rate of tumor cells in the later stage. We further investigated the optimal timing of combining VEGFR inhibition with EGFR inhibition and predicted that the drug combination targeting both the EGFR pathway and VEGFR pathway has a synergistic effect. The experimental data validated the prediction of drug synergy, confirming the effectiveness of our model. In addition, the combination of EGFR and VEGFR genes showed clinical relevance in glioma patients.

CONCLUSIONS

The developed multiscale model revealed angiogenesis-induced drug resistance mechanisms of brain tumors to EGFRI treatment and predicted a synergistic drug combination targeting both EGFR and VEGFR pathways with optimal combination timing. This study explored the mechanistic and functional mechanisms of the angiogenesis underlying tumor growth and drug resistance, which advances our understanding of novel mechanisms of drug resistance and provides implications for designing more effective cancer therapies.

Predicting breast cancer response to neoadjuvant chemotherapy based on tumor vascular features in needle biopsies

In clinical breast cancer intervention, selection of the optimal treatment protocol based on predictive biomarkers remains an elusive goal. Here, we present a modeling tool to predict the likelihood of breast cancer response to neoadjuvant chemotherapy using patient specific tumor vasculature biomarkers. A semi-automated analysis was implemented and performed on 3990 histological images from 48 patients, with 10-208 images analyzed for each patient. We applied a histology-based model to resected primary breast cancer tumors (n = 30), and then evaluated a cohort of patients (n = 18) undergoing neoadjuvant chemotherapy, collecting pre- and post-treatment pathology specimens and MRI data. We found that core biopsy samples can be used with acceptable accuracy (r = 0.76) to determine histological parameters representative of the whole tissue region. Analysis of model histology parameters obtained from tumor vasculature measurements, specifically diffusion distance divided by radius of drug source (L/rb) and blood volume fraction (BVF), provides a statistically significant separation of patients obtaining a pathologic complete response (pCR) from those that do not (Student's t-test; P < 0.05). With this model, it is feasible to evaluate primary breast tumor vasculature biomarkers in a patient specific manner, thereby allowing a precision approach to breast cancer treatment.

Mathematical modeling of tumor-immune cell interactions

The anti-tumor activity of the immune system is increasingly recognized as critical for the mounting of a prolonged and effective response to cancer growth and invasion, and for preventing recurrence following resection or treatment. As the knowledge of tumor-immune cell interactions has advanced, experimental investigation has been complemented by mathematical modeling with the goal to quantify and predict these interactions. This succinct review offers an overview of recent tumor-immune continuum modeling approaches, highlighting spatial models. The focus is on work published in the past decade, incorporating one or more immune cell types and evaluating immune cell effects on tumor progression. Due to their relevance to cancer, the following immune cells and their combinations are described: macrophages, Cytotoxic T Lymphocytes, Natural Killer cells, dendritic cells, T regulatory cells, and CD4+ T helper cells. Although important insight has been gained from a mathematical modeling perspective, the development of models incorporating patient-specific data remains an important goal yet to be realized for potential clinical benefit.

Dynamic Targeting in Cancer Treatment

With the advent of personalized medicine, design and development of anti-cancer drugs that are specifically targeted to individual or sets of genes or proteins has been an active research area in both academia and industry. The underlying motivation for this approach is to interfere with several pathological crosstalk pathways in order to inhibit or at the very least control the proliferation of cancer cells. However, after initially conferring beneficial effects, if sub-lethal, these artificial perturbations in cell function pathways can inadvertently activate drug-induced up- and down-regulation of feedback loops, resulting in dynamic changes over time in the molecular network structure and potentially causing drug resistance as seen in clinics. Hence, the targets or their combined signatures should also change in accordance with the evolution of the network (reflected by changes to the structure and/or functional output of the network) over the course of treatment. This suggests the need for a "dynamic targeting" strategy aimed at optimizing tumor control by interfering with different molecular targets, at varying stages. Understanding the dynamic changes of this complex network under various perturbed conditions due to drug treatment is extremely challenging under experimental conditions let alone in clinical settings. However, mathematical modeling can facilitate studying these effects at the network level and beyond, and also accelerate comparison of the impact of different dosage regimens and therapeutic modalities prior to sizeable investment in risky and expensive clinical trials. A dynamic targeting strategy based on the use of mathematical modeling can be a new, exciting research avenue in the discovery and development of therapeutic drugs.

An agent-based model for drug-radiation interactions in the tumour microenvironment: Hypoxia-activated prodrug SN30000 in multicellular tumour spheroids

Multicellular tumour spheroids capture many characteristics of human tumour microenvironments, including hypoxia, and represent an experimentally tractable in vitro model for studying interactions between radiotherapy and anticancer drugs. However, interpreting spheroid data is challenging because of limited ability to observe cell fate within spheroids dynamically. To overcome this limitation, we have developed a hybrid continuum/agent-based model (ABM) for HCT116 tumour spheroids, parameterised using experimental models (monolayers and multilayers) in which reaction and diffusion can be measured directly. In the ABM, cell fate is simulated as a function of local oxygen, glucose and drug concentrations, determined by solving diffusion equations and intracellular reactions. The model is lattice-based, with cells occupying discrete locations on a 3D grid embedded within a coarser grid that encompasses the culture medium; separate solvers are employed for each grid. The generated concentration fields account for depletion in the medium and specify concentration-time profiles within the spheroid. Cell growth and survival are determined by intracellular oxygen and glucose concentrations, the latter based on direct measurement of glucose diffusion/reaction (in multilayers) for the first time. The ABM reproduces known features of spheroids including overall growth rate, its oxygen and glucose dependence, peripheral cell proliferation, central hypoxia and necrosis. We extended the ABM to describe in detail the hypoxia-dependent interaction between ionising radiation and a hypoxia-activated prodrug (SN30000), again using experimentally determined parameters; the model accurately simulated clonogenic cell killing in spheroids, while inclusion of reversible cell cycle delay was required to account for the marked spheroid growth delay after combined radiation and SN30000. This ABM of spheroid growth and response exemplifies the utility of integrating computational and experimental tools for investigating radiation/drug interactions, and highlights the critical importance of understanding oxygen, glucose and drug concentration gradients in interpreting activity of therapeutic agents in spheroid models.

Studies in 3D cultures, notably multicellular tumour spheroids that mimic many features of solid tumours, have great potential for speeding up anticancer drug development. However the increased complexity of 3D cultures makes interpretation of experiments more difficult. We have developed a hybrid continuum/agent-based mathematical model, validated by experiments, to aid interpretation of spheroid experiments in developing drugs designed to eliminate radiation-resistant hypoxic cells. This model includes key features of the tumour microenvironment including oxygen and glucose transport and regions of hypoxia where the cells are resistant to radiation, but sensitive to hypoxia-activated prodrugs such as SN30000. This enables us to predict the growth and cell response in untreated spheroids and compare the results to spheroids treated with radiation and SN30000. We demonstrate good prediction of cellular responses in spheroids treated with radiation and SN30000 and good agreement with spheroid regrowth after treatment when additional effects of cellular growth delay are added. This demonstrates that the modelling approach has potential to improve interpretation of experimental investigations of drug and radiation combinations.

Systems Pharmacology: Defining the Interactions of Drug Combinations

The majority of diseases are associated with alterations in multiple molecular pathways and complex interactions at the cellular and organ levels. Single-target monotherapies therefore have intrinsic limitations with respect to their maximum therapeutic benefits. The potential of combination drug therapies has received interest for the treatment of many diseases and is well established in some areas, such as oncology. Combination drug treatments may allow us to identify synergistic drug effects, reduce adverse drug reactions, and address variability in disease characteristics between patients. Identification of combination therapies remains challenging. We discuss current state-of-the-art systems pharmacology approaches to enable rational identification of combination therapies. These approaches, which include characterization of mechanisms of disease and drug action at a systems level, can enable understanding of drug interactions at the molecular, cellular, physiological, and organismal levels. Such multiscale understanding can enable precision medicine by promoting the rational development of combination therapy at the level of individual patients for many diseases.

In silico drug absorption tract: An agent-based biomimetic model for human oral drug absorption

Background

An agent-based modeling approach has been suggested as an alternative to traditional, equation-based modeling methods for describing oral drug absorption. It enables researchers to gain a better understanding of the pharmacokinetic (PK) mechanisms of a drug. This project demonstrates that a biomimetic agent-based model can adequately describe the absorption and disposition kinetics both of midazolam and clonazepam.

Methods

An agent-based biomimetic model, in silico drug absorption tract (ISDAT), was built to mimic oral drug absorption in humans. The model consisted of distinct spaces, membranes, and metabolic enzymes, and it was altogether representative of human physiology relating to oral drug absorption. Simulated experiments were run with the model, and the results were compared to the referent data from clinical equivalence trials. Acceptable similarity was verified by pre-specified criteria, which included 1) qualitative visual matching between the clinical and simulated concentration-time profiles, 2) quantitative similarity indices, namely, weighted root mean squared error (RMSE), and weighted mean absolute percentage error (MAPE) and 3) descriptive similarity which requires less than 25% difference between key PK parameters calculated by the clinical and the simulated concentration-time profiles. The model and its parameters were iteratively refined until all similarity criteria were met. Furthermore, simulated PK experiments were conducted to predict bioavailability (F). For better visualization, a graphical user interface for the model was developed and a video is available in Supporting Information.

Results

Simulation results satisfied all three levels of similarity criteria for both drugs. The weighted RMSE was 0.51 and 0.92, and the weighted MAPE was 5.99% and 8.43% for midazolam and clonazepam, respectively. Calculated PK parameter values, including area under the curve (AUC), peak plasma drug concentration (C_max), time to reach C_max (T_max), terminal elimination rate constant (Kel), terminal elimination half life (T_1/2), apparent oral clearance (CL/F), and apparent volume of distribution (V/F), were reasonable compared to the referent values. The predicted absolute oral bioavailability (F) was 44% for midazolam (literature reported value, 31–72%) and 93% (literature reported value, ≥ 90%) for clonazepam.

Conclusion

The ISDAT met all the pre-specified similarity criteria for both midazolam and clonazepam, and demonstrated its ability to describe absorption kinetics of both drugs. Therefore, the validated ISDAT can be a promising platform for further research into the use of similar in silico models for drug absorption kinetics.

Multiscale Tumor Modeling With Drug Pharmacokinetic and Pharmacodynamic Profile Using Stochastic Hybrid System

Effective cancer treatment strategy requires an understanding of cancer behavior and development across multiple temporal and spatial scales. This has resulted into a growing interest in developing multiscale mathematical models that can simulate cancer growth, development, and response to drug treatments. This study thus investigates multiscale tumor modeling that integrates drug pharmacokinetic and pharmacodynamic (PK/PD) information using stochastic hybrid system modeling framework. Specifically, (1) pathways modeled by differential equations are adopted for gene regulations at the molecular level; (2) cellular automata (CA) model is proposed for the cellular and multicellular scales. Markov chains are used to model the cell behaviors by taking into account the gene expression levels, cell cycle, and the microenvironment. The proposed model enables the prediction of tumor growth under given molecular properties, microenvironment conditions, and drug PK/PD profile. Simulation results demonstrate the effectiveness of the proposed approach and the results agree with observed tumor behaviors.

Applying optimization algorithms to tuberculosis antibiotic treatment regimens

Introduction

Tuberculosis (TB), one of the most common infectious diseases, requires treatment with multiple antibiotics taken over at least 6 months. This long treatment often results in poor patient-adherence, which can lead to the emergence of multi-drug resistant TB. New antibiotic treatment strategies are sorely needed. New antibiotics are being developed or repurposed to treat TB, but as there are numerous potential antibiotics, dosing sizes and potential schedules, the regimen design space for new treatments is too large to search exhaustively. Here we propose a method that combines an agent-based multi-scale model capturing TB granuloma formation with algorithms for mathematical optimization to identify optimal TB treatment regimens.

Methods

We define two different single-antibiotic treatments to compare the efficiency and accuracy in predicting optimal treatment regimens of two optimization algorithms: genetic algorithms (GA) and surrogate-assisted optimization through radial basis function (RBF) networks. We also illustrate the use of RBF networks to optimize double-antibiotic treatments.

Results

We found that while GAs can locate optimal treatment regimens more accurately, RBF networks provide a more practical strategy to TB treatment optimization with fewer simulations, and successfully estimated optimal double-antibiotic treatment regimens.

Conclusions

Our results indicate surrogate-assisted optimization can locate optimal TB treatment regimens from a larger set of antibiotics, doses and schedules, and could be applied to solve optimization problems in other areas of research using systems biology approaches. Our findings have important implications for the treatment of diseases like TB that have lengthy protocols or for any disease that requires multiple drugs.

Theory and Experimental Validation of a Spatio-temporal Model of Chemotherapy Transport to Enhance Tumor Cell Kill

It has been hypothesized that continuously releasing drug molecules into the tumor over an extended period of time may significantly improve the chemotherapeutic efficacy by overcoming physical transport limitations of conventional bolus drug treatment. In this paper, we present a generalized space- and time-dependent mathematical model of drug transport and drug-cell interactions to quantitatively formulate this hypothesis. Model parameters describe: perfusion and tissue architecture (blood volume fraction and blood vessel radius); diffusion penetration distance of drug (i.e., a function of tissue compactness and drug uptake rates by tumor cells); and cell death rates (as function of history of drug uptake). We performed preliminary testing and validation of the mathematical model using in vivo experiments with different drug delivery methods on a breast cancer mouse model. Experimental data demonstrated a 3-fold increase in response using nano-vectored drug vs. free drug delivery, in excellent quantitative agreement with the model predictions. Our model results implicate that therapeutically targeting blood volume fraction, e.g., through vascular normalization, would achieve a better outcome due to enhanced drug delivery.

Mathematical Modeling of Therapy-induced Cancer Drug Resistance: Connecting Cancer Mechanisms to Population Survival Rates

Drug resistance significantly limits the long-term effectiveness of targeted therapeutics for cancer patients. Recent experimental studies have demonstrated that cancer cell heterogeneity and microenvironment adaptations to targeted therapy play important roles in promoting the rapid acquisition of drug resistance and in increasing cancer metastasis. The systematic development of effective therapeutics to overcome drug resistance mechanisms poses a major challenge. In this study, we used a modeling approach to connect cellular mechanisms underlying cancer drug resistance to population-level patient survival. To predict progression-free survival in cancer patients with metastatic melanoma, we developed a set of stochastic differential equations to describe the dynamics of heterogeneous cell populations while taking into account micro-environment adaptations. Clinical data on survival and circulating tumor cell DNA (ctDNA) concentrations were used to confirm the effectiveness of our model. Moreover, our model predicted distinct patterns of dose-dependent synergy when evaluating a combination of BRAF and MEK inhibitors versus a combination of BRAF and PI3K inhibitors. These predictions were consistent with the findings in previously reported studies. The impact of the drug metabolism rate on patient survival was also discussed. The proposed model might facilitate the quantitative evaluation and optimization of combination therapeutics and cancer clinical trial design.

The Tumor Microenvironment as a Barrier to Cancer Nanotherapy

Although extensive research effort and resources have been dedicated to the development of nanotherapeutics to treat cancer, few formulations have reached clinical application. A major reason is that the large number of parameters available to tune nanotherapy characteristics coupled with the variability in tumor tissue precludes evaluation of complex interactions through experimentation alone. In order to optimize the nanotechnology design and gain further insight into these phenomena, mathematical modeling and computational simulation have been applied to complement empirical work. In this chapter, we discuss modeling work related to nanotherapy and the tumor microenvironment. We first summarize the biology underlying the dysregulated tumor microenvironment, followed by a description of major nano-scale parameters. We then present an overview of the mathematical modeling of cancer nanotherapy, including evaluation of nanotherapy in multi-dimensional tumor tissue, coupling of nanotherapy with vascular flow, modeling of nanotherapy in combination with in vivo imaging, modeling of nanoparticle transport based on in vitro data, modeling of vasculature-bound nanoparticles, evaluation of nanotherapy using pharmacokinetic modeling, and modeling of nano-based hyperthermia. We conclude that an even tighter interdisciplinary effort between biological, material, and physical scientists is needed in order to eventually overcome the tumor microenvironment barrier to successful nanotherapy.

Simulation of the Protein-Shedding Kinetics of a Fully Vascularized Tumor

Circulating biomarkers are of significant interest for cancer detection and treatment personalization. However, the biophysical processes that determine how proteins are shed from cancer cells or their microenvironment, diffuse through tissue, enter blood vasculature, and persist in circulation remain poorly understood. Since approaches primarily focused on experimental evaluation are incapable of measuring the shedding and persistence for every possible marker candidate, we propose an interdisciplinary computational/experimental approach that includes computational modeling of tumor tissue heterogeneity. The model implements protein production, transport, and shedding based on tumor vascularization, cell proliferation, hypoxia, and necrosis, thus quantitatively relating the tumor and circulating proteomes. The results highlight the dynamics of shedding as a function of protein diffusivity and production. Linking the simulated tumor parameters to clinical tumor and vascularization measurements could potentially enable this approach to reveal the tumor-specific conditions based on the protein detected in circulation and thus help to more accurately manage cancer diagnosis and treatment.

Evaluation of uptake and distribution of gold nanoparticles in solid tumors

Although nanotherapeutics offer a targeted and potentially less toxic alternative to systemic chemotherapy in cancer treatment, nanotherapeutic transport is typically hindered by abnormal characteristics of tumor tissue. Once nanoparticles targeted to tumor cells arrive in the circulation of tumor vasculature, they must extravasate from irregular vessels and diffuse through the tissue to ideally reach all malignant cells in cytotoxic concentrations. The enhanced permeability and retention effect can be leveraged to promote extravasation of appropriately sized particles from tumor vasculature; however, therapeutic success remains elusive partly due to inadequate intra-tumoral transport promoting heterogeneous nanoparticle uptake and distribution. Irregular tumor vasculature not only hinders particle transport but also sustains hypoxic tissue kregions with quiescent cells, which may be unaffected by cycle-dependent chemotherapeutics released from nanoparticles and thus regrow tumor tissue following nanotherapy. Furthermore, a large proportion of systemically injected nanoparticles may become sequestered by the reticuloendothelial system, resulting in overall diminished efficacy. We review recent work evaluating the uptake and distribution of gold nanoparticles in pre-clinical tumor models, with the goal to help improve nanotherapy outcomes. We also examine the potential role of novel layered gold nanoparticles designed to address some of these critical issues, assessing their uptake and transport in cancerous tissue.