A QSP Model for Predicting Clinical Responses to Monotherapy, Combination and Sequential Therapy Following CTLA-4, PD-1, and PD-L1 Checkpoint Blockade

Using mathematical modelling and AI to improve delivery and efficacy of therapies in cancer

Mathematical modelling has proven to be a valuable tool in predicting the delivery and efficacy of molecular, antibody-based, nano and cellular therapy in solid tumours. Mathematical models based on our understanding of the biological processes at subcellular, cellular and tissue level are known as mechanistic models that, in turn, are divided into continuous and discrete models. Continuous models are further divided into lumped parameter models - for describing the temporal distribution of medicine in tumours and normal organs - and distributed parameter models - for studying the spatiotemporal distribution of therapy in tumours. Discrete models capture interactions at the cellular and subcellular levels. Collectively, these models are useful for optimizing the delivery and efficacy of molecular, nanoscale and cellular therapy in tumours by incorporating the biological characteristics of tumours, the physicochemical properties of drugs, the interactions among drugs, cancer cells and various components of the tumour microenvironment, and for enabling patient-specific predictions when combined with medical imaging. Artificial intelligence-based methods, such as machine learning, have ushered in a new era in oncology. These data-driven approaches complement mechanistic models and have immense potential for improving cancer detection, treatment and drug discovery. Here we review these diverse approaches and suggest ways to combine mechanistic and artificial intelligence-based models to further improve patient treatment outcomes.

Mathematical modeling of the synergetic effect between radiotherapy and immunotherapy

The synergy between radiotherapy and immunotherapy plays a pivotal role in enhancing tumor control and treatment outcomes. To explore the underlying mechanisms of synergy, we investigated a novel treatment approach known as personalized ultra-fractionated stereotactic adaptive radiation (PULSAR) therapy, which emphasizes the impact of radiation timing. Unlike conventional daily treatments, PULSAR delivers high-dose radiation in spaced intervals over weeks or months, enabling tumors to adapt and potentially enhancing synergy with immunotherapy. Drawing on insights from small-animal radiation studies, we developed a discrete-time model based on multiple difference equations to elucidate the temporal dynamics of tumor control driven by both radiation and the adaptive immune response. By accounting for the migration and infiltration of T cells within the tumor microenvironment, we established a quantitative link between radiation therapy and immunotherapy. Model parameters were estimated using a simulated annealing algorithm applied to training data, and our model achieved high accuracy for the test data with a root mean square error of 287 mm3. Notably, our framework replicated the PULSAR effect observed in animal studies, revealing that longer intervals between radiation treatments in the context of immunotherapy yielded enhanced tumor control. Specifically, mice receiving immunotherapy alongside radiation pulses delivered at extended intervals, ten days, showed markedly improved tumor responses, whereas those treated with shorter intervals did not achieve comparable benefits. Moreover, our model offers an in-silico tool for designing future personalized ultra-fractionated stereotactic adaptive radiation trials. Overall, these findings underscore the critical importance of treatment timing in harnessing the synergy between radiotherapy and immunotherapy and highlight the potential of our model to optimize and individualize treatment protocols.

Predicting survival in prospective clinical trials using weakly-supervised QSP

Quantitative systems pharmacology (QSP) models of cancer immunity provide mechanistic insights into cellular dynamics and drug effects that are difficult to study clinically. However, their inability to predict patient survival mechanistically limits their utility in anti-cancer drug development. To overcome this, we link virtual patients from a QSP model to real clinical trial patients. Using data from atezolizumab trials in non-small cell lung cancer, we show that tumor-based linkage effectively captures survival outcomes. By treating linked survival and censoring as weak supervision labels, we trained survival models using only QSP model covariates, without clinical covariates. Our approach also predicts survival for treatments not included in training data. Specifically, we accurately estimated survival hazard ratios (HR) for chemotherapy monotherapy and atezolizumab plus chemotherapy combination. The predicted HR of 0.70 (95% prediction interval [PI] 0.55-0.86) closely matches the observed HR of 0.79 (95% PI 0.64-0.98) from the IMpower130 trial.

A mechanistic quantitative systems pharmacology model platform for translational efficacy evaluation and checkpoint combination design of bispecific immuno-modulatory antibodies

Over the past 2 decades, tumor immunotherapies have witnessed remarkable advancements, especially with the emergence of immune checkpoint-targeting bispecific antibodies. However, a quantitative understanding of the dynamic cross-talking mechanisms underlying different immune checkpoints as well as the optimal dosing and target design of checkpoint-targeting bispecific antibodies still remain challenging to researchers. To address this challenge, we have here developed a multi-scale quantitative systems pharmacology (QSP) model platform that integrates a diverse array of immune checkpoints and their interactive functions. The model has been calibrated and validated against an extensive collection of multiscale experimental datasets covering 20+ different monoclonal and bispecific antibody treatments at over 60 administered dose levels. Based on high-throughput simulations, the QSP model platform comprehensively screened and characterized the potential efficacy of different bispecific antibody target combination designs, and model-based preclinical population-level simulations revealed target-specific dose-response relationships as well as alternative dosing strategies that can maintain anti-tumor treatment efficacy while reducing dosing frequencies. Model simulations also pointed out that combining checkpoint-targeting bispecific antibodies with monoclonal antibodies can lead to significantly enhanced anti-tumor efficacy. Our mechanistic QSP model can serve as an integrated precision medicine simulation platform to guide the translational research and clinical development of checkpoint-targeting immuno-modulatory bispecific antibodies.

A Multiple-Model-Informed Drug-Development Approach for Optimal Regimen Selection of an Oncolytic Virus in Combination With Pembrolizumab

The antitumor efficacy of an intratumoral injection of a genetically engineered oncolytic vaccinia virus carrying human IL-7 and murine IL-12 genes (hIL-7/mIL-12-VV) was demonstrated in CT26.WT-bearing mice. In the CT26.WT-bearing mouse model, the efficacy of the combination of hIL-7/mIL-12-VV plus the anti-programmed cell death protein (PD)-1 antibody was determined to be correlated with the timing of administration: greater efficacy was observed when hIL-7/mIL-12-VV was administered before the anti-PD-1 agent instead of simultaneous administration. To identify an optimal dosing regimen for first-in-human clinical trials, a multiple model-informed drug-development (MIDD) approach was used through development of a quantitative systems pharmacology (QSP) model and an agent-based model (ABM). All models were built and verified using available literature and preclinical study data. Multiple dosing scenarios were explored using virtual populations by altering the interval between hIL-7/hIL-12-VV and pembrolizumab administration. In contrast with observations from preclinical studies, both the QSP and the ABM models demonstrated no antagonistic effect on the dose-dependent antitumor efficacy of hIL-7/hIL-12-VV by pembrolizumab in simulations of clinical therapy. Based on the MIDD strategy, it was recommended that the highest dose of hIL-7/hIL-12-VV and pembrolizumab should be administered on the same day, but with pembrolizumab administration following hIL-7/hIL-12-VV administration. Multiple different modeling approaches uniquely supported and informed the first-in-human clinical trial design by guiding the optimal dose and regimen selection.

An overview of immunotoxicity in drug discovery and development

The immune system is one of the common targets of drugs' toxicity (Immunotoxicity) and/or efficacy (Immunotherapy). Immunotoxicity leads to adverse effects on human health, which raises serious concerns for the regulatory agencies. Currently, immunotoxicity assessment is conducted using different in vitro and in vivo assays. In silico and in vitro human cell-based immunotoxicity assays should also be explored for screening purposes as these are time and cost effective as well as for ethical reasons. For in vivo studies, tier 1-3 assessments (Tier 1: hematology, serum globulin levels, lymphoid organ's weight and histopathology; Tier 2: immunophenotyping, TDAR and cell mediated immunity; and Tier 3: host resistance) should be used. These non-clinical in vivo assessments are useful to select immunological endpoints for clinical trials as well as for precautionary labeling. As per regulatory guidelines, adverse immunogenicity information of drug should be included in product's labeling to make health care practitioner aware of safety concerns before prescribing medicines and patient management (USFDA, 2022a, 2022b). This review mainly focuses on the importance of immunotoxicity assessment during drug discovery and development.

Quantitative Systems Pharmacology Modeling in Immuno-Oncology: Hypothesis Testing, Dose Optimization, and Efficacy Prediction

Despite an increasing number of clinical trials, cancer is one of the leading causes of death worldwide in the past decade. Among all complex diseases, clinical trials in oncology have among the lowest success rates, in part due to the high intra- and inter-tumoral heterogeneity. There are more than a thousand cancer drugs and treatment combinations being investigated in ongoing clinical trials for various cancer subtypes, germline mutations, metastasis, etc. Particularly, treatments relying on the (re)activation of the immune system have become increasingly present in the clinical trial pipeline. However, the complexities of the immune response and cancer-immune interactions pose a challenge to the development of these therapies. Quantitative systems pharmacology (QSP), as a computational approach to predict tumor response to treatments of interest, can be used to conduct in silico clinical trials with virtual patients (and emergent use of digital twins) in place of real patients, thus lowering the time and cost of clinical trials. In line with improved mechanistic understanding of the human immune system and promising results from recent cancer immunotherapy, QSP models can play critical roles in model-informed drug development in immuno-oncology. In this chapter, we discuss how QSP models were designed to serve different study objectives, including hypothesis testing, dose optimization, and efficacy prediction, via case studies in immuno-oncology.

Assessing tumor volumetric reduction with consideration for setup errors based on mathematical tumor model and microdosimetric kinetic model in single-isocenter VMAT for brain metastases

The volumetric reduction rate (VRR) was evaluated with consideration for six degrees-of-freedom (6DoF) patient setup errors based on a mathematical tumor model in single-isocenter volumetric modulated arc therapy (SI-VMAT) for brain metastases. Simulated gross tumor volumes (GTV) of 1.0 cm and dose distribution were created (27 Gy/3 fractions). The distance between the GTV center and isocenter (d) was set at 0-10 cm. The GTV was translated within 0-1.0 mm (Trans) and rotated within 0-1.0° (Rot) in the three axis directions using affine transformation. The tumor growth volume was calculated using a multicomponent mathematical model (MCTM), and lethal effects of irradiation and repair from damage during irradiation were calculated by a microdosimetric kinetic model (MKM) for non-small cell lung cancer (NSCLC) A549 and NCI-H460 (H460) cells. The VRRs were calculated 5 days after the end of irradiation using the physical dose to the GTV for varying d and 6DoF setup errors. The tolerance value of VRR, the GTV volume reduction rate, was set at 5%, based on the pre-irradiation GTV volume. With the exception of the only one A549 condition where (Trans, Rot) = (1.0 mm, 1.0°) was repeated for 3 fractions, all conditions met all the tolerance VRR values for A549 and H460 cells with varying d from 0 to 10 cm. Evaluation based on the mathematical tumor model suggested that if the 6DoF setup errors at each irradiation could be kept within 1.0 mm and 1.0°, there would be little effect on tumor volume regardless of the distance from the isocenter in SI-VMAT.

Assessing the performance of QSP models: biology as the driver for validation

Validation of a quantitative model is a critical step in establishing confidence in the model's suitability for whatever analysis it was designed. While processes for validation are well-established in the statistical sciences, the field of quantitative systems pharmacology (QSP) has taken a more piecemeal approach to defining and demonstrating validation. Although classical statistical methods can be used in a QSP context, proper validation of a mechanistic systems model requires a more nuanced approach to what precisely is being validated, and what role said validation plays in the larger context of the analysis. In this review, we summarize current thoughts of QSP validation in the scientific community, contrast the aims of statistical validation from several contexts (including inference, pharmacometrics analysis, and machine learning) with the challenges faced in QSP analysis, and use examples from published QSP models to define different stages or levels of validation, any of which may be sufficient depending on the context at hand.

An industry perspective on current QSP trends in drug development

2023 marks the 10th anniversary of Natpara's submission to the US FDA, which led to the first recorded regulatory interaction where a decision was supported by Quantitative and Systems Pharmacology (QSP) simulations. It had taken about 5 years for the timid QSP discipline to emerge as an effective Model-Informed Drug Development (MIDD) tool with visible impact in the pharmaceutical industry. Since then, the presence of QSP in the regulatory environment has continued to increase, to the point that the Agency reported 60 QSP submissions in 2020 alone, representing ~ 4% of their annual IND submissions [1]. What sort of industry mindset has enabled QSP to reach this level of success? How does QSP fit within the MIDD paradigm? Does QSP mean the same to Discovery and to Clinical Development projects? How do 'platforms' compare to 'fit-for-purpose' QSP models in an industrial setting? Can QSP and empirical Pharmacokinetic-Pharmacodynamic (PKPD) modelling be complementary? What level of validation is required to inform drug development decisions? This article reflects on all these questions, in particular addressing those audiences with limited line-of-sight into the drug industry decision-making machinery.

Dose Optimization in Oncology Drug Development: An International Consortium for Innovation and Quality in Pharmaceutical Development White Paper

The landscape of oncology drug development has witnessed remarkable advancements over the last few decades, significantly improving clinical outcomes and quality of life for patients with cancer. Project Optimus, introduced by the U.S. Food and Drug Administration, stands as a groundbreaking endeavor to reform dose selection of oncology drugs, presenting both opportunities and challenges for the field. To address complex dose optimization challenges, an Oncology Dose Optimization IQ Working Group was created to characterize current practices, provide recommendations for improvement, develop a clinical toolkit, and engage Health Authorities. Historically, dose selection for cytotoxic chemotherapeutics has focused on the maximum tolerated dose, a paradigm that is less relevant for targeted therapies and new treatment modalities. A survey conducted by this group gathered insights from member companies regarding industry practices in oncology dose optimization. Given oncology drug development is a complex effort with multidimensional optimization and high failure rates due to lack of clinically relevant efficacy, this Working Group advocates for a case-by-case approach to inform the timing, specific quantitative targets, and strategies for dose optimization, depending on factors such as disease characteristics, patient population, mechanism of action, including associated resistance mechanisms, and therapeutic index. This white paper highlights the evolving nature of oncology dose optimization, the impact of Project Optimus, and the need for a tailored and evidence-based approach to optimize oncology drug dosing regimens effectively.

Assessing the Role of Patient Generation Techniques in Virtual Clinical Trial Outcomes

Virtual clinical trials (VCTs) are growing in popularity as a tool for quantitatively predicting heterogeneous treatment responses across a population. In the context of a VCT, a plausible patient is an instance of a mathematical model with parameter (or attribute) values chosen to reflect features of the disease and response to treatment for that particular patient. A number of techniques have been introduced to determine the set of model parametrizations to include in a virtual patient cohort. These methodologies generally start with a prior distribution for each model parameter and utilize some criteria to determine whether a parameter set sampled from the priors should be included or excluded from the plausible population. No standard technique exists, however, for generating these prior distributions and choosing the inclusion/exclusion criteria. In this work, we rigorously quantify the impact that VCT design choices have on VCT predictions. Rather than use real data and a complex mathematical model, a spatial model of radiotherapy is used to generate simulated patient data and the mathematical model used to describe the patient data is a two-parameter ordinary differential equations model. This controlled setup allows us to isolate the impact of both the prior distribution and the inclusion/exclusion criteria on both the heterogeneity of plausible populations and on predicted treatment response. We find that the prior distribution, rather than the inclusion/exclusion criteria, has a larger impact on the heterogeneity of the plausible population. Yet, the percent of treatment responders in the plausible population was more sensitive to the inclusion/exclusion criteria utilized. This foundational understanding of the role of virtual clinical trial design should help inform the development of future VCTs that use more complex models and real data.

Predicting efficacy assessment of combined treatment of radiotherapy and nivolumab for NSCLC patients through virtual clinical trials using QSP modeling

Non-Small Cell Lung Cancer (NSCLC) remains one of the main causes of cancer death worldwide. In the urge of finding an effective approach to treat cancer, enormous therapeutic targets and treatment combinations are explored in clinical studies, which are not only costly, suffer from a shortage of participants, but also unable to explore all prospective therapeutic solutions. Within the evolving therapeutic landscape, the combined use of radiotherapy (RT) and checkpoint inhibitors (ICIs) emerged as a promising avenue. Exploiting the power of quantitative system pharmacology (QSP), we undertook a study to anticipate the therapeutic outcomes of these interventions, aiming to address the limitations of clinical trials. After enhancing a pre-existing QSP platform and accurately replicating clinical data outcomes, we conducted an in-depth study, examining different treatment protocols with nivolumab and RT, both as monotherapy and in combination, by assessing their efficacy through clinical endpoints, namely time to progression (TTP) and duration of response (DOR). As result, the synergy of combined protocols showcased enhanced TTP and extended DOR, suggesting dual advantages of extended response and slowed disease progression with certain combined regimens. Through the lens of QSP modeling, our findings highlight the potential to fine-tune combination therapies for NSCLC, thereby providing pivotal insights for tailoring patient-centric therapeutic interventions.

Practical QSP application from the preclinical phase to enhance the probability of clinical success: Insights from case studies in oncology

Quantitative Systems Pharmacology (QSP) has emerged as a promising modeling and simulation (M&S) approach in drug development, with potential to improve clinical success rates. While conventional M&S has significantly contributed to quantitative understanding in late preclinical and clinical phases, it falls short in explaining unexpected phenomena and testing hypotheses in the early research phase. QSP presents a solution to these limitations. To harness the full potential of QSP in early preclinical stages, preclinical modelers who are familiar with conventional M&S need to update their understanding of the differences between conventional M&S and QSP. This review focuses on QSP applications during the preclinical stage, citing case examples and sharing our experiences in oncology. We emphasize the critical role of QSP in increasing the probability of success for clinical proof of concept (PoC) when applied from the early preclinical stage. Enhancing the quality of both hypotheses and QSP models from early preclinical stage is of critical importance. Once a QSP model achieves credibility, it facilitates predictions of clinical responses and potential biomarkers. We propose that sequential QSP applications from preclinical stages can improve success rates of clinical PoC, and emphasize the importance of refining both hypotheses and QSP models throughout the process.

Effects of Short-Term Lenvatinib Administration Prior to Transarterial Chemoembolization for Hepatocellular Carcinoma

AIM

Transarterial chemoembolization (TACE) combined with lenvatinib, employing a 4-day lenvatinib administration followed by TACE without an interval (short-term LEN-TACE), was performed for hepatocellular carcinoma (HCC). The aim was to assess tumor hemodynamics following the 4-day lenvatinib and to evaluate the treatment outcomes after the short-term LEN-TACE.

METHODS

25 unresectable HCC patients received this combined therapy. Lenvatinib (4-12 mg) was administrated for 4 days prior to TACE. Perfusion CT scans were obtained before and after the lenvatinib administration. Either cTACE (76%) or DEB-TACE (24%) were performed.

RESULTS

intra-tumor blood flow significantly decreased after the 4-day lenvatinib (p < 0.05). The TACE procedure was successful with no severe adverse events in all patients. The overall complete response (CR) rate was 75% (cTACE 84%, DEB-TACE 40%). The lipiodol-washout ratio between 1 week and 4 months after cTACE correlated with the arterial flow reduction ratio by lenvatinib prior to TACE (r = -0.55). The 12-month progression-free survival (PFS) rate was 75.0%.

CONCLUSIONS

The short-term LEN-TACE is feasible and safe, demonstrating promising outcomes with a high CR ratio, contributing to lipiodol retention in the tumor after cTACE, and extended PFS. To confirm the advantages of this treatment protocol, a prospective clinical trial is mandatory.

Utility and impact of quantitative pharmacology on dose selection and clinical development of immuno-oncology therapy

Immuno-oncology (IO) therapies have changed the cancer treatment landscape. Immune checkpoint inhibitors (ICIs) have improved overall survival in 20-40% of patients with malignancies that were previously refractory. Due to the uniqueness in biology, modalities and patient responses, drug development strategies for IO differed from that traditionally used for cytotoxic and target therapies in oncology, and quantitative pharmacology utilizing modeling approach can be applied in all phases of the development process. In this review, we used case studies to showcase how various modeling methodologies were applied from translational science and dose selection through to label change, using examples that included anti-programmed-death-1 (anti-PD-1), anti-programmed-death ligand-1 (anti-PD-L1), anti-cytotoxic T-lymphocyte-associated protein 4 (anti-CTLA-4), and anti-glucocorticoid-induced tumor necrosis factor receptor-related protein (anti-GITR) antibodies. How these approaches were utilized to support phase I-III dose selection, the design of phase III trials, and regulatory decisions on label change are discussed to illustrate development strategies. Model-based quantitative approaches have positively impacted IO drug development, and a better understanding of the biology and exposure-response relationship may benefit the development and optimization of new IO therapies.

Transport Barriers Influence the Activation of Anti-Tumor Immunity: A Systems Biology Analysis

Effective anti-cancer immune responses require activation of one or more naïve T cells. If the correct naïve T cell encounters its cognate antigen presented by an antigen presenting cell, then the T cell can activate and proliferate. Here, mathematical modeling is used to explore the possibility that immune activation in lymph nodes is a rate-limiting step in anti-cancer immunity and can affect response rates to immune checkpoint therapy. The model provides a mechanistic framework for optimizing cancer immunotherapy and developing testable solutions to unleash anti-tumor immune responses for more patients with cancer. The results show that antigen production rate and trafficking of naïve T cells into the lymph nodes are key parameters and that treatments designed to enhance tumor antigen production can improve immune checkpoint therapies. The model underscores the potential of radiation therapy in augmenting tumor immunogenicity and neoantigen production for improved ICB therapy, while emphasizing the need for careful consideration in cases where antigen levels are already sufficient to avoid compromising the immune response.

A mean-field description for the expansion kinetics of activated T cell populations

When lymphocytes encounter their cognate antigen, they become activated and undergo a limited number of cell divisions during which they differentiate into memory or effector cells or die. While the dynamics of individual cells are often heterogeneous, the expansion kinetics at the population level are highly reproducible, suggesting a mean-field description. To generate a finite division destiny, we consider two scenarios: Cells stop dividing after a certain number of iterations or their death rate increases with each cell division. The dynamics of the combined system can be mapped to a partial differential equation, and for a suitable choice of the activation rate, we obtain simple analytical solutions for the total cell number and the mean number of divisions per cell which can well describe the signal-dependent T cell expansion kinetics from in vitro experiments. Interestingly, only the division cessation mechanism yields an expression for the division destiny that does not contradict experiments. We show that the generation-dependent decrease of the division rate in individual cells leads to a time-dependent decrease at the population level which is consistent with a "time-to-die" control mechanism for the division destiny as suggested previously. We also derive mean-field equations for the total cell number which provide a basis for implementing T cell expansion kinetics into quantitative systems pharmacology models for immuno-oncology and CAR-T cell therapies.

Knowledge-based mechanistic modeling accurately predicts disease progression with gefitinib in EGFR-mutant lung adenocarcinoma

Lung adenocarcinoma (LUAD) is associated with a low survival rate at advanced stages. Although the development of targeted therapies has improved outcomes in LUAD patients with identified and specific genetic alterations, such as activating mutations on the epidermal growth factor receptor gene (EGFR), the emergence of tumor resistance eventually occurs in all patients and this is driving the development of new therapies. In this paper, we present the In Silico EGFR-mutant LUAD (ISELA) model that links LUAD patients' individual characteristics, including tumor genetic heterogeneity, to tumor size evolution and tumor progression over time under first generation EGFR tyrosine kinase inhibitor gefitinib. This translational mechanistic model gathers extensive knowledge on LUAD and was calibrated on multiple scales, including in vitro, human tumor xenograft mouse and human, reproducing more than 90% of the experimental data identified. Moreover, with 98.5% coverage and 99.4% negative logrank tests, the model accurately reproduced the time to progression from the Lux-Lung 7 clinical trial, which was unused in calibration, thus supporting the model high predictive value. This knowledge-based mechanistic model could be a valuable tool in the development of new therapies targeting EGFR-mutant LUAD as a foundation for the generation of synthetic control arms.

Mathematical model combined with microdosimetric kinetic model for tumor volume calculation in stereotactic body radiation therapy

We proposed a new mathematical model that combines an ordinary differential equation (ODE) and microdosimetric kinetic model (MKM) to predict the tumor-cell lethal effect of Stereotactic body radiation therapy (SBRT) applied to non-small cell lung cancer (NSCLC). The tumor growth volume was calculated by the ODE in the multi-component mathematical model (MCM) for the cell lines NSCLC A549 and NCI-H460 (H460). The prescription doses 48 Gy/4 fr and 54 Gy/3 fr were used in the SBRT, and the effect of the SBRT on tumor cells was evaluated by the MKM. We also evaluated the effects of (1) linear quadratic model (LQM) and the MKM, (2) varying the ratio of active and quiescent tumors for the total tumor volume, and (3) the length of the dose-delivery time per fractionated dose (tinter) on the initial tumor volume. We used the ratio of the tumor volume at 1 day after the end of irradiation to the tumor volume before irradiation to define the radiation effectiveness value (REV). The combination of MKM and MCM significantly reduced REV at 48 Gy/4 fr compared to the combination of LQM and MCM. The ratio of active tumors and the prolonging of tinter affected the decrease in the REV for A549 and H460 cells. We evaluated the tumor volume considering a large fractionated dose and the dose-delivery time by combining the MKM with a mathematical model of tumor growth using an ODE in lung SBRT for NSCLC A549 and H460 cells.

A transcriptome-informed QSP model of metastatic triple-negative breast cancer identifies predictive biomarkers for PD-1 inhibition

Triple-negative breast cancer (TNBC), a highly metastatic breast cancer subtype, has limited treatment options. While a small number of patients attain clinical benefit with single-agent checkpoint inhibitors, identifying these patients before the therapy remains challenging. Here, we developed a transcriptome-informed quantitative systems pharmacology model of metastatic TNBC by integrating heterogenous metastatic tumors. In silico clinical trial with an anti-PD-1 drug, pembrolizumab, predicted that several features, such as the density of antigen-presenting cells, the fraction of cytotoxic T cells in lymph nodes, and the richness of cancer clones in tumors, could serve individually as biomarkers but had a higher predictive power as combinations of two biomarkers. We showed that PD-1 inhibition neither consistently enhanced all antitumorigenic factors nor suppressed all protumorigenic factors but ultimately reduced the tumor carrying capacity. Collectively, our predictions suggest several candidate biomarkers that might effectively predict the response to pembrolizumab monotherapy and potential therapeutic targets to develop treatment strategies for metastatic TNBC.

Incorporating lesion-to-lesion heterogeneity into early oncology decision making

RECISTv1.1 (Response Evaluation Criteria In Solid Tumors) is the most commonly used response grading criteria in early oncology trials. In this perspective, we argue that RECISTv1.1 is ambiguous regarding lesion-to-lesion variation that can introduce bias in decision making. We show theoretical examples of how lesion-to-lesion variability causes bias in RECISTv1.1, leading to misclassification of patient response. Next, we review immune checkpoint inhibitor (ICI) clinical trial data and find that lesion-to-lesion heterogeneity is widespread in ICI-treated patients. We illustrate the implications of ignoring lesion-to-lesion heterogeneity in interpreting biomarker data, selecting treatments for patients with progressive disease, and go/no-go decisions in drug development. Further, we propose that Quantitative Systems Pharmacology (QSP) models can aid in developing better metrics of patient response and treatment efficacy by capturing patient responses robustly by considering lesion-to-lesion heterogeneity. Overall, we believe patient response evaluation with an appreciation of lesion-to-lesion heterogeneity can potentially improve decision-making at the early stage of oncology drug development and benefit patient care.

Converging on a Cure: The Roads to Predictive Immunotherapy

SUMMARY

Convergence science teams integrating clinical, biological, engineering, and computational expertise are inventing new forecast systems to monitor and predict evolutionary changes in tumor and immune interactions during early cancer progression and therapeutic response. The resulting methods should inform a new predictive medicine paradigm to select adaptive immunotherapeutic regimens personalized to patients' tumors at a given time during their cancer progression for durable patient response.

In silico cancer immunotherapy trials uncover the consequences of therapy-specific response patterns for clinical trial design and outcome

Late-stage cancer immunotherapy trials often lead to unusual survival curve shapes, like delayed curve separation or a plateauing curve in the treatment arm. It is critical for trial success to anticipate such effects in advance and adjust the design accordingly. Here, we use in silico cancer immunotherapy trials - simulated trials based on three different mathematical models - to assemble virtual patient cohorts undergoing late-stage immunotherapy, chemotherapy, or combination therapies. We find that all three simulation models predict the distinctive survival curve shapes commonly associated with immunotherapies. Considering four aspects of clinical trial design - sample size, endpoint, randomization rate, and interim analyses - we demonstrate how, by simulating various possible scenarios, the robustness of trial design choices can be scrutinized, and possible pitfalls can be identified in advance. We provide readily usable, web-based implementations of our three trial simulation models to facilitate their use by biomedical researchers, doctors, and trialists.

Modeling Clinical Phenotype Variability: Consideration of Genomic Variations, Computational Methods, and Quantitative Proteomics

Advances in biomedical and computer technologies have presented the modeling community the opportunity for mechanistically modeling and simulating the variability in a disease phenotype or in a drug response. The capability to quantify response variability can inform a drug development program. Quantitative systems pharmacology scientists have published various computational approaches for creating virtual patient populations (VPops) to model and simulate drug response variability. Genomic variations can impact disease characteristics and drug exposure and response. Quantitative proteomics technologies are increasingly used to facilitate drug discovery and development and inform patient care. Incorporating variations in genomics and quantitative proteomics may potentially inform creation of VPops to model and simulate virtual patient trials, and may help account for, in a predictive manner, phenotypic variations observed clinically.

Multicomponent mathematical model for tumor volume calculation with setup error using single-isocenter stereotactic radiotherapy for multiple brain metastases

We evaluated the tumor residual volumes considering six degrees-of-freedom (6DoF) patient setup errors in stereotactic radiotherapy (SRT) with multicomponent mathematical model using single-isocenter irradiation for brain metastases. Simulated spherical gross tumor volumes (GTVs) with 1.0 (GTV 1), 2.0 (GTV 2), and 3.0 (GTV 3)-cm diameters were used. The distance between the GTV center and isocenter (d) was set at 0-10 cm. The GTV was simultaneously translated within 0-1.0 mm (T) and rotated within 0°-1.0° (R) in the three axis directions using affine transformation. We optimized the tumor growth model parameters using measurements of non-small cell lung cancer cell lines' (A549 and NCI-H460) growth. We calculated the GTV residual volume at the irradiation's end using the physical dose to the GTV when the GTV size, d, and 6DoF setup error varied. The d-values that satisfy tolerance values (10%, 35%, and 50%) of the GTV residual volume rate based on the pre-irradiation GTV volume were determined. The larger the tolerance value set for both cell lines, the longer the distance to satisfy the tolerance value. In GTV residual volume evaluations based on the multicomponent mathematical model on SRT with single-isocenter irradiation, the smaller the GTV size and the larger the distance and 6DoF setup error, the shorter the distance that satisfies the tolerance value might need to be.

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.

Cell state-directed therapy - epigenetic modulation of gene transcription demonstrated with a quantitative systems pharmacology model of temozolomide

Cancer therapy continues to be plagued by modest therapeutic advances. This is particularly evident in glioblastoma multiforme (GBM) wherein treatment failures are attributed to intratumoral heterogeneity (ITH), a dynamic process of cell state transitions or plasticity. To address ITH, we introduce the concept of cell state-directed (CSD) therapy through a quantitative systems pharmacology model of temozolomide (TMZ), a cornerstone of GBM drug therapy. The model consisting of multiple modules incorporated an epigenetic-based gene transcription-translation module that enabled CSD therapy. Numerous model simulations were conducted to demonstrate the potential impact of CSD therapy on TMZ activity. The simulations included those based on global sensitivity analyses to identify fragile nodes - MDM2 and XIAP - in the network, and also how an epigenetic modifier (birabresib) could overcome a mechanism of TMZ resistance. The positive results of CSD therapy on TMZ activity supports continued efforts to develop CSD therapy as a new anticancer approach.

Current studies and future promises of PD-1 signal inhibitors in cervical cancer therapy

PD-1 (Programmed cell death-1) is a receptor that inhibits the activation of T cells and is an important target for cancer immunotherapy. PD-1 expression stays high on antigen-specific T cells that have been stimulated for a long time, making them less responsive to stimuli. Consequently, there has been a recent surge in the number of researchers focusing on how the PD-1 axis delivers inhibitory signals to uncover new therapeutic targets. As an inhibitory signaling mechanism, the PD-1 axis controls immunological responses. Blocking the PD-1 axis has been shown to have long-lasting effects on various cancers, demonstrating the crucial role of PD-1 in blocking anti-tumor immunity. Despite this role, most patients do not respond to PD-1 monotherapy, and some have experienced adverse events. Many challenges remain regarding the PD-1 signaling axis to be addressed. In this review, we outline the most recent research and prospects of PD-1 signal inhibitors to enhance cervical cancer therapy.

Virtual clinical trials of anti-PD-1 and anti-CTLA-4 immunotherapy in advanced hepatocellular carcinoma using a quantitative systems pharmacology model

BACKGROUND

Hepatocellular carcinoma (HCC) is the most common form of primary liver cancer and is the third-leading cause of cancer-related death worldwide. Most patients with HCC are diagnosed at an advanced stage, and the median survival for patients with advanced HCC treated with modern systemic therapy is less than 2 years. This leaves the advanced stage patients with limited treatment options. Immune checkpoint inhibitors (ICIs) targeting programmed cell death protein 1 (PD-1) or its ligand, are widely used in the treatment of HCC and are associated with durable responses in a subset of patients. ICIs targeting cytotoxic T-lymphocyte-associated protein 4 (CTLA-4) also have clinical activity in HCC. Combination therapy of nivolumab (anti-PD-1) and ipilimumab (anti-CTLA-4) is the first treatment option for HCC to be approved by Food and Drug Administration that targets more than one immune checkpoints.

METHODS

In this study, we used the framework of quantitative systems pharmacology (QSP) to perform a virtual clinical trial for nivolumab and ipilimumab in HCC patients. Our model incorporates detailed biological mechanisms of interactions of immune cells and cancer cells leading to antitumor response. To conduct virtual clinical trial, we generate virtual patient from a cohort of 5,000 proposed patients by extending recent algorithms from literature. The model was calibrated using the data of the clinical trial CheckMate 040 (ClinicalTrials.gov number, NCT01658878).

RESULTS

Retrospective analyses were performed for different immune checkpoint therapies as performed in CheckMate 040. Using machine learning approach, we predict the importance of potential biomarkers for immune blockade therapies.

CONCLUSIONS

This is the first QSP model for HCC with ICIs and the predictions are consistent with clinically observed outcomes. This study demonstrates that using a mechanistic understanding of the underlying pathophysiology, QSP models can facilitate patient selection and design clinical trials with improved success.

Integration of lncRNAs, Protein-Coding Genes and Pathology Images for Detecting Metastatic Melanoma

Melanoma is a lethal skin disease that develops from moles. This study aimed to integrate multimodal data to predict metastatic melanoma, which is highly aggressive and difficult to treat. The proposed EnsembleSKCM method evaluated the prediction performances of long noncoding RNAs (lncRNAs), protein-coding messenger genes (mRNAs) and pathology images (images) for metastatic melanoma. Feature selection was used to screen for metastatic biomarkers in the lncRNA and mRNA datasets. The integrated EnsembleSKCM model was built based on the weighted results of the lncRNA-, mRNA- and image-based models. EnsembleSKCM achieved 0.9444 in the prediction accuracy of metastatic melanoma and outperformed the single-modal prediction models based on the lncRNA, mRNA and image data. The experimental data suggest the importance of integrating the complementary information from the three data modalities. WGCNA was used to analyze the relationship of molecular-level features and image features, and the results show connections between them. Another cohort was used to validate our prediction.

Quantitative systems pharmacology modeling provides insight into inter-mouse variability of Anti-CTLA4 response

Clinical responses of immuno-oncology therapies are highly variable among patients. Similar response variability has been observed in syngeneic mouse models. Understanding of the variability in the mouse models may shed light on patient variability. Using a murine anti-CTLA4 antibody as a case study, we developed a quantitative systems pharmacology model to capture the molecular interactions of the antibody and relevant cellular interactions that lead to tumor cell killing. Nonlinear mixed effect modeling was incorporated to capture the inter-animal variability of tumor growth profiles in response to anti-CTLA4 treatment. The results suggested that intratumoral CD8+ T cell kinetics and tumor proliferation rate were the main drivers of the variability. In addition, simulations indicated that nonresponsive mice to anti-CTLA4 treatment could be converted to responders by increasing the number of intratumoral CD8+ T cells. The model provides a mechanistic starting point for translation of CTLA4 inhibitors from syngeneic mice to the clinic.

Simulations of tumor growth and response to immunotherapy by coupling a spatial agent-based model with a whole-patient quantitative systems pharmacology model

Quantitative systems pharmacology (QSP) models and spatial agent-based models (ABM) are powerful and efficient approaches for the analysis of biological systems and for clinical applications. Although QSP models are becoming essential in discovering predictive biomarkers and developing combination therapies through in silico virtual trials, they are inadequate to capture the spatial heterogeneity and randomness that characterize complex biological systems, and specifically the tumor microenvironment. Here, we extend our recently developed spatial QSP (spQSP) model to analyze tumor growth dynamics and its response to immunotherapy at different spatio-temporal scales. In the model, the tumor spatial dynamics is governed by the ABM, coupled to the QSP model, which includes the following compartments: central (blood system), tumor, tumor-draining lymph node, and peripheral (the rest of the organs and tissues). A dynamic recruitment of T cells and myeloid-derived suppressor cells (MDSC) from the QSP central compartment has been implemented as a function of the spatial distribution of cancer cells. The proposed QSP-ABM coupling methodology enables the spQSP model to perform as a coarse-grained model at the whole-tumor scale and as an agent-based model at the regions of interest (ROIs) scale. Thus, we exploit the spQSP model potential to characterize tumor growth, identify T cell hotspots, and perform qualitative and quantitative descriptions of cell density profiles at the invasive front of the tumor. Additionally, we analyze the effects of immunotherapy at both whole-tumor and ROI scales under different tumor growth and immune response conditions. A digital pathology computational analysis of triple-negative breast cancer specimens is used as a guide for modeling the immuno-architecture of the invasive front.

Quantitative systems pharmacology modeling sheds light into the dose response relationship of a trispecific T cell engager in multiple myeloma

In relapsed and refractory multiple myeloma (RRMM), there are few treatment options once patients progress from the established standard of care. Several bispecific T-cell engagers (TCE) are in clinical development for multiple myeloma (MM), designed to promote T-cell activation and tumor killing by binding a T-cell receptor and a myeloma target. In this study we employ both computational and experimental tools to investigate how a novel trispecific TCE improves activation, proliferation, and cytolytic activity of T-cells against MM cells. In addition to binding CD3 on T-cells and CD38 on tumor cells, the trispecific binds CD28, which serves as both co-stimulation for T-cell activation and an additional tumor target. We have established a robust rule-based quantitative systems pharmacology (QSP) model trained against T-cell activation, cytotoxicity, and cytokine data, and used it to gain insight into the complex dose response of this drug. We predict that CD3-CD28-CD38 killing capacity increases rapidly in low dose levels, and with higher doses, killing plateaus rather than following the bell-shaped curve typical of bispecific TCEs. We further predict that dose–response curves are driven by the ability of tumor cells to form synapses with activated T-cells. When competition between cells limits tumor engagement with active T-cells, response to therapy may be diminished. We finally suggest a metric related to drug efficacy in our analysis—“effective” receptor occupancy, or the proportion of receptors engaged in synapses. Overall, this study predicts that the CD28 arm on the trispecific antibody improves efficacy, and identifies metrics to inform potency of novel TCEs.

Virtual Populations for Quantitative Systems Pharmacology Models

Quantitative systems pharmacology (QSP) places an emphasis on dynamic systems modeling, incorporating considerations from systems biology modeling and pharmacodynamics. The goal of QSP is often to quantitatively predict the effects of clinical therapeutics, their combinations, and their doses on clinical biomarkers and endpoints. In order to achieve this goal, strategies for incorporating clinical data into model calibration are critical. Virtual population (VPop) approaches facilitate model calibration while faced with challenges encountered in QSP model application, including modeling a breadth of clinical therapies, biomarkers, endpoints, utilizing data of varying structure and source, capturing observed clinical variability, and simulating with models that may require more substantial computational time and resources than often found in pharmacometrics applications. VPops are frequently developed in a process that may involve parameterization of isolated pathway models, integration into a larger QSP model, incorporation of clinical data, calibration, and quantitative validation that the model with the accompanying, calibrated VPop is suitable to address the intended question or help with the intended decision. Here, we introduce previous strategies for developing VPops in the context of a variety of therapeutic and safety areas: metabolic disorders, drug-induced liver injury, autoimmune diseases, and cancer. We introduce methodological considerations, prior work for sensitivity analysis and VPop algorithm design, and potential areas for future advancement. Finally, we give a more detailed application example of a VPop calibration algorithm that illustrates recent progress and many of the methodological considerations. In conclusion, although methodologies have varied, VPop strategies have been successfully applied to give valid clinical insights and predictions with the assistance of carefully defined and designed calibration and validation strategies. While a uniform VPop approach for all potential QSP applications may be challenging given the heterogeneity in use considerations, we anticipate continued innovation will help to drive VPop application for more challenging cases of greater scale while developing new rigorous methodologies and metrics.

Data-driven learning how oncogenic gene expression locally alters heterocellular networks

Developing drugs increasingly relies on mechanistic modeling and simulation. Models that capture causal relations among genetic drivers of oncogenesis, functional plasticity, and host immunity complement wet experiments. Unfortunately, formulating such mechanistic cell-level models currently relies on hand curation, which can bias how data is interpreted or the priority of drug targets. In modeling molecular-level networks, rules and algorithms are employed to limit a priori biases in formulating mechanistic models. Here we combine digital cytometry with Bayesian network inference to generate causal models of cell-level networks linking an increase in gene expression associated with oncogenesis with alterations in stromal and immune cell subsets from bulk transcriptomic datasets. We predict how increased Cell Communication Network factor 4, a secreted matricellular protein, alters the tumor microenvironment using data from patients diagnosed with breast cancer and melanoma. Predictions are then tested using two immunocompetent mouse models for melanoma, which provide consistent experimental results.

While mechanistic models play increasing roles in immuno-oncology, hand network curation is current practice. Here the authors use a Bayesian data-driven approach to infer how expression of a secreted oncogene alters the cellular landscape within the tumor.

Predicting efficacy of 5-fluorouracil therapy via a mathematical model with fuzzy uncertain parameters

Background:

Due to imprecise/missing data used for parameterization of ordinary differential equations (ODEs), model parameters are uncertain. Uncertainty of parameters has hindered the application of ODEs that require accurate parameters.

Methods:

We extended an available ODE model of tumor-immune system interactions via fuzzy logic to illustrate the fuzzification procedure of an ODE model. The fuzzy ODE (FODE) model assigns a fuzzy number to the parameters, to capture parametric uncertainty. We used the FODE model to predict tumor and immune cell dynamics and to assess the efficacy of 5-fluorouracil (5-FU) chemotherapy.

Result:

FODE model investigates how parametric uncertainty affects the uncertainty band of cell dynamics in the presence and absence of 5-FU treatment. In silico experiments revealed that the frequent 5-FU injection created a beneficial tumor microenvironment that exerted detrimental effects on tumor cells by enhancing the infiltration of CD8+ T cells, and natural killer cells, and decreasing that of myeloid-derived suppressor cells. The global sensitivity analysis was proved model robustness against random perturbation to parameters.

Conclusion:

ODE models with fuzzy uncertain kinetic parameters cope with insufficient/imprecise experimental data in the field of mathematical oncology and can predict cell dynamics uncertainty band.

How translational modeling in oncology needs to get the mechanism just right

Translational model‐based approaches have played a role in increasing success in the development of novel anticancer treatments. However, despite this, significant translational uncertainty remains from animal models to patients. Optimization of dose and scheduling (regimen) of drugs to maximize the therapeutic utility (maximize efficacy while avoiding limiting toxicities) is still predominately driven by clinical investigations. Here, we argue that utilizing pragmatic mechanism‐based translational modeling of nonclinical data can further inform this optimization. Consequently, a prototype model is demonstrated that addresses the required fundamental mechanisms.

Recent applications of quantitative systems pharmacology and machine learning models across diseases

Quantitative systems pharmacology (QSP) is a quantitative and mechanistic platform describing the phenotypic interaction between drugs, biological networks, and disease conditions to predict optimal therapeutic response. In this meta-analysis study, we review the utility of the QSP platform in drug development and therapeutic strategies based on recent publications (2019-2021). We gathered recent original QSP models and described the diversity of their applications based on therapeutic areas, methodologies, software platforms, and functionalities. The collection and investigation of these publications can assist in providing a repository of recent QSP studies to facilitate the discovery and further reusability of QSP models. Our review shows that the largest number of QSP efforts in recent years is in Immuno-Oncology. We also addressed the benefits of integrative approaches in this field by presenting the applications of Machine Learning methods for drug discovery and QSP models. Based on this meta-analysis, we discuss the advantages and limitations of QSP models and propose fields where the QSP approach constitutes a valuable interface for more investigations to tackle complex diseases and improve drug development.

Combination therapy with T cell engager and PD-L1 blockade enhances the antitumor potency of T cells as predicted by a QSP model

Background

T cells have been recognized as core effectors for cancer immunotherapy. How to restore the anti-tumor ability of suppressed T cells or improve the lethality of cytotoxic T cells has become the main focus in immunotherapy. Bispecific antibodies, especially bispecific T cell engagers (TCEs), have shown their unique ability to enhance the patient’s immune response to tumors by stimulating T cell activation and cytokine production in an MHC-independent manner. Antibodies targeting the checkpoint inhibitory molecules such as programmed cell death protein 1 (PD-1), PD-ligand 1 (PD-L1) and cytotoxic lymphocyte activated antigen 4 are able to restore the cytotoxic effect of immune suppressed T cells and have also shown durable responses in patients with malignancies. However, both types have their own limitations in treating certain cancers. Preclinical and clinical results have emphasized the potential of combining these two antibodies to improve tumor response and patients’ survival. However, the selection and evaluation of combination partners clinically is a costly endeavor. In addition, despite advances made in immunotherapy, there are subsets of patients who are non-responders, and reliable biomarkers for different immunotherapies are urgently needed to improve the ability to prospectively predict patients’ response and improve clinical study design. Therefore, mathematical and computational models are essential to optimize patient benefit, and guide combination approaches with lower cost and in a faster manner.

Method

In this study, we continued to extend the quantitative systems pharmacology (QSP) model we developed for a bispecific TCE to explore efficacy of combination therapy with an anti-PD-L1 monoclonal antibody in patients with colorectal cancer.

Results

Patient-specific response to TCE monotherapy, anti-PD-L1 monotherapy and the combination therapy were predicted using this model according to each patient’s individual characteristics.

Conclusions

Individual biomarkers for TCE monotherapy, anti-PD-L1 monotherapy and their combination have been determined based on the QSP model. Best treatment options for specific patients could be suggested based on their own characteristics to improve clinical trial efficiency. The model can be further used to assess plausible combination strategies for different TCEs and immune checkpoint inhibitors in different types of cancer.

Chimeric Antigen Receptor T Cell Therapies: A Review of Cellular Kinetic-Pharmacodynamic Modeling Approaches

Chimeric antigen receptor T cell (CAR-T cell) therapies have shown significant efficacy in CD19+ leukemias and lymphomas. There remain many challenges and questions for improving next-generation CAR-T cell therapies, and mathematical modeling of CAR-T cells may play a role in supporting further development. In this review, we introduce a mathematical modeling taxonomy for a set of relatively simple cellular kinetic-pharmacodynamic models that describe the in vivo dynamics of CAR-T cell and their interactions with cancer cells. We then discuss potential extensions of this model to include target binding, tumor distribution, cytokine-release syndrome, immunophenotype differentiation, and genotypic heterogeneity.

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.

A Spatial Quantitative Systems Pharmacology Platform spQSP-IO for Simulations of Tumor-Immune Interactions and Effects of Checkpoint Inhibitor Immunotherapy

Quantitative systems pharmacology (QSP) models have become increasingly common in fundamental mechanistic studies and drug discovery in both academic and industrial environments. With imaging techniques widely adopted and other spatial quantification of tumor such as spatial transcriptomics gaining traction, it is crucial that these data reflecting tumor spatial heterogeneity be utilized to inform the QSP models to enhance their predictive power. We developed a hybrid computational model platform, spQSP-IO, to extend QSP models of immuno-oncology with spatially resolved agent-based models (ABM), combining their powers to track whole patient-scale dynamics and recapitulate the emergent spatial heterogeneity in the tumor. Using a model of non-small-cell lung cancer developed based on this platform, we studied the role of the tumor microenvironment and cancer-immune cell interactions in tumor development and applied anti-PD-1 treatment to virtual patients and studied how the spatial distribution of cells changes during tumor growth in response to the immune checkpoint inhibition treatment. Using parameter sensitivity analysis and biomarker analysis, we are able to identify mechanisms and pretreatment measurements correlated with treatment efficacy. By incorporating spatial data that highlight both heterogeneity in tumors and variability among individual patients, spQSP-IO models can extend the QSP framework and further advance virtual clinical trials.

The Role of Mathematical Models in Immuno-Oncology: Challenges and Future Perspectives

Immuno-oncology (IO) focuses on the ability of the immune system to detect and eliminate cancer cells. Since the approval of the first immune checkpoint inhibitor, immunotherapies have become a major player in oncology treatment and, in 2021, represented the highest number of approved drugs in the field. In spite of this, there is still a fraction of patients that do not respond to these therapies and develop resistance mechanisms. In this sense, mathematical models offer an opportunity to identify predictive biomarkers, optimal dosing schedules and rational combinations to maximize clinical response. This work aims to outline the main therapeutic targets in IO and to provide a description of the different mathematical approaches (top-down, middle-out, and bottom-up) integrating the cancer immunity cycle with immunotherapeutic agents in clinical scenarios. Among the different strategies, middle-out models, which combine both theoretical and evidence-based description of tumor growth and immunological cell-type dynamics, represent an optimal framework to evaluate new IO strategies.

The Combination of Cell Cultured Technology and In Silico Model to Inform the Drug Development

Human-derived in vitro models can provide high-throughput efficacy and toxicity data without a species gap in drug development. Challenges are still encountered regarding the full utilisation of massive data in clinical settings. The lack of translated methods hinders the reliable prediction of clinical outcomes. Therefore, in this study, in silico models were proposed to tackle these obstacles from in vitro to in vivo translation, and the current major cell culture methods were introduced, such as human-induced pluripotent stem cells (hiPSCs), 3D cells, organoids, and microphysiological systems (MPS). Furthermore, the role and applications of several in silico models were summarised, including the physiologically based pharmacokinetic model (PBPK), pharmacokinetic/pharmacodynamic model (PK/PD), quantitative systems pharmacology model (QSP), and virtual clinical trials. These credible translation cases will provide templates for subsequent in vitro to in vivo translation. We believe that synergising high-quality in vitro data with existing models can better guide drug development and clinical use.

A mechanistic systems pharmacology modeling platform to investigate the effect of PD-L1 expression heterogeneity and dynamics on the efficacy of PD-1 and PD-L1 blocking antibodies in cancer

Tumors have developed multitude of ways to evade immune response and suppress cytotoxic T cells. Programed cell death protein 1 (PD-1) and programed cell death ligand 1 (PD-L1) are immune checkpoints that when activated, rapidly inactivate the cytolytic activity of T cells. Expression heterogeneity of PD-L1 and the surface receptor dynamics of both PD-1 and PD-L1 may be important parameters in modulating the immune response. PD-L1 is expressed on both tumor and non-tumor immune cells and this differential expression reflects different aspects of anti-tumor immunity. Here, we developed a mechanistic computational model to investigate the role of PD-1 and PD-L1 dynamics in modulating the efficacy of PD-1 and PD-L1 blocking antibodies. Our model incorporates immunological synapse restricted interaction of PD-1 and PD-L1, basal parameters for receptor dynamics, and T cell interaction with tumor and non-tumor immune cells. Simulations predict the existence of a threshold in PD-1 expression above which there is no efficacy for both anti-PD-1 and anti-PD-L1. Model also predicts that anti-tumor response is more sensitive to PD-L1 expression on non-tumor immune cells than tumor cells. New combination strategies are suggested that may enhance efficacy in resistant cases such as combining anti-PD-1 with a low dose of anti-PD-L1 or with inhibitors of PD-L1 recycling and synthesis. Another combination strategy suggested by the model is the combination of anti-PD-1 and anti-PD-L1 with enhancers of PD-L1 degradation rate. Virtual patients are then generated to test specific biomarkers of response. Intriguing predictions that emerge from the virtual patient simulations are that PD-1 blocking antibody results in higher response rate than PD-L1 blockade and that PD-L1 expression density on non-tumor immune cells rather than tumor cells is a predictor of response.

Modeling Radioimmune Response-Current Status and Perspectives

The combination of immune therapy with radiation offers an exciting and promising treatment modality in cancer therapy. It has been hypothesized that radiation induces damage signals within the tumor, making it more detectable for the immune system. In combination with inhibiting immune checkpoints an effective anti-tumor immune response may be established. This inversion from tumor immune evasion raises numerous questions to be solved to support an effective clinical implementation: These include the optimum immune drug and radiation dose time courses, the amount of damage and associated doses required to stimulate an immune response, and the impact of lymphocyte status and dynamics. Biophysical modeling can offer unique insights, providing quantitative information addressing these factors and highlighting mechanisms of action. In this work we review the existing modeling approaches of combined ‘radioimmune’ response, as well as associated fields of study. We propose modeling attempts that appear relevant for an effective and predictive model. We emphasize the importance of the time course of drug and dose delivery in view to the time course of the triggered biological processes. Special attention is also paid to the dose distribution to circulating blood lymphocytes and the effect this has on immune competence.

In silico trials predict that combination strategies for enhancing vesicular stomatitis oncolytic virus are determined by tumor aggressivity

Background

Immunotherapies, driven by immune-mediated antitumorigenicity, offer the potential for significant improvements to the treatment of multiple cancer types. Identifying therapeutic strategies that bolster antitumor immunity while limiting immune suppression is critical to selecting treatment combinations and schedules that offer durable therapeutic benefits. Combination oncolytic virus (OV) therapy, wherein complementary OVs are administered in succession, offer such promise, yet their translation from preclinical studies to clinical implementation is a major challenge. Overcoming this obstacle requires answering fundamental questions about how to effectively design and tailor schedules to provide the most benefit to patients.

Methods

We developed a computational biology model of combined oncolytic vaccinia (an enhancer virus) and vesicular stomatitis virus (VSV) calibrated to and validated against multiple data sources. We then optimized protocols in a cohort of heterogeneous virtual individuals by leveraging this model and our previously established in silico clinical trial platform.

Results

Enhancer multiplicity was shown to have little to no impact on the average response to therapy. However, the duration of the VSV injection lag was found to be determinant for survival outcomes. Importantly, through treatment individualization, we found that optimal combination schedules are closely linked to tumor aggressivity. We predicted that patients with aggressively growing tumors required a single enhancer followed by a VSV injection 1 day later, whereas a small subset of patients with the slowest growing tumors needed multiple enhancers followed by a longer VSV delay of 15 days, suggesting that intrinsic tumor growth rates could inform the segregation of patients into clinical trials and ultimately determine patient survival. These results were validated in entirely new cohorts of virtual individuals with aggressive or non-aggressive subtypes.

Conclusions

Based on our results, improved therapeutic schedules for combinations with enhancer OVs can be studied and implemented. Our results further underline the impact of interdisciplinary approaches to preclinical planning and the importance of computational approaches to drug discovery and development.

Dynamical systems analysis as an additional tool to inform treatment outcomes: The case study of a quantitative systems pharmacology model of immuno-oncology

Quantitative systems pharmacology (QSP) proved to be a powerful tool to elucidate the underlying pathophysiological complexity that is intensified by the biological variability and overlapped by the level of sophistication of drug dosing regimens. Therapies combining immunotherapy with more traditional therapeutic approaches, including chemotherapy and radiation, are increasingly being used. These combinations are purposed to amplify the immune response against the tumor cells and modulate the suppressive tumor microenvironment (TME). In order to get the best performance from these combinatorial approaches and derive rational regimen strategies, a better understanding of the interaction of the tumor with the host immune system is needed. The objective of the current work is to provide new insights into the dynamics of immune-mediated TME and immune-oncology treatment. As a case study, we will use a recent QSP model by Kosinsky et al. [J. Immunother. Cancer 6, 17 (2018)] that aimed to reproduce the dynamics of interaction between tumor and immune system upon administration of radiation therapy and immunotherapy. Adopting a dynamical systems approach, we here investigate the qualitative behavior of the representative components of this QSP model around its key parameters. The ability of T cells to infiltrate tumor tissue, originally identified as responsible for individual therapeutic inter-variability [Y. Kosinsky et al., J. Immunother. Cancer 6, 17 (2018)], is shown here to be a saddle-node bifurcation point for which the dynamical system oscillates between two states: tumor-free or maximum tumor volume. By performing a bifurcation analysis of the physiological system, we identified equilibrium points and assessed their nature. We then used the traditional concept of basin of attraction to assess the performance of therapy. We showed that considering the therapy as input to the dynamical system translates into the changes of the trajectory shapes of the solutions when approaching equilibrium points and thus providing information on the issue of therapy.

A Mathematical Model to Estimate Chemotherapy Concentration at the Tumor-Site and Predict Therapy Response in Colorectal Cancer Patients with Liver Metastases

Simple Summary

It is known that drug transport barriers in the tumor determine drug concentration at the tumor site, causing disparity from the systemic (plasma) drug concentration. However, current clinical standard of care still bases dosage and treatment optimization on the systemic concentration of drugs. Here, we present a proof of concept observational cohort study to accurately estimate drug concentration at the tumor site from mathematical modeling using biologic, clinical, and imaging/perfusion data, and correlate it with outcome in colorectal cancer liver metastases. We demonstrate that drug concentration at the tumor site, not in systemic circulation, can be used as a credible biomarker for predicting chemotherapy outcome, and thus our mathematical modeling approach can be applied prospectively in the clinic to personalize treatment design to optimize outcome.

Abstract

Chemotherapy remains a primary treatment for metastatic cancer, with tumor response being the benchmark outcome marker. However, therapeutic response in cancer is unpredictable due to heterogeneity in drug delivery from systemic circulation to solid tumors. In this proof-of-concept study, we evaluated chemotherapy concentration at the tumor-site and its association with therapy response by applying a mathematical model. By using pre-treatment imaging, clinical and biologic variables, and chemotherapy regimen to inform the model, we estimated tumor-site chemotherapy concentration in patients with colorectal cancer liver metastases, who received treatment prior to surgical hepatic resection with curative-intent. The differential response to therapy in resected specimens, measured with the gold-standard Tumor Regression Grade (TRG; from 1, complete response to 5, no response) was examined, relative to the model predicted systemic and tumor-site chemotherapy concentrations. We found that the average calculated plasma concentration of the cytotoxic drug was essentially equivalent across patients exhibiting different TRGs, while the estimated tumor-site chemotherapeutic concentration (eTSCC) showed a quadratic decline from TRG = 1 to TRG = 5 (p < 0.001). The eTSCC was significantly lower than the observed plasma concentration and dropped by a factor of ~5 between patients with complete response (TRG = 1) and those with no response (TRG = 5), while the plasma concentration remained stable across TRG groups. TRG variations were driven and predicted by differences in tumor perfusion and eTSCC. If confirmed in carefully planned prospective studies, these findings will form the basis of a paradigm shift in the care of patients with potentially curable colorectal cancer and liver metastases.