Model for in vivo progression of tumors based on co-evolving cell population and vasculature

Modeling iontophoretic drug delivery in a microfluidic device

Iontophoresis employs low-intensity electrical voltage and continuous constant current to direct a charged drug into a tissue. Iontophoretic drug delivery has recently been used as a novel method for cancer treatment in vivo. There is an urgent need to precisely model the low-intensity electric fields in cell culture systems to optimize iontophoretic drug delivery to tumors. Here, we present an iontophoresis-on-chip (IOC) platform to precisely quantify carboplatin drug delivery and its corresponding anti-cancer efficacy under various voltages and currents. In this study, we use an in vitro heparin-based hydrogel microfluidic device to model the movement of a charged drug across an extracellular matrix (ECM) and in MDA-MB-231 triple-negative breast cancer (TNBC) cells. Transport of the drug through the hydrogel was modeled based on diffusion and electrophoresis of charged drug molecules in the direction of an oppositely charged electrode. The drug concentration in the tumor extracellular matrix was computed using finite element modeling of transient drug transport in the heparin-based hydrogel. The model predictions were then validated using the IOC platform by comparing the predicted concentration of a fluorescent cationic dye (Alexa Fluor 594®) to the actual concentration in the microfluidic device. Alexa Fluor 594® was used because it has a molecular weight close to paclitaxel, the gold standard drug for treating TNBC, and carboplatin. Our results demonstrated that a 50 mV DC electric field and a 3 mA electrical current significantly increased drug delivery and tumor cell death by 48.12% ± 14.33 and 39.13% ± 12.86, respectively (n = 3, p-value <0.05). The IOC platform and mathematical drug delivery model of iontophoresis are promising tools for precise delivery of chemotherapeutic drugs into solid tumors. Further improvements to the IOC platform can be made by adding a layer of epidermal cells to model the skin.

Anti-vascular nano agents: a promising approach for cancer treatment

Anti-vascular agents (AVAs) are a class of promising therapeutic agents with tumor vasculature targeting properties, which can be divided into two types: anti-angiogenic agents (AAAs, inhibit angiogenesis factors) and vascular disrupting agents (VDAs, disrupt established tumor vasculature). AVAs exhibit an enhanced anti-cancer effect by cutting off the oxygen and nutrition supplement channels of tumors. However, the intrinsic drawbacks, such as poor hydrophilicity, undesirable membrane permeability and inferior tumor targeting ability, discount their anti-vascular efficacy. Fortunately, the development of nanotechnology has brought an opportunity for efficient delivery of AVAs to tumour sites with great therapeutic efficacy. The works summarized in this review will provide an understanding of recent advances of anti-vascular nano agents (AVNAs) with a goal to define the mechanism of anti-vascular-based cancer therapy and discuss the challenges and opportunities of AVNAs for clinical translation.

Predicting Patient-Specific Radiotherapy Protocols Based on Mathematical Model Choice for Proliferation Saturation Index

Radiation is commonly used in cancer treatment. Over 50% of all cancer patients will undergo radiotherapy (RT) as part of cancer care. Scientific advances in RT have primarily focused on the physical characteristics of treatment including beam quality and delivery. Only recently have inroads been made into utilizing tumor biology and radiobiology to design more appropriate RT protocols. Tumors are composites of proliferating and growth-arrested cells, and overall response depends on their respective proportions at irradiation. Prokopiou et al. (Radiat Oncol 10:159, 2015) developed the concept of the proliferation saturation index (PSI) to augment the clinical decision process associated with RT. This framework is based on the application of the logistic equation to pre-treatment imaging data in order to estimate a patient-specific tumor carrying capacity, which is then used to recommend a specific RT protocol. It is unclear, however, how dependent clinical recommendations are on the underlying tumor growth law. We discuss a PSI framework with a generalized logistic equation that can capture kinetics of different well-known growth laws including logistic and Gompertzian growth. Estimation of model parameters on the basis of clinical data revealed that the generalized logistic model can describe data equally well for a wide range of the generalized logistic exponent value. Clinical recommendations based on the calculated PSI, however, are strongly dependent on the specific growth law assumed. Our analysis suggests that the PSI framework may best be utilized in clinical practice when the underlying tumor growth law is known, or when sufficiently many tumor growth models suggest similar fractionation protocols.

Role of mathematical medicine in gastrointestinal carcinoma: Current status and perspectives

Mathematical medicine has already played an important role in clinical and basic research as a major interdisciplinary branch of medicine. Mathematical medicine has an important role not only in imaging diagnosis, image storage and transmission in gastrointestinal (GI) cancer, but also in tumor precision therapy. Specifically, in the field of minimally invasive treatment such as precise ablation, 3-dimension modeling, navigation, and surgical simulation significantly improve the therapeutic safety and efficiency in GI cancer. In addition, in the era of big data, data analysis and individualized therapy using mathematical medicine will become a trend in the future, offering an effective method for diagnosing and treating GI cancer and promoting clinical and scientific research.

In silico modeling for tumor growth visualization

BACKGROUND

Cancer is a complex disease. Fundamental cellular based studies as well as modeling provides insight into cancer biology and strategies to treatment of the disease. In silico models complement in vivo models. Research on tumor growth involves a plethora of models each emphasizing isolated aspects of benign and malignant neoplasms. Biologists and clinical scientists are often overwhelmed by the mathematical background knowledge necessary to grasp and to apply a model to their own research.

RESULTS

We aim to provide a comprehensive and expandable simulation tool to visualizing tumor growth. This novel Web-based application offers the advantage of a user-friendly graphical interface with several manipulable input variables to correlate different aspects of tumor growth. By refining model parameters we highlight the significance of heterogeneous intercellular interactions on tumor progression. Within this paper we present the implementation of the Cellular Potts Model graphically presented through Cytoscape.js within a Web application. The tool is available under the MIT license at https://github.com/davcem/cpm-cytoscape and http://styx.cgv.tugraz.at:8080/cpm-cytoscape/ .

CONCLUSION

In-silico methods overcome the lack of wet experimental possibilities and as dry method succeed in terms of reduction, refinement and replacement of animal experimentation, also known as the 3R principles. Our visualization approach to simulation allows for more flexible usage and easy extension to facilitate understanding and gain novel insight. We believe that biomedical research in general and research on tumor growth in particular will benefit from the systems biology perspective.

Modelling tumour cell proliferation from vascular structure using tissue decomposition into avascular elements

Computer models allow the mechanistically detailed study of tumour proliferation and its dependency on nutrients. However, the computational study of large vascular tumours requires detailed information on the 3-dimensional vessel network and rather high computation times due to complex geometries. This study puts forward the idea of partitioning vascularised tissue into connected avascular elements that can exchange cells and nutrients between each other. Our method is able to rapidly calculate the evolution of proliferating as well as dead and quiescent cells, and hence a proliferative index, from a given amount and distribution of vascularisation of arbitrary complexity. Applying our model, we found that a heterogeneous vessel distribution provoked a higher proliferative index, suggesting increased malignancy, and increased the amount of dead cells compared to a more static tumour environment when a homogenous vessel distribution was assumed. We subsequently demonstrated that under certain amounts of vascularisation, cell proliferation may even increase when vessel density decreases, followed by a subsequent decrease of proliferation. This effect was due to a trade-off between an increase in compensatory proliferation for replacing dead cells and a decrease of cell population due to lack of oxygen supply in lowly vascularised tumours. Findings were illustrated by an ectopic colorectal cancer mouse xenograft model. Our presented approach can be in the future applied to study the effect of cytostatic, cytotoxic and anti-angiogenic chemotherapy and is ideally suited for translational systems biology, where rapid interaction between theory and experiment is essential.

A spatial model predicts that dispersal and cell turnover limit intratumour heterogeneity

Most cancers in humans are large, measuring centimetres in diameter, and composed of many billions of cells. An equivalent mass of normal cells would be highly heterogeneous as a result of the mutations that occur during each cell division. What is remarkable about cancers is that virtually every neoplastic cell within a large tumour often contains the same core set of genetic alterations, with heterogeneity confined to mutations that emerge late during tumour growth. How such alterations expand within the spatially constrained three-dimensional architecture of a tumour, and come to dominate a large, pre-existing lesion, has been unclear. Here we describe a model for tumour evolution that shows how short-range dispersal and cell turnover can account for rapid cell mixing inside the tumour. We show that even a small selective advantage of a single cell within a large tumour allows the descendants of that cell to replace the precursor mass in a clinically relevant time frame. We also demonstrate that the same mechanisms can be responsible for the rapid onset of resistance to chemotherapy. Our model not only provides insights into spatial and temporal aspects of tumour growth, but also suggests that targeting short-range cellular migratory activity could have marked effects on tumour growth rates.

A computational model incorporating neural stem cell dynamics reproduces glioma incidence across the lifespan in the human population

Glioma is the most common form of primary brain tumor. Demographically, the risk of occurrence increases until old age. Here we present a novel computational model to reproduce the probability of glioma incidence across the lifespan. Previous mathematical models explaining glioma incidence are framed in a rather abstract way, and do not directly relate to empirical findings. To decrease this gap between theory and experimental observations, we incorporate recent data on cellular and molecular factors underlying gliomagenesis. Since evidence implicates the adult neural stem cell as the likely cell-of-origin of glioma, we have incorporated empirically-determined estimates of neural stem cell number, cell division rate, mutation rate and oncogenic potential into our model. We demonstrate that our model yields results which match actual demographic data in the human population. In particular, this model accounts for the observed peak incidence of glioma at approximately 80 years of age, without the need to assert differential susceptibility throughout the population. Overall, our model supports the hypothesis that glioma is caused by randomly-occurring oncogenic mutations within the neural stem cell population. Based on this model, we assess the influence of the (experimentally indicated) decrease in the number of neural stem cells and increase of cell division rate during aging. Our model provides multiple testable predictions, and suggests that different temporal sequences of oncogenic mutations can lead to tumorigenesis. Finally, we conclude that four or five oncogenic mutations are sufficient for the formation of glioma.

Cancer systems biology: embracing complexity to develop better anticancer therapeutic strategies

The transformation of normal cells into cancer cells and maintenance of the malignant state and phenotypes are associated with genetic and epigenetic deregulations, altered cellular signaling responses and aberrant interactions with the microenvironment. These alterations are constantly evolving as tumor cells face changing selective pressures induced by the cells themselves, the microenvironment and drug treatments. Tumors are also complex ecosystems where different, sometime heterogeneous, subclonal tumor populations and a variety of nontumor cells coexist in a constantly evolving manner. The interactions between molecules and between cells that arise as a result of these alterations and ecosystems are even more complex. The cancer research community is increasingly embracing this complexity and adopting a combination of systems biology methods and integrated analyses to understand and predictively model the activity of cancer cells. Systems biology approaches are helping to understand the mechanisms of tumor progression and design more effective cancer therapies. These approaches work in tandem with rapid technological advancements that enable data acquisition on a broader scale, with finer accuracy, higher dimensionality and higher throughput than ever. Using such data, computational and mathematical models help identify key deregulated functions and processes, establish predictive biomarkers and optimize therapeutic strategies. Moving forward, implementing patient-specific computational and mathematical models of cancer will significantly improve the specificity and efficacy of targeted therapy, and will accelerate the adoption of personalized and precision cancer medicine.

Current advances in mathematical modeling of anti-cancer drug penetration into tumor tissues

Delivery of anti-cancer drugs to tumor tissues, including their interstitial transport and cellular uptake, is a complex process involving various biochemical, mechanical, and biophysical factors. Mathematical modeling provides a means through which to understand this complexity better, as well as to examine interactions between contributing components in a systematic way via computational simulations and quantitative analyses. In this review, we present the current state of mathematical modeling approaches that address phenomena related to drug delivery. We describe how various types of models were used to predict spatio-temporal distributions of drugs within the tumor tissue, to simulate different ways to overcome barriers to drug transport, or to optimize treatment schedules. Finally, we discuss how integration of mathematical modeling with experimental or clinical data can provide better tools to understand the drug delivery process, in particular to examine the specific tissue- or compound-related factors that limit drug penetration through tumors. Such tools will be important in designing new chemotherapy targets and optimal treatment strategies, as well as in developing non-invasive diagnosis to monitor treatment response and detect tumor recurrence.

A possible explanation for the variable frequencies of cancer stem cells in tumors

A controversy surrounds the frequency of cancer stem cells (CSCs) in solid tumors. Initial studies indicated that these cells had a frequency ranging from 0.0001 to 0.1% of the total cells. Recent studies have shown that this does not always seem to be the case. Some of these studies have indicated a frequency of [Formula: see text]. In this paper we propose a stochastic model that is able to capture this potential variability in the frequency of CSCs among the various type of tumors. Considerations regarding the heterogeneity of the tumor cells and its consequences are included. Possible effects on conventional treatments in clinical practice are also described. The model results suggest that traditional attempts to combat cancer cells with rapid cycling can be very stimulating for the cancer stem cell populations.

Tumor growth dynamics: insights into evolutionary processes

Identifying the types of event that drive tumor evolution and progression is crucial for understanding cancer. We suggest that the analysis of tumor growth dynamics can provide a window into tumor biology and evolution by connecting them with the types of genetic change that have occurred. Although fundamentally important, the documentation of tumor growth kinetics is more sparse in the literature than is the molecular analysis of cells. Here, we provide a historical summary of tumor growth patterns and argue that they can be classified into five basic categories. We then illustrate how those categories can provide insights into events that drive tumor progression, by discussing a particular evolutionary model as an example and encouraging such analysis in a more general setting.

Systems pharmacological analysis of paclitaxel-mediated tumor priming that enhances nanocarrier deposition and efficacy

Paclitaxel (PAC)-mediated apoptosis decompresses and primes tumors for enhanced deposition of nanoparticulate agents such as pegylated liposomal doxorubicin (DXR). A quantitative pharmacokinetic/pharmacodynamic (PK/PD) approach was developed to analyze efficacy and identify optima for PAC combined with sterically stabilized liposome (SSL)-DXR. Using data extracted from diverse literature sources, Cremophor-paclitaxel (Taxol(®)) PK was described by a carrier-mediated dispositional model and SSL-DXR PK was described by a two-compartment model with first-order drug release. A hybrid-physiologic, well-stirred model with partition coefficients (Kp) captured intratumor concentrations. Apoptotic responses driving tumor priming were modeled using nonlinear, time-dependent transduction functions. The tumor growth model used net first-order growth and death rate constants, and two transit compartments that captured the temporal displacement of tumor exposure versus effect, and apoptotic signals from each agent were used to drive cytotoxic effects of the combination. The final model captured plasma and intratumor PK data, apoptosis induction profiles, and tumor growth for all treatments/sequences. A feedback loop representing PAC-induced apoptosis effects on Kp(_DXR) enabled the model to capture tumor-priming effects. Simulations to explore time- and sequence-dependent effects of priming indicated that PAC priming increased K(p_DXR) 3-fold. The intratumor concentrations producing maximal and half-maximal effects were 18 and 7.2 μg/ml for PAC, and 17.6 and 14.3 μg/ml for SSL-DXR. The duration of drug-induced apoptosis was 27.4 h for PAC and 15.8 h for SSL-DXR. Simulations suggested that PAC administered 24 h before peak priming could increase efficacy 2.5-fold over experimentally reported results. The quantitative approach developed in this article is applicable for evaluating tumor-priming strategies using diverse agents.

Multiscale imaging and computational modeling of blood flow in the tumor vasculature

The evolution in our understanding of tumor angiogenesis has been the result of pioneering imaging and computational modeling studies spanning the endothelial cell, microvasculature and tissue levels. Many of these primary data on the tumor vasculature are in the form of images from pre-clinical tumor models that provide a wealth of qualitative and quantitative information in many dimensions and across different spatial scales. However, until recently, the visualization of changes in the tumor vasculature across spatial scales remained a challenge due to a lack of techniques for integrating micro- and macroscopic imaging data. Furthermore, the paucity of three-dimensional (3-D) tumor vascular data in conjunction with the challenges in obtaining such data from patients presents a serious hurdle for the development and validation of predictive, multiscale computational models of tumor angiogenesis. In this review, we discuss the development of multiscale models of tumor angiogenesis, new imaging techniques capable of reproducing the 3-D tumor vascular architecture with high fidelity, and the emergence of "image-based models" of tumor blood flow and molecular transport. Collectively, these developments are helping us gain a fundamental understanding of the cellular and molecular regulation of tumor angiogenesis that will benefit the development of new cancer therapies. Eventually, we expect this exciting integration of multiscale imaging and mathematical modeling to have widespread application beyond the tumor vasculature to other diseases involving a pathological vasculature, such as stroke and spinal cord injury.