A mathematical model of drug transport in human breast cancer

Quantitative imaging of doxorubicin diffusion and cellular uptake in biomimetic gels with human liver tumor cells

Novel tumor-on-a-chip approaches are increasingly used to investigate tumor progression and potential treatment options. To improve the effect of any cancer treatment it is important to have an in depth understanding of drug diffusion, penetration through the tumor extracellular matrix and cellular uptake. In this study, we have developed a miniaturized chip where drug diffusion and cellular uptake in different hydrogel environments can be quantified at high resolution using live imaging. Diffusion of doxorubicin was reduced in a biomimetic hydrogel mimicking tissue properties of cirrhotic liver and early stage hepatocellular carcinoma (373 ± 108 µm2/s) as compared to an agarose gel (501 ± 77 µm2/s, p = 0.019). The diffusion was further lowered to 256 ± 30 µm2/s (p = 0.028) by preparing the biomimetic gel in cell media instead of phosphate buffered saline. The addition of liver tumor cells (Huh7 or HepG2) to the gel, at two different densities, did not significantly influence drug diffusion. Clinically relevant and quantifiable doxorubicin concentration gradients (1-20 µM) were established in the chip within one hour. Intracellular increases in doxorubicin fluorescence correlated with decreasing fluorescence of the DNA-binding stain Hoechst 33342 and based on the quantified intracellular uptake of doxorubicin an apparent cell permeability (9.00 ± 0.74 × 10-4 µm/s for HepG2) was determined. Finally, the data derived from the in vitro model were applied to a spatio-temporal tissue concentration model to evaluate the potential clinical impact of a cirrhotic extracellular matrix on doxorubicin diffusion and tumor cell uptake.

A Mathematical Model of Stroma-Supported Allometric Tumor Growth

Mounting empirical research suggests that the stroma, or interface between healthy and cancerous tissue, is a critical determinate of cancer invasion. At the same time, a cancer cell's location and potential to proliferate can influence its sensitivity to cancer treatments. In this paper, we use ordinary differential equations to develop spatially structured models for solid tumors wherein the growth of tumor components is coordinated. The model tumors feature two components, a proliferating peripheral growth region, which potentially includes a mix of cancerous and noncancerous stroma cells, and a solid tumor core. Mathematical and numerical analysis are used to investigate how coordinated expansion of the tumor growth region and core can influence overall growth dynamics in a variety of tumor types. Model assumptions, which are motivated by empirical and in silico solid tumor research, are evaluated through comparison to tumor volume data and existing models of tumor growth.

Predicting drug delivery efficiency into tumor tissues through molecular simulation of transport in complex vascular networks

Efficient delivery of anticancer drugs into tumor tissues at maximally effective and minimally toxic concentrations is vital for therapeutic success. At present, no method exists that can predict the spatial and temporal distribution of drugs into a target tissue after administration of a specific dose. This prevents accurate estimation of optimal dosage regimens for cancer therapy. Here we present a new method that predicts quantitatively the time-dependent spatial distribution of drugs in tumor tissues at sub-micrometer resolution. This is achieved by modeling the diffusive flow of individual drug molecules through the three-dimensional network of blood-vessels that vascularize the tumor, and into surrounding tissues, using molecular mechanics techniques. By evaluating delivery into tumors supplied by a series of blood-vessel networks with varying degrees of complexity, we show that the optimal dose depends critically on the precise vascular structure. Finally, we apply our method to calculate the optimal dosage of the cancer drug doxil into a section of a mouse ovarian tumor, and demonstrate the enhanced delivery of liposomally administered doxorubicin when compared to free doxorubicin. Comparison with experimental data and a multiple-compartment model show that the model accurately recapitulates known pharmacokinetics and drug-load predictions. In addition, it provides, for the first time, a detailed picture of the spatial dependence of drug uptake into tissues surrounding tumor vasculatures. This approach is fundamentally different to current continuum models, and reveals that the target tumor vascular topology is as important for therapeutic success as the transport properties of the drug delivery platform itself. This sets the stage for revisiting drug dosage calculations.

In vivo mimicking model for solid tumor towards hydromechanics of tissue deformation and creation of necrosis

The present work addresses transvascular and interstitial fluid transport inside a solid tumor surrounded by normal tissue (close to an in vivo mimicking setup). In general, biological tissues behave like a soft porous material and show mechanical behavior towards the fluid motion through the interstitial space. In general, forces like viscous drag that are associated with the fluid flow may compress the tissue material. On the macroscopic level, we try to model the motion of fluids and macromolecules through the interstitial space of solid tumor and the normal tissue layer. The transvascular fluid transport is assumed to be governed by modified Starling's law. The poroelastohydrodynamics (interstitial hydrodynamics and the deformation of tissue material) inside the tumor and normal tissue regions is modeled using linearized biphasic mixture theory. Correspondingly, the velocity distribution of fluid is coupled to the displacement field of the solid phase (mainly cellular phase and extracellular matrix) in both the normal and tumor tissue regions. The corresponding velocity field is used within the transport reaction equation for fluids and macromolecules through interstitial space to get the overall solute (e.g., nutrients, drug, and other macromolecules) distribution. This study justifies that the presence of the normal tissue layer plays a significant role in delaying/assisting necrosis inside the tumor tissue. It is observed that the exchange process of fluids and macromolecules across the interface of the tumor and normal tissue affects the effectiveness factor corresponding to the tumor tissue.

Mathematical Based Calculation of Drug Penetration Depth in Solid Tumors

Cancer is a class of diseases characterized by out-of-control cells' growth which affect cells and make them damaged. Many treatment options for cancer exist. Chemotherapy as an important treatment option is the use of drugs to treat cancer. The anticancer drug travels to the tumor and then diffuses in it through capillaries. The diffusion of drugs in the solid tumor is limited by penetration depth which is different in case of different drugs and cancers. The computation of this depth is important as it helps physicians to investigate about treatment of infected tissue. Although many efforts have been made on studying and measuring drug penetration depth, less works have been done on computing this length from a mathematical point of view. In this paper, first we propose phase lagging model for diffusion of drug in the tumor. Then, using this model on one side and considering the classic diffusion on the other side, we compute the drug penetration depth in the solid tumor. This computed value of drug penetration depth is corroborated by comparison with the values measured by experiments.

Hydrodynamics and convection enhanced macromolecular fluid transport in soft biological tissues: Application to solid tumor

This work addresses a theoretical framework for transvascular exchange and extravascular transport of solute macromolecules through soft interstitial space inside a solid tumor. Most of the soft biological tissues show materialistic properties similar to deformable porous material. They exhibit mechanical behavior towards the fluid motion since the solid phase of the tumor tissue gets compressed by the drag force that is associated with the extracellular fluid flow. This paper presents a general view about the transvascular and interstitial transport of solute nutrients inside a tumor in the macroscopic level. Modified Starling׳s equation is used to describe transvascular nutrient transport. On the macroscopic level, motion of extracellular fluid within the tumor interstitium is modeled with the help of biphasic mixture theory and a spherical symmetry solution is given as a simpler case. This present model describes the average interstitial fluid pressure (IFP), extracellular fluid velocity (EFV) and flow rate of extracellular fluid, as well as the deformation of the solid phase of the tumor tissue as an immediate cause of extracellular fluid flow. When the interstitial transport is diffusion dominated, an analytical treatment of advection-diffusion-reaction equation finds the overall nutrient distribution. We propose suitable criteria for the formation of necrosis within the tumor interstitium. This study introduces some parameters that represent the nutrient supply from tumor blood vessels into the tumor extracellular space. These transport parameters compete with the reversible nutrient metabolism of the tumor cells present in the interstitium. The present study also shows that the effectiveness factor corresponding to a first order nutrient metabolism may reach beyond unity if the strength of the distributive solute source assumes positive non-zero values.

A microneedle-based method for the characterization of diffusion in skin tissue using doxorubicin as a model drug

Hollow microneedles can overcome the stratum corneum (SC) barrier and deposit a compound directly into the viable epidermis or the dermis, unlike adhesive patches that rely on drug diffusion across the SC. The traditional one-dimensional methods used to study the diffusivity of drugs across the skin layers are not very accurate for hollow microneedles, since the ejection of compounds out of microneedle lumens resembles a point-source spreading in all directions and is highly dependent on injection depth. This paper presents a technique that is useful for studying drug injection using hollow microneedles at various depths below the SC. This technique uses confocal microscopy to image the distribution of a fluorescent compound in the skin after injection. The fluorescence distribution in the skin is observed over time and applied to a spherical Gaussian diffusion model for limited source diffusion to determine the diffusion coefficient of the compound in the skin. Applied to freshly excised pig skin, the diffusion coefficient for the anti-cancer drug doxorubicin was measured as 4.61 × 10(-9) cm(2)/s, while the diffusion coefficient in previously refrigerated or frozen pig skin was 1.31 × 10(-8) cm(2)/s and 4.21 × 10(-8) cm(2)/s, respectively. Our data suggests that skin storage conditions can substantially alter the diffusion of drugs. The use of refrigerated and, even more so, previously frozen skin should be avoided for quantitative transdermal drug delivery studies.

Multiphysics and Multiscale Analysis for Chemotherapeutic Drug

This paper presents a three-dimensional dynamic model for the chemotherapy design based on a multiphysics and multiscale approach. The model incorporates cancer cells, matrix degrading enzymes (MDEs) secreted by cancer cells, degrading extracellular matrix (ECM), and chemotherapeutic drug. Multiple mechanisms related to each component possible in chemotherapy are systematically integrated for high reliability of computational analysis of chemotherapy. Moreover, the fidelity of the estimated efficacy of chemotherapy is enhanced by atomic information associated with the diffusion characteristics of chemotherapeutic drug, which is obtained from atomic simulations. With the developed model, the invasion process of cancer cells in chemotherapy treatment is quantitatively investigated. The performed simulations suggest a substantial potential of the presented model for a reliable design technology of chemotherapy treatment.

Mathematical Modelling and Prediction of the Effect of Chemotherapy on Cancer Cells

Cancer is a class of diseases characterized by out-of-control cells' growth which affect DNAs and make them damaged. Many treatment options for cancer exist, with the primary ones including surgery, chemotherapy, radiation therapy, hormonal therapy, targeted therapy and palliative care. Which treatments are used depends on the type, location, and grade of the cancer as well as the person's health and wishes. Chemotherapy is the use of medication (chemicals) to treat disease. More specifically, chemotherapy typically refers to the destruction of cancer cells. Considering the diffusion of drugs in cancer cells and fractality of DNA walks, in this research we worked on modelling and prediction of the effect of chemotherapy on cancer cells using Fractional Diffusion Equation (FDE). The employed methodology is useful not only for analysis of the effect of special drug and cancer considered in this research but can be expanded in case of different drugs and cancers.

A reason for intermittent fasting to suppress the awakening of dormant breast tumors

For their growth, dormant tumors, which lack angiogenesis may critically depend on gradients of nutrients and oxygen from the nearest blood vessel. Because for oxygen depletion the distance from the nearest blood vessel to depletion will generally be shorter than for glucose depletion, such tumors will contain anoxic living tumor cells. These cells are dangerous, because they are capable of inducing angiogenesis, which will "wake up" the tumor. Anoxic cells are dependent on anaerobic glucose breakdown for ATP generation. The local extracellular glucose concentration gradient is determined by the blood glucose concentration and by consumption by cells closer to the nearest blood vessel. The blood glucose concentration can be lowered by 20-40% during fasting. We calculated that glucose supply to the potentially hazardous anoxic cells can thereby be reduced significantly, resulting in cell death specifically of the anoxic tumor cells. We hypothesize that intermittent fasting will help to reduce the incidence of tumor relapse via reducing the number of anoxic tumor cells and tumor awakening.

Mathematical and computational models of drug transport in tumours

The ability to predict how far a drug will penetrate into the tumour microenvironment within its pharmacokinetic (PK) lifespan would provide valuable information about therapeutic response. As the PK profile is directly related to the route and schedule of drug administration, an in silico tool that can predict the drug administration schedule that results in optimal drug delivery to tumours would streamline clinical trial design. This paper investigates the application of mathematical and computational modelling techniques to help improve our understanding of the fundamental mechanisms underlying drug delivery, and compares the performance of a simple model with more complex approaches. Three models of drug transport are developed, all based on the same drug binding model and parametrized by bespoke in vitro experiments. Their predictions, compared for a 'tumour cord' geometry, are qualitatively and quantitatively similar. We assess the effect of varying the PK profile of the supplied drug, and the binding affinity of the drug to tumour cells, on the concentration of drug reaching cells and the accumulated exposure of cells to drug at arbitrary distances from a supplying blood vessel. This is a contribution towards developing a useful drug transport modelling tool for informing strategies for the treatment of tumour cells which are 'pharmacokinetically resistant' to chemotherapeutic strategies.

A new mathematical pharmacodynamic model of clonogenic cancer cell death by doxorubicin

Previous models for predicting tumor cell growth are mostly based on measurements of total cell numbers. The purpose of this paper is to provide a new simple mathematical model for calculating tumor cell growth focusing on the fraction of cells that is clonogenic. The non-clonogenic cells are considered to be relatively harmless. We performed a number of different types of experiments: a long-term drug "treatment", several concentrations/fixed time experiments and time-series experiments, in which human MCF-7 breast cancer cells were exposed to doxorubicin and the total number of cells were counted. In the latter two types, at every measurement point a plating efficiency experiment was started. The final number of colonies formed is equal to the number of clonogenic cells at the onset of the experiment. Based on the intracellular drug concentration, our model predicts cell culture effects taking clonogenic ability and growth inhibition by neighboring cells into account. The model fitted well to the experimental data. The estimated damage parameter which represents the chance of an MCF-7 cell to become non-clonogenic per unit time and per unit intracellular doxorubicin concentration was found to be 0.0025 ± 0.0008 (mean ± SD) nM(-1) h(-1). The model could be used to calculate the effect of every doxorubicin concentration versus time (C-t) profile. Although in vivo parameters may well be different from those found in vitro, the model can be used to predict trends, e.g. by comparing effects of different in vivo C-t profiles.

Microfluidic device for recreating a tumor microenvironment in vitro

We have developed a microfluidic device that mimics the delivery and systemic clearance of drugs to heterogeneous three-dimensional tumor tissues in vitro. Nutrients delivered by vasculature fail to reach all parts of tumors, giving rise to heterogeneous microenvironments consisting of viable, quiescent and necrotic cell types. Many cancer drugs fail to effectively penetrate and treat all types of cells because of this heterogeneity. Monolayers of cancer cells do not mimic this heterogeneity, making it difficult to test cancer drugs with a suitable in vitro model. Our microfluidic devices were fabricated out of PDMS using soft lithography. Multicellular tumor spheroids, formed by the hanging drop method, were inserted and constrained into rectangular chambers on the device and maintained with continuous medium perfusion on one side. The rectangular shape of chambers on the device created linear gradients within tissue. Fluorescent stains were used to quantify the variability in apoptosis within tissue. Tumors on the device were treated with the fluorescent chemotherapeutic drug doxorubicin, time-lapse microscopy was used to monitor its diffusion into tissue, and the effective diffusion coefficient was estimated. The hanging drop method allowed quick formation of uniform spheroids from several cancer cell lines. The device enabled growth of spheroids for up to 3 days. Cells in proximity of flowing medium were minimally apoptotic and those far from the channel were more apoptotic, thereby accurately mimicking regions in tumors adjacent to blood vessels. The estimated value of the doxorubicin diffusion coefficient agreed with a previously reported value in human breast cancer. Because the penetration and retention of drugs in solid tumors affects their efficacy, we believe that this device is an important tool in understanding the behavior of drugs, and developing new cancer therapeutics.

Predicting DNA-mediated drug delivery in interior carcinoma using electromagnetically excited nanoparticles

Tumor-site-specific delivery of anti-cancer drugs remains one of the most prevailing problems in cancer treatment. While conventional means of chemo-delivery invariably leave different degrees of side-effects on healthy tissues, in recent times, intelligent chemical designs have been exploited to reduce the cross-consequences. In particular, the strategies involving superparamaganetic nanoparticles with surface assembled oligonucleotides as therapeutic carrier have raised affirmative promises. Process is designed in such a way that the therapeutic molecules are released preferentially at target site as the complementary oligonucleotide chains dissociate over the heat generated by the nanoparticles under the excitation of low frequency electromagnetic energy. In spite of the preliminary demonstrations, analytical comprehension of the entire process especially on the purview of non-trivial interactions between stochastic phase-transition phenomena of oligonucleotide chains and hierarchical organization of in vivo transport processes remains unknown. Here, we propose an integrated computational predictive model to interpret the efficacy of drug delivery in the aforementioned process. The basic physics of heat generation by superparamagnetic nanoparticles in presence of external electromagnetic field has been coupled with transient biological heat transfer model and the statistical mechanics based oligonucleotide denaturation dynamics. Conjunctionally, we have introduced a set of hierarchically appropriate transport processes to mimic the in vivo drug delivery system. The subsequent interstitial diffusion and convection of the various species involved in the process over time was simulated assuming a porous media model of the carcinoma. As a result, the model predictions exhibit excellent congruence with available experimental results. To delineate a broader spectrum of a priori speculations, we have investigated the effects of different tunable parameters such as magnetizing field strength, nanoparticle size, diffusion coefficients, porous media parameters and different oligonucleotide sequences on temperature rise and site-specific drug release. The proposed model, thus, provides a generic framework for the betterment of nanoparticle mediated drug delivery, which is expected to impart significant impact on cancer therapy.

A theoretical quantitative model for evolution of cancer chemotherapy resistance

Background

Disseminated cancer remains a nearly uniformly fatal disease. While a number of effective chemotherapies are available, tumors inevitably evolve resistance to these drugs ultimately resulting in treatment failure and cancer progression. Causes for chemotherapy failure in cancer treatment reside in multiple levels: poor vascularization, hypoxia, intratumoral high interstitial fluid pressure, and phenotypic resistance to drug-induced toxicity through upregulated xenobiotic metabolism or DNA repair mechanisms and silencing of apoptotic pathways. We propose that in order to understand the evolutionary dynamics that allow tumors to develop chemoresistance, a comprehensive quantitative model must be used to describe the interactions of cell resistance mechanisms and tumor microenvironment during chemotherapy.

Ultimately, the purpose of this model is to identify the best strategies to treat different types of tumor (tumor microenvironment, genetic/phenotypic tumor heterogeneity, tumor growth rate, etc.). We predict that the most promising strategies are those that are both cytotoxic and apply a selective pressure for a phenotype that is less fit than that of the original cancer population. This strategy, known as double bind, is different from the selection process imposed by standard chemotherapy, which tends to produce a resistant population that simply upregulates xenobiotic metabolism. In order to achieve this goal we propose to simulate different tumor progression and therapy strategies (chemotherapy and glucose restriction) targeting stabilization of tumor size and minimization of chemoresistance.

Results

This work confirms the prediction of previous mathematical models and simulations that suggested that administration of chemotherapy with the goal of tumor stabilization instead of eradication would yield better results (longer subject survival) than the use of maximum tolerated doses. Our simulations also indicate that the simultaneous administration of chemotherapy and 2-deoxy-glucose does not optimize treatment outcome because when simultaneously administered these drugs are antagonists. The best results were obtained when 2-deoxy-glucose was followed by chemotherapy in two separate doses.

Conclusions

These results suggest that the maximum potential of a combined therapy may depend on how each of the drugs modifies the evolutionary landscape and that a rational use of these properties may prevent or at least delay relapse.

Reviewers

This article was reviewed by Dr Marek Kimmel and Dr Mark Little.

A multipurpose microfluidic device designed to mimic microenvironment gradients and develop targeted cancer therapeutics

The heterogeneity of cellular microenvironments in tumors severely limits the efficacy of most cancer therapies. We have designed a microfluidic device that mimics the microenvironment gradients present in tumors that will enable the development of more effective cancer therapies. Tumor cell masses were formed within micron-scale chambers exposed to medium perfusion on one side to create linear nutrient gradients. The optical accessibility of the PDMS and glass device enables quantitative transmitted and fluorescence microscopy of all regions of the cell masses. Time-lapse microscopy was used to measure the growth rate and show that the device can be used for long-term efficacy studies. Fluorescence microscopy was used to demonstrate that the cell mass contained viable, apoptotic, and acidic regions similar to in vivo tumors. The diffusion coefficient of doxorubicin was accurately measured, and the accumulation of therapeutic bacteria was quantified. The device is simple to construct, and it can easily be reproduced to create an array of in vitro tumors. Because microenvironment gradients and penetration play critical roles controlling drug efficacy, we believe that this microfluidic device will be vital for understanding the behavior of common cancer drugs in solid tumors and designing novel intratumorally targeted therapeutics.

Integrating cell-cycle progression, drug penetration and energy metabolism to identify improved cancer therapeutic strategies

The effectiveness of chemotherapeutic drugs in tumors is reduced by multiple effects including drug diffusion and variable susceptibility of local cell populations. We hypothesized that quantifying the interactions between drugs and tumor microenvironments could be used to identify more effective anti-cancer strategies. To test this hypothesis we created a mathematical model that integrated intracellular metabolism, nutrient and drug diffusion, cell-cycle progression, cellular drug effects, and drug pharmacokinetics. To our knowledge, this is the first model that combines these elements and has coupled them to experimentally derived parameters. Drug cytotoxicity was assumed to be cell-cycle phase specific, and progression through the cell cycle was assumed to be dependent on ATP generation. The model consisted of a coupled set of nonlinear partial differential, ordinary differential and algebraic equations with an outer free boundary, which was solved using orthogonal collocation on a moving grid of finite elements. Model simulations showed the existence of an optimum drug diffusion coefficient: a low diffusivity prevents effective penetration before the drug is cleared from the blood and a high diffusivity limits drug retention. This result suggests that increasing the molecular weight of the anti-cancer drug paclitaxel from 854 to approximately 20,000 by nanoparticle conjugation would improve its efficacy. The simulations also showed that fast growing tumors are less responsive to therapy than are slower tumors with more quiescent cells, demonstrating the competing effects of regrowth and cytotoxicity. The therapeutic implications of the simulation results are that (1) monolayer cultures are inadequate for accurately determining therapeutic effects in vitro, (2) decreasing the diffusivity of paclitaxel could increase its efficacy, and (3) measuring the proliferation fraction in tumors could enhance the prediction of therapeutic efficacy.

Enhanced efficacy of anti-tumor liposomal doxorubicin by hyperthermia

The efficiency of novel tumor chemotherapeutics could be increased using targeted drug delivery by hyperthermia. In this paper, the 3D liposomal doxorubicin distribution in the tumor tissue enhanced by local hyperthermia was quantitatively studied in real time using laser confocal microscopy. Results showed that the thermally induced liposomal doxorubicin extravasation was non-uniform and more excessive in the peripheral region than that in the tumor center. The effect of the thermally targeted drug delivery was also investigated. On the 1st, 3rd day after the thermally targeted drug treatment, histological examination showed that many nucleolus were condensed and collapsed in the peripheral region. But, in the tumor center, there were no such changes found until the 3rd day. While on the 6th day, tumor cells in both the peripheral and center region were found necrotic. The enhancement of the nanoparticle anti-tumor drug effect was significant. A theoretical analysis of liposomal doxorubicin diffusion to the tumor cells in vivo was performed. Results showed that it took more than 40 hrs for the doxorubicin to get into the tumor cells in the center region from the periphery region. The theoretical results well explained the experimental observations.

Induction of p53 Up-Regulated Modulator of Apoptosis Messenger RNA by Chemotherapeutic Treatment of Locally Advanced Breast Cancer

PURPOSE

In biopsies of patients with locally advanced breast cancer, we investigated the in vivo changes of the gene expression pattern induced by chemotherapy to find genes that are potentially responsible for the efficacy of the drug.

EXPERIMENTAL DESIGN

Early cellular responses to chemotherapy-induced damage, both in vivo and in vitro, were investigated by analyzing chemotherapy-induced changes in gene expression profiles. Core biopsies were taken from nine patients with locally advanced breast cancer, before and at 6 hours after initiation of doxorubicin-based chemotherapy. Both samples were cohybridized on the same microarray containing 18,000 cDNA spots.

RESULTS

The analysis revealed marked differences in gene expression profile between treated and untreated samples. The gene which was most frequently found to be differentially expressed was p53 up-regulated modulator of apoptosis (PUMA). This gene was up-regulated in eight of nine patients with an average factor of 1.80 (range, 1.36-2.73). In vitro MCF-7 breast cancer cells exposed to clinically achievable doxorubicin concentrations for 6 hours revealed marked induction of PUMA mRNA, as well.

CONCLUSIONS

This is the first report describing PUMA mRNA to be up-regulated as a response to chemotherapy in patients. Because PUMA is a known member of the family of BH3-only proapoptotic proteins, this finding suggests PUMA's potential importance for the response to anticancer drugs.

Mathematical Modeling and Optimization of Drug Delivery from Intratumorally Injected Microspheres

Purpose: Paclitaxel is a highly promising phase-sensitive antitumor drug that could conceivably be improved by extended lower dosing as opposed to intermittent higher dosing. Although intratumoral delivery of paclitaxel to the whole tumor at different loads and rates has already been achieved, determining an optimal release mode of paclitaxel for tumor eradication remains difficult. This study set out to rationally design such an optimal microsphere release mode based on mathematical modeling.

Experimental Design: A computational reaction-diffusion framework was used to model drug release from intratumorally injected microspheres, drug transport and binding in tumor interstitum, and drug clearance by microvasculature and intracellular uptake and binding.

Results: Numerical simulations suggest that interstitial drug concentration is characterized by a fast spatially inhomogeneous rise phase, during which interstitial and intracellular binding sites are saturated, followed by a slow spatially homogeneous phase that is governed by the rate of drug release from microspheres. For zero-order drug release, the slow phase corresponds to a plateau drug concentration that is proportional to the ratio of the rate of blood clearance of drug to the rate of drug release from microspheres. Consequently, increasing the duration of intratumoral drug release extends the duration of cell exposure to the drug but lowers the plateau drug concentration. This tradeoff implies that intratumoral drug release can be designed to optimize tumor cell kill. Synthesizing our modeling predictions with published dose-response data, we propose an optimal protocol for the delivery of paclitaxel-loaded microspheres to small solid tumors.

Simulation model of doxorubicin activity in islets of human breast cancer cells

During cytotoxic chemotherapy, cancer cells are exposed to a dynamic concentration-versus-time curve. Besides the area under this curve, the shape of this curve may determine the cytotoxic effect. This report describes the concept that cell damage is determined by the molar drug accumulation history inside the tumor cells. Cell numbers of large populations of human MCF-7 cells exposed to three different doxorubicin concentration-versus-time profiles were recorded for 31 days. The drug accumulation history in the cells was calculated using cellular drug transport parameters derived from doxorubicin uptake and efflux measurements on MCF-7 cells attached to culture dishes. Recovery of the proliferation rate of a cell population after drug exposure was described using a mathematical model of cell damage. The model fitted well to the proliferation assays. It allowed for comparison of the effects of changes in doxorubicin concentration-versus-time profiles in vitro. The model was then used to predict the effect of the changes in the doxorubicin concentration profile in vivo, in tumor islets, after a bolus injection of doxorubicin. In the model doxorubicin exposure resulted in less cell damage inside the tumor islets than at the rim.