Mathematical modelling of drug transport in tumour multicell spheroids and monolayer cultures

Multiscale modeling of the dynamic growth of cancerous tumors under the influence of chemotherapy drugs

A comprehensive model of chemotherapy treatment of cancer can help us to optimize the drug administration/dosage and improve the treatment outcome. In the present study, a multiscale mathematical model of tumor growth during chemotherapy treatment is developed to predict its response to the medication and cancer progression. The modeling is a continuous multiscale simulation consisting of three tissue phases including cancer cells, normal cells, and extracellular matrix. In addition to the drug administration, the impacts of immune cells, programmed cell death, nutrient competition, and glucose concentration are included. The outputs of our mathematical model conform to the published experimental and clinical data, and it can be used in optimizing chemotherapy, and personalized cancer treatment.

Delivery of Anticancer Drugs Using Microbubble-Assisted Ultrasound in a 3D Spheroid Model

Tumor spheroids are promising three-dimensional (3D) in vitro tumor models for the evaluation of drug delivery methods. The design of noninvasive and targeted drug methods is required to improve the intratumoral bioavailability of chemotherapeutic drugs and reduce their adverse off-target effects. Among such methods, microbubble-assisted ultrasound (MB-assisted US) is an innovative modality for noninvasive targeted drug delivery. The aim of the present study is to evaluate the efficacy of this US modality for the delivery of bleomycin, doxorubicin, and irinotecan in colorectal cancer (CRC) spheroids. MB-assisted US permeabilized the CRC spheroids to propidium iodide, which was used as a drug model without affecting their growth and viability. Histological analysis and electron microscopy revealed that MB-assisted US affected only the peripheral layer of the CRC spheroids. The acoustically mediated bleomycin delivery induced a significant decrease in CRC spheroid growth in comparison to spheroids treated with bleomycin alone. However, this US modality did not improve the therapeutic efficacy of doxorubicin and irinotecan on CRC spheroids. In conclusion, this study demonstrates that tumor spheroids are a relevant approach to evaluate the efficacy of MB-assisted US for the delivery of chemotherapeutics.

Tumor Spheroids as Model to Design Acoustically Mediated Drug Therapies: A Review

Tumor spheroids as well as multicellular tumor spheroids (MCTSs) are promising 3D in vitro tumor models for drug screening, drug design, drug targeting, drug toxicity, and validation of drug delivery methods. These models partly reflect the tridimensional architecture of tumors, their heterogeneity and their microenvironment, which can alter the intratumoral biodistribution, pharmacokinetics, and pharmacodynamics of drugs. The present review first focuses on current spheroid formation methods and then on in vitro investigations exploiting spheroids and MCTS for designing and validating acoustically mediated drug therapies. We discuss the limitations of the current studies and future perspectives. Various spheroid formation methods enable the easy and reproducible generation of spheroids and MCTSs. The development and assessment of acoustically mediated drug therapies have been mainly demonstrated in spheroids made up of tumor cells only. Despite the promising results obtained with these spheroids, the successful evaluation of these therapies will need to be addressed in more relevant 3D vascular MCTS models using MCTS-on-chip platforms. These MTCSs will be generated from patient-derived cancer cells and nontumor cells, such as fibroblasts, adipocytes, and immune cells.

Three-dimensional in vitro culture models in oncology research

Cancer is a multifactorial disease that is responsible for 10 million deaths per year. The intra- and inter-heterogeneity of malignant tumors make it difficult to develop single targeted approaches. Similarly, their diversity requires various models to investigate the mechanisms involved in cancer initiation, progression, drug resistance and recurrence. Of the in vitro cell-based models, monolayer adherent (also known as 2D culture) cell cultures have been used for the longest time. However, it appears that they are often less appropriate than the three-dimensional (3D) cell culture approach for mimicking the biological behavior of tumor cells, in particular the mechanisms leading to therapeutic escape and drug resistance. Multicellular tumor spheroids are widely used to study cancers in 3D, and can be generated by a multiplicity of techniques, such as liquid-based and scaffold-based 3D cultures, microfluidics and bioprinting. Organoids are more complex 3D models than multicellular tumor spheroids because they are generated from stem cells isolated from patients and are considered as powerful tools to reproduce the disease development in vitro. The present review provides an overview of the various 3D culture models that have been set up to study cancer development and drug response. The advantages of 3D models compared to 2D cell cultures, the limitations, and the fields of application of these models and their techniques of production are also discussed.

The Adrenergic Receptor Antagonist Carvedilol Elicits Anti-Tumor Responses in Uveal Melanoma 3D Tumor Spheroids and May Serve as Co-Adjuvant Therapy with Radiation

Uveal melanoma (UM) is the most common intraocular tumor in adults. Despite local tumor control, no effective therapy has been found to prevent metastasis, resulting in a high mortality rate. In the present study, we evaluated the anti-tumor potential of non-selective ß-blockers in 3D tumor spheroids grown from UM cell lines. Of the various ß-blockers tested, carvedilol and its enantiomers were most potent in decreasing the viability of Mel270 spheroids. Carvedilol at a concentration of 10–50 µM significantly elicited cytotoxicity and induced apoptosis in spheroid cells. In result, carvedilol inhibited tumor spheroid growth and compactness, and furthermore prevented the long-term survival and repopulation of spreading spheroid cells. The drug sensitivity of the different spheroids grown from Mel270, 92-1, UPMD2, or UPMM3 cell lines was dependent on 3D morphology rather than on high-risk cytogenetic profile or adrenergic receptor expression levels. In fact, the monosomy-3-containing UPMM3 cell line was most responsive to carvedilol treatment compared to the other cell lines. The concurrent treatment of UPMM3 spheroids with carvedilol and 5 or 10 Gy irradiation revealed additive cytotoxic effects that provided tumor control. Collectively, our data demonstrate the anti-tumor properties of carvedilol and its enantiomers, which may serve as candidates for the co-adjuvant therapy of UM.

Kinetics of Nanomedicine in Tumor Spheroid as an In Vitro Model System for Efficient Tumor-Targeted Drug Delivery With Insights From Mathematical Models

Numerous strategies have been developed to treat cancer conventionally. Most importantly, chemotherapy shows its huge promise as a better treatment modality over others. Nonetheless, the very complex behavior of the tumor microenvironment frequently impedes successful drug delivery to the tumor sites that further demands very urgent and effective distribution mechanisms of anticancer drugs specifically to the tumor sites. Hence, targeted drug delivery to tumor sites has become a major challenge to the scientific community for cancer therapy by assuring drug effects to selective tumor tissue and overcoming undesired toxic side effects to the normal tissues. The application of nanotechnology to the drug delivery system pays heed to the design of nanomedicine for specific cell distribution. Aiming to limit the use of traditional strategies, the adequacy of drug-loaded nanocarriers (i.e., nanomedicine) proves worthwhile. After systemic blood circulation, a typical nanomedicine follows three levels of disposition to tumor cells in order to exhibit efficient pharmacological effects induced by the drug candidates residing within it. As a result, nanomedicine propounds the assurance towards the improved bioavailability of anticancer drug candidates, increased dose responses, and enhanced targeted efficiency towards delivery and distribution of effective therapeutic concentration, limiting toxic concentration. These aspects emanate the proficiency of drug delivery mechanisms. Understanding the potential tumor targeting barriers and limiting conditions for nanomedicine extravasation, tumor penetration, and final accumulation of the anticancer drug to tumor mass, experiments with in vivo animal models for nanomedicine screening are a key step before it reaches clinical translation. Although the study with animals is undoubtedly valuable, it has many associated ethical issues. Moreover, individual experiments are very expensive and take a longer time to conclude. To overcome these issues, nowadays, multicellular tumor spheroids are considered a promising in vitro model system that proposes better replication of in vivo tumor properties for the future development of new therapeutics. In this review, we will discuss how tumor spheroids could be used as an in vitro model system to screen nanomedicine used in targeted drug delivery, aiming for better therapeutic benefits. In addition, the recent proliferation of mathematical modeling approaches gives profound insight into the underlying physical principles and produces quantitative predictions. The hierarchical tumor structure is already well decorous to be treated mathematically. To study targeted drug delivery, mathematical modeling of tumor architecture, its growth, and the concentration gradient of oxygen are the points of prime focus. Not only are the quantitative models circumscribed to the spheroid, but also the role of modeling for the nanoparticle is equally inevitable. Abundant mathematical models have been set in motion for more elaborative and meticulous designing of nanomedicine, addressing the question regarding the objective of nanoparticle delivery to increase the concentration and the augmentative exposure of the therapeutic drug molecule to the core. Thus, to diffuse the dichotomy among the chemistry involved, biological data, and the underlying physics, the mathematical models play an indispensable role in assisting the experimentalist with further evaluation by providing the admissible quantitative approach that can be validated. This review will provide an overview of the targeted drug delivery mechanism for spheroid, using nanomedicine as an advantageous tool.

A Bayesian approach to estimate the diffusion coefficient of Rhodamine 6G in breast cancer spheroids

Multicellular spheroids have emerged as a robust platform to model tumor growth and are widely used for studying drug sensitivity. Diffusion is the main mechanism for transporting nutrients and chemotherapeutic drugs into spheroids, since they are typically avascular. In this study, the Bayesian inference was used to solve the inverse problem of determining the light attenuation coefficient and diffusion coefficient of Rhodamine 6G (R6G) in breast cancer spheroids, as a mock drug for the tyrosine kinase inhibitor, Neratinib. Four types of breast cancer spheroids were formed and the diffusion coefficient was estimated assuming a linear relationship between the intensity and concentration. The mathematical model used for prediction is the solution to the diffusion problem in spherical coordinates, accounting for the light attenuation. The Gaussian likelihood was used to account for the error between the measurements and model predictions. The Markov Chain Monte Carlo algorithm (MCMC) was used to sample from the posterior. The posterior predictions for the diffusion and light attenuation coefficients were provided. The results indicate that the diffusion coefficient values do not significantly vary across a HER2+ breast cancer cell line as a function of transglutaminase 2 levels, even in the presence of fibroblast cells. However, we demonstrate that different diffusion coefficient values can be ascertained from tumorigenic compared to nontumorigenic spheroids and from nonmetastatic compared to post-metastatic breast cancer cells using this approach. We also report agreement between spheroid radius, attenuation coefficient, and subsequent diffusion coefficient to give evidence of cell packing in self-assembled spheroids. The methodology presented here will allow researchers to determine diffusion in spheroids to decouple transport and drug penetration changes from biological resistivity.

A Microfluidic Multisize Spheroid Array for Multiparametric Screening of Anticancer Drugs and Blood-Brain Barrier Transport Properties

Physiological-relevant in vitro tissue models with their promise of better predictability have the potential to improve drug screening outcomes in preclinical studies. Despite the advances of spheroid models in pharmaceutical screening applications, variations in spheroid size and consequential altered cell responses often lead to nonreproducible and unpredictable results. Here, a microfluidic multisize spheroid array is established and characterized using liver, lung, colon, and skin cells as well as a triple-culture model of the blood-brain barrier (BBB) to assess the effects of spheroid size on (a) anticancer drug toxicity and (b) compound penetration across an advanced BBB model. The reproducible on-chip generation of 360 spheroids of five dimensions on a well-plate format using an integrated microlens technology is demonstrated. While spheroid size-related IC50 values vary up to 160% using the anticancer drugs cisplatin (CIS) or doxorubicin (DOX), reduced CIS:DOX drug dose combinations eliminate all lung microtumors independent of their sizes. A further application includes optimizing cell seeding ratios and size-dependent compound uptake studies in a perfused BBB model. Generally, smaller BBB-spheroids reveal an 80% higher compound penetration than larger spheroids while verifying the BBB opening effect of mannitol and a spheroid size-related modulation on paracellular transport properties.

Cell spheroids as a versatile research platform: formation mechanisms, high throughput production, characterization and applications

Three-dimensional cell culture has tremendous advantages to closely mimic the in vivo architecture and microenvironment of healthy tissue and organs, as well as of solid tumors. Spheroids are currently the most attractive 3D model to produce uniform reproducible cell structures as well as a potential basis for engineering large tissues and complex organs. In this review we discuss, from an engineering perspective, processes to obtain uniform 3D cell spheroids, comparing dynamic and static cultures and considering aspects such as mass transfer and shear stress. In addition, computational and mathematical modelling of complex cell spheroid systems are discussed. The non-cell-adhesive hydrogel-based method and dynamic cell culture in bioreactors are focused in detail and the myriad of developed spheroid characterization techniques is presented. The main bottlenecks and weaknesses are discussed, especially regarding the analysis of morphological parameters, cell quantification and viability, gene expression profiles, metabolic behavior and high-content analysis. Finally, a vast set of applications of spheroids as tools for in vitro study model systems is examined, including drug screening, tissue formation, pathologies development, tissue engineering and biofabrication, 3D bioprinting and microfluidics, together with their use in high-throughput platforms.

Pumpless, unidirectional microphysiological system for testing metabolism-dependent chemotherapeutic toxicity

Drug development is often hindered by the failure of preclinical models to accurately assess and predict the efficacy and safety of drug candidates. Body-on-a-chip (BOC) microfluidic devices, a subset of microphysiological systems (MPS), are being created to better predict human responses to drugs. Each BOC is designed with separate organ chambers interconnected with microfluidic channels mimicking blood recirculation. Here, we describe the design of the first pumpless, unidirectional, multiorgan system and apply this design concept for testing anticancer drug treatments. HCT-116 colon cancer spheroids, HepG2/C3A hepatocytes, and HL-60 promyeloblasts were embedded in collagen hydrogels and cultured within compartments representing "colon tumor", "liver," and "bone marrow" tissue, respectively. Operating on a pumpless platform, the microfluidic channel design provides unidirectional perfusion at physiologically realistic ratios to multiple channels simultaneously. The metabolism-dependent toxic effect of Tegafur, an oral prodrug of 5-fluorouracil, combined with uracil was examined in each cell type. Tegafur-uracil treatment induced substantial cell death in HCT-116 cells and this cytotoxic response was reduced for multicellular spheroids compared to single cells, likely due to diffusion-limited drug penetration. Additionally, off-target toxicity was detected by HL-60 cells, which demonstrate that such systems can provide useful information on dose-limiting side effects. Collectively, this microscale cell culture analog is a valuable physiologically-based pharmacokinetic drug screening platform that may be used to support cancer drug development.

From tumour perfusion to drug delivery and clinical translation of in silico cancer models

In silico cancer models have demonstrated great potential as a tool to improve drug design, optimise the delivery of drugs to target sites in the host tissue and, hence, improve therapeutic efficacy and patient outcome. However, there are significant barriers to the successful translation of in silico technology from bench to bedside. More precisely, the specification of unknown model parameters, the necessity for models to adequately reflect in vivo conditions, and the limited amount of pertinent validation data to evaluate models' accuracy and assess their reliability, pose major obstacles in the path towards their clinical translation. This review aims to capture the state-of-the-art in in silico cancer modelling of vascularised solid tumour growth, and identify the important advances and barriers to success of these models in clinical oncology. Particular emphasis has been put on continuum-based models of cancer since they - amongst the class of mechanistic spatio-temporal modelling approaches - are well-established in simulating transport phenomena and the biomechanics of tissues, and have demonstrated potential for clinical translation. Three important avenues in in silico modelling are considered in this contribution: first, since systemic therapy is a major cancer treatment approach, we start with an overview of the tumour perfusion and angiogenesis in silico models. Next, we present the state-of-the-art in silico work encompassing the delivery of chemotherapeutic agents to cancer nanomedicines through the bloodstream, and then review continuum-based modelling approaches that demonstrate great promise for successful clinical translation. We conclude with a discussion of what we view to be the key challenges and opportunities for in silico modelling in personalised and precision medicine.

Gradient-sized control of tumor spheroids on a single chip

Multicellular tumor spheroids are attracting more attention as a physiologically relevant in vitro tumor model for biomedical research. The size of spheroids is one of the critical parameters related to drug penetration and cellular responses. It remains challenging to generate a large number of gradient-sized spheroids in one culture vessel. Here, a liquid-dome method was used to simultaneously produce more than 200 gradient-sized spheroids on an agarose chip. Surface tension effect was used to modulate the liquid spatial distribution and achieve a range of spheroid sizes. MCF-7 cells formed multiple spheroids on the chips for concept validation. It showed that different configurations of the liquid domes exhibited different levels of size control. Relative to the smallest spheroids in the configuration, hemispheric and square domes produced spheroids up to 3.4 and 12.8-fold larger in area, respectively. In addition, the co-culture of MCF-7 and fibroblasts helped to elucidate the tendency of fibroblasts towards the spheroid center. Other size-dependent behaviors were profiled; larger spheroids behaved differently from smaller spheroids in terms of spheroid growth, drug penetration and cellular responses. This method breaks the boundary between the preparation of gradient-sized spheroids and significant time/labour demand. It can be useful for drug screening and in vitro tumor modelling.

Boyden chamber-based compartmentalized tumor spheroid culture system to implement localized anticancer drug treatment

In anticancer drug development, it is important to simultaneously evaluate both the effect of drugs on cell proliferation and their ability to penetrate tissues. To realize such an evaluation process, here, we present a compartmentalized tumor spheroid culture system utilizing a thin membrane with a through-hole to conduct localized anticancer treatment of tumor spheroids and monitor spheroid dimensions as an indicator of cell proliferation. The system is based on a commercialized Boyden chamber plate; a through-hole was bored through a porous membrane of the chamber, and the pre-existing 0.4 μm membrane pores were filled with parylene C. A HepG2 spheroid was immobilized onto the through-hole, separating the upper and lower compartments. Fluorescein (to verify the isolation between the compartments) and tirapazamine (TPZ; to treat only the lower part of the spheroid) were added to the upper and lower compartments, respectively. Since the transportation of fluorescein was blocked during treatment, i.e., the upper and lower compartments were isolated, it was confirmed that localized TPZ treatment was successfully conducted using the developed system. The effect of localized TPZ treatment on cell proliferation was estimated by measuring the maximum horizontal cross-sectional areas in the upper and lower parts of the spheroid by microscopic observations. This system can, thus, be used to perform localized anticancer drug treatment of tumor spheroids and evaluate the effect of drugs on cell proliferation.

Anticancer Drug Affects Metabolomic Profiles in Multicellular Spheroids: Studies Using Mass Spectrometry Imaging Combined with Machine Learning

Multicellular spheroids (hereinafter referred to as spheroids) are 3D biological models. The metabolomic profiles inside spheroids provide crucial information reflecting the molecular phenotypes and microenvironment of cells. To study the influence of an anticancer drug on the spatially resolved metabolites, spheroids were cultured using HCT-116 colorectal cancer cells, treated with the anticancer drug Irinotecan under a series of time- and concentration-dependent conditions. The Single-probe mass spectrometry imaging (MSI) technique was utilized to conduct the experiments. The MSI data were analyzed using advanced data analysis methods to efficiently extract metabolomic information. Multivariate curve resolution alternating least square (MCR-ALS) was used to decompose each MS image into different components with grouped species. To improve the efficiency of data analysis, both supervised (Random Forest) and unsupervised (cluster large applications (CLARA)) machine learning (ML) methods were employed to cluster MS images according to their metabolomic features. Our results indicate that anticancer drug significantly affected the abundances of a variety of metabolites in different regions of spheroids. This integrated experiment and data analysis approach can facilitate the studies of metabolites in different types of 3D tumor models and tissues and potentially benefit the drug discovery, therapeutic resistance, and other biological research fields.

Mathematical modeling of the proliferation gradient in multicellular tumor spheroids

MultiCellular Tumor Spheroids are 3D cell cultures that can accurately reproduce the behavior of solid tumors. It has been experimentally observed that large spheroids exhibit a decreasing gradient of proliferation from the periphery to the center of these multicellular 3D models: the proportion of proliferating cells is higher in the periphery while the non-proliferating quiescent cells increase in depth. In this paper, we propose to investigate the key mechanisms involved in the establishment of this gradient with a Partial Differential Equations model that mimics the experimental set-up of growing spheroids under different nutrients supply conditions. The model consists of mass balance equations on the two cell populations observed in the data: the proliferating cells and the quiescent cells. The spherical symmetry is used to rewrite the model in radial and relative coordinates. Thanks to a rigorous data postprocessing the model is then fit and compared quantitatively with the experimental quantification of the percentage of proliferating cells from EdU immunodetection on 2D spheroid cryosection images. The results of this calibration show that the proliferation gradient observed in spheroids can be quantitatively reproduced by our model.

Dynamical density-functional-theory-based modeling of tissue dynamics: Application to tumor growth

We present a theoretical framework based on an extension of dynamical density-functional theory (DDFT) for describing the structure and dynamics of cells in living tissues and tumors. DDFT is a microscopic statistical mechanical theory for the time evolution of the density distribution of interacting many-particle systems. The theory accounts for cell-pair interactions, different cell types, phenotypes, and cell birth and death processes (including cell division), to provide a biophysically consistent description of processes bridging across the scales, including describing the tissue structure down to the level of the individual cells. Analysis of the model is presented for single-species and two-species cases, the latter aimed at describing competition between tumor and healthy cells. In suitable parameter regimes, model results are consistent with biological observations. Of particular note, divergent tumor growth behavior, mirroring metastatic and benign growth characteristics, are shown to be dependent on the cell-pair-interaction parameters.

Sarcoma Spheroids and Organoids-Promising Tools in the Era of Personalized Medicine

Cancer treatment is rapidly evolving toward personalized medicine, which takes into account the individual molecular and genetic variability of tumors. Sophisticated new in vitro disease models, such as three-dimensional cell cultures, may provide a tool for genetic, epigenetic, biomedical, and pharmacological research, and help determine the most promising individual treatment. Sarcomas, malignant neoplasms originating from mesenchymal cells, may have a multitude of genomic aberrations that give rise to more than 70 different histopathological subtypes. Their low incidence and high level of histopathological heterogeneity have greatly limited progress in their treatment, and trials of clinical sarcoma are less frequent than trials of other carcinomas. The main advantage of 3D cultures from tumor cells or biopsy is that they provide patient-specific models of solid tumors, and they overcome some limitations of traditional 2D monolayer cultures by reflecting cell heterogeneity, native histologic architectures, and cell-extracellular matrix interactions. Recent advances promise that these models can help bridge the gap between preclinical and clinical research by providing a relevant in vitro model of human cancer useful for drug testing and studying metastatic and dormancy mechanisms. However, additional improvements of 3D models are expected in the future, specifically the inclusion of tumor vasculature and the immune system, to enhance their full ability to capture the biological features of native tumors in high-throughput screening. Here, we summarize recent advances and future perspectives of spheroid and organoid in vitro models of rare sarcomas that can be used to investigate individual molecular biology and predict clinical responses. We also highlight how spheroid and organoid culture models could facilitate the personalization of sarcoma treatment, provide specific clinical scenarios, and discuss the relative strengths and limitations of these models.

Emerging tumor spheroids technologies for 3D in vitro cancer modeling

Cancer is a leading cause of mortality and morbidity worldwide. Around 90% of deaths are caused by metastasis and just 10% by primary tumor. The advancement of treatment approaches is not at the same rhythm of the disease; making cancer a focal target of biomedical research. To enhance the understanding and prompts the therapeutic delivery; concepts of tissue engineering are applied in the development of in vitro models that can bridge between 2D cell culture and animal models, mimicking tissue microenvironment. Tumor spheroid represents highly suitable 3D organoid-like framework elucidating the intra and inter cellular signaling of cancer, like that formed in physiological niche. However, spheroids are of limited value in studying critical biological phenomenon such as tumor-stroma interactions involving extra cellular matrix or immune system. Therefore, a compelling need of tailoring spheroid technologies with physiologically relevant biomaterials or in silico models, is ever emerging. The diagnostic and prognostic role of spheroids rearrangements within biomaterials or microfluidic channel is indicative of patient management; particularly for the decision of targeted therapy. Fragmented information on available in vitro spheroid models and lack of critical analysis on transformation aspects of these strategies; pushes the urge to comprehensively overview the recent technological advancements (e.g. bioprinting, micro-fluidic technologies or use of biomaterials to attain the third dimension) in the shed of translationable cancer research. In present article, relationships between current models and their possible exploitation in clinical success is explored with the highlight of existing challenges in defining therapeutic targets and screening of drug efficacy.

Drug delivery to solid tumors: the predictive value of the multicellular tumor spheroid model for nanomedicine screening

The increasing number of publications on the subject shows that nanomedicine is an attractive field for investigations aiming to considerably improve anticancer chemotherapy. Based on selective tumor targeting while sparing healthy tissue, carrier-mediated drug delivery has been expected to provide significant benefits to patients. However, despite reduced systemic toxicity, most nanodrugs approved for clinical use have been less effective than previously anticipated. The gap between experimental results and clinical outcomes demonstrates the necessity to perform comprehensive drug screening by using powerful preclinical models. In this context, in vitro three-dimensional models can provide key information on drug behavior inside the tumor tissue. The multicellular tumor spheroid (MCTS) model closely mimics a small avascular tumor with the presence of proliferative cells surrounding quiescent cells and a necrotic core. Oxygen, pH and nutrient gradients are similar to those of solid tumor. Furthermore, extracellular matrix (ECM) components and stromal cells can be embedded in the most sophisticated spheroid design. All these elements together with the physicochemical properties of nanoparticles (NPs) play a key role in drug transport, and therefore, the MCTS model is appropriate to assess the ability of NP to penetrate the tumor tissue. This review presents recent developments in MCTS models for a better comprehension of the interactions between NPs and tumor components that affect tumor drug delivery. MCTS is particularly suitable for the high-throughput screening of new nanodrugs.

A novel individual-cell-based mathematical model based on multicellular tumour spheroids for evaluating doxorubicin-related delivery in avascular regions

BACKGROUND AND PURPOSE

Effective drug delivery in the avascular regions of tumours, which is crucial for the promising antitumour activity of doxorubicin-related therapy, is governed by two inseparable processes: intercellular diffusion and intracellular retention. To accurately evaluate doxorubicin-related delivery in the avascular regions, these two processes should be assessed together. Here we describe a new approach to such an assessment.

EXPERIMENTAL APPROACH

An individual-cell-based mathematical model based on multicellular tumour spheroids was developed that describes the different intercellular diffusion and intracellular retention kinetics of doxorubicin in each cell layer. The different effects of a P-glycoprotein inhibitor (LY335979) and a hypoxia inhibitor (YC-1) were quantitatively evaluated and compared, in vitro (tumour spheroids) and in vivo (HepG2 tumours in mice). This approach was further tested by evaluating in these models, an experimental doxorubicin derivative, INNO 206, which is in Phase II clinical trials.

KEY RESULTS

Inhomogeneous, hypoxia-induced, P-glycoprotein expression compromised active transport of doxorubicin in the central area, that is, far from the vasculature. LY335979 inhibited efflux due to P-glycoprotein but limited levels of doxorubicin outside the inner cells, whereas YC-1 co-administration specifically increased doxorubicin accumulation in the inner cells without affecting the extracellular levels. INNO 206 exhibited a more effective distribution profile than doxorubicin.

CONCLUSIONS AND IMPLICATIONS

The individual-cell-based mathematical model accurately evaluated and predicted doxorubicin-related delivery and regulation in the avascular regions of tumours. The described framework provides a mechanistic basis for the proper development of doxorubicin-related drug co-administration profiles and nanoparticle development and could avoid unnecessary clinical trials.

Evaluating the influence of mechanical stress on anticancer treatments through a multiphase porous media model

Drug resistance is one of the leading causes of poor therapy outcomes in cancer. As several chemotherapeutics are designed to target rapidly dividing cells, the presence of a low-proliferating cell population contributes significantly to treatment resistance. Interestingly, recent studies have shown that compressive stresses acting on tumor spheroids are able to hinder cell proliferation, through a mechanism of growth inhibition. However, studies analyzing the influence of mechanical compression on therapeutic treatment efficacy have still to be performed. In this work, we start from an existing mathematical model for avascular tumors, including the description of mechanical compression. We introduce governing equations for transport and uptake of a chemotherapeutic agent, acting on cell proliferation. Then, model equations are adapted for tumor spheroids and the combined effect of compressive stresses and drug action is investigated. Interestingly, we find that the variation in tumor spheroid volume, due to the presence of a drug targeting cell proliferation, considerably depends on the compressive stress level of the cell aggregate. Our results suggest that mechanical compression of tumors may compromise the efficacy of chemotherapeutic agents. In particular, a drug dose that is effective in reducing tumor volume for stress-free conditions may not perform equally well in a mechanically compressed environment.

Strategy for constructing vascularized adipose units in poly(l-glutamic acid) hydrogel porous scaffold through inducing in-situ formation of ASCs spheroids

Vascularization is of great importance to adipose tissue regeneration. Here we introduced a paradigm that using scaffold to induce ASC spheroids, so to promote vascularized adipose tissue regeneration. Poly (l-glutamic acid) (PLGA) was activated by EDC, followed by being cross-linked by Adipic dihydrazide (ADH) to form a homogeneous hydrogel. Lyophilization was then carried out to create porous structure. The PLGA hydrogel scaffold possessed a significant swollen hydrophilic network to weaken cell-scaffold adhesion but drive ASCs to aggregate to form spheroids. Increase of seeding cell density was proved to result in the increase of spheroid size, upregulating angiogenic genes (VEGF and FGF-2) expression by enhancing the hypoxia-induced paracrine secretion. Also, the adipogenic differentiation of ASCs was achieved in spheroids in vitro. Moreover, the in vivo vascularized adipose tissue regeneration was evaluated in the dorsum of nude mice. After 12weeks post-implantation, the significant angiogenesis was found in both adipogenic induced and non-induced engineered tissue. In adipogenic induced group, the clear ring-like morphology, the large vacuole in the middle of the cell and the Oil red O staining demonstrated adipose tissue formation.

STATEMENT OF SIGNIFICANCE

Vascularization is of great importance to adipose tissue regeneration. Adipose derived stem cell (ASC) spheroids possessed not only the high efficiency of vascularization, but also the improved differentiation ability. Several research works have illustrated the advantage of ASC spheroids in vascularization. However, in adipose regeneration, ASC spheroid was rarely used. Even so, it is reasonable to believe that ASC spheroids hold a great promise in vascularized adipose tissue engineering. Thus in the present study, we introduced a method to create lots of ASC spheroids that acted as lots of individual adipogenesis and angiogenesis units inside of a porous hydrogel scaffold. Then, the scaffold carrying ASC spheroids was implanted subcutaneously in nude mice to preliminarily evaluate the adipose tissue generation and blood vessel formation.

Reversible Monolayer/Spheroid Cell Culture Switching by UCST-Type Thermoresponsive Ureido Polymers

Multicellular spheroids have been studied in the fields of oncology, stem cell biology, and tissue engineering. In this study, we found a new polymer material for thermo-controlled spheroid/monolayer cell culture switching. The polymers that have pendant ureido groups (ureido polymers) exhibited upper critical solution temperature-type phase separation behavior. Cells in monolayer culture were converted to spheroids by the addition of ureido polymers below phase separation temperature (T_p). Time-lapse observations indicated that cells began to migrate and aggregate to form the spheroids to avoid contact with phase-separated polymer (coacervates) on the surface of the culture dish. We supposed that the coacervates seemingly suppressed interaction between cell and the dish surface or extracellular matrices. By increasing culture temperature above T_p, the spheroids began to collapse into a monolayer of cells due to dissolution of the coacervates. These results indicated that cell morphology could be repeatedly switched by changing the culture temperature in the presence of ureido polymers.

3D tumor spheroids: an overview on the tools and techniques used for their analysis

In comparison with 2D cell culture models, 3D spheroids are able to accurately mimic some features of solid tumors, such as their spatial architecture, physiological responses, secretion of soluble mediators, gene expression patterns and drug resistance mechanisms. These unique characteristics highlight the potential of 3D cellular aggregates to be used as in vitro models for screening new anticancer therapeutics, both at a small and large scale. Nevertheless, few reports have focused on describing the tools and techniques currently available to extract significant biological data from these models. Such information will be fundamental to drug and therapeutic discovery process using 3D cell culture models. The present review provides an overview of the techniques that can be employed to characterize and evaluate the efficacy of anticancer therapeutics in 3D tumor spheroids.

Constructal approach to cell membranes transport: Amending the 'Norton-Simon' hypothesis for cancer treatment

To investigate biosystems, we propose a new thermodynamic concept that analyses ion, mass and energy flows across the cell membrane. This paradigm-shifting approach has a wide applicability to medically relevant topics including advancing cancer treatment. To support this claim, we revisit ‘Norton-Simon’ and evolving it from an already important anti-cancer hypothesis to a thermodynamic theorem in medicine. We confirm that an increase in proliferation and a reduction in apoptosis trigger a maximum of ATP consumption by the tumor cell. Moreover, we find that positive, membrane-crossing ions lead to a decrease in the energy used by the tumor, supporting the notion of their growth inhibitory effect while negative ions apparently increase the cancer’s consumption of energy hence reflecting a growth promoting impact. Our results not only represent a thermodynamic proof of the original Norton-Simon hypothesis but, more concretely, they also advance the clinically intriguing and experimentally testable, diagnostic hypothesis that observing an increase in negative ions inside a cell in vitro, and inside a diseased tissue in vivo, may indicate growth or recurrence of a tumor. We conclude with providing theoretical evidence that applying electromagnetic field therapy early on in the treatment cycle may maximize its anti-cancer efficacy.

An analytical model for nanoparticles concentration resulting from infusion into poroelastic brain tissue

We consider the infusion of a diluted suspension of nanoparticles (NPs) into poroelastic brain tissue, in view of relevant biomedical applications such as intratumoral thermotherapy. Indeed, the high impact of the related pathologies motivates the development of advanced therapeutic approaches, whose design also benefits from theoretical models. This study provides an analytical expression for the time-dependent NPs concentration during the infusion into poroelastic brain tissue, which also accounts for particle binding onto cells (by recalling relevant results from the colloid filtration theory). Our model is computationally inexpensive and, compared to fully numerical approaches, permits to explicitly elucidate the role of the involved physical aspects (tissue poroelasticity, infusion parameters, NPs physico-chemical properties, NP-tissue interactions underlying binding). We also present illustrative results based on parameters taken from the literature, by considering clinically relevant ranges for the infusion parameters. Moreover, we thoroughly assess the model working assumptions besides discussing its limitations. While not laying any claims of generality, our model can be used to support the development of more ambitious numerical approaches, towards the preliminary design of novel therapies based on NPs infusion into brain tissue.

Inhibition of hexokinase-2 with targeted liposomal 3-bromopyruvate in an ovarian tumor spheroid model of aerobic glycolysis

BACKGROUND

The objective of this study was to evaluate the expression levels of glycolytic markers, especially hexokinase-2 (HK2), using a three-dimensional multicellular spheroid model of human ovarian adenocarcinoma (SKOV-3) cells and to develop an epidermal growth factor receptor-targeted liposomal formulation for improving inhibition of HK2 and the cytotoxicity of 3-bromopyruvate (3-BPA).

METHODS

Multicellular SKOV-3 tumor spheroids were developed using the hanging drop method and expression levels of glycolytic markers were examined. Non-targeted and epidermal growth factor receptor-targeted liposomal formulations of 3-BPA were formulated and characterized. Permeability and cellular uptake of the liposomal formulations in three-dimensional SKOV-3 spheroids was evaluated using confocal microscopy. The cytotoxicity and HK2 inhibition potential of solution form of 3-BPA was compared to the corresponding liposomal formulation by using cell proliferation and HK2 enzymatic assays.

RESULTS

SKOV-3 spheroids were reproducibly developed using the 96-well hanging drop method, with an average size of 900 µm by day 5. HK2 enzyme activity levels under hypoxic conditions were found to be higher than under normoxic conditions (P<0.0001, Student's t-test, unpaired and two-tailed). Liposomal formulations (both non-targeted and targeted) of 3-BPA showed a more potent inhibitory effect (P<0.001, Student's t-test, unpaired and two-tailed) at a dose of 50 µM than the aqueous solution form at 3, 6, and 24 hours post administration. Similarly, the cytotoxic activity 3-BPA at various concentrations (10 µM-100 µM) showed that the liposomal formulations had an enhanced cytotoxic effect of 2-5-fold (P<0.0001, Student's t-test, unpaired and two-tailed) when compared to the aqueous solution form for both 10 µM and 25 µM concentrations.

CONCLUSION

SKOV-3 spheroids developed by the hanging drop method can be used as a tumor aerobic glycolysis model for evaluation of therapies targeting the glycolytic pathway in cancer cells. Encapsulation of 3-BPA in a liposomal formulation improved permeability, HK2 inhibition, and cytotoxicity in the multicellular spheroid model.

Mathematical modeling of efficient protocols to control glioma growth

In this paper we propose a mathematical model to describe the evolution of glioma cells taking into account the viscoelastic properties of brain tissue. The mathematical model is established considering that the glioma cells are of two phenotypes: migratory and proliferative. The evolution of the migratory cells is described by a diffusion-reaction equation of non Fickian type deduced considering a mass conservation law with a non Fickian migratory mass flux. The evolution of the proliferative cells is described by a reaction equation. A stability analysis that leads to the design of efficient protocols is presented. Numerical simulations that illustrate the behavior of the mathematical model are included.

Application of mathematical modeling in sustained release delivery systems

INTRODUCTION

This review, presenting as starting point the concept of the mathematical modeling, is aimed at the physical and mathematical description of the most important mechanisms regulating drug delivery from matrix systems. The precise knowledge of the delivery mechanisms allows us to set up powerful mathematical models which, in turn, are essential for the design and optimization of appropriate drug delivery systems.

AREAS COVERED

The fundamental mechanisms for drug delivery from matrices are represented by drug diffusion, matrix swelling, matrix erosion, drug dissolution with possible recrystallization (e.g., as in the case of amorphous and nanocrystalline drugs), initial drug distribution inside the matrix, matrix geometry, matrix size distribution (in the case of spherical matrices of different diameter) and osmotic pressure. Depending on matrix characteristics, the above-reported variables may play a different role in drug delivery; thus the mathematical model needs to be built solely on the most relevant mechanisms of the particular matrix considered.

EXPERT OPINION

Despite the somewhat diffident behavior of the industrial world, in the light of the most recent findings, we believe that mathematical modeling may have a tremendous potential impact in the pharmaceutical field. We do believe that mathematical modeling will be more and more important in the future especially in the light of the rapid advent of personalized medicine, a novel therapeutic approach intended to treat each single patient instead of the 'average' patient.

Vital imaging of multicellular spheroids

Cell behavior is significantly different in two-dimensional and three-dimensional culture conditions, and a number of methods have been developed to establish and study three-dimensional cellular arrays in vitro. When grown under nonadherent conditions, many types of cells form structures called multicellular spheroids (MCSs), which have been popular models to study cell behavior in a three-dimensional environment. The histoarchitecture of MCSs derived from malignant cells resembles that of tumors, and there is rapidly increasing interest in using these structures to more accurately understand the dynamics of cancer cells in situ, including their responses to chemotherapeutics. Confocal microscopy is an extremely useful method to investigate cell behavior in MCSs due to its ability to more clearly image fluorescent probes at some depth in three-dimensional structures. This chapter describes some basic approaches toward visualizing a variety of fluorescent probes in MCSs.

Therapeutic angiogenesis of three-dimensionally cultured adipose-derived stem cells in rat infarcted hearts

BACKGROUND AIMS

To successfully treat myocardial infarction (MI), blood must be resupplied to the ischemic myocardium by inducing angiogenesis. Many studies report enhanced angiogenesis using stem cells; however, the therapeutic efficacy of cell transplant remains low because transplanted cells may not survive, be retained at the site of transplant, or develop into vascular tissue. In this study, we assessed the therapeutic potential of three-dimensional cell masses (3DCM) composed of human adipose-derived stem cells (hASC) in a rat MI model.

METHODS

For formation of 3DCM, hASC were cultured on a substrate with immobilized fibroblast growth factor 2. The morphology and phenotypes of 3DCM were analyzed 1 day after culture. The cells (hASC and 3DCM, 5 × 10(5) cells) were injected into ischemic regions after ligation of the left coronary artery (n = 6 in each group). Cell retention ratio, therapeutic efficacy and vascularization were evaluated 4 weeks after transplant.

RESULTS

A spheroid-type 3DCM, which included vascular cells (CD34(+)/CD31(+)/KDR(+)/α-SMA(+)) with high production of human vascular endothelial growth factor, was obtained. Infarct size and cardiomyocyte apoptosis were reduced in the 3DCM-injected group compared with the hASC-injected group. The retention ratio of hASC was 14-fold higher in the 3DCM-injected group. Many transplanted cells differentiated into endothelial and smooth muscle cells and formed vascular networks incorporated into host vessels.

CONCLUSIONS

Transplant of 3DCM may be useful for angiogenic cell therapy to treat MI.

Opportunities and challenges for use of tumor spheroids as models to test drug delivery and efficacy

Multicellular spheroids are three dimensional in vitro microscale tissue analogs. The current article examines the suitability of spheroids as an in vitro platform for testing drug delivery systems. Spheroids model critical physiologic parameters present in vivo, including complex multicellular architecture, barriers to mass transport, and extracellular matrix deposition. Relative to two-dimensional cultures, spheroids also provide better target cells for drug testing and are appropriate in vitro models for studies of drug penetration. Key challenges associated with creation of uniformly sized spheroids, spheroids with small number of cells and co-culture spheroids are emphasized in the article. Moreover, the assay techniques required for the characterization of drug delivery and efficacy in spheroids and the challenges associated with such studies are discussed. Examples for the use of spheroids in drug delivery and testing are also emphasized. By addressing these challenges with possible solutions, multicellular spheroids are becoming an increasingly useful in vitro tool for drug screening and delivery to pathological tissues and organs.

Understanding cancer mechanisms through network dynamics

Cancer is a complex, multifaceted disease. Cellular systems are perturbed both during the onset and development of cancer, and the behavioural change of tumour cells usually involves a broad range of dynamic variations. To an extent, the difficulty of monitoring the systemic change has been alleviated by recent developments in the high-throughput technologies. At both the genomic as well as proteomic levels, the technological advances in microarray and mass spectrometry, in conjunction with computational simulations and the construction of human interactome maps have facilitated the progress of identifying disease-associated genes. On a systems level, computational approaches developed for network analysis are becoming especially useful for providing insights into the mechanism behind tumour development and metastasis. This review emphasizes network approaches that have been developed to study cancer and provides an overview of our current knowledge of protein-protein interaction networks, and how their systemic perturbation can be analysed by two popular network simulation methods: Boolean network and ordinary differential equations.

Antitumor efficacy following the intracellular and interstitial release of liposomal doxorubicin

pH-triggered lipid-membranes designed from biophysical principles are evaluated in the form of targeted liposomal doxorubicin with the aim to ultimately better control the growth of vascularized tumors. We compare the antitumor efficacy of anti-HER2/neu pH-triggered lipid vesicles encapsulating doxorubicin to the anti-HER2/neu form of an FDA approved liposomal doxorubicin of DSPC/cholesterol-based vesicles. The HER2/neu receptor is chosen due to its abundance in human breast cancers and its connection to low prognosis. On a subcutaneous murine BT474 xenograft model, superior control of tumor growth is demonstrated by targeted pH-triggered vesicles relative to targeted DSPC/cholesterol-based vesicles (35% vs. 19% decrease in tumor volume after 32 days upon initiation of treatment). Superior tumor control is also confirmed on SKBR3 subcutaneous xenografts of lower HER2/neu expression. The non-targeted form of pH-triggered vesicles encapsulating doxorubicin results also in better tumor control relative to the non-targeted DSPC/cholesterol-based vesicles (34% vs. 41% increase in tumor volume). Studies in BT474 multicellular spheroids suggest that the observed efficacy could be attributed to release of doxorubicin directly into the acidic tumor interstitium from pH-triggered vesicles extravasated into the tumor but not internalized by cancer cells. pH-triggered liposome carriers engineered from gel-phase bilayers that reversibly phase-separate with lowering pH, form transiently defective interfacial boundaries resulting in fast release of encapsulated doxorubicin. Our studies show that pH-triggered liposomes release encapsulated doxorubicin intracellularly and intratumorally, and may improve tumor control at the same or even lower administered doses relative to FDA approved liposomal chemotherapy.

Use of mathematical models to understand anticancer drug delivery and its effect on solid tumors

The transport of anticancer drugs and their effect on tumor cells involve a number of physical and biochemical processes. Mathematical modeling provides a tool to help us understand the interaction of these complex processes, thereby contributing to the improvement and optimization of drug delivery. This article starts with a discussion of the biological and physiological properties of tumors, which are often found as barriers to anticancer drug transport and effect. A broad spectrum of mathematical models is reviewed to give an overview of the current state of modeling approaches and different categories of models are outlined. These include pharmacokinetic and transport-based models for the prediction of temporal and temporal-spatial profiles of antidrug concentrations, as well as empirical or deterministic models to describe the effect of drug. We conclude that the systematic elucidation and integration of cellular signal transduction with the biophysical aspects of drug transport will lead to a better understanding of the entire drug-delivery process.

Angiogenesis in ischemic tissue produced by spheroid grafting of human adipose-derived stromal cells

Stem cells offer significant therapeutic promise for the treatment of ischemic disease. However, stem cells transplanted into ischemic tissue exhibit limited therapeutic efficacy due to poor engraftment in vivo. Several strategies for improving the survival and engraftment of stem cells in ischemic tissue have been developed including transplantation in combination with growth factor delivery, genetic modification of stem cells, and the use of cell-transplantation scaffolds. Here, we demonstrate that human adipose-derived stromal cells (hADSCs) cultured and grafted as spheroids exhibit improved therapeutic efficacy for ischemia treatment. hADSCs were cultured in monolayer or spheroids. Spheroid cultures were more effective in preconditioning hADSCs to a hypoxic environment, upregulating hypoxia-adaptive signals (i.e., stromal cell-derived factor-1α and hypoxia-inducible factor-1α), inhibiting apoptosis, and enhancing secretion of both angiogenic and anti-apoptotic factors (i.e., hepatocyte growth factor, vascular endothelial growth factor, and fibroblast growth factor 2) compared to monolayer cultures. Moreover, cell harvesting following spheroid cultures avoided damage to extracellular matrices due to harsh proteolytic enzyme treatment, thereby preventing anoikis (apoptosis induced by a lack of cell-matrix interaction). Following intramuscular transplantation to ischemic hindlimbs of athymic mice, hADSC spheroids showed improved cell survival, angiogenic factor secretion, neovascularization, and limb survival as compared to hADSCs grafted as dissociated cells. Taken together, spheroid cultures precondition hADSCs to a hypoxic environment, and grafting hADSCs as spheroids to ischemic limbs improves therapeutic efficacy for ischemia treatment due to enhanced cell survival and paracrine effects. Spheroid-based cell delivery could be a simple and effective strategy for improving stem cell therapy for ischemic diseases, eliminating the need for growth factor delivery, biomaterial scaffolds or genetic modification.

Nonlinear modelling of cancer: bridging the gap between cells and tumours

Despite major scientific, medical and technological advances over the last few decades, a cure for cancer remains elusive. The disease initiation is complex, and including initiation and avascular growth, onset of hypoxia and acidosis due to accumulation of cells beyond normal physiological conditions, inducement of angiogenesis from the surrounding vasculature, tumour vascularization and further growth, and invasion of surrounding tissue and metastasis. Although the focus historically has been to study these events through experimental and clinical observations, mathematical modelling and simulation that enable analysis at multiple time and spatial scales have also complemented these efforts. Here, we provide an overview of this multiscale modelling focusing on the growth phase of tumours and bypassing the initial stage of tumourigenesis. While we briefly review discrete modelling, our focus is on the continuum approach. We limit the scope further by considering models of tumour progression that do not distinguish tumour cells by their age. We also do not consider immune system interactions nor do we describe models of therapy. We do discuss hybrid-modelling frameworks, where the tumour tissue is modelled using both discrete (cell-scale) and continuum (tumour-scale) elements, thus connecting the micrometre to the centimetre tumour scale. We review recent examples that incorporate experimental data into model parameters. We show that recent mathematical modelling predicts that transport limitations of cell nutrients, oxygen and growth factors may result in cell death that leads to morphological instability, providing a mechanism for invasion via tumour fingering and fragmentation. These conditions induce selection pressure for cell survivability, and may lead to additional genetic mutations. Mathematical modelling further shows that parameters that control the tumour mass shape also control its ability to invade. Thus, tumour morphology may serve as a predictor of invasiveness and treatment prognosis.

The influence of P-glycoprotein expression and its inhibitors on the distribution of doxorubicin in breast tumors

Background

Anti-cancer drugs access solid tumors via blood vessels, and must penetrate tumor tissue to reach all cancer cells. Previous studies have demonstrated steep gradients of decreasing doxorubicin fluorescence with increasing distance from blood vessels, such that many tumor cells are not exposed to drug. Studies using multilayered cell cultures show that increased P-glycoprotein (PgP) is associated with better penetration of doxorubicin, while PgP inhibitors decrease drug penetration in tumor tissue. Here we evaluate the effect of PgP expression on doxorubicin distribution in vivo.

Methods

Mice bearing tumor sublines with either high or low expression of PgP were treated with doxorubicin, with or without pre-treatment with the PgP inhibitors verapamil or PSC 833. The distribution of doxorubicin in relation to tumor blood vessels was quantified using immunofluorescence.

Results

Our results indicate greater uptake of doxorubicin by cells near blood vessels in wild type as compared to PgP-overexpressing tumors, and pre-treatment with verapamil or PSC 833 increased uptake in PgP-overexpressing tumors. However, there were steeper gradients of decreasing doxorubicin fluorescence in wild-type tumors compared to PgP overexpressing tumors, and treatment of PgP overexpressing tumors with PgP inhibitors led to steeper gradients and greater heterogeneity in the distribution of doxorubicin.

Conclusion

PgP inhibitors increase uptake of doxorubicin in cells close to blood vessels, have little effect on drug uptake into cells at intermediate distances, and might have a paradoxical effect to decrease doxorubicin uptake into distal cells. This effect probably contributes to the limited success of PgP inhibitors in clinical trials.

Prediction of drug response in breast cancer using integrative experimental/computational modeling

Nearly 30% of women with early-stage breast cancer develop recurrent disease attributed to resistance to systemic therapy. Prevailing models of chemotherapy failure describe three resistant phenotypes: cells with alterations in transmembrane drug transport, increased detoxification and repair pathways, and alterations leading to failure of apoptosis. Proliferative activity correlates with tumor sensitivity. Cell-cycle status, controlling proliferation, depends on local concentration of oxygen and nutrients. Although physiologic resistance due to diffusion gradients of these substances and drugs is a recognized phenomenon, it has been difficult to quantify its role with any accuracy that can be exploited clinically. We implement a mathematical model of tumor drug response that hypothesizes specific functional relationships linking tumor growth and regression to the underlying phenotype. The model incorporates the effects of local drug, oxygen, and nutrient concentrations within the three-dimensional tumor volume, and includes the experimentally observed resistant phenotypes of individual cells. We conclude that this integrative method, tightly coupling computational modeling with biological data, enhances the value of knowledge gained from current pharmacokinetic measurements, and, further, that such an approach could predict resistance based on specific tumor properties and thus improve treatment outcome.

Recent advances in three-dimensional multicellular spheroid culture for biomedical research

Many types of mammalian cells can aggregate and differentiate into 3-D multicellular spheroids when cultured in suspension or a nonadhesive environment. Compared to conventional monolayer cultures, multicellular spheroids resemble real tissues better in terms of structural and functional properties. Multicellular spheroids formed by transformed cells are widely used as avascular tumor models for metastasis and invasion research and for therapeutic screening. Many primary or progenitor cells on the other hand, show significantly enhanced viability and functional performance when grown as spheroids. Multicellular spheroids in this aspect are ideal building units for tissue reconstruction. Here we review the current understanding of multicellular spheroid formation mechanisms, their biomedical applications, and recent advances in spheroid culture, manipulation, and analysis techniques.

Predicting drug pharmacokinetics and effect in vascularized tumors using computer simulation

In this paper, we investigate the pharmacokinetics and effect of doxorubicin and cisplatin in vascularized tumors through two-dimensional simulations. We take into account especially vascular and morphological heterogeneity as well as cellular and lesion-level pharmacokinetic determinants like P-glycoprotein (Pgp) efflux and cell density. To do this we construct a multi-compartment PKPD model calibrated from published experimental data and simulate 2-h bolus administrations followed by 18-h drug washout. Our results show that lesion-scale drug and nutrient distribution may significantly impact therapeutic efficacy and should be considered as carefully as genetic determinants modulating, for example, the production of multidrug-resistance protein or topoisomerase II. We visualize and rigorously quantify distributions of nutrient, drug, and resulting cell inhibition. A main result is the existence of significant heterogeneity in all three, yielding poor inhibition in a large fraction of the lesion, and commensurately increased serum drug concentration necessary for an average 50% inhibition throughout the lesion (the IC(50) concentration). For doxorubicin the effect of hypoxia and hypoglycemia ("nutrient effect") is isolated and shown to further increase cell inhibition heterogeneity and double the IC(50), both undesirable. We also show how the therapeutic effectiveness of doxorubicin penetration therapy depends upon other determinants affecting drug distribution, such as cellular efflux and density, offering some insight into the conditions under which otherwise promising therapies may fail and, more importantly, when they will succeed. Cisplatin is used as a contrast to doxorubicin since both published experimental data and our simulations indicate its lesion distribution is more uniform than that of doxorubicin. Because of this some of the complexity in predicting its therapeutic efficacy is mitigated. Using this advantage, we show results suggesting that in vitro monolayer assays using this drug may more accurately predict in vivo performance than for drugs like doxorubicin. The nonlinear interaction among various determinants representing cell and lesion phenotype as well as therapeutic strategies is a unifying theme of our results. Throughout it can be appreciated that macroscopic environmental conditions, notably drug and nutrient distributions, give rise to considerable variation in lesion response, hence clinical resistance. Moreover, the synergy or antagonism of combined therapeutic strategies depends heavily upon this environment.

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.

Modelling the cell cycle and cell movement in multicellular tumour spheroids

This paper analyses a recent mathematical model of avascular tumour spheroid growth which accounts for both cell cycle dynamics and chemotactic driven cell movement. The model considers cells to exist in one of two compartments: proliferating and quiescent, as well as accounting for necrosis and apoptosis. One particular focus of this paper is the behaviour created when proliferating and quiescent cells have different chemotactic responses to an extracellular nutrient supply. Two very different steady-state behaviours are identified corresponding to those cases where proliferating cells move either more quickly or more slowly than quiescent cells in response to a gradient in the extracellular nutrient supply. The case where proliferating cells move more rapidly leads to the commonly accepted spheroid structure of a thin layer of proliferating cells surrounding an inner quiescent core. In the case where proliferating cells move more slowly than quiescent cells the model predicts an interesting structure of a thin layer of quiescent cells surrounding an inner core of proliferating and quiescent cells. The sensitivity of this tumour structure to the cell cycle model parameters is also discussed. In particular variations in the steady-state size of the tumour and the types of transient behaviour are explored. The model reveals interesting transient behaviour with sharply delineated regions of proliferating and quiescent cells.

Macrophage-based anti-cancer therapy: modelling different modes of tumour targeting

Tumour hypoxia is associated with poor drug delivery and low rates of cell proliferation, factors that limit the efficacy of therapies that target proliferating cells. Since macrophages localise within hypoxic regions, a promising way to target hypoxic tumour cells involves engineering macrophages to express therapeutic genes under hypoxia. In this paper we develop mathematical models to compare the responses of avascular tumour spheroids to two modes of action: either the macrophages deliver an enzyme that activates an externally applied prodrug (bystander model), or they deliver cytotoxic factors directly (local model). The models we develop comprise partial differential equations for a multiphase mixture of tumour cells, macrophages and extracellular fluid, coupled to a moving boundary representing the spheroid surface. Chemical constituents, such as oxygen and drugs, diffuse within the multiphase mixture. Simulations of both models show the spheroid evolving to an equilibrium or to a travelling wave (multiple stable solutions are also possible). We uncover the parameter dependence of the wave speed and steady-state tumour size, and bifurcations between these solution forms. For some parameter sets, adding extra macrophages has a counterintuitive deleterious effect, triggering a bifurcation from bounded to unbounded tumour growth. While these features are common to the bystander and local models, the crucial difference is where cell death occurs. The bystander model is comparable to traditional chemotherapy, with poor targeting of hypoxic tumour cells; however, the local mode of action is more selective for hypoxic regions. We conclude that effective targeting of hypoxic tumour cells may require the use of drugs with limited mobility or whose action does not depend on cell proliferation.

The minimal, phase-transition model for the cell-number maintenance by the hyperplasia-extended homeorhesis

Oncogenic hyperplasia is the first and inevitable stage of formation of a (solid) tumor. This stage is also the core of many other proliferative diseases. The present work proposes the first minimal model that combines homeorhesis with oncogenic hyperplasia where the latter is regarded as a genotoxically activated homeorhetic dysfunction. This dysfunction is specified as the transitions of the fluid of cells from a fluid, homeorhetic state to a solid, hyperplastic-tumor state, and back. The key part of the model is a nonlinear reaction-diffusion equation (RDE) where the biochemical-reaction rate is generalized to the one in the well-known Schlögl physical theory of the non-equilibrium phase transitions. A rigorous analysis of the stability and qualitative aspects of the model, where possible, are presented in detail. This is related to the spatially homogeneous case, i.e. when the above RDE is reduced to a nonlinear ordinary differential equation. The mentioned genotoxic activation is treated as a prevention of the quiescent G0-stage of the cell cycle implemented with the threshold mechanism that employs the critical concentration of the cellular fluid and the nonquiescent-cell-duplication time. The continuous tumor morphogeny is described by a time-space-dependent cellular-fluid concentration. There are no sharp boundaries (i.e. no concentration jumps exist) between the domains of the homeorhesis- and tumor-cell populations. No presumption on the shape of a tumor is used. To estimate a tumor in specific quantities, the model provides the time-dependent tumor locus, volume, and boundary that also points out the tumor shape and size. The above features are indispensable in the quantitative development of antiproliferative drugs or therapies and strategies to prevent oncogenic hyperplasia in cancer and other proliferative diseases. The work proposes an analytical-numerical method for solving the aforementioned RDE. A few topics for future research are suggested.