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Doxorubicin (Dox) IC50 for murine Eμ-myc/Arf-/- and Eμ-myc/p53-/- lymphoma cells used in this study compared to well characterized Daudi and Jurkat cell lines.
Source publication
We combine mathematical modeling with experiments in living mice to quantify the relative roles of intrinsic cellular vs. tissue-scale physiological contributors to chemotherapy drug resistance, which are difficult to understand solely through experimentation. Experiments in cell culture and in mice with drug-sensitive (Eµ-myc/Arf-/-) and drug-resi...
Citations
... Most of the previously-published mathematical models use systemic pharmacokinetics and kinetics of cell-death for evaluating drug delivery efficacy, but few involve both the spatio-temporal drug transport in tissue scale and tumor microenvironment (TME) heterogeneity, implying that most of the literature studies have used PK/PD models, which is just temporal, instead of full spatio-temporal models. These comprehensive studies have considered TME heterogeneity (e.g., interstitial fluid flow, microvascular network, elevated interstitial fluid pressure (IFP), inefficient lymphatic system, to name a few) and also employed spatial-temporal representations of tumor tissue to mathematically model drug transport in the TME [23][24][25][26][27][28][29] . Desirable transport properties of drug are crucial for efficient treatment of solid tumor 30,31 . ...
... Additionally, the characteristics of a drug-diffusivity, associating rate, and systemic clearance rate-determine its capability to penetrate solid tumors 34,35 . Additionally, there have been many computational attempts to examine the effects of different drug parameters on the efficacy of drug delivery 23,32,35,36 , but their impact on successive treatment cycles have not yet been investigated. In this study, the great potential of mathematical modeling and computational oncology is investigated for evaluating long-term response of treatment. ...
The development of an in silico approach that evaluates and identifies appropriate treatment protocols for individuals could help grow personalized treatment and increase cancer patient lifespans. With this motivation, the present study introduces a novel approach for sequential treatment cycles based on simultaneously examining drug delivery, tumor growth, and chemotherapy efficacy. This model incorporates the physical conditions of tumor geometry, including tumor, capillary network, and normal tissue assuming real circumstances, as well as the intravascular and interstitial fluid flow, drug concentration, chemotherapy efficacy, and tumor recurrence. Three treatment approaches—maximum tolerated dose (MTD), metronomic chemotherapy (MC), and chemo-switching (CS)—as well as different chemotherapy schedules are investigated on a real tumor geometry extracted from image. Additionally, a sensitivity analysis of effective parameters of drug is carried out to evaluate the potential of using different other drugs in cancer treatment. The main findings are: (i) CS, MC, and MTD have the best performance in reducing tumor cells, respectively; (ii) multiple doses raise the efficacy of drugs that have slower clearance, higher diffusivity, and lower to medium binding affinities; (iii) the suggested approach to eradicating tumors is to reduce their cells to a predetermined rate through chemotherapy and then apply adjunct therapy.
... Drug concentration at the tumor site can differ significantly from systemic concentrations, and may be a better determinant of therapeutic efficacy. To correctly estimate drug concentration at the tumor site, we have developed and validated a mechanistic mathematical model of diffusion-based drug transport, based on patient-derived data, to account for and describe the role of tumor biophysical attributes in drug efficacy [34][35][36][37]. Our mathematical model allows for the estimation of drug concentration at the tumor-site based on systemic drug pharmacokinetics, patient features, and tumor characteristics quantified through routine clinical parameters and standard imaging. ...
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.
... With this compartmentalized representation of tumor vascular-induced heterogeneity and its consequences on protein shedding, the model can be formulated with constraints based on observable tumor characteristics. In particular, tissue spatial constraints, e.g., as can be observed from histology 21,22 , are used here as model parameters. ...
Identification of protein biomarkers for cancer diagnosis and prognosis remains a critical unmet clinical need. A major reason is that the dynamic relationship between proliferating and necrotic cell populations during vascularized tumor growth, and the associated extra- and intra-cellular protein outflux from these populations into blood circulation remains poorly understood. Complementary to experimental efforts, mathematical approaches have been employed to effectively simulate the kinetics of detectable surface proteins (e.g., CA-125) shed into the bloodstream. However, existing models can be difficult to tune and may be unable to capture the dynamics of non-extracellular proteins, such as those shed from necrotic and apoptosing cells. The models may also fail to account for intra-tumoral spatial and microenvironmental heterogeneity. We present a new multi-compartment model to simulate heterogeneously vascularized growing tumors and the corresponding protein outflux. Model parameters can be tuned from histology data, including relative vascular volume, mean vessel diameter, and distance from vasculature to necrotic tissue. The model enables evaluating the difference in shedding rates between extra- and non-extracellular proteins from viable and necrosing cells as a function of heterogeneous vascularization. Simulation results indicate that under certain conditions it is possible for non-extracellular proteins to have superior outflux relative to extracellular proteins. This work contributes towards the goal of cancer biomarker identification by enabling simulation of protein shedding kinetics based on tumor tissue-specific characteristics. Ultimately, we anticipate that models like the one introduced herein will enable examining origins and circulating dynamics of candidate biomarkers, thus facilitating marker selection for validation studies.
... Over the last two decades, considerable progress has been achieved in basic or translational research involving PDAC. However, the application of mathematical and computational tools to support explorations in PDAC biology, diagnosis, prognosis, and treatment has lagged behind, and this becomes even more evident when compared to the progress made in quantitative investigations of other cancer types ( Fig. 1) [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41]. This gap highlights the need for the development and application of novel quantitative tools to improve the understanding of PDAC progression and support clinical care. ...
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.
... Mathematical modeling has been extensively used in mechanistically explaining the observed data and in deriving new experimentally and/or clinically testable predictions in many cancer research fields [10][11][12][13][14][15][16][17][18][19][20][21][22][23]. In cancer nanomedicine, previous mathematical models have revealed valuable insights into the in vivo dynamics of NPs [24]. ...
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.
... Our group has recently demonstrated the application of PK modeling to disposition kinetics data of mesoporous silica NPs (MSNs) acquired through SPECT/CT imaging in vivo ( Fig. 9) (Dogra et al. 2018). Guided by the data and built on our prior work (Das et al. 2013;Pascal et al. 2013b;Frieboes et al. 2015), we developed simple master equations in closed form to model the kinetics of MSN biodistribution and clearance with the goal of establishing the structure-activity relationships of MSNs. By systematically varying MSN physicochemical variables (including size, surface charge, and surface coatings) in the therapeutically relevant size range of~25-150 nm, we examined the effect of size, zeta potential, and surface chemistry on in vivo disposition of hydrodynamically stable, monodisperse, nontargeted MSNs administered via intravenous (i.v.) or intraperitoneal (i.p.) injection. ...
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.
... Over the years, our group has proposed that the characteristics of the tumor vasculature might be a biologic predictor of response to chemotherapy. This mechanistic hypothesis has been examined in a series of modeling studies to evaluate the prediction of treatment outcomes based on chemotherapy drug diffusion and the physical properties of several tumor types (13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28)(29). We and other investigators have proposed that diffusion barriers may prevent drugs from reaching malignant tumor cells, a functional mechanism that might partially underlie drug resistance (30). ...
... The semi-automated histology analysis described here can potentially be used for other solid tumors, although thresholding based on vascular staining and tumor types may need to be optimized for each. The general applicability of the mechanistic fkill model to predict response in several other cancer types has been examined and confirmed, including CRC with metastasis to liver, glioblastoma, pancreatic cancer, and lymphoma (13,16,18,21). The observed consistency across tumor types is attributed to the fact that the fkill model was derived from fundamental principles of mass transport common to many solid tumor types (13), and evaluates vasculature characteristics in the tumor prior to treatment, thereby determining the efficiency of the vascular network to deliver drugs to the tumor. ...
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.
... Data-driven modeling approaches that integrate statistical analysis of large-scale cancer multi-omics (e.g., genomics, proteomics, and other omics technologies) with clinical data have been used to identify key biological processes underlying cancer pathogenesis, prognostic biomarkers, and predictive signatures for drug response (Jerby and Ruppin, 2012;Casado et al., 2013;Niepel et al., 2013). On the other hand, mechanistic modeling approaches have been used to understand the roles of individual proteins in regulating cell fate and how signaling pathways interact to influence cancer progression (Prasasya et al., 2011;Hass et al., 2017), the dynamic interactions among cancer cells and between cells and the constantly changing microenvironment (Faratian et al., 2009;Klinger et al., 2013;Almendro et al., 2014;Leder et al., 2014), biophysical drug-cell interactions, and drug transport processes across tissues ( Das et al., 2013;Pascal et al., 2013a,b;Koay et al., 2014;Frieboes et al., 2015;Wang et al., 2016;Brocato et al., 2018). In addition, mechanistic models are being generated to account for pharmacokinetics and pharmacodynamics to analyze drug action, dose-response relationships, and the time-course effect resulting from a drug dose, ultimately leading to the discovery of more effective dosing schedules (Swat et al., 2011;Vandamme et al., 2014;Wang et al., 2015a;Dogra et al., 2018). ...
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.
... On a patient-specific basis, the tumor model can be calibrated to fit morphological and phenotypical parameters of actual tumors after obtaining this information through imaging and histological analysis 17,[57][58][59][60][61][62] . Incorporation of further biological data, such as tumor vessel density, the amount of blood perfusion, integrity of endothelial cell layer, extracellular matrix protein, interstitial pressure, infiltrated immune cells, rate of tumor cell proliferation, resistant/anti-apoptotic mechanisms in tumor cells and their heterogeneities inside the tumor, would be expected to refine the prediction of drug delivery and therapeutic potency. ...
Abstract Nanotherapy may constitute a promising approach to target tumors with anticancer drugs while minimizing systemic toxicity. Computational modeling can enable rapid evaluation of nanoparticle (NP) designs and numerical optimization. Here, an optimization study was performed using an existing tumor model to find NP size and ligand density that maximize tumoral NP accumulation while minimizing tumor size. Optimal NP avidity lies at lower bound of feasible values, suggesting reduced ligand density to prolong NP circulation. For the given set of tumor parameters, optimal NP diameters were 288 nm to maximize NP accumulation and 334 nm to minimize tumor diameter, leading to uniform NP distribution and adequate drug load. Results further show higher dependence of NP biodistribution on the NP design than on tumor morphological parameters. A parametric study with respect to drug potency was performed. The lower the potency of the drug, the bigger the difference is between the maximizer of NP accumulation and the minimizer of tumor size, indicating the existence of a specific drug potency that minimizes the differential between the two optimal solutions. This study shows the feasibility of applying optimization to NP designs to achieve efficacious cancer nanotherapy, and offers a first step towards a quantitative tool to support clinical decision making.
... Semi-mechanistic mathematical modeling and PK analysis. Different from our prior work on modeling free drug [60][61][62][63][64][65][66] and targeted nanocarrier delivery to tumors 67-70 , we here used a parsimonious, semi-mechanistic model to describe the macroscopic concentration-time behavior of MSNs in individual "black box-like" ROIs and estimate relevant PK parameters. As shown in Fig. 1b, an organ i receives an influx of NPs from the major feeding artery. ...
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.
