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

Multiphysics simulation of liposome release from hydrogels for cavity filling following patient-specific breast tumor surgery

Several studies have recommended the use of hydrogels for localized targeted delivery of chemotherapeutic drugs following tumor removal surgery. This approach aims to both fill the cavity and prevent cancer recurrence. The use of Multiphysics-based simulation emerges as a valuable strategy for minimizing experimental work, providing detailed insights into how drug release occurs in the tissue, and enabling the optimization of the design. In this study, we introduced a mathematical model, utilizing experimental data, to investigate the transport of liposomes carrying MZ1 from a thermosensitive hydrogel and their impact on the viability of breast cancer cells. The proposed comprehensive model considers not just the transport within the interstitial tissue, represented as a porous medium, but also the uptake by cells and its influence on cell viability, along with the potential lymphatic drainage. The six real patient-specific tumor shapes extracted from MRI scans were used to investigate how the size and form of the tumor can modify the transport pattern. The computational results revealed that the concentration of liposomes in the tissue is significantly influenced by their release from the hydrogel, which proved to be the limiting step. Liposome concentrations of approximately 0.1 % weight were found to be sufficient in ensuring minimal cell survival in the vicinity of the tumor.

Insights from a multiscale framework on metabolic rate variation driving glioblastoma multiforme growth and invasion

Non-physiological levels of oxygen and nutrients within the tumors result in heterogeneous cell populations that exhibit distinct necrotic, hypoxic, and proliferative zones. Among these zonal cellular properties, metabolic rates strongly affect the overall growth and invasion of tumors. Here, we report on a hybrid discrete-continuum (HDC) mathematical framework that uses metabolic data from a biomimetic two-dimensional (2D) in-vitro cancer model to predict three-dimensional (3D) behaviour of in-vitro human glioblastoma (hGB). The mathematical model integrates modules of continuum, discrete, and neurons. Results indicated that the HDC model is capable of quantitatively predicting growth, invasion length, and the asymmetric finger-type invasion pattern in in-vitro hGB tumors. Additionally, the model could predict the reduction in invasion length of hGB tumoroids in response to temozolomide (TMZ). This model has the potential to incorporate additional modules, including immune cells and signaling pathways governing cancer/immune cell interactions, and can be used to investigate targeted therapies.

Applications of Machine Learning (ML) and Mathematical Modeling (MM) in Healthcare with Special Focus on Cancer Prognosis and Anticancer Therapy: Current Status and Challenges

The use of data-driven high-throughput analytical techniques, which has given rise to computational oncology, is undisputed. The widespread use of machine learning (ML) and mathematical modeling (MM)-based techniques is widely acknowledged. These two approaches have fueled the advancement in cancer research and eventually led to the uptake of telemedicine in cancer care. For diagnostic, prognostic, and treatment purposes concerning different types of cancer research, vast databases of varied information with manifold dimensions are required, and indeed, all this information can only be managed by an automated system developed utilizing ML and MM. In addition, MM is being used to probe the relationship between the pharmacokinetics and pharmacodynamics (PK/PD interactions) of anti-cancer substances to improve cancer treatment, and also to refine the quality of existing treatment models by being incorporated at all steps of research and development related to cancer and in routine patient care. This review will serve as a consolidation of the advancement and benefits of ML and MM techniques with a special focus on the area of cancer prognosis and anticancer therapy, leading to the identification of challenges (data quantity, ethical consideration, and data privacy) which are yet to be fully addressed in current studies.

Analytical Models of Intra- and Extratumoral Cell Interactions at Avascular Stage of Growth in the Presence of Targeted Chemotherapy

In this study, we propose a set of nonlinear differential equations to model the dynamic growth of avascular stage tumors, considering nutrient supply from underlying tissue, innate immune response, contact inhibition of cell migration, and interactions with a chemotherapeutic agent. The model has been validated against available experimental data from the literature for tumor growth. We assume that the size of the modeled tumor is already detectable, and it represents all clinically observed existent cell populations; initial conditions are selected accordingly. Numerical results indicate that the tumor size and regression significantly depend on the strength of the host immune system. The effect of chemotherapy is investigated, not only within the malignancy, but also in terms of the responding immune cells and healthy tissue in the vicinity of a tumor.

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.

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. ANNUAL INTERNATIONAL CONFERENCE OF THE IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. ANNUAL INTERNATIONAL CONFERENCE 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.

Targeting a cell surface vitamin D receptor on tumor-associated macrophages in triple-negative breast cancer

Triple-negative breast cancer (TNBC) is an aggressive tumor with limited treatment options and poor prognosis. We applied the in vivo phage display technology to isolate peptides homing to the immunosuppressive cellular microenvironment of TNBC as a strategy for non-malignant target discovery. We identified a cyclic peptide (CSSTRESAC) that specifically binds to a vitamin D receptor, protein disulfide-isomerase A3 (PDIA3) expressed on the cell surface of tumor-associated macrophages (TAM), and targets breast cancer in syngeneic TNBC, non-TNBC xenograft, and transgenic mouse models. Systemic administration of CSSTRESAC to TNBC-bearing mice shifted the cytokine profile toward an antitumor immune response and delayed tumor growth. Moreover, CSSTRESAC enabled ligand-directed theranostic delivery to tumors and a mathematical model confirmed our experimental findings. Finally, in silico analysis showed PDIA3-expressing TAM in TNBC patients. This work uncovers a functional interplay between a cell surface vitamin D receptor in TAM and antitumor immune response that could be therapeutically exploited.

Conversion of RNA Aptamer into Modified DNA Aptamers Provides for Prolonged Stability and Enhanced Antitumor Activity

Aptamers, synthetic single-strand oligonucleotides that are similar in function to antibodies, are promising as therapeutics because of their minimal side effects. However, the stability and bioavailability of the aptamers pose a challenge. We developed aptamers converted from RNA aptamer to modified DNA aptamers that target phospho-AXL with improved stability and bioavailability. On the basis of the comparative analysis of a library of 17 converted modified DNA aptamers, we selected aptamer candidates, GLB-G25 and GLB-A04, that exhibited the highest bioavailability, stability, and robust antitumor effect in in vitro experiments. Backbone modifications such as thiophosphate or dithiophosphate and a covalent modification of the 5'-end of the aptamer with polyethylene glycol optimized the pharmacokinetic properties, improved the stability of the aptamers in vivo by reducing nuclease hydrolysis and renal clearance, and achieved high and sustained inhibition of AXL at a very low dose. Treatment with these modified aptamers in ovarian cancer orthotopic mouse models significantly reduced tumor growth and the number of metastases. This effective silencing of the phospho-AXL target thus demonstrated that aptamer specificity and bioavailability can be improved by the chemical modification of existing aptamers for phospho-AXL. These results lay the foundation for the translation of these aptamer candidates and companion biomarkers to the clinic.

Targeted Phage Display-based Pulmonary Vaccination in Mice and Non-human Primates

BACKGROUND

The extensive alveolar capillary network of the lungs is an attractive route for administration of several agents. One key functional attribute is the rapid onset of systemic action due to the absence of first-pass metabolism.

METHODS

Here we applied a combinatorial approach for ligand-directed pulmonary delivery as a unique route for systemic targeting in vaccination.

FINDINGS

We screened a phage display random peptide library in vivo to select, identify, and validate a ligand (CAKSMGDIVC) that specifically targets and is internalized through its receptor, α3β1 integrin, on the surface of cells lining the lung airways and alveoli and mediates CAKSMGDIVC-displaying phage binding and systemic delivery without compromising lung homeostasis. As a proof-of-concept, we show that the pulmonary delivery of targeted CAKSMGDIVC-displaying phage particles in mice and non-human primates elicit a systemic and specific humoral response.

CONCLUSIONS

This broad methodology blueprint represents a robust and versatile platform tool enabling new ligand-receptor discovery with many potential translational applications.

FUNDING

Cancer Center Support Grants to the University of Texas M.D. Anderson Cancer Center (CA016672), University of New Mexico Comprehensive Cancer Center (CA118100), Rutgers Cancer Institute of New Jersey (CA072720), research awards from the Gillson Longenbaugh Foundation, and National Institutes of Health (NIH) grant no. 1R01CA226537.

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.

ncRNA therapy with miRNA-22-3p suppresses the growth of triple-negative breast cancer

Deregulation of noncoding RNAs, including microRNAs (miRs), is implicated in the pathogenesis of many human cancers, including breast cancer. Through extensive analysis of The Cancer Genome Atlas, we found that expression of miR-22-3p is markedly lower in triple-negative breast cancer (TNBC) than in normal breast tissue. The restoration of miR-22-3p expression led to significant inhibition of TNBC cell proliferation, colony formation, migration, and invasion. We demonstrated that miR-22-3p reduces eukaryotic elongation factor 2 kinase (eEF2K) expression by directly binding to the 3' untranslated region of eEF2K mRNA. Inhibition of EF2K expression recapitulated the effects of miR-22-3p on TNBC cell proliferation, motility, invasion, and suppression of phosphatidylinositol 3-kinase/Akt and Src signaling. Systemic administration of miR-22-3p in single-lipid nanoparticles significantly suppressed tumor growth in orthotopic MDA-MB-231 and MDA-MB-436 TNBC models. Evaluation of the tumor response, following miR-22-3p therapy in these models using a novel mathematical model factoring in various in vivo parameters, demonstrated that the therapy is highly effective against TNBC. These findings suggest that miR-22-3p functions as a tumor suppressor by targeting clinically significant oncogenic pathways and that miR-22-3p loss contributes to TNBC growth and progression. The restoration of miR-22-3p expression is a potential novel noncoding RNA-based therapy for TNBC.

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.

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.

Therapeutic potential of FLANC, a novel primate-specific long non-coding RNA in colorectal cancer

OBJECTIVE

To investigate the function of a novel primate-specific long non-coding RNA (lncRNA), named FLANC, based on its genomic location (co-localised with a pyknon motif), and to characterise its potential as a biomarker and therapeutic target.

DESIGN

FLANC expression was analysed in 349 tumours from four cohorts and correlated to clinical data. In a series of multiple in vitro and in vivo models and molecular analyses, we characterised the fundamental biological roles of this lncRNA. We further explored the therapeutic potential of targeting FLANC in a mouse model of colorectal cancer (CRC) metastases.

RESULTS

FLANC, a primate-specific lncRNA feebly expressed in normal colon cells, was significantly upregulated in cancer cells compared with normal colon samples in two independent cohorts. High levels of FLANC were associated with poor survival in two additional independent CRC patient cohorts. Both in vitro and in vivo experiments demonstrated that the modulation of FLANC expression influenced cellular growth, apoptosis, migration, angiogenesis and metastases formation ability of CRC cells. In vivo pharmacological targeting of FLANC by administration of 1,2-dioleoyl-sn-glycero-3-phosphatidylcholine nanoparticles loaded with a specific small interfering RNA, induced significant decrease in metastases, without evident tissue toxicity or pro-inflammatory effects. Mechanistically, FLANC upregulated and prolonged the half-life of phosphorylated STAT3, inducing the overexpression of VEGFA, a key regulator of angiogenesis.

CONCLUSIONS

Based on our findings, we discovered, FLANC as a novel primate-specific lncRNA that is highly upregulated in CRC cells and regulates metastases formation. Targeting primate-specific transcripts such as FLANC may represent a novel and low toxic therapeutic strategy for the treatment of patients.

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

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

Sequential deconstruction of composite drug transport in metastatic breast cancer

It is challenging to design effective drug delivery systems (DDS) that target metastatic breast cancers (MBC) because of lack of competent imaging and image analysis protocols that suitably capture the interactions between DDS and metastatic lesions. Here, we integrate high temporal resolution of in vivo whole-body PET-CT, ex vivo whole-organ optical imaging, high spatial resolution of confocal microscopy, and mathematical modeling, to systematically deconstruct the trafficking of injectable nanoparticle generators encapsulated with polymeric doxorubicin (iNPG-pDox) in pulmonary MBC. iNPG-pDox accumulated substantially in metastatic lungs, compared to healthy lungs. Intratumoral distribution and retention of iNPG-pDox varied with lesion size, possibly induced by locally remodeled microenvironment. We further used multiscale imaging and mathematical simulations to provide improved drug delivery strategies for MBC. Our work presents a multidisciplinary translational toolbox to evaluate transport and interactions of DDS within metastases. This knowledge can be recursively applied to rationally design advanced therapies for metastatic cancers.

A modeling platform for the lymphatic system

We present a physiologically-based pharmacokinetic modeling platform capable of simulating the biodistribution of different therapeutic agents, including cells, their interactions within the immune system, redistribution across lymphoid compartments, and infiltration into tumor tissues. This transport-based platform comprises a distinctive implementation of a tumor compartment with spatial heterogeneity which enables the modeling of tumors of different size, necrotic state, and agent infiltration capacity. We provide three validating and three exploratory examples that illustrate the capabilities of the proposed approach. The results show that the model can recapitulate immune cell balance across different compartments, respond to antigen stimulation, simulate immune vaccine effects, and immune cell infiltration to tumors. Based on the results, the model can be used to study problems pertinent to current immunotherapies and has the potential to assist medical techniques that rely on the transport of biological species.

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.

Modeling the Spatiotemporal Dynamics of Oncolytic Viruses and Radiotherapy as a Treatment for Cancer

Virotherapy is a novel treatment for cancer, which may be delivered as a single agent or in combination with other therapies. Research studies indicated that the combination of viral therapy and radiation therapy has synergistic antitumor effects in in vitro and in vivo. In this paper, we proposed two models in the form of partial differential equations to investigate the spatiotemporal dynamics of tumor cells under virotherapy and radiovirotherapy. We first presented a virotherapy model and solved it numerically for different values of the parameters related to the oncolytic virus, which is administered continuously. The results showed that virotherapy alone cannot eradicate cancer, and thus, we extended the model to include the effect of radiotherapy in combination with virotherapy. Numerical investigations were carried out for three modes of radiation delivery which are constant, decaying, and periodic. The numerical results showed that radiovirotherapy leads to complete eradication of the tumor provided that the delivery of radiation is constant. Moreover, there is an optimal timing for administering radiation, as well as an ideal dose that improves the results of the treatment. The virotherapy in our model is given continuously over a certain period of time, and bolus treatment (where virotherapy is given in cycles) could be considered and compared with our results.

A mathematical model to predict nanomedicine pharmacokinetics and tumor delivery

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

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

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

Mathematical Modeling to Address Challenges in Pancreatic Cancer

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

Tumor core biopsies adequately represent immune microenvironment of high-grade serous carcinoma

The prognostic and therapeutic value of the tumor microenvironment (TME) in various cancer types is of major interest. Characterization of the TME often relies on a small representative tissue sample. However, the adequacy of such a sample for assessing components of the TME is not yet known. Here, we used immunohistochemical (IHC) staining and 7-color multiplex staining to evaluate CD8 (cluster of differentiation 8), CD68, PD-L1 (programmed death-ligand 1), CD34, FAP (fibroblast activation protein), and cytokeratin in 220 tissue cores from 26 high-grade serous ovarian cancer samples. Comparisons were drawn between a larger tumor specimen and smaller core biopsies based on number and location (central tumor vs. peripheral tumor) of biopsies. Our analysis found that the correlation between marker-specific cell subsets in larger tumor versus smaller core was stronger with two core biopsies and was not further strengthened with additional biopsies. Moreover, this correlation was consistently strong regardless of whether the biopsy was taken at the center or at the periphery of the original tumor sample. These findings could have a substantial impact on longitudinal assessment for detection of biomarkers in clinical trials.

Size-Optimized Ultrasmall Porous Silica Nanoparticles Depict Vasculature-Based Differential Targeting in Triple Negative Breast Cancer

Rapid sequestration and prolonged retention of intravenously injected nanoparticles by the liver and spleen (reticuloendothelial system (RES)) presents a major barrier to effective delivery to the target site and hampers clinical translation of nanomedicine. Inspired by biological macromolecular drugs, synthesis of ultrasmall (diameter ≈12-15 nm) porous silica nanoparticles (UPSNs), capable of prolonged plasma half-life, attenuated RES sequestration, and accelerated hepatobiliary clearance, is reported. The study further investigates the effect of tumor vascularization on uptake and retention of UPSNs in two mouse models of triple negative breast cancer with distinctly different microenvironments. A semimechanistic mathematical model is developed to gain mechanistic insights into the interactions between the UPSNs and the biological entities of interest, specifically the RES. Despite similar systemic pharmacokinetic profiles, UPSNs demonstrate strikingly different tumor responses in the two models. Histopathology confirms the differences in vasculature and stromal status of the two models, and corresponding differences in the microscopic distribution of UPSNs within the tumors. The studies demonstrate the successful application of multidisciplinary and complementary approaches, based on laboratory experimentation and mathematical modeling, to concurrently design optimized nanomaterials, and investigate their complex biological interactions, in order to drive innovation and translation.

Mathematical modeling in cancer nanomedicine: a review

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.

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

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

Dynamic Targeting in Cancer Treatment

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

Understanding Ductal Carcinoma In Situ Invasion using a Multiscale Agent-Based Model

Ductal carcinoma in situ (DCIS) is commonly treated clinically through surgical resection. Although surgical options exist for resection, it is unclear which is optimal to reduce the likelihood of future invasive disease. This is further complicated by challenges in determining correct surgical margins from disease diagnostics, with mammographic imaging misidentifying surgical margins by as much as 2 cm vs. histological examination. We have implemented a threedimensional, hybrid multiscale model of DCIS to study disease initiation and progression. In order to shed new light on current biological questions and clinical challenges surrounding the disease, we present here an improved version of this model, with more biologically relevant molecular signaling pathways, cell phenotype hierarchies, and duct architecture variation. In particular, a cell necrosis, lysis and calcification pathway has been incorporated into the model to help better understand the relationship between diagnostic imaging and the true extent of disease invasion. We observe that deficiencies in availability of molecular signaling molecules that upregulate cell proliferation may be overcome by dynamic shifts in phenotypic distributions within the disease mass. Hypoxia, necrosis, and calcification together functioned as a hypoxia relief mechanism, and were observed to maintain a consistent distance between the DCIS leading edge and the site of necrosis onset, providing insights for improving surgical margins.

Establishing the effects of mesoporous silica nanoparticle properties on in vivo disposition using imaging-based pharmacokinetics

The progress of nanoparticle (NP)-based drug delivery has been hindered by an inability to establish structure-activity relationships in vivo. Here, using stable, monosized, radiolabeled, mesoporous silica nanoparticles (MSNs), we apply an integrated SPECT/CT imaging and mathematical modeling approach to understand the combined effects of MSN size, surface chemistry and routes of administration on biodistribution and clearance kinetics in healthy rats. We show that increased particle size from ~32- to ~142-nm results in a monotonic decrease in systemic bioavailability, irrespective of route of administration, with corresponding accumulation in liver and spleen. Cationic MSNs with surface exposed amines (PEI) have reduced circulation, compared to MSNs of identical size and charge but with shielded amines (QA), due to rapid sequestration into liver and spleen. However, QA show greater total excretion than PEI and their size-matched neutral counterparts (TMS). Overall, we provide important predictive functional correlations to support the rational design of nanomedicines.

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.

Understanding the Connection between Nanoparticle Uptake and Cancer Treatment Efficacy using Mathematical Modeling

Nanoparticles have shown great promise in improving cancer treatment efficacy while reducing toxicity and treatment side effects. Predicting the treatment outcome for nanoparticle systems by measuring nanoparticle biodistribution has been challenging due to the commonly unmatched, heterogeneous distribution of nanoparticles relative to free drug distribution. We here present a proof-of-concept study that uses mathematical modeling together with experimentation to address this challenge. Individual mice with 4T1 breast cancer were treated with either nanoparticle-delivered or free doxorubicin, with results demonstrating improved cancer kill efficacy of doxorubicin loaded nanoparticles in comparison to free doxorubicin. We then developed a mathematical theory to render model predictions from measured nanoparticle biodistribution, as determined using graphite furnace atomic absorption. Model analysis finds that treatment efficacy increased exponentially with increased nanoparticle accumulation within the tumor, emphasizing the significance of developing new ways to optimize the delivery efficiency of nanoparticles to the tumor microenvironment.

Targeting Ligand Specificity Linked to Tumor Tissue Topological Heterogeneity via Single-Cell Micro-Pharmacological Modeling

Targeted therapy has held promise to be a successful anticancer treatment due to its specificity towards tumor cells that express the target receptors. However, not all targeting drugs used in the clinic are equally effective in tumor eradication. To examine which biochemical and biophysical properties of targeted agents are pivotal for their effective distribution inside the tumor and their efficient cellular uptake, we combine mathematical micro-pharmacological modeling with in vivo imaging of targeted human xenograft tumors in SCID mice. The mathematical model calibrated to experimental data was used to explore properties of the targeting ligand (diffusion and affinity) and ligand release schemes (rates and concentrations) with a goal to identify the properties of cells and ligands that enable high receptor saturation. By accounting for heterogeneities typical of in vivo tumors, our model was able to identify cell- and tissue-level barriers to efficient drug uptake. This work provides a base for utilizing experimentally measurable properties of a ligand-targeted agent and patient-specific attributes of the tumor tissue to support the development of novel targeted imaging agents and for improvement in their delivery to individual tumor cells.

The influence of soluble fragments of extracellular matrix (ECM) on tumor growth and morphology

A major challenge in matrix-metalloproteinase (MMP) target validation and MMP-inhibitor-drug development for anti-cancer clinical trials is to better understand their complex roles (often competing with each other) in tumor progression. While there is extensive research on the growth-promoting effects of MMPs, the growth-inhibiting effects of MMPs has not been investigated thoroughly. So we develop a continuum model of tumor growth and invasion including chemotaxis and haptotaxis in order to examine the complex interaction between the tumor and its host microenvironment and to explore the inhibiting influence of the gradients of soluble fragments of extracellular matrix (ECM) density on tumor growth and morphology. Previously, it was shown both computationally (in one spatial dimension) and experimentally that the chemotactic pull due to soluble ECM gradients is anti-invasive, contrary to the traditional view of the role of chemotaxis in malignant invasion [1]. With two-dimensional numerical simulation and using a level set based tumor-host interface capturing method, we examine the effects of chemotaxis on the progression and morphology of a tumor growing in nutrient-rich and nutrient-poor microenvironments which was not investigated before. In particular we examine how the geometry of the growing tumor is affected when placed in different environments. We also investigate the effects of varying ECM degradation rate, the production rate of matrix degrading enzymes (MDE), and the conversion of ECM into soluble ECM. We find that chemotaxis due to ECM-fragment gradients strongly influences tumor growth and morphology, and that the instabilities caused by tumor cell proliferation and haptotactic movements can be prevented if chemotaxis is sufficiently strong. The influence of chemotaxis and the above factors on tumor growth and morphology are found to be more prominent in nutrient-poor environments than in nutrient-rich environments. So we extend our investigations of these antinvasive chemotactic influences by examining the effects of cell-cell and cell-ECM adhesion and low proliferation rate for tumors growing in low-nutrient environments. We find that as the extent of chemotaxis increases, the effects of adhesion on tumor growth and shape become negligible. Under conditions of low cell mitosis, chemotaxis may cause the tumor to shrink, as the extent of chemotaxis increases. Both stable and unstable tumor shrinkage are predicted by our model. Unexpectedly, in some cases chemotaxis may contribute toward developing instability where haptotaxis alone induces stable growth.

Mechanistic Model for Cancer Growth and Response to Chemotherapy

Cancer treatment has developed over the years; however not all patients respond to this treatment, and therefore further research is needed. In this paper, we employ mathematical modeling to understand the behavior of cancer and its interaction with therapy. We study a drug delivery and drug-cell interaction model along with cell proliferation. Due to the fact that cancer cells grow when there are enough nutrients and oxygen, proliferation can be a barrier against a response to therapy. To understand the effect of this factor, we perform numerical simulations of the model for different values of the parameters with a continuous delivery of the drug. The numerical results showed that cancer dies after short apoptotic cycles if the cancer is highly vascularized or if the penetration of the drug is high. This suggests promoting angiogenesis or perfusion of the drug. This result is similar to the situation where proliferation is not considered since the constant release of drug overcomes the growth of the cells and thus the effect of proliferation can be neglected.