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.

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

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. 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. 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 regimen to prevent antagonistic effects. Thus, 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.

Mechanistic modeling of anti-microRNA-155 therapy combinations in lung cancer

To improve treatment outcomes in non-small cell lung cancer (NSCLC), it is crucial to identify treatment strategies with the potential to exhibit drug synergism. This can lower the required effective dose, reducing exposure to drugs and associated toxicities, while improving treatment efficacy. In previous studies, drugs targeting the microRNA-155 or PD-L1 have been promising in restraining NSCLC tumor growth. We have developed a mathematical model that simulates the in vivo pharmacokinetics and pharmacodynamics of the novel nanoparticle-delivered anti-microRNA-155 for potential use with standard-of-care drug atezolizumab for NSCLC. Through modeling and simulation, we identified possible drug synergism between the two drugs that holds promise to improve tumor response at reduced drug exposure.Clinical Relevance-Identifying the possibility of drug synergism for an anti-microRNA-155 based nanotherapeutic with standard-of-care immunotherapy to improve lung cancer treatment outcomes.

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.

A Phase 2 Trial of Enhancing Immune Checkpoint Blockade by Stereotactic Radiation and In Situ Virus Gene Therapy in Metastatic Triple-Negative Breast Cancer

PURPOSE

A Phase 2 trial of stereotactic radiotherapy and in situ cytotoxic virus therapy in patients with metastatic triple-negative breast cancer (mTNBC) followed by pembrolizumab (STOMP) was designed to evaluate dual approach of enhancing single-agent immune checkpoint blockade with adenovirus-mediated expression of herpes-simplex-virus thymidine-kinase (ADV/HSV-tk) plus valacyclovir gene therapy and stereotactic body radiotherapy (SBRT) in patients with mTNBC.

PATIENTS AND METHODS

In this single-arm, open-label Phase 2 trial, patients with mTNBC were treated with ADV/HSV-tk [5 × 1011 virus particles (vp)] intratumoral injection, followed by SBRT to the injected tumor site, then pembrolizumab (200 mg, every 3 weeks). The primary endpoint was clinical benefit rate [CBR; complete response (CR), partial response (PR), or stable disease (SD) ≥ 24 weeks per RECIST version1.1 at non-irradiated site]. Secondary endpoints included duration on treatment (DoT), overall survival (OS), and safety. Exploratory endpoints included immune response to treatment assessed by correlative tissue and blood-based biomarkers.

RESULTS

Twenty-eight patients were enrolled and treated. CBR was seen in 6 patients (21.4%), including 2 CR (7.1%), 1 PR (3.6%), and 3 SD (10.7%). Patients with clinical benefit had durable responses, with median DoT of 9.6 months and OS of 14.7 months. The median OS was 6.6 months in the total population. The combination was well tolerated. Correlative studies with Cytometry by Time of Flight (CyTOF) and imaging mass cytometry (IMC) revealed a significant increase of CD8 T cells in responders and of myeloid cells in non-responders.

CONCLUSIONS

The median OS increased by more than 2-fold in patients with clinical benefit. The therapy is a well-tolerated treatment in heavily pretreated patients with mTNBC. Early detection of increased effector and effector memory CD8 T cells and myeloids correlate with response and non-response, respectively.

Mass Transport Model of Radiation Response: Calibration and Application to Chemoradiation for Pancreatic Cancer

PURPOSE

The benefit of radiation therapy for pancreatic ductal adenocarcinoma (PDAC) remains unclear. We hypothesized that a new mechanistic mathematical model of chemotherapy and radiation response could predict clinical outcomes a priori, using a previously described baseline measurement of perfusion from computed tomography scans, normalized area under the enhancement curve (nAUC).

METHODS AND MATERIALS

We simplified an existing mass transport model that predicted cancer cell death by replacing previously unknown variables with averaged direct measurements from randomly selected pathologic sections of untreated PDAC. This allowed using nAUC as the sole model input to approximate tumor perfusion. We then compared the predicted cancer cell death to the actual cell death measured from corresponding resected tumors treated with neoadjuvant chemoradiation in a calibration cohort (n = 80) and prospective cohort (n = 25). After calibration, we applied the model to 2 separate cohorts for pathologic and clinical associations: targeted therapy cohort (n = 101), cetuximab/bevacizumab + radiosensitizing chemotherapy, and standard chemoradiation cohort (n = 81), radiosensitizing chemotherapy to 50.4 Gy in 28 fractions.

RESULTS

We established the relationship between pretreatment computed v nAUC to pathologically verified blood volume fraction of the tumor (r = 0.65; P = .009) and fractional tumor cell death (r = 0.97-0.99; P < .0001) in the calibration and prospective cohorts. On multivariate analyses, accounting for traditional covariates, nAUC independently associated with overall survival in all cohorts (mean hazard ratios, 0.14-0.31). Receiver operator characteristic analyses revealed discrimination of good and bad prognostic groups in the cohorts with area under the curve values of 0.64 to 0.71.

CONCLUSIONS

This work presents a new mathematical modeling approach to predict clinical response from chemotherapy and radiation for PDAC. Our findings indicate that oxygen/drug diffusion strongly influences clinical responses and that nAUC is a potential tool to select patients with PDAC for radiation therapy.

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

Purpose

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

Methods

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

Results

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

Conclusions

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

Supplementary Information

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

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.

A Multiscale Model to Identify Limiting Factors in Nanoparticle-Based miRNA Delivery for Tumor Inhibition. Annu Int Conf IEEE Eng Med Biol Soc 2021;2021:4230-4233. [PMID: 34892157 PMCID: PMC8712117 DOI: 10.1109/embc46164.2021.9630862]

MicroRNA-based gene therapy for cancer treatment via nanoparticles (NPs) requires navigation of multiple physical and physiological barriers in order to efficiently deliver the miRNAs to the cancer cell cytoplasm. We here present a mathematical model to investigate the variability associated with tumor, NP, and miRNA characteristics, and identify the limiting factors in miRNA delivery to tumors. Through global parameter analysis, the miRNA release rate from NPs and NP degradability were found to have the most significant impact on cytosolic accumulation of miRNAs. These NP properties can be fine-tuned in order to optimize the delivery system for enhancing the efficacy of miRNA-based therapy.Clinical Relevance-Understanding the effect of nanoparticle, tumor, and miRNA characteristics in governing the efficacy of miRNA-based cancer therapy will support its clinical translation.

Innate Immunity Plays a Key Role in Controlling Viral Load in COVID-19: Mechanistic Insights from a Whole-Body Infection Dynamics Model

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is a pathogen of immense public health concern. Efforts to control the disease have only proven mildly successful, and the disease will likely continue to cause excessive fatalities until effective preventative measures (such as a vaccine) are developed. To develop disease management strategies, a better understanding of SARS-CoV-2 pathogenesis and population susceptibility to infection are needed. To this end, mathematical modeling can provide a robust in silico tool to understand COVID-19 pathophysiology and the in vivo dynamics of SARS-CoV-2. Guided by ACE2-tropism (ACE2 receptor dependency for infection) of the virus and by incorporating cellular-scale viral dynamics and innate and adaptive immune responses, we have developed a multiscale mechanistic model for simulating the time-dependent evolution of viral load distribution in susceptible organs of the body (respiratory tract, gut, liver, spleen, heart, kidneys, and brain). Following parameter quantification with in vivo and clinical data, we used the model to simulate viral load progression in a virtual patient with varying degrees of compromised immune status. Further, we ranked model parameters through sensitivity analysis for their significance in governing clearance of viral load to understand the effects of physiological factors and underlying conditions on viral load dynamics. Antiviral drug therapy, interferon therapy, and their combination were simulated to study the effects on viral load kinetics of SARS-CoV-2. The model revealed the dominant role of innate immunity (specifically interferons and resident macrophages) in controlling viral load, and the importance of timing when initiating therapy after infection.

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.

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

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

Innate immunity plays a key role in controlling viral load in COVID-19: mechanistic insights from a whole-body infection dynamics model

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is a pathogen of immense public health concern. Efforts to control the disease have only proven mildly successful, and the disease will likely continue to cause excessive fatalities until effective preventative measures (such as a vaccine) are developed. To develop disease management strategies, a better understanding of SARS-CoV-2 pathogenesis and population susceptibility to infection are needed. To this end, physiologically-relevant mathematical modeling can provide a robust in silico tool to understand COVID-19 pathophysiology and the in vivo dynamics of SARS-CoV-2. Guided by ACE2-tropism (ACE2 receptor dependency for infection) of the virus, and by incorporating cellular-scale viral dynamics and innate and adaptive immune responses, we have developed a multiscale mechanistic model for simulating the time-dependent evolution of viral load distribution in susceptible organs of the body (respiratory tract, gut, liver, spleen, heart, kidneys, and brain). Following calibration with in vivo and clinical data, we used the model to simulate viral load progression in a virtual patient with varying degrees of compromised immune status. Further, we conducted global sensitivity analysis of model parameters and ranked them for their significance in governing clearance of viral load to understand the effects of physiological factors and underlying conditions on viral load dynamics. Antiviral drug therapy, interferon therapy, and their combination was simulated to study the effects on viral load kinetics of SARS-CoV-2. The model revealed the dominant role of innate immunity (specifically interferons and resident macrophages) in controlling viral load, and the importance of timing when initiating therapy following infection.

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

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

Mathematical prediction of clinical outcomes in advanced cancer patients treated with checkpoint inhibitor immunotherapy

We present a mechanistic mathematical model of immune checkpoint inhibitor therapy to address the oncological need for early, broadly applicable readouts (biomarkers) of patient response to immunotherapy. The model is built upon the complex biological and physical interactions between the immune system and cancer, and is informed using only standard-of-care CT. We have retrospectively applied the model to 245 patients from multiple clinical trials treated with anti-CTLA-4 or anti-PD-1/PD-L1 antibodies. We found that model parameters distinctly identified patients with common (n = 18) and rare (n = 10) malignancy types who benefited and did not benefit from these monotherapies with accuracy as high as 88% at first restaging (median 53 days). Further, the parameters successfully differentiated pseudo-progression from true progression, providing previously unidentified insights into the unique biophysical characteristics of pseudo-progression. Our mathematical model offers a clinically relevant tool for personalized oncology and for engineering immunotherapy regimens.

A Multiscale Agent-Based Model of Ductal Carcinoma In Situ

OBJECTIVE

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

METHODS

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

RESULTS

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

CONCLUSION

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

SIGNIFICANCE

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

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

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

A mathematical model to predict nanomedicine pharmacokinetics and tumor delivery

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

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

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

Development of a three dimensional, multiscale agent-based model of ductal carcinoma in situ

Ductal carcinoma in situ (DCIS) is the most commonly diagnosed form of non-invasive breast cancer, constituting 20% of all new breast cancer cases in the United States. Although non-invasive, DCIS is usually treated surgically through resection. Interestingly, long-term survival studies have shown that patient survival rates are not significantly impacted by the type or resection, indicating that increased breast conservation through minimized surgical resection may indeed be possible. This requires a greater understanding of disease development, so that clinicians may more accurately determine surgical margins which minimize patient impact while maintaining survival rates. To this end, we have developed a three-dimensional, lattice-free multiscale agent based model of DCIS designed to help quantify ductal invasion rates, in order to allow clinicians to better estimate disease age and extent of invasion, and to predict surgical margins based on parameters obtainable from non-invasive testing (i.e., mammography). Here, we present the model development to date, and discuss some preliminary results.

Development of a three dimensional, lattice-free multiscale model of the mammary terminal end bud

The terminal end bud (TEB) is a bulbous structure composed of highly proliferative cells that is responsible for mammary gland development during the pubertal stage. This is a highly organized process, involving cellular differentiation hierarchies regulated by endocrine and paracrine signaling. Here, we present development of a lattice-free, three dimensional multiscale agent based model of the TEB to study the effects of cellular phenotypic hierarchies, endocrine and paracrine signaling, and proliferation demographics on pubertal mammary gland development. Cells in the TEB experience complex physical interaction during the active growth involved in pubertal ductal elongation, which we represent mathematically based on the physical forces involved in cell-cell and cell-microenvironment interactions. We observe that maximum ductal elongation rates are achievable due to each progenitive phenotype cell only undergoing a couple proliferation cycles before losing the progenitive capability, and that molecular signaling is necessary to restrict ductal elongation to biologically relevant rates. Cellular proliferation and growth is sufficient to achieve these elongation rates in the absence of other cellular behaviors such as migration or conformational changes. This model serves as a valuable tool to gain insights into the cell population dynamics of mammary gland development, and can serve as a foundation to study the early stages of breast cancer development based on endocrine-mediated phenotypic population shifts.

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

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

A modeling approach to study the normal mammary gland growth process

Terminal end buds (TEBs) are bulb-like structures at the growing tips of elongating mammary ducts, and the growth of a TEB is a complex, organized biological process. In this paper, we present a hybrid continuum-discrete agent-based model to provide quantitative insight into the properties of cell symmetric and asymmetric division on the spatial and developing cell rearrangement within the TEB during ductal elongation. An interplay of endocrine-paracrine signaling and cell lineage has been implemented in the model. Our results show that higher symmetric division rates resulted in more progenitor cells remaining in the TEB, while lower rates resulted in more differentiated cells in the TEB. Moreover, pure proliferation alone was enough to result in ductal elongation in the absence of any cellular migration, a result consistent with current experimental data. This model can also serve as a platform to study how mutation-induced phenotypic changes contribute to developmental defects in mammary gland development.

Integrated PK-PD and agent-based modeling in oncology

Mathematical modeling has become a valuable tool that strives to complement conventional biomedical research modalities in order to predict experimental outcome, generate new medical hypotheses, and optimize clinical therapies. Two specific approaches, pharmacokinetic-pharmacodynamic (PK-PD) modeling, and agent-based modeling (ABM), have been widely applied in cancer research. While they have made important contributions on their own (e.g., PK-PD in examining chemotherapy drug efficacy and resistance, and ABM in describing and predicting tumor growth and metastasis), only a few groups have started to combine both approaches together in an effort to gain more insights into the details of drug dynamics and the resulting impact on tumor growth. In this review, we focus our discussion on some of the most recent modeling studies building on a combined PK-PD and ABM approach that have generated experimentally testable hypotheses. Some future directions are also discussed.

Simulating cancer growth with multiscale agent-based modeling

There have been many techniques developed in recent years to in silico model a variety of cancer behaviors. Agent-based modeling is a specific discrete-based hybrid modeling approach that allows simulating the role of diversity in cell populations as well as within each individual cell; it has therefore become a powerful modeling method widely used by computational cancer researchers. Many aspects of tumor morphology including phenotype-changing mutations, the adaptation to microenvironment, the process of angiogenesis, the influence of extracellular matrix, reactions to chemotherapy or surgical intervention, the effects of oxygen and nutrient availability, and metastasis and invasion of healthy tissues have been incorporated and investigated in agent-based models. In this review, we introduce some of the most recent agent-based models that have provided insight into the understanding of cancer growth and invasion, spanning multiple biological scales in time and space, and we further describe several experimentally testable hypotheses generated by those models. We also discuss some of the current challenges of multiscale agent-based cancer models.

Mechanistic modeling identifies drug-uptake history as predictor of tumor drug resistance and nano-carrier-mediated response

A quantitative understanding of the advantages of nanoparticle-based drug delivery vis-à-vis conventional free drug chemotherapy has yet to be established for cancer or other diseases despite numerous investigations. Here, we employ first-principles cell biophysics, drug pharmaco-kinetics, and drug pharmaco-dynamics to model the delivery of doxorubicin (DOX) to hepatocellular carcinoma (HCC) tumor cells and predict the resultant experimental cytotoxicity data. The fundamental, mechanistic hypothesis of our mathematical model is that the integrated history of drug uptake by the cells over time of exposure, which sets the cell death rate parameter, and the uptake rate are the sole determinants of the dose response relationship. A universal solution of the model equations is capable of predicting the entire, nonlinear dose response of the cells to any drug concentration based on just two separate measurements of these cellular parameters. This analysis reveals that nanocarrier-mediated delivery overcomes resistance to the free drug because of improved cellular uptake rates, and that dose response curves to nanocarrier mediated drug delivery are equivalent to those for free-drug, but "shifted to the left;" that is, lower amounts of drug achieve the same cell kill. We then demonstrate the model's general applicability to different tumor and drug types, and cell-exposure time courses by investigating HCC cells exposed to cisplatin and 5-fluorouracil, breast cancer MCF-7 cells exposed to DOX, and pancreatic adenocarcinoma PANC-1 cells exposed to gemcitabine. The model will help in the optimal design of nanocarriers for clinical applications and improve the current, largely empirical understanding of in vivo drug transport and tumor response.