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

Gradient-induced instability in tumour spheroids unveils the impact of microenvironmental nutrient changes

Tumours often display invasive behaviours that induce fingering, branching and fragmentation processes. The phenomenon, known as diffusional instability, is driven by differential cell proliferation, migration, and death due to the presence of metabolite and catabolite concentration gradients. An understanding of the intricate dynamics of this spatially heterogeneous process plays a key role in the investigation of tumour growth and invasion. In this study, we developed an in vitro tumour invasion assay to investigate cell invasiveness in tumour spheroids under a chemotactic stimulus. Our method, employing tumour spheroids seeded in a 3D collagen gel within a microfluidic chemotaxis chamber, focuses on the role of diffusive gradients. Using Time-Lapse Microscopy, the dynamic evolution of tumour spheroids was monitored in real-time, providing a comprehensive view of the morphological changes and cell migration patterns under different chemotactic conditions. Specifically, we explored the impact of fetal bovine serum (FBS) gradients on the behaviour of CT26 mouse colon carcinoma cells and compared the effects of varying FBS concentrations to two isotropic control conditions. Furthermore, a finite element in silico model was developed to quantify the diffusive flow of nutrients in the chemotaxis chamber and obtain a detailed understanding of tumour dynamics. Our findings reveal that the presence of a chemotactic gradient significantly influences tumour invasiveness, with higher concentrations of nutrients associated with increased cancer growth and cell migration.

Hybridizing mechanistic modeling and deep learning for personalized survival prediction after immune checkpoint inhibitor immunotherapy

We present a study where predictive mechanistic modeling is combined with deep learning methods to predict individual patient survival probabilities under immune checkpoint inhibitor (ICI) immunotherapy. This hybrid approach enables prediction based on both measures that are calculable from mechanistic models of key mechanisms underlying ICI therapy that may not be directly measurable in the clinic and easily measurable quantities or patient characteristics that are not always readily incorporated into predictive mechanistic models. A deep learning time-to-event predictive model trained on a hybrid mechanistic + clinical data set from 93 patients achieved higher per-patient predictive accuracy based on event-time concordance, Brier score, and negative binomial log-likelihood-based criteria than when trained on only mechanistic model-derived values or only clinical data. Feature importance analysis revealed that both clinical and model-derived parameters play prominent roles in increasing prediction accuracy, further supporting the advantage of our hybrid approach.

Translational modeling-based evidence for enhanced efficacy of standard-of-care drugs in combination with anti-microRNA-155 in non-small-cell lung cancer

BACKGROUND

Elevated microRNA-155 (miR-155) expression in non-small-cell lung cancer (NSCLC) promotes cisplatin resistance and negatively impacts treatment outcomes. However, miR-155 can also boost anti-tumor immunity by suppressing PD-L1 expression. Therapeutic targeting of miR-155 through its antagonist, anti-miR-155, has proven challenging due to its dual molecular effects.

METHODS

We developed a multiscale mechanistic model, calibrated with in vivo data and then extrapolated to humans, to investigate the therapeutic effects of nanoparticle-delivered anti-miR-155 in NSCLC, alone or in combination with standard-of-care drugs.

RESULTS

Model simulations and analyses of the clinical scenario revealed that monotherapy with anti-miR-155 at a dose of 2.5 mg/kg administered once every three weeks has substantial anti-cancer activity. It led to a median progression-free survival (PFS) of 6.7 months, which compared favorably to cisplatin and immune checkpoint inhibitors. Further, we explored the combinations of anti-miR-155 with standard-of-care drugs, and found strongly synergistic two- and three-drug combinations. A three-drug combination of anti-miR-155, cisplatin, and pembrolizumab resulted in a median PFS of 13.1 months, while a two-drug combination of anti-miR-155 and cisplatin resulted in a median PFS of 11.3 months, which emerged as a more practical option due to its simple design and cost-effectiveness. Our analyses also provided valuable insights into unfavorable dose ratios for drug combinations, highlighting the need for optimizing dose regimens to prevent antagonistic effects.

CONCLUSIONS

This work bridges the gap between preclinical development and clinical translation of anti-miR-155 and unravels the potential of anti-miR-155 combination therapies in NSCLC.

Mathematical modeling of brain metastases growth and response to therapies: A review

Brain metastases (BMs) are the most common intracranial tumor type and a significant health concern, affecting approximately 10% to 30% of all oncological patients. Although significant progress is being made, many aspects of the metastatic process to the brain and the growth of the resulting lesions are still not well understood. There is a need for an improved understanding of the growth dynamics and the response to treatment of these tumors. Mathematical models have been proven valuable for drawing inferences and making predictions in different fields of cancer research, but few mathematical works have considered BMs. This comprehensive review aims to establish a unified platform and contribute to fostering emerging efforts dedicated to enhancing our mathematical understanding of this intricate and challenging disease. We focus on the progress made in the initial stages of mathematical modeling research regarding BMs and the significant insights gained from such studies. We also explore the vital role of mathematical modeling in predicting treatment outcomes and enhancing the quality of clinical decision-making for patients facing BMs.

Clinical Validation of Mathematically Derived Early Tumor Dynamics for Solid Tumors in Response to Durvalumab

PURPOSE

Early prediction of response to immunotherapy may help guide patient management by identifying resistance to treatment and allowing adaptation of therapies. This analysis evaluated a mathematical model of response to immunotherapy that provides patient-specific prediction of outcome using the initial change in tumor size/burden from baseline to the first follow-up visit on standard imaging scans.

METHODS

We applied the model to 600 patients with advanced solid tumors who received durvalumab in Study 1108, a phase I/II trial, and compared outcome prediction performance versus size-based criteria with RECIST version 1.1 best overall response (BOR), baseline circulating tumor (ct)DNA level, and other clinical/pathologic predictors of immunotherapy response.

RESULTS

In multiple solid tumors, the mathematical parameter representing net tumor growth rate at the first on-treatment computed tomography (CT) scan assessed around 6 weeks after starting durvalumab (α1) had a concordance index to predict overall survival (OS) of 0.66-0.77 on multivariate analyses. This measurement of early tumor dynamics significantly improved multivariate OS models that included standard RECIST v1.1 criteria, baseline ctDNA levels, and other clinical/pathologic factors in predicting OS. Furthermore, α1 was assessed consistently at the first on-treatment CT scan, whereas all traditional RECIST BOR groups were confirmed only after this time.

CONCLUSION

These results support further exploring α1 as an integral biomarker of response to immunotherapy. This biomarker may be predictive of further benefit and can be assessed before RECIST response groups can be assigned, potentially providing an opportunity to personalize oncologic management.

Hybridizing mechanistic mathematical modeling with deep learning methods to predict individual cancer patient survival after immune checkpoint inhibitor therapy

We present a study where predictive mechanistic modeling is used in combination with deep learning methods to predict individual patient survival probabilities under immune checkpoint inhibitor (ICI) therapy. This hybrid approach enables prediction based on both measures that are calculable from mechanistic models (but may not be directly measurable in the clinic) and easily measurable quantities or characteristics (that are not always readily incorporated into predictive mechanistic models). The mechanistic model we have applied here can predict tumor response from CT or MRI imaging based on key mechanisms underlying checkpoint inhibitor therapy, and in the present work, its parameters were combined with readily-available clinical measures from 93 patients into a hybrid training set for a deep learning time-to-event predictive model. Analysis revealed that training an artificial neural network with both mechanistic modeling-derived and clinical measures achieved higher per-patient predictive accuracy based on event-time concordance, Brier score, and negative binomial log-likelihood-based criteria than when only mechanistic model-derived values or only clinical data were used. Feature importance analysis revealed that both clinical and model-derived parameters play prominent roles in neural network decision making, and in increasing prediction accuracy, further supporting the advantage of our hybrid approach. We anticipate that many existing mechanistic models may be hybridized with deep learning methods in a similar manner to improve predictive accuracy through addition of additional data that may not be readily implemented in mechanistic descriptions.

Dose optimization of an adjuvanted peptide-based personalized neoantigen melanoma vaccine

The advancements in next-generation sequencing have made it possible to effectively detect somatic mutations, which has led to the development of personalized neoantigen cancer vaccines that are tailored to the unique variants found in a patient's cancer. These vaccines can provide significant clinical benefit by leveraging the patient's immune response to eliminate malignant cells. However, determining the optimal vaccine dose for each patient is a challenge due to the heterogeneity of tumors. To address this challenge, we formulate a mathematical dose optimization problem based on a previous mathematical model that encompasses the immune response cascade produced by the vaccine in a patient. We propose an optimization approach to identify the optimal personalized vaccine doses, considering a fixed vaccination schedule, while simultaneously minimizing the overall number of tumor and activated T cells. To validate our approach, we perform in silico experiments on six real-world clinical trial patients with advanced melanoma. We compare the results of applying an optimal vaccine dose to those of a suboptimal dose (the dose used in the clinical trial and its deviations). Our simulations reveal that an optimal vaccine regimen of higher initial doses and lower final doses may lead to a reduction in tumor size for certain patients. Our mathematical dose optimization offers a promising approach to determining an optimal vaccine dose for each patient and improving clinical outcomes.

Current status and future prospective of breast cancer immunotherapy

The immune system is complicated, interconnected, and offers a powerful defense system that protects its host from foreign pathogens. Immunotherapy involves boosting the immune system to kill cancer cells, and nowadays, is a major emerging treatment for cancer. With the advances in our understanding of the immunology of cancer, there has been an explosion of studies to develop and evaluate therapies that engage the immune system in the fight against cancer. Nevertheless, conventional therapies have been effective in reducing tumor burden and prolonging patient life, but the overall efficacy of these treatment regimens has been somewhat mixed and often with severe side effects. A common reason for this is the activation of molecular mechanisms that lead to apoptosis of anti-tumor effector cells. The competency to block tumor escape entirely depends on our understanding of the cellular and molecular pathways which operate in the tumor microenvironment. Numerous strategies have been developed for activating the immune system to kill tumor cells. Breast cancer is one of the major causes of cancer death in women, and is characterized by complex molecular and cellular events that closely intertwine with the host immune system. In this regard, predictive biomarkers of immunotherapy, use of nanotechnology, personalized cancer vaccines, antibodies to checkpoint inhibitors, engineered chimeric antigen receptor-T cells, and the combination with other therapeutic modalities have transformed cancer therapy and optimized the therapeutic effect. In this chapter, we will offer a holistic view of the different therapeutic modalities and recent advances in immunotherapy. Additionally, we will summarize the recent advances and future prospective of breast cancer immunotherapies, as a case study.

Global stability and parameter analysis reinforce therapeutic targets of PD-L1-PD-1 and MDSCs for glioblastoma

Glioblastoma (GBM) is an aggressive primary brain cancer that currently has minimally effective treatments. Like other cancers, immunosuppression by the PD-L1-PD-1 immune checkpoint complex is a prominent axis by which glioma cells evade the immune system. Myeloid-derived suppressor cells (MDSCs), which are recruited to the glioma microenviroment, also contribute to the immunosuppressed GBM microenvironment by suppressing T cell functions. In this paper, we propose a GBM-specific tumor-immune ordinary differential equations model of glioma cells, T cells, and MDSCs to provide theoretical insights into the interactions between these cells. Equilibrium and stability analysis indicates that there are unique tumorous and tumor-free equilibria which are locally stable under certain conditions. Further, the tumor-free equilibrium is globally stable when T cell activation and the tumor kill rate by T cells overcome tumor growth, T cell inhibition by PD-L1-PD-1 and MDSCs, and the T cell death rate. Bifurcation analysis suggests that a treatment plan that includes surgical resection and therapeutics targeting immune suppression caused by the PD-L1-PD1 complex and MDSCs results in the system tending to the tumor-free equilibrium. Using a set of preclinical experimental data, we implement the approximate Bayesian computation (ABC) rejection method to construct probability density distributions that estimate model parameters. These distributions inform an appropriate search curve for global sensitivity analysis using the extended fourier amplitude sensitivity test. Sensitivity results combined with the ABC method suggest that parameter interaction is occurring between the drivers of tumor burden, which are the tumor growth rate and carrying capacity as well as the tumor kill rate by T cells, and the two modeled forms of immunosuppression, PD-L1-PD-1 immune checkpoint and MDSC suppression of T cells. Thus, treatment with an immune checkpoint inhibitor in combination with a therapeutic targeting the inhibitory mechanisms of MDSCs should be explored.

On fast simulation of dynamical system with neural vector enhanced numerical solver

The large-scale simulation of dynamical systems is critical in numerous scientific and engineering disciplines. However, traditional numerical solvers are limited by the choice of step sizes when estimating integration, resulting in a trade-off between accuracy and computational efficiency. To address this challenge, we introduce a deep learning-based corrector called Neural Vector (NeurVec), which can compensate for integration errors and enable larger time step sizes in simulations. Our extensive experiments on a variety of complex dynamical system benchmarks demonstrate that NeurVec exhibits remarkable generalization capability on a continuous phase space, even when trained using limited and discrete data. NeurVec significantly accelerates traditional solvers, achieving speeds tens to hundreds of times faster while maintaining high levels of accuracy and stability. Moreover, NeurVec's simple-yet-effective design, combined with its ease of implementation, has the potential to establish a new paradigm for fast-solving differential equations based on deep learning.

Global stability and parameter analysis reinforce therapeutic targets of PD-L1-PD-1 and MDSCs for glioblastoma

Glioblastoma (GBM) is an aggressive primary brain cancer that currently has minimally effective treatments. Like other cancers, immunosuppression by the PD-L1-PD-1 immune checkpoint complex is a prominent axis by which glioma cells evade the immune system. Myeloid-derived suppressor cells (MDSCs), which are recruited to the glioma microenviroment, also contribute to the immunosuppressed GBM microenvironment by suppressing T cell functions. In this paper, we propose a GBM-specific tumor-immune ordinary differential equations model of glioma cells, T cells, and MDSCs to provide theoretical insights into the interactions between these cells. Equilibrium and stability analysis indicates that there are unique tumorous and tumor-free equilibria which are locally stable under certain conditions. Further, the tumor-free equilibrium is globally stable when T cell activation and the tumor kill rate by T cells overcome tumor growth, T cell inhibition by PD-L1-PD-1 and MDSCs, and the T cell death rate. Bifurcation analysis suggests that a treatment plan that includes surgical resection and therapeutics targeting immune suppression caused by the PD-L1-PD1 complex and MDSCs results in the system tending to the tumor-free equilibrium. Using a set of preclinical experimental data, we implement the Approximate Bayesian Computation (ABC) rejection method to construct probability density distributions that estimate model parameters. These distributions inform an appropriate search curve for global sensitivity analysis using the extended Fourier Amplitude Sensitivity Test (eFAST). Sensitivity results combined with the ABC method suggest that parameter interaction is occurring between the drivers of tumor burden, which are the tumor growth rate and carrying capacity as well as the tumor kill rate by T cells, and the two modeled forms of immunosuppression, PD-L1-PD-1 immune checkpoint and MDSC suppression of T cells. Thus, treatment with an immune checkpoint inhibitor in combination with a therapeutic targeting the inhibitory mechanisms of MDSCs should be explored.

Harnessing progress in radiotherapy for global cancer control

The pace of technological innovation over the past three decades has transformed the field of radiotherapy into one of the most technologically intense disciplines in medicine. However, the global barriers to access this highly effective treatment are complex and extend beyond technological limitations. Here, we review the technological advancement and current status of radiotherapy and discuss the efforts of the global radiation oncology community to formulate a more integrative 'diagonal approach' in which the agendas of science-driven advances in individual outcomes and the sociotechnological task of global cancer control can be aligned to bring the benefit of this proven therapy to patients with cancer everywhere.

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.

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.

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.

Protocol for mathematical prediction of patient response and survival to immune checkpoint inhibitor immunotherapy

This protocol describes the application of a mechanistic mathematical model of immune checkpoint inhibitor (ICI) immunotherapy to patient tumor imaging data for predicting solid tumor response and patient survival under ICI intervention. We describe steps for data collection and processing, data pipelines, and approaches to increase precision. The protocol is highly predictive as early as the first restaging after treatment start and can be used with standard-of-care imaging measures. For complete details on the use and execution of this protocol, please refer to Butner et al. (2020)¹ and Butner et al. (2021).².

Distinct Dynamics of Migratory Response to PD-1 and CTLA-4 Blockade Reveals New Mechanistic Insights for Potential T-Cell Reinvigoration following Immune Checkpoint Blockade

Cytotoxic T-lymphocyte-associated antigen 4 (CTLA-4) and programmed cell death protein 1 (PD-1), two clinically relevant targets for the immunotherapy of cancer, are negative regulators of T-cell activation and migration. Optimizing the therapeutic response to CTLA-4 and PD-1 blockade calls for a more comprehensive insight into the coordinated function of these immune regulators. Mathematical modeling can be used to elucidate nonlinear tumor-immune interactions and highlight the underlying mechanisms to tackle the problem. Here, we investigated and statistically characterized the dynamics of T-cell migration as a measure of the functional response to these pathways. We used a previously developed three-dimensional organotypic culture of patient-derived tumor spheroids treated with anti-CTLA-4 and anti-PD-1 antibodies for this purpose. Experiment-based dynamical modeling revealed the delayed kinetics of PD-1 activation, which originates from the distinct characteristics of PD-1 and CTLA-4 regulation, and followed through with the modification of their contributions to immune modulation. The simulation results show good agreement with the tumor cell reduction and active immune cell count in each experiment. Our findings demonstrate that while PD-1 activation provokes a more exhaustive intracellular cascade within a mature tumor environment, the time-delayed kinetics of PD-1 activation outweighs its preeminence at the individual cell level and consequently confers a functional dominance to the CTLA-4 checkpoint. The proposed model explains the distinct immunostimulatory pattern of PD-1 and CTLA-4 blockade based on mechanisms involved in the regulation of their expression and may be useful for planning effective treatment schemes targeting PD-1 and CTLA-4 functions.

Opportunities for improving brain cancer treatment outcomes through imaging-based mathematical modeling of the delivery of radiotherapy and immunotherapy

Immunotherapy has become a fourth pillar in the treatment of brain tumors and, when combined with radiation therapy, may improve patient outcomes and reduce the neurotoxicity. As with other combination therapies, the identification of a treatment schedule that maximizes the synergistic effect of radiation- and immune-therapy is a fundamental challenge. Mechanism-based mathematical modeling is one promising approach to systematically investigate therapeutic combinations to maximize positive outcomes within a rigorous framework. However, successful clinical translation of model-generated combinations of treatment requires patient-specific data to allow the models to be meaningfully initialized and parameterized. Quantitative imaging techniques have emerged as a promising source of high quality, spatially and temporally resolved data for the development and validation of mathematical models. In this review, we will present approaches to personalize mechanism-based modeling frameworks with patient data, and then discuss how these techniques could be leveraged to improve brain cancer outcomes through patient-specific modeling and optimization of treatment strategies.

Dedifferentiation-mediated stem cell niche maintenance in early-stage ductal carcinoma in situ progression: insights from a multiscale modeling study

We present a multiscale agent-based model of ductal carcinoma in situ (DCIS) to study how key phenotypic and signaling pathways are involved in the early stages of disease progression. The model includes a phenotypic hierarchy, and key endocrine and paracrine signaling pathways, and simulates cancer ductal growth in a 3D lattice-free domain. In particular, by considering stochastic cell dedifferentiation plasticity, the model allows for study of how dedifferentiation to a more stem-like phenotype plays key roles in the maintenance of cancer stem cell populations and disease progression. Through extensive parameter perturbation studies, we have quantified and ranked how DCIS is sensitive to perturbations in several key mechanisms that are instrumental to early disease development. Our studies reveal that long-term maintenance of multipotent stem-like cell niches within the tumor are dependent on cell dedifferentiation plasticity, and that disease progression will become arrested due to dilution of the multipotent stem-like population in the absence of dedifferentiation. We have identified dedifferentiation rates necessary to maintain biologically relevant multipotent cell populations, and also explored quantitative relationships between dedifferentiation rates and disease progression rates, which may potentially help to optimize the efficacy of emerging anti-cancer stem cell therapeutics.

Mathematical Modeling to Simulate the Effect of Adding Radiation Therapy to Immunotherapy and Application to Hepatocellular Carcinoma

PURPOSE

To develop a comprehensive framework to simulate the response to immune checkpoint inhibitors (ICIs) in combination with radiation therapy (RT) and to apply the framework for investigating ICI-RT combination regimen in patients with hepatocellular carcinoma (HCC).

METHODS AND MATERIALS

The mechanistic mathematical model is based on dynamic biological interactions between the immune system and the tumor using input data from patient blood samples and outcomes of clinical trials. The cell compartments are described by ordinary differential equations and represent irradiated and nonirradiated tumor cells and lymphocytes. The effect of ICI is modeled using an immune activation term that is based on tumor size changes observed in a phase 1/2 clinical trial for HCC. Simulated combination regimen are based on ongoing ICI-RT trials.

RESULTS

The proposed framework successfully describes tumor volume trajectories observed in early-stage clinical trials of durvalumab monotherapy in patients with HCC. For ICI-RT treatment regimen the irradiated tumor fraction is the most important parameter for the efficacy. For 90% of the tumor cells being irradiated, adding RT to ICI yields an increase in clinical benefit from 33% to 71% in nonirradiated tumor sites. The model agrees with clinical data showing an association of outcome with initial tumor volume and lymphocyte counts. We demonstrate model application in clinical trial design to predict progression-free survival curves, showing that the cohort size to show significant improvement heavily depends on the irradiated tumor fraction.

CONCLUSIONS

We present a framework extending radiation cell kill models to include circulating lymphocytes and the effect of ICIs and enable simulation of combination strategies. The simulations predict that a significant amount of the benefit from RT in combination with ICI stems from the reduction in irradiated tumor burden and associated immune suppression. This aspect needs to be included in the interpretation of outcomes and the design of novel combination trials.

Early prediction of clinical response to checkpoint inhibitor therapy in human solid tumors through mathematical modeling

Background:

Checkpoint inhibitor therapy of cancer has led to markedly improved survival of a subset of patients in multiple solid malignant tumor types, yet the factors driving these clinical responses or lack thereof are not known. We have developed a mechanistic mathematical model for better understanding these factors and their relations in order to predict treatment outcome and optimize personal treatment strategies.

Methods:

Here, we present a translational mathematical model dependent on three key parameters for describing efficacy of checkpoint inhibitors in human cancer: tumor growth rate (α), tumor-immune infiltration (Λ), and immunotherapy-mediated amplification of anti-tumor response (µ). The model was calibrated by fitting it to a compiled clinical tumor response dataset (n = 189 patients) obtained from published anti-PD-1 and anti-PD-L1 clinical trials, and then validated on an additional validation cohort (n = 64 patients) obtained from our in-house clinical trials.

Results:

The derived parameters Λ and µ were both significantly different between responding versus nonresponding patients. Of note, our model appropriately classified response in 81.4% of patients by using only tumor volume measurements and within 2 months of treatment initiation in a retrospective analysis. The model reliably predicted clinical response to the PD-1/PD-L1 class of checkpoint inhibitors across multiple solid malignant tumor types. Comparison of model parameters to immunohistochemical measurement of PD-L1 and CD8+ T cells confirmed robust relationships between model parameters and their underlying biology.

Conclusions:

These results have demonstrated reliable methods to inform model parameters directly from biopsy samples, which are conveniently obtainable as early as the start of treatment. Together, these suggest that the model parameters may serve as early and robust biomarkers of the efficacy of checkpoint inhibitor therapy on an individualized per-patient basis.

Funding:

We gratefully acknowledge support from the Andrew Sabin Family Fellowship, Center for Radiation Oncology Research, Sheikh Ahmed Center for Pancreatic Cancer Research, GE Healthcare, Philips Healthcare, and institutional funds from the University of Texas M.D. Anderson Cancer Center. We have also received Cancer Center Support Grants from the National Cancer Institute (P30CA016672 to the University of Texas M.D. Anderson Cancer Center and P30CA072720 the Rutgers Cancer Institute of New Jersey). This research has also been supported in part by grants from the National Science Foundation Grant DMS-1930583 (ZW, VC), the National Institutes of Health (NIH) 1R01CA253865 (ZW, VC), 1U01CA196403 (ZW, VC), 1U01CA213759 (ZW, VC), 1R01CA226537 (ZW, RP, WA, VC), 1R01CA222007 (ZW, VC), U54CA210181 (ZW, VC), and the University of Texas System STARS Award (VC). BC acknowledges support through the SER Cymru II Programme, funded by the European Commission through the Horizon 2020 Marie Skłodowska-Curie Actions (MSCA) COFUND scheme and the Welsh European Funding Office (WEFO) under the European Regional Development Fund (ERDF). EK has also received support from the Project Purple, NIH (U54CA210181, U01CA200468, and U01CA196403), and the Pancreatic Cancer Action Network (16-65-SING). MF was supported through NIH/NCI center grant U54CA210181, R01CA222959, DoD Breast Cancer Research Breakthrough Level IV Award W81XWH-17-1-0389, and the Ernest Cockrell Jr. Presidential Distinguished Chair at Houston Methodist Research Institute. RP and WA received serial research awards from AngelWorks, the Gillson-Longenbaugh Foundation, and the Marcus Foundation. This work was also supported in part by grants from the National Cancer Institute to SHC (R01CA109322, R01CA127483, R01CA208703, and U54CA210181 CITO pilot grant) and to PYP (R01CA140243, R01CA188610, and U54CA210181 CITO pilot grant). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

The Role of the Immune Response in Brain Metastases: Novel Imaging Biomarkers for Immunotherapy

Brain metastases are a major clinical problem, and immunotherapy offers a novel treatment paradigm with the potential to synergize with existing focal therapies like surgery and radiosurgery or even replace them in future. The brain is a unique microenvironment structurally and immunologically. The immune response is likely to be crucial to the adaptation of systemic immune modulating agents against this disease. Imaging is frequently employed in the clinical diagnosis and management of brain metastasis, so it is logical that brain imaging techniques are investigated as a source of biomarkers of the immune response in these tumors. Current imaging techniques in clinical use include structural MRI (post-contrast T1W sequences, T2, and FLAIR), physiological sequences (perfusion- and diffusion-weighted imaging), and molecular imaging (MR spectroscopy and PET). These are reviewed for their application to predicting and measuring the response to immunotherapy in brain metastases.

A Mathematical Model of Breast Tumor Progression Based on Immune Infiltration

Breast cancer is the most prominent type of cancer among women. Understanding the microenvironment of breast cancer and the interactions between cells and cytokines will lead to better treatment approaches for patients. In this study, we developed a data-driven mathematical model to investigate the dynamics of key cells and cytokines involved in breast cancer development. We used gene expression profiles of tumors to estimate the relative abundance of each immune cell and group patients based on their immune patterns. Dynamical results show the complex interplay between cells and molecules, and sensitivity analysis emphasizes the direct effects of macrophages and adipocytes on cancer cell growth. In addition, we observed the dual effect of IFN-γ on cancer proliferation, either through direct inhibition of cancer cells or by increasing the cytotoxicity of CD8+ T-cells.

Current Landscape and Future Directions of Biomarkers for Immunotherapy in Hepatocellular Carcinoma

Hepatocellular carcinoma (HCC) is the most common liver cancer and one of the leading causes of cancer-related deaths in the world. Multiple immunotherapeutic approaches have been investigated to date, and immunotherapy has become the new standard of care therapy in HCC. However, the current role of immunotherapy in HCC remains non-curative. Given this context, a high priority for oncology is understanding the biomarkers that predict clinical response to immunotherapy, have the potential to improve patient selection to maximize the clinical benefit, and spare unnecessary toxicity. In this review, we summarize the key predictive and prognostic biomarkers investigated in immunotherapy clinical trials in HCC and the emerging biomarkers to serve as a roadmap for future clinical trials. Biomarkers from tumoral tissues including PDL-1 expression, tissue infiltrating lymphocytes, tumor mutational burden (TMB) and specific immune signatures, and from peripheral blood including neutrophil-to-lymphocytes ratio, platelet-to-lymphocytes ratio, circulating tumor DNA (ctDNA), circulating tumor cells (CTCs), and specific cytokines, along with gut microbiota are among the studied biomarkers to date in the HCC era. More integrative approaches, including mathematical biomarkers to predict immunotherapy outcomes, are yet to be studied in HCC.

Cancer Physical Hallmarks as New Targets for Improved Immunotherapy

A low response rate is the major challenge for existing cancer immunotherapies. Physical cues in the tumor microenvironment (TME) have been recognized as new hallmarks of cancer, which may synergistically contribute to low immunotherapy response. Recent evidence indicates that the physical hallmarks of cancer hold great potential as new targets for improved immunotherapy.

Modelling treatment-response rates

The time course of tumour responses to immunotherapies can be mathematically predicted on the basis of tumour-growth rates, the rates of immune activation and of tumour–immune-cell interactions, and the efficacy of immune-mediated tumour killing.

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.