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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).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.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.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.

Supplementary Figure from 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.

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

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 DiscoveryNanomedicine for Oncologic Disease.

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.

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.

Graphical abstract, 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.

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.

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.

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 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. 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. 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 for TNBC, providing a basis for rational therapeutic combinations for improved response.

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.

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. 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 validated 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. The derived parameters Λ and µ were both significantly different between responding versus non-responding patients. Of note, our model appropriately classified response in 81.4% of patients by using only tumor volume measurements and within two 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, demonstrating reliable methods to inform model parameters directly from biopsy samples, which are conveniently obtainable as early as the start of treatment. Together, these results 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.SIGNIFICANCECheckpoint inhibitors have revolutionized cancer immunotherapy, but only a subset of patients with solid tumors responds clinically. The ability to predict tumor responses a priori or soon after starting therapy would allow for personalized and timely adaptive clinical applications of checkpoint inhibitor- based immunotherapy in patients. By applying a mechanistic mathematical model, we show that checkpoint inhibitor therapeutic effectiveness is accurately predictable in most patients within two months after treatment initiation. Our method may be implemented directly into clinical practice, as it relies on standard-of-care imaging and pathology. If successful in prospective studies, this model will improve selection of cancer patients for checkpoint inhibitor therapy, and perhaps for other forms of humoral- or cell-based immunotherapy.

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.

Siliceous nanomaterials are attractive candidates for applications in cancer theranostics due to their precise synthesis control, ease of surface functionalization, accuracy of characterization, controllable release of cargo, and predictable pharmacokinetics. However, the inorganic silica core inherent to these nanomaterials has colloidal instability and can be cytotoxic, presenting notable challenges for their clinical translation. Surface coatings may be used to overcome this hurdle, by improving their stability, safety, and biological activity and thereby supporting their development for various biomedical applications. Out of the various surface coatings tested to date, lipid-based coatings have shown notable potential due to their biocompatibility and low immunogenicity, where lipids have demonstrated clinical success in the form of liposomal drug delivery systems. In this chapter, we will discuss lipid-coated siliceous nanomaterials, with an emphasis on the principles of lipid coating, the enhanced biocompatibility brought about by the lipid shell, and the use of lipid-coated silica nanoparticles in cancer therapy.

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., Graphical Abstract

A mathematical model of checkpoint inhibitor immunotherapy yields patient-specific prognosis of tumor kill and patient survival., 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.

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 DiseaseDiagnostic Tools > in vivo Nanodiagnostics and ImagingNanotechnology Approaches to Biology > Nanoscale Systems in Biology, Pharmacological evaluation of nanoparticles and antibodies performed through quantitative imaging‐guided mathematical models.

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.

Cancer continues to be among the leading healthcare problems worldwide, and efforts continue not just to find better drugs, but also better drug delivery methods. The need for delivering cytotoxic agents selectively to cancerous cells, for improved safety and efficacy, has triggered the application of nanotechnology in medicine. This effort has provided drug delivery systems that can potentially revolutionize cancer treatment. Nanocarriers, due to their capacity for targeted drug delivery, can shift the balance of cytotoxicity from healthy to cancerous cells. The field of cancer nanomedicine has made significant progress, but challenges remain that impede its clinical translation. Several biophysical barriers to the transport of nanocarriers to the tumor exist, and a much deeper understanding of nano-bio interactions is necessary to change the status quo. Mathematical modeling has been instrumental in improving our understanding of the physicochemical and physiological underpinnings of nanomaterial behavior in biological systems. Here, we present a comprehensive review of literature on mathematical modeling works that have been and are being employed towards a better understanding of nano-bio interactions for improved tumor delivery efficacy.

Corrections to the acknowledgment of grant support for the above named paper are presented here.

Mammary gland ductal elongation is spearheaded by terminal end buds (TEBs), where populations of highly proliferative cells are maintained throughout post-pubertal organogenesis in virgin mice until the mammary fat pad is filled by a mature ductal tree. We have developed a hybrid multiscale agent-based model to study how cellular differentiation pathways, cellular proliferation capacity, and endocrine and paracrine signaling play a role during development of the mammary gland. A simplified cellular phenotypic hierarchy that includes stem, progenitor, and fully differentiated cells within the TEB was implemented. Model analysis finds that mammary gland development was highly sensitive to proliferation events within the TEB, with progenitors likely undergoing 2-3 proliferation cycles before transitioning to a non-proliferative phenotype, and this result is in agreement with our previous experimental work. Endocrine and paracrine signaling were found to provide reliable ductal elongation rate regulation, while variations in the probability a new daughter cell will be of a proliferative phenotype were seen to have minimal effects on ductal elongation rates. Moreover, the distribution of cellular phenotypes within the TEB was highly heterogeneous, demonstrating significant allowable plasticity in possible phenotypic distributions while maintaining biologically relevant growth behavior. Finally, simulation results indicate ductal elongation rates due to cellular proliferation within the TEB may have a greater sensitivity to upstream endocrine signaling than endothelial to stromal paracrine signaling within the TEB. This model provides a useful tool to gain quantitative insights into cellular population dynamics and the effects of endocrine and paracrine signaling within the pubertal terminal end bud.

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.

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.

Rekindled interest has developed in pulsed vacuum systems due to their use for Xenon Difluoride (XeF2) etching systems and their usefulness in the fabrication of MEMS and nanostructures. Despite numerous applications of pulsed vacuum systems, little information is available in the literature on their design considerations. In this paper mathematical models and their experimental verification are presented for various important design considerations of pulsed vacuum systems. Control of the chambers' pressures and pulse durations are typically the most important design considerations for processes involving pulsed vacuum systems. Pressure sensors give the exact pressure, but accurate chamber volumes are unknown. Thus a methodology is developed for accurate determination of chamber volumes that involves the introduction of a calibrated volume into a chamber. Then it is demonstrated that allowing a known pressure and volume of gas to move between two chambers leads to accurate temporal control of the chambers' pressures. Furthermore, by varying chambers' volumes, configurations, pressures, and the conductances between the chambers it is shown that the pulse duration could be accurately controlled. Though the model and demonstrations are presented in the context of a pulsed XeF 2 etching system, they are general and useful for all pulsed vacuum systems.

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.

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.

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. Author Summary Cancer treatment efficacy can be significantly enhanced through the elution of drug from nano-carriers that can temporarily stay in the tumor vasculature. Here we present a relatively simple yet powerful mathematical model that accounts for both spatial and temporal heterogeneities of drug dosing to help explain, examine, and prove this concept. We find that the delivery of systemic chemotherapy through a certain form of nano-carriers would have enhanced tumor kill by a factor of 2 to 4 over the standard therapy that the patients actually received. We also find that targeting blood volume fraction (a parameter of the model) through vascular normalization can achieve more effective drug delivery and tumor kill. More importantly, this model only requires a limited number of parameters which can all be readily assessed from standard clinical diagnostic measurements (e.g., histopathology and CT). This addresses an important challenge in current translational research and justifies further development of the model towards clinical translation.