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

Systematic evaluation of MRI-based characterization of tumor-associated vascular morphology and hemodynamics via a dynamic digital phantom

Purpose

Validation of quantitative imaging biomarkers is a challenging task, due to the difficulty in measuring the ground truth of the target biological process. A digital phantom-based framework is established to systematically validate the quantitative characterization of tumor-associated vascular morphology and hemodynamics based on dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI).

Approach

A digital phantom is employed to provide a ground-truth vascular system within which 45 synthetic tumors are simulated. Morphological analysis is performed on high-spatial resolution DCE-MRI data (spatial/temporal resolution = 30 to 300    μ m / 60    s ) to determine the accuracy of locating the arterial inputs of tumor-associated vessels (TAVs). Hemodynamic analysis is then performed on the combination of high-spatial resolution and high-temporal resolution (spatial/temporal resolution = 60 to 300    μ m / 1 to 10 s) DCE-MRI data, determining the accuracy of estimating tumor-associated blood pressure, vascular extraction rate, interstitial pressure, and interstitial flow velocity.

Results

The observed effects of acquisition settings demonstrate that, when optimizing the DCE-MRI protocol for the morphological analysis, increasing the spatial resolution is helpful but not necessary, as the location and arterial input of TAVs can be recovered with high accuracy even with the lowest investigated spatial resolution. When optimizing the DCE-MRI protocol for hemodynamic analysis, increasing the spatial resolution of the images used for vessel segmentation is essential, and the spatial and temporal resolutions of the images used for the kinetic parameter fitting require simultaneous optimization.

Conclusion

An in silico validation framework was generated to systematically quantify the effects of image acquisition settings on the ability to accurately estimate tumor-associated characteristics.

The effect of tumor vascular remodeling and immune microenvironment activation induced by radiotherapy: quantitative evaluation with magnetic resonance/photoacoustic dual-modality imaging

Background

Tumor radiotherapy combined with immunotherapy for solid tumors has been proposed, but tumor vascular structure abnormalities and immune microenvironment often affect the therapeutic effect of tumor, and multimodal imaging technology can provide more accurate and comprehensive information in tumor research. The purpose of this study was to evaluate the dynamic monitoring of tumor blood vessels and microenvironment induced by radiotherapy by magnetic resonance/photoacoustic (MR/PA) imaging, and to explore its application value in radiotherapy combined with immunotherapy.

Methods

The tumor-bearing mice were randomly allocated into six groups, which received different doses of radiation therapy (2 Gy ×14 or 8 Gy ×3) and anti-programmed death ligand-1 (PD-L1) antibody for two consecutive weeks. MR/PA imaging was used to noninvasively evaluate the response of tumor to different doses of radiotherapy, combined with histopathological techniques to observe the tumor vessels and microenvironment.

Results

The inhibitory effect of high-dose radiotherapy on tumors was significantly greater than that of low-dose radiotherapy, with the MR images revealing that the signal intensity decreased significantly (P<0.05). Compared with those in the other groups, the tumor vascular density decreased significantly (P<0.01), and the vascular maturity index increased significantly in the low-dose group (P<0.05). The PA images showed that the deoxyhemoglobin and total hemoglobin levels decreased and the SO2 level increased after radiation treatment (P<0.05). In addition, the high-dose group had an increased number of tumor-infiltrating lymphocytes (CD4+ T and CD8+ T cells) (P<0.01, P<0.05) and natural killer cells (P<0.001) and increased PD-L1 expression in the tumors (P<0.05). The combination of radiotherapy and immunotherapy increased the survival rate of the mice (P<0.05), and a regimen of an 8 Gy dose of radiation combined with immunotherapy inhibited tumor growth and increased the survival rate of the mice to a greater degree than the 2 Gy radiation dose with immunotherapy combination (P=0.002).

Conclusions

Differential fractionation radiotherapy doses exert biological effects on tumor vascular and the immune microenvironment, and MR/PA can be used to evaluate tumor vascular remodeling after radiotherapy, which has certain value for the clinical applications of radiotherapy combined with immunotherapy.

Vascular phenotyping of the invasive front in breast cancer using a 3D angiogenesis atlas

OBJECTIVE

Vascular remodeling at the invasive tumor front (ITF) plays a critical role in progression and metastasis of triple negative breast cancer (TNBC). Therefore, there is a crucial need to characterize the vascular phenotype (i.e. changes in the structure and function of vasculature) of the ITF and tumor core (TC) in TNBC. This requires high-resolution, 3D structural and functional microvascular data that spans the ITF and TC (i.e. ∼4-5 mm from the tumor's edge). Since such data are often challenging to obtain with most conventional imaging approaches, we employed a unique "3D whole-tumor angiogenesis atlas" derived from orthotopic xenografts to characterize the vascular phenotype of the ITF and TC in TNBC.

METHODS

First, high-resolution (8 μm) computed tomography (CT) images of "whole-tumor" microvasculature were acquired from eight orthotopic TNBC xenografts, of which three tumors were excised at post-inoculation day 21 (i.e. early-stage) and five tumors were excised at post-inoculation day 35 (i.e. advanced-stage). These 3D morphological CT data were combined with soft tissue contrast from MRI as well as functional data generated in silico using image-based hemodynamic modeling to generate a multi-layered "angiogenesis atlas". Employing this atlas, blood vessels were first spatially stratified within the ITF (i.e. ≤1 mm from the tumor's edge) and TC (i.e. >1 mm from the tumor's edge) of each tumor xenograft. Then, a novel method was developed to visualize and characterize microvascular remodeling and perfusion changes in terms of distance from the tumor's edge.

RESULTS

The angiogenesis atlas enabled the 3D visualization of changes in tumor vessel growth patterns, morphology and perfusion within the ITF and TC. Early and advanced stage tumors demonstrated significant differences in terms of their edge-to-center distributions for vascular surface area density, vascular length density, intervessel distance and simulated perfusion density (p ≪ 0.01). Elevated vascular length density, vascular surface area density and perfusion density along the circumference of the ITF was suggestive of a preferential spatial pattern of angiogenic growth in this tumor cohort. Finally, we demonstrated the feasibility of differentiating the vascular phenotypes of ITF and TC in these TNBC xenografts.

CONCLUSIONS

The combination of a 3D angiogenesis atlas and image-based hemodynamic modeling heralds a new approach for characterizing the role of vascular remodeling in cancer and other diseases.

SMoRe ParS: A novel methodology for bridging modeling modalities and experimental data applied to 3D vascular tumor growth

Multiscale systems biology is having an increasingly powerful impact on our understanding of the interconnected molecular, cellular, and microenvironmental drivers of tumor growth and the effects of novel drugs and drug combinations for cancer therapy. Agent-based models (ABMs) that treat cells as autonomous decision-makers, each with their own intrinsic characteristics, are a natural platform for capturing intratumoral heterogeneity. Agent-based models are also useful for integrating the multiple time and spatial scales associated with vascular tumor growth and response to treatment. Despite all their benefits, the computational costs of solving agent-based models escalate and become prohibitive when simulating millions of cells, making parameter exploration and model parameterization from experimental data very challenging. Moreover, such data are typically limited, coarse-grained and may lack any spatial resolution, compounding these challenges. We address these issues by developing a first-of-its-kind method that leverages explicitly formulated surrogate models (SMs) to bridge the current computational divide between agent-based models and experimental data. In our approach, Surrogate Modeling for Reconstructing Parameter Surfaces (SMoRe ParS), we quantify the uncertainty in the relationship between agent-based model inputs and surrogate model parameters, and between surrogate model parameters and experimental data. In this way, surrogate model parameters serve as intermediaries between agent-based model input and data, making it possible to use them for calibration and uncertainty quantification of agent-based model parameters that map directly onto an experimental data set. We illustrate the functionality and novelty of Surrogate Modeling for Reconstructing Parameter Surfaces by applying it to an agent-based model of 3D vascular tumor growth, and experimental data in the form of tumor volume time-courses. Our method is broadly applicable to situations where preserving underlying mechanistic information is of interest, and where computational complexity and sparse, noisy calibration data hinder model parameterization.

VascuViz: a multimodality and multiscale imaging and visualization pipeline for vascular systems biology

Despite advances in imaging, image-based vascular systems biology has remained challenging because blood vessel data are often available only from a single modality or at a given spatial scale, and cross-modality data are difficult to integrate. Therefore, there is an exigent need for a multimodality pipeline that enables ex vivo vascular imaging with magnetic resonance imaging, computed tomography and optical microscopy of the same sample, while permitting imaging with complementary contrast mechanisms from the whole-organ to endothelial cell spatial scales. To achieve this, we developed 'VascuViz'-an easy-to-use method for simultaneous three-dimensional imaging and visualization of the vascular microenvironment using magnetic resonance imaging, computed tomography and optical microscopy in the same intact, unsectioned tissue. The VascuViz workflow permits multimodal imaging with a single labeling step using commercial reagents and is compatible with diverse tissue types and protocols. VascuViz's interdisciplinary utility in conjunction with new data visualization approaches opens up new vistas in image-based vascular systems biology.

Modified microvessel density based on perfusion distance: a preferable NSCLC prognostic factor

Background

Despite the vital role of blood perfusion in tumor progression, the prognostic value of typical blood perfusion markers, such as microvessel density (MVD) or microvessel area (MVA), in patients with non-small cell lung cancer (NSCLC) is still unclear. This study established a modified MVD (mMVD) measurement based on perfusion distance and determined its prognostic value in patients with NSCLC.

Methods

A total of 100 patients with NSCLC were enrolled in this retrospective study. The intratumor microvessels of NSCLC patients were visualized using immunohistochemical staining for CD31. The blood perfusion distance was evaluated as the distance from each vessel to its nearest cancer cell (D_mvcc), and the cutoff value for prognosis was determined. Apart from the total MVD (tMVD), microvessels near cancer cells within the cutoff-D_mvcc were counted as mMVD. Predictive values for mortality and recurrence were evaluated and compared.

Results

The D_mvcc ranged from 1.6 to 269.8 µm (median, 13.1 µm). The mMVD (range: 2-70; median 23) was counted from tMVD according to the cutoff-D_mvcc (~20 µm). Compared with tMVD, a larger fraction of mMVD (80% vs. 2.9%) played a significant role in overall survival, with an improved area under the receiver operating characteristic (ROC) curve (AUC) (0.74 vs. 0.56). A high mMVD was an independent positive indicator of overall survival (OS) and progression-free survival (PFS). In contrast, tMVD was only related to PFS at the optimal cutoff.

Conclusions

Perfusion-distance-based mMVD is a promising prognostic factor for NSCLC patients with superior sensitivity, specificity, and clinical applicability compared to tMVD. This study provides novel insights into the prognostic role of tumor vessel perfusion in patients with NSCLC.

Cross-Modality Imaging of Murine Tumor Vasculature-a Feasibility Study

Tumor vasculature and angiogenesis play a crucial role in tumor progression. Their visualization is therefore of utmost importance to the community. In this proof-of-principle study, we have established a novel cross-modality imaging (CMI) pipeline to characterize exactly the same murine tumors across scales and penetration depths, using orthotopic models of melanoma cancer. This allowed the acquisition of a comprehensive set of vascular parameters for a single tumor. The workflow visualizes capillaries at different length scales, puts them into the context of the overall tumor vessel network and allows quantification and comparison of vessel densities and morphologies by different modalities. The workflow adds information about hypoxia and blood flow rates. The CMI approach includes well-established technologies such as magnetic resonance imaging (MRI), positron emission tomography (PET), computed tomography (CT), and ultrasound (US), and modalities that are recent entrants into preclinical discovery such as optical coherence tomography (OCT) and high-resolution episcopic microscopy (HREM). This novel CMI platform establishes the feasibility of combining these technologies using an extensive image processing pipeline. Despite the challenges pertaining to the integration of microscopic and macroscopic data across spatial resolutions, we also established an open-source pipeline for the semi-automated co-registration of the diverse multiscale datasets, which enables truly correlative vascular imaging. Although focused on tumor vasculature, our CMI platform can be used to tackle a multitude of research questions in cancer biology.

Pilot Clinical Study Investigating the Thermal Physiology of Breast Cancer via High-Resolution Infrared Imaging

This descriptive study investigates breast thermal characteristics in females histologically diagnosed with unilateral breast cancer and in their contralateral normal breasts. The multi-institutional clinical pilot study was reviewed and approved by the Institutional Review Boards (IRBs) at participating institutions. Eleven female subjects with radiologic breast abnormalities were enrolled in the study between June 2019 and September 2019 after informed consent was obtained. Static infrared images were recorded for each subject. The Wilcoxon signed rank test was used to conduct paired comparisons in temperature data between breasts among the eight histologically diagnosed breast cancer subjects (n = 8). Localized temperatures of cancerous breast lesions were significantly warmer than corresponding regions in contralateral breasts (34.0 ± 0.9 °C vs. 33.2 ± 0.5 °C, p = 0.0142, 95% CI 0.25-1.5 °C). Generalized temperatures over cancerous breasts, in contrast, were not significantly warmer than corresponding regions in contralateral breasts (33.9 ± 0.8 °C vs. 33.4 ± 0.4 °C, p = 0.0625, 95% CI -0.05-1.45 °C). Among the breast cancers enrolled, breast cancers elevated temperatures locally at the site of the lesion (localized hyperthermia), but not over the entire breast (generalized hyperthermia).

Biologically-Based Mathematical Modeling of Tumor Vasculature and Angiogenesis via Time-Resolved Imaging Data

Tumor-associated vasculature is responsible for the delivery of nutrients, removal of waste, and allowing growth beyond 2-3 mm3. Additionally, the vascular network, which is changing in both space and time, fundamentally influences tumor response to both systemic and radiation therapy. Thus, a robust understanding of vascular dynamics is necessary to accurately predict tumor growth, as well as establish optimal treatment protocols to achieve optimal tumor control. Such a goal requires the intimate integration of both theory and experiment. Quantitative and time-resolved imaging methods have emerged as technologies able to visualize and characterize tumor vascular properties before and during therapy at the tissue and cell scale. Parallel to, but separate from those developments, mathematical modeling techniques have been developed to enable in silico investigations into theoretical tumor and vascular dynamics. In particular, recent efforts have sought to integrate both theory and experiment to enable data-driven mathematical modeling. Such mathematical models are calibrated by data obtained from individual tumor-vascular systems to predict future vascular growth, delivery of systemic agents, and response to radiotherapy. In this review, we discuss experimental techniques for visualizing and quantifying vascular dynamics including magnetic resonance imaging, microfluidic devices, and confocal microscopy. We then focus on the integration of these experimental measures with biologically based mathematical models to generate testable predictions.

Cross-Modality Imaging of Murine Tumor Vasculature-a Feasibility Study

Tumor vasculature and angiogenesis play a crucial role in tumor progression. Their visualization is therefore of utmost importance to the community. In this proof-of-principle study, we have established a novel cross-modality imaging (CMI) pipeline to characterize exactly the same murine tumors across scales and penetration depths, using orthotopic models of melanoma cancer. This allowed the acquisition of a comprehensive set of vascular parameters for a single tumor. The workflow visualizes capillaries at different length scales, puts them into the context of the overall tumor vessel network and allows quantification and comparison of vessel densities and morphologies by different modalities. The workflow adds information about hypoxia and blood flow rates. The CMI approach includes well-established technologies such as magnetic resonance imaging (MRI), positron emission tomography (PET), computed tomography (CT), and ultrasound (US), and modalities that are recent entrants into preclinical discovery such as optical coherence tomography (OCT) and high-resolution episcopic microscopy (HREM). This novel CMI platform establishes the feasibility of combining these technologies using an extensive image processing pipeline. Despite the challenges pertaining to the integration of microscopic and macroscopic data across spatial resolutions, we also established an open-source pipeline for the semi-automated co-registration of the diverse multiscale datasets, which enables truly correlative vascular imaging. Although focused on tumor vasculature, our CMI platform can be used to tackle a multitude of research questions in cancer biology.

Computational Simulation of Exosome Transport in Tumor Microenvironment

Cellular exosome-mediated crosstalk in tumor microenvironment (TME) is a critical component of anti-tumor immune responses. In addition to particle size, exosome transport and uptake by target cells is influenced by physical and physiological factors, including interstitial fluid pressure, and exosome concentration. These variables differ under both normal and pathological conditions, including cancer. The transport of exosomes in TME is governed by interstitial flow and diffusion. Based on these determinants, mathematical models were adapted to simulate the transport of exosomes in the TME with specified exosome release rates from the tumor cells. In this study, the significance of spatial relationship in exosome-mediated intercellular communication was established by treating their movement in the TME as a continuum using a transport equation, with advection due to interstitial flow and diffusion due to concentration gradients. To quantify the rate of release of exosomes by biomechanical forces acting on the tumor cells, we used a transwell platform with confluent triple negative breast cancer cells 4T1.2 seeded in BioFlex plates exposed to an oscillatory force. Exosome release rates were quantified from 4T1.2 cells seeded at the bottom of the well following the application of either no force or an oscillatory force, and these rates were used to model exosome transport in the transwell. The simulations predicted that a larger number of exosomes reached the membrane of the transwell for 4T1.2 cells exposed to the oscillatory force when compared to controls. Additionally, we simulated the interstitial fluid flow and exosome transport in a 2-dimensional TME with macrophages, T cells, and mixtures of these two populations at two different stages of a tumor growth. Computational simulations were carried out using the commercial computational simulation package, ANSYS/Fluent. The results of this study indicated higher exosome concentrations and larger interstitial fluid pressure at the later stages of the tumor growth. Quantifying the release of exosomes by cancer cells, their transport through the TME, and their concentration in TME will afford a deeper understanding of the mechanisms of these interactions and aid in deriving predictive models for therapeutic intervention.

Vessel-on-a-chip models for studying microvascular physiology, transport, and function in vitro

To understand how the microvasculature grows and remodels, researchers require reproducible systems that emulate the function of living tissue. Innovative contributions toward fulfilling this important need have been made by engineered microvessels assembled in vitro with microfabrication techniques. Microfabricated vessels, commonly referred to as "vessels-on-a-chip," are from a class of cell culture technologies that uniquely integrate microscale flow phenomena, tissue-level biomolecular transport, cell-cell interactions, and proper three-dimensional (3-D) extracellular matrix environments under well-defined culture conditions. Here, we discuss the enabling attributes of microfabricated vessels that make these models more physiological compared with established cell culture techniques and the potential of these models for advancing microvascular research. This review highlights the key features of microvascular transport and physiology, critically discusses the strengths and limitations of different microfabrication strategies for studying the microvasculature, and provides a perspective on current challenges and future opportunities for vessel-on-a-chip models.

Digitally Fabricated and Naturally Augmented In Vitro Tissues

Human in vitro tissues are extracorporeal 3D cultures of human cells embedded in biomaterials, commonly hydrogels, which recapitulate the heterogeneous, multiscale, and architectural environment of the human body. Contemporary strategies used in 3D tissue and organ engineering integrate the use of automated digital manufacturing methods, such as 3D printing, bioprinting, and biofabrication. Human tissues and organs, and their intra- and interphysiological interplay, are particularly intricate. For this reason, attentiveness is rising to intersect materials science, medicine, and biology with arts and informatics. This report presents advances in computational modeling of bioink polymerization and its compatibility with bioprinting, the use of digital design and fabrication in the development of fluidic culture devices, and the employment of generative algorithms for modeling the natural and biological augmentation of in vitro tissues. As a future direction, the use of serially linked in vitro tissues as human body-mimicking systems and their application in drug pharmacokinetics and metabolism, disease modeling, and diagnostics are discussed.

Abnormal morphology biases hematocrit distribution in tumor vasculature and contributes to heterogeneity in tissue oxygenation

Oxygen heterogeneity in solid tumors is recognized as a limiting factor for therapeutic efficacy. This heterogeneity arises from the abnormal tumor vascular structure. We investigate the role that anomalies in red blood cell transport plays in establishing oxygen heterogeneity in tumor tissue. We introduce a metric to characterize tumor vasculature (mean vessel length-to-diameter ratio, λ) and demonstrate how it predicts tissue-oxygen heterogeneity. We also report an increase in λ following treatment with the antiangiogenic agent DC101. Together, we propose λ as an effective way of monitoring the action of antiangiogenic agents and a proxy measure of oxygen heterogeneity in tumor tissue. Unraveling the causal relationship between tumor vascular structure and tissue oxygenation will pave the way for new personalized therapeutic approaches.

Oxygen heterogeneity in solid tumors is recognized as a limiting factor for therapeutic efficacy. This heterogeneity arises from the abnormal vascular structure of the tumor, but the precise mechanisms linking abnormal structure and compromised oxygen transport are only partially understood. In this paper, we investigate the role that red blood cell (RBC) transport plays in establishing oxygen heterogeneity in tumor tissue. We focus on heterogeneity driven by network effects, which are challenging to observe experimentally due to the reduced fields of view typically considered. Motivated by our findings of abnormal vascular patterns linked to deviations from current RBC transport theory, we calculated average vessel lengths L¯ and diameters d¯ from tumor allografts of three cancer cell lines and observed a substantial reduction in the ratio λ=L¯/d¯ compared to physiological conditions. Mathematical modeling reveals that small values of the ratio λ (i.e., λ<6) can bias hematocrit distribution in tumor vascular networks and drive heterogeneous oxygenation of tumor tissue. Finally, we show an increase in the value of λ in tumor vascular networks following treatment with the antiangiogenic cancer agent DC101. Based on our findings, we propose λ as an effective way of monitoring the efficacy of antiangiogenic agents and as a proxy measure of perfusion and oxygenation in tumor tissue undergoing antiangiogenic treatment.

Computational feasibility of simulating whole-organ vascular networks

The human body contains approximately 20 billion blood vessels, which transport nutrients, oxygen, immune cells, and signals throughout the body. The brain's vasculature includes up to 9 billion of these vessels to support cognition, motor processes, and myriad other vital functions. To model blood flowing through a vasculature, a geometric description of the vessels is required. Previously reported attempts to model vascular geometries have produced highly-detailed models. These models, however, are limited to a small fraction of the human brain, and little was known about the feasibility of computationally modeling whole-organ-sized networks. We implemented a fractal-based algorithm to construct a vasculature the size of the human brain and evaluated the algorithm's speed and memory requirements. Using high-performance computing systems, the algorithm constructed a vasculature comprising 17 billion vessels in 1960 core-hours, or 49 minutes of wall-clock time, and required less than 32 GB of memory per node. We demonstrated strong scalability that was limited mainly by input/output operations. The results of this study demonstrated, for the first time, that it is feasible to computationally model the vasculature of the whole human brain. These findings provide key insights into the computational aspects of modeling whole-organ vasculature.

Patient-Specific Characterization of Breast Cancer Hemodynamics Using Image-Guided Computational Fluid Dynamics

The overall goal of this study is to employ quantitative magnetic resonance imaging (MRI) data to constrain a patient-specific, computational fluid dynamics (CFD) model of blood flow and interstitial transport in breast cancer. We develop image processing methodologies to generate tumor-related vasculature-interstitium geometry and realistic material properties, using dynamic contrast enhanced MRI (DCE-MRI) and diffusion weighted MRI (DW-MRI) data. These data are used to constrain CFD simulations for determining the tumor-associated blood supply and interstitial transport characteristics unique to each patient. We then perform a proof-of-principle statistical comparison between these hemodynamic characteristics in 11 malignant and 5 benign lesions from 12 patients. Significant differences between groups (i.e., malignant versus benign) were observed for the median of tumor-associated interstitial flow velocity ( P = 0.028 ), and the ranges of tumor-associated blood pressure (P = 0.016) and vascular extraction rate (P = 0.040). The implication is that malignant lesions tend to have larger magnitude of interstitial flow velocity, and higher heterogeneity in blood pressure and vascular extraction rate. Multivariable logistic models based on combinations of these hemodynamic data achieved excellent differentiation between malignant and benign lesions with an area under the receiver operator characteristic curve of 1.0, sensitivity of 1.0, and specificity of 1.0. This image-based model system is a fundamentally new way to map flow and pressure fields related to breast tumors using only non-invasive, clinically available imaging data and established laws of fluid mechanics. Furthermore, the results provide preliminary evidence for this methodology's utility for the quantitative characterization of breast cancer.

A multi-scale model for determining the effects of pathophysiology and metabolic disorders on tumor growth

The search for efficient chemotherapy drugs and other anti-cancer treatments would benefit from a deeper understanding of the tumor microenvironment (TME) and its role in tumor progression. Because in vivo experimental methods are unable to isolate or control individual factors of the TME and in vitro models often do not include all the contributing factors, some questions are best addressed with systems biology mathematical models. In this work, we present a new fully-coupled, agent-based, multi-scale mathematical model of tumor growth, angiogenesis and metabolism that includes important aspects of the TME spanning subcellular-, cellular- and tissue-level scales. The mathematical model is computationally implemented for a three-dimensional TME, and a double hybrid continuous-discrete (DHCD) method is applied to solve the governing equations. The model recapitulates the distinct morphological and metabolic stages of a solid tumor, starting with an avascular tumor and progressing through angiogenesis and vascularized tumor growth. To examine the robustness of the model, we simulated normal and abnormal blood conditions, including hyperglycemia/hypoglycemia, hyperoxemia/hypoxemia, and hypercarbia/hypocarbia - conditions common in cancer patients. The results demonstrate that tumor progression is accelerated by hyperoxemia, hyperglycemia and hypercarbia but inhibited by hypoxemia and hypoglycemia; hypocarbia had no appreciable effect. Because of the importance of interstitial fluid flow in tumor physiology, we also examined the effects of hypo- or hypertension, and the impact of decreased hydraulic conductivity common in desmoplastic tumors. The simulations show that chemotherapy-increased blood pressure, or reduction of interstitial hydraulic conductivity increase tumor growth rate and contribute to tumor malignancy.

Ginsenoside Rh2 pretreatment and withdrawal reactivated the pentose phosphate pathway to ameliorate intracellular redox disturbance and promoted intratumoral penetration of adriamycin

Improving the limited penetration, accumulation and therapeutic effects of antitumor drugs in the avascular region of the tumor mass is crucial during chemotherapy. P-gp inhibitors have achieved little success despite significant efforts. Excessive P-gp inhibition disturbed the kinetic balance between intracellular accumulation and intercellular penetration, thus resulting in a more inhomogeneous distribution of substrate drugs. Here, we found that ginsenoside Rh2 pretreatment mildly downregulated P-gp expression through reactivating the pentose phosphate pathway and rebalancing redox status. This mild P-gp inhibition not only significantly increased the growth inhibition effect and accumulation profile of adriamycin (ADR) throughout the multicellular tumor spheroid (MCTS) but also had unique advantages in improving drug penetration. Furthermore, we developed a novel individual-cell-based PK-PD integrated model and proved that metabolic reprogramming and redox rebalancing-based P-gp regulation was sufficient to increase the ADR effect in both central and peripheral cells of MCTS. Thus, a “ginsenoside Rh2-ADR” sequential regimen was proposed and exhibited a potent antitumor effect in vivo. This novel P-gp inhibition via metabolic reprogramming and redox rebalancing provided a new idea for achieving better antitumor effects in the tumor avascular region during chemotherapy.

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Rh2 pretreatment downregulated P-gp expression through metabolic reprogramming and redox rebalancing.

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Rh2-pretreatment improved ADR penetration into the core of MCTS and tumour mass.

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“Ginsenoside Rh2-ADR” sequential regimen exhibited potent antitumor effects in vivo.

Glioblastoma multiforme restructures the topological connectivity of cerebrovascular networks

Glioblastoma multiforme alters healthy tissue vasculature by inducing angiogenesis and vascular remodeling. To fully comprehend the structural and functional properties of the resulting vascular network, it needs to be studied collectively by considering both geometric and topological properties. Utilizing Single Plane Illumination Microscopy (SPIM), the detailed capillary structure in entire healthy and tumor-bearing mouse brains could be resolved in three dimensions. At the scale of the smallest capillaries, the entire vascular systems of bulk U87- and GL261-glioblastoma xenografts, their respective cores, and healthy brain hemispheres were modeled as complex networks and quantified with fundamental topological measures. All individual vessel segments were further quantified geometrically and modular clusters were uncovered and characterized as meta-networks, facilitating an analysis of large-scale connectivity. An inclusive comparison of large tissue sections revealed that geometric properties of individual vessels were altered in glioblastoma in a relatively subtle way, with high intra- and inter-tumor heterogeneity, compared to the impact on the vessel connectivity. A network topology analysis revealed a clear decomposition of large modular structures and hierarchical network organization, while preserving most fundamental topological classifications, in both tumor models with distinct growth patterns. These results augment our understanding of cerebrovascular networks and offer a topological assessment of glioma-induced vascular remodeling. The findings may help understand the emergence of hypoxia and necrosis, and prove valuable for therapeutic interventions such as radiation or antiangiogenic therapy.

Modelling the transport of fluid through heterogeneous, whole tumours in silico

Cancers exhibit spatially heterogeneous, unique vascular architectures across individual samples, cell-lines and patients. This inherently disorganised collection of leaky blood vessels contribute significantly to suboptimal treatment efficacy. Preclinical tools are urgently required which incorporate the inherent variability and heterogeneity of tumours to optimise and engineer anti-cancer therapies. In this study, we present a novel computational framework which incorporates whole, realistic tumours extracted ex vivo to efficiently simulate vascular blood flow and interstitial fluid transport in silico for validation against in vivo biomedical imaging. Our model couples Poiseuille and Darcy descriptions of vascular and interstitial flow, respectively, and incorporates spatially heterogeneous blood vessel lumen and interstitial permeabilities to generate accurate predictions of tumour fluid dynamics. Our platform enables highly-controlled experiments to be performed which provide insight into how tumour vascular heterogeneity contributes to tumour fluid transport. We detail the application of our framework to an orthotopic murine glioma (GL261) and a human colorectal carcinoma (LS147T), and perform sensitivity analysis to gain an understanding of the key biological mechanisms which determine tumour fluid transport. Finally we mimic vascular normalization by modifying parameters, such as vascular and interstitial permeabilities, and show that incorporating realistic vasculatures is key to modelling the contrasting fluid dynamic response between tumour samples. Contrary to literature, we show that reducing tumour interstitial fluid pressure is not essential to increase interstitial perfusion and that therapies should seek to develop an interstitial fluid pressure gradient. We also hypothesise that stabilising vessel diameters and permeabilities are not key responses following vascular normalization and that therapy may alter interstitial hydraulic conductivity. Consequently, we suggest that normalizing the interstitial microenvironment may provide a more effective means to increase interstitial perfusion within tumours.

The structure of tumours varies widely, with dense and chaotically-formed networks of blood vessels that differ between each individual tumour and even between different regions of the same tumour. This atypical environment can inhibit the delivery of anti-cancer therapies. Computational tools are urgently required which facilitate a deeper understanding of the relationship between blood vessel architectures and therapeutic response. We have developed a computational framework which integrates the complex tumour vascular architecture to predict fluid transport across all lengths scales in whole tumours. We apply our model to two tumour cell-lines and show that differences in their inherent vascular structures influence flow through cancerous tissue. We also use our platform to predict the fluid dynamic response following vascular normalization therapy in realistic, static tumour networks and show that the response is dependent on tumour vascular architecture. We hypothesise that therapy may alter the permeability of interstitial tissue to fluid transport and show that lowering interstitial fluid pressure is not a necessary therapeutic outcome to increase tumour perfusion.

Monitoring of tumor vascular normalization: the key points from basic research to clinical application

Tumor vascular normalization alleviates hypoxia in the tumor microenvironment, reduces the degree of malignancy, and increases the efficacy of traditional therapy. However, the time window for vascular normalization is narrow; therefore, how to determine the initial and final points of the time window accurately is a key factor in combination therapy. At present, the gold standard for detecting the normalization of tumor blood vessels is histological staining, including tumor perfusion, microvessel density (MVD), vascular morphology, and permeability. However, this detection method is almost unrepeatable in the same individual and does not dynamically monitor the trend of the time window; therefore, finding a relatively simple and specific monitoring index has important clinical significance. Imaging has long been used to assess changes in tumor blood vessels and tumor changes caused by the oxygen environment in clinical practice; some preclinical and clinical research studies demonstrate the feasibility to assess vascular changes, and some new methods were in preclinical research. In this review, we update the most recent insights of evaluating tumor vascular normalization.

Computational modelling of drug delivery to solid tumour: Understanding the interplay between chemotherapeutics and biological system for optimised delivery systems

Drug delivery to solid tumour involves multiple physiological, biochemical and biophysical processes taking place across a wide range of length and time scales. The therapeutic efficacy of anticancer drugs is influenced by the complex interplays among the intrinsic properties of tumours, biophysical aspects of drug transport and cellular uptake. Mathematical and computational modelling allows for a well-controlled study on the individual and combined effects of a wide range of parameters on drug transport and therapeutic efficacy, which would not be possible or economically viable through experimental means. A wide spectrum of mathematical models has been developed for the simulation of drug transport and delivery in solid tumours, including PK/PD-based compartmental models, microscopic and macroscopic transport models, and molecular dynamics drug loading and release models. These models have been used as a tool to identify the limiting factors and for optimal design of efficient drug delivery systems. This article gives an overview of the currently available computational models for drug transport in solid tumours, together with their applications to novel drug delivery systems, such as nanoparticle-mediated drug delivery and convection-enhanced delivery.

Microvascular hemodynamics in the chick chorioallantoic membrane

OBJECTIVE

The microvasculature of the CAM in the developing chick embryo is characterized by interdigitating arteriolar and venular trees, connected at multiple points along their lengths to a mesh-like capillary plexus. Theoretical modeling techniques were employed to investigate the resulting hemodynamic characteristics of the CAM.

METHODS

Based on previously obtained anatomical data, a model was developed in which the capillary plexus was treated as a porous medium. Supply of blood from arterioles and drainage into venules were represented by distributions of flow sources and sinks. Predicted flow velocities were compared with measurements in arterioles and venules obtained via video microscopy.

RESULTS

If it was assumed that blood flowed into and out of the capillary plexus only at the ends of terminal arterioles and venules, the predicted velocities increased with decreasing diameter in vessels below 50 μm in diameter, contrary to the observations. Distributing sources/sinks along arterioles/venules led to velocities consistent with the data.

CONCLUSIONS

These results imply that connections to the capillary plexus distributed along the arterioles and venules strongly affect the hemodynamic characteristics of the CAM. The theoretical model provides a basis for quantitative simulations of structural adaptation in CAM networks in response to hemodynamic stimuli.

Image-based modelling of skeletal muscle oxygenation

The supply of oxygen in sufficient quantity is vital for the correct functioning of all organs in the human body, in particular for skeletal muscle during exercise. Disease is often associated with both an inhibition of the microvascular supply capability and is thought to relate to changes in the structure of blood vessel networks. Different methods exist to investigate the influence of the microvascular structure on tissue oxygenation, varying over a range of application areas, i.e. biological in vivo and in vitro experiments, imaging and mathematical modelling. Ideally, all of these methods should be combined within the same framework in order to fully understand the processes involved. This review discusses the mathematical models of skeletal muscle oxygenation currently available that are based upon images taken of the muscle microvasculature in vivo and ex vivo Imaging systems suitable for capturing the blood vessel networks are discussed and respective contrasting methods presented. The review further informs the association between anatomical characteristics in health and disease. With this review we give the reader a tool to understand and establish the workflow of developing an image-based model of skeletal muscle oxygenation. Finally, we give an outlook for improvements needed for measurements and imaging techniques to adequately investigate the microvascular capability for oxygen exchange.

Modelling drug transport during intraperitoneal chemotherapy

Despite a strong rationale for intraperitoneal (IP) chemotherapy, the actual use of the procedure is limited by the poor penetration depth of the drug into the tissue. Drug penetration into solid tumours is a complex mass transport process that involves multiple parameters not only related to the used cytotoxic agent but also to the tumour tissue properties and even the therapeutic setup. Mathematical modelling can provide unique insights into the different transport barriers that occur during IP chemotherapy as well as offer the possibility to test different protocols or drugs without the need for in vivo experiments. In this work, a distinction is made between three different types of model: the lumped parameter model, the distributed model and the cell-based model. For each model, we discuss which steps of the transport process are included and where assumptions are made. Finally, we focus on the advantages and main limitations of each category and discuss some future perspectives for the modelling of IP chemotherapy.

Creating High-Resolution Multiscale Maps of Human Tissue Using Multi-beam SEM

Multi-beam scanning electron microscopy (mSEM) enables high-throughput, nano-resolution imaging of macroscopic tissue samples, providing an unprecedented means for structure-function characterization of biological tissues and their cellular inhabitants, seamlessly across multiple length scales. Here we describe computational methods to reconstruct and navigate a multitude of high-resolution mSEM images of the human hip. We calculated cross-correlation shift vectors between overlapping images and used a mass-spring-damper model for optimal global registration. We utilized the Google Maps API to create an interactive map and provide open access to our reconstructed mSEM datasets to both the public and scientific communities via our website www.mechbio.org. The nano- to macro-scale map reveals the tissue’s biological and material constituents. Living inhabitants of the hip bone (e.g. osteocytes) are visible in their local extracellular matrix milieu (comprising collagen and mineral) and embedded in bone’s structural tissue architecture, i.e. the osteonal structures in which layers of mineralized tissue are organized in lamellae around a central blood vessel. Multi-beam SEM and our presented methodology enable an unprecedented, comprehensive understanding of health and disease from the molecular to organ length scale.

Until recently, the assessment of organ and tissue health relied on site-sampling (biopsy) of micro-scale regions and was fraught with sampling errors. Overcoming these limitations requires a means for seamless imaging of organs, from their cellular inhabitants to whole organs, akin to charting a map of the organ and its resident cells. Map navigation necessitates the capacity to zoom in and out of regions of interest, with high precision, as well as to analyze relationships between cells, tissue degeneration and organ (patho-)physiology. Here we describe the process, in technical detail, based on a world-first case study of a human hip sample and its resident cell population. We acquired 55,000 nm-resolution images of the hip using multi-beam scanning electron microscopy (mSEM). To reconstruct the entire dataset, we developed stitching algorithms to maximize map precision at smallest length scales, and rendered them using the Google Maps API. This enabled the exploration of the hip and its inhabitants in a seamless manner, from a global to a high-resolution local view of a single cell. The resulting navigable maps are available for research teams and the public alike to explore and to elucidate the cellular basis of tissue degeneration and organ failure (mechbio.org).

Effects of endothelial cell proliferation and migration rates in a computational model of sprouting angiogenesis

Angiogenesis, the recruitment of new blood vessels, is a critical process for the growth, expansion, and metastatic dissemination of developing tumors. Three types of cells make up the new vasculature: tip cells, which migrate in response to gradients of vascular endothelial growth factor (VEGF), stalk cells, which proliferate and extend the vessels, and phalanx cells, which are quiescent and support the sprout. In this study we examine the contribution of tip cell migration rate and stalk cell proliferation rate on the formation of new vasculature. We calculate several vascular metrics, such as the number of vascular bifurcations per unit volume, vascular segment length per unit volume, and vascular tortuosity. These measurements predict that proliferation rate has a greater effect on the spread and extent of vascular growth compared to migration rate. Together, these findings provide strong implications for designing anti-angiogenic therapies that may differentially target endothelial cell proliferation and migration. Computational models can be used to predict optimal anti-angiogenic therapies in combination with other therapeutics to improve outcome.

Development of a mathematical model to estimate intra-tumor oxygen concentrations through multi-parametric imaging

Background

Tumor hypoxia is involved in every stage of solid tumor development: formation, progression, metastasis, and apoptosis. Two types of hypoxia exist in tumors—chronic hypoxia and acute hypoxia. Recent studies indicate that the regional hypoxia kinetics is closely linked to metastasis and therapeutic responses, but regional hypoxia kinetics is hard to measure. We propose a novel approach to determine the local pO₂ by fusing the parameters obtained from in vivo functional imaging through the use of a modified multivariate Krogh model.

Methods

To test our idea and its potential to translate into an in vivo setting through the use of existing imaging techniques, simulation studies were performed comparing the local partial oxygen pressure (pO₂) from the proposed multivariate image fusion model to the referenced pO₂ derived by Green’s function, which considers the contribution from every vessel segment of an entire three-dimensional tumor vasculature to profile tumor oxygen with high spatial resolution.

Results

pO₂ derived from our fusion approach were close to the referenced pO₂ with regression slope near 1.0 and an r² higher than 0.8 if the voxel size (or the spatial resolution set by functional imaging modality) was less than 200 μm. The simulation also showed that the metabolic rate, blood perfusion, and hemoglobin concentration were dominant factors in tissue oxygenation. The impact of the measurement error of functional imaging to the pO₂ precision and accuracy was simulated. A Gaussian error function with FWHM equal to 20 % of blood perfusion or fractional vascular volume measurement contributed to average 7 % statistical error in pO₂.

Conclusion

The simulation results indicate that the fusion of multiple parametric maps through the biophysically derived mathematical models can monitor the intra-tumor spatial variations of hypoxia in tumors with existing imaging methods, and the potential to further investigate different forms of hypoxia, such as chronic and acute hypoxia, in response to cancer therapies.

Electronic supplementary material

The online version of this article (doi:10.1186/s12938-016-0235-5) contains supplementary material, which is available to authorized users.

Rapid short-pulse sequences enhance the spatiotemporal uniformity of acoustically driven microbubble activity during flow conditions

Despite the promise of microbubble-mediated focused ultrasound therapies, in vivo findings have revealed over-treated and under-treated regions distributed throughout the focal volume. This poor distribution cannot be improved by conventional pulse shapes and sequences, due to their limited ability to control acoustic cavitation dynamics within the ultrasonic focus. This paper describes the design of a rapid short-pulse (RaSP) sequence which is comprised of short pulses separated by μs off-time intervals. Improved acoustic cavitation distribution was based on the hypothesis that microbubbles can freely move during the pulse off-times. Flowing SonoVue^® microbubbles (flow velocity: 10 mm/s) were sonicated with a 0.5 MHz focused ultrasound transducer using RaSP sequences (peak-rarefactional pressures: 146-900 kPa, pulse repetition frequency: 1.25 kHz, and pulse lengths: 5-50 cycles). The distribution of cavitation activity was evaluated using passive acoustic mapping. RaSP sequences generated uniform distributions within the focus in contrast to long pulses (50 000 cycles) that produced non-uniform distributions. Fast microbubble destruction occurred for long pulses, whereas microbubble activity was sustained for longer durations for shorter pulses. High-speed microscopy revealed increased mobility in the direction of flow during RaSP sonication. In conclusion, RaSP sequences produced spatiotemporally uniform cavitation distributions and could result in efficient therapies by spreading cavitation throughout the treatment area.

Computational Model for Tumor Oxygenation Applied to Clinical Data on Breast Tumor Hemoglobin Concentrations Suggests Vascular Dilatation and Compression

We present a computational model for trans-vascular oxygen transport in synthetic tumor and host tissue blood vessel networks, aiming at qualitatively explaining published data of optical mammography, which were obtained from 87 breast cancer patients. The data generally show average hemoglobin concentration to be higher in tumors versus host tissue whereas average oxy-to total hemoglobin concentration (vascular segment RBC-volume-weighted blood oxygenation) can be above or below normal. Starting from a synthetic arterio-venous initial network the tumor vasculature was generated by processes involving cooption, angiogenesis, and vessel regression. Calculations of spatially resolved blood flow, hematocrit, oxy- and total hemoglobin concentrations, blood and tissue oxygenation were carried out for ninety tumor and associated normal vessel networks starting from various assumed geometries of feeding arteries and draining veins. Spatial heterogeneity in the extra-vascular partial oxygen pressure distribution can be related to various tumor compartments characterized by varying capillary densities and blood flow characteristics. The reported higher average hemoglobin concentration of tumors is explained by growth and dilatation of tumor blood vessels. Even assuming sixfold metabolic rate of oxygen consumption in tumorous versus host tissue, the predicted oxygen hemoglobin concentrations are above normal. Such tumors are likely associated with high tumor blood flow caused by high-caliber blood vessels crossing the tumor volume and hence oxygen supply exceeding oxygen demand. Tumor oxy- to total hemoglobin concentration below normal could only be achieved by reducing tumor vessel radii during growth by a randomly selected factor, simulating compression caused by intra-tumoral solid stress due to proliferation of cells and extracellular matrix. Since compression of blood vessels will impede chemotherapy we conclude that tumors with oxy- to total hemoglobin concentration below normal are less likely to respond to chemotherapy. Such behavior was recently reported for neo-adjuvant chemotherapy of locally advanced breast tumors.

A generative modeling approach to connectivity-Electrical conduction in vascular networks

The physiology of biological structures is inherently dynamic and emerges from the interaction and assembly of large collections of small entities. The extent of coupled entities complicates modeling and increases computational load. Here, microvascular networks are used to present a novel generative approach to connectivity based on the observation that biological organization is hierarchical and composed of a limited set of building blocks, i.e. a vascular network consists of blood vessels which in turn are composed by one or more cell types. Fast electrical communication is crucial to synchronize vessel tone across the vast distances within a network. We hypothesize that electrical conduction capacity is delimited by the size of vascular structures and connectivity of the network. Generation and simulation of series of dynamical models of electrical spread within vascular networks of different size and composition showed that (1) Conduction is enhanced in models harboring long and thin endothelial cells that couple preferentially along the longitudinal axis. (2) Conduction across a branch point depends on endothelial connectivity between branches. (3) Low connectivity sub-networks are more sensitive to electrical perturbations. In summary, the capacity for electrical signaling in microvascular networks is strongly shaped by the morphology and connectivity of vascular (particularly endothelial) cells. While the presented software can be used by itself or as a starting point for more sophisticated models of vascular dynamics, the generative approach can be applied to other biological systems, e.g. nervous tissue, the lymphatics, or the biliary system.

Modeling microcirculatory blood flow: current state and future perspectives

Microvascular blood flow determines a number of important physiological processes of an organism in health and disease. Therefore, a detailed understanding of microvascular blood flow would significantly advance biophysical and biomedical research and its applications. Current developments in modeling of microcirculatory blood flow already allow to go beyond available experimental measurements and have a large potential to elucidate blood flow behavior in normal and diseased microvascular networks. There exist detailed models of blood flow on a single cell level as well as simplified models of the flow through microcirculatory networks, which are reviewed and discussed here. The combination of these models provides promising prospects for better understanding of blood flow behavior and transport properties locally as well as globally within large microvascular networks.

Biomimetic on-a-chip platforms for studying cancer metastasis

Cancer metastasis is a multi-step, secondary tumor formation that is responsible for the vast majority of deaths in cancer patients. Animal models have served as one of the major tools for studying metastatic diseases. However, these metastasis models inherently lack the ability to decouple many of the key parameters that might contribute to cancer progression, and therefore ultimately limit detailed, mechanistic investigation of metastasis. Recently, organ-on-a-chip model systems have been developed for various tissue types with the potential to recapitulate major components of metastasis. Here, we discuss recent advances in in vitro biomimetic on-a-chip models for cancer metastasis.

Three-dimensional reconstruction of neovasculature in solid tumors and basement membrane matrix using ex vivo X-ray microcomputed tomography

OBJECTIVE

To create accurate, high-resolution 3D reconstructions of neovasculature structures in xenografted tumors and Matrigel plugs for quantitative analyses in angiogenesis studies in animal models.

METHODS

The competent neovasculature within xenografted solid tumors or Matrigel plugs in mice was perfused with Microfil, a radioopaque, hydrophilic polymerizing contrast agent, by systemic perfusion of the blood circulation via the heart. The perfused tumors and plugs were resected and scanned by X-ray micro-CT to generate stacks of 2D images showing the radioopaque material. A nonbiased, precise postprocessing scheme was employed to eliminate background X-ray absorbance from the extravascular tissue. The revised binary image stacks were compiled to reveal the Microfil-casted neovasculature as 3D reconstructions. Vascular structural parameters were calculated from the refined 3D reconstructions using the scanner software.

RESULTS

Clarified 3D reconstructions were sufficiently precise to allow measurements of vascular architecture to a diametric limit of resolution of 3 μm in tumors and plugs.

CONCLUSIONS

Ex vivo micro-CT can be used for 3D reconstruction and quantitative analysis of neovasculature including microcirculation in solid tumors and Matrigel plugs. This method can be generally applied for reconstructing and measuring vascular structures in three dimensions.

Simulation predicts IGFBP2-HIF1α interaction drives glioblastoma growth

Tremendous strides have been made in improving patients’ survival from cancer with one glaring exception: brain cancer. Glioblastoma is the most common, aggressive and highly malignant type of primary brain tumor. The average overall survival remains less than 1 year. Notably, cancer patients with obesity and diabetes have worse outcomes and accelerated progression of glioblastoma. The root cause of this accelerated progression has been hypothesized to involve the insulin signaling pathway. However, while the process of invasive glioblastoma progression has been extensively studied macroscopically, it has not yet been well characterized with regards to intracellular insulin signaling. In this study we connect for the first time microscale insulin signaling activity with macroscale glioblastoma growth through the use of computational modeling. Results of the model suggest a novel observation: feedback from IGFBP2 to HIF1α is integral to the sustained growth of glioblastoma. Our study suggests that downstream signaling from IGFI to HIF1α, which has been the target of many insulin signaling drugs in clinical trials, plays a smaller role in overall tumor growth. These predictions strongly suggest redirecting the focus of glioma drug candidates on controlling the feedback between IGFBP2 and HIF1α.

Current treatment for glioblastoma patients is limited to nonspecific methods: surgery followed by a combination of radio- and chemotherapy. With these methods, glioma patient survival is less than one year post-diagnosis. Targeting specific protein signaling pathways offers potentially more potent therapies. One promising potential target is the insulin signaling pathway, which is known to contribute to glioblastoma progression. However, drugs targeting this pathway have shown mixed results in clinical trials, and the detailed mechanisms of how the insulin signaling pathway promotes glioblastoma growth remain to be elucidated. Here, we developed a computational model of insulin signaling in glioblastoma in order to study this pathway’s role in tumor progression. Using the model, we systematically test contributions of different insulin signaling protein interactions on glioblastoma growth. Our model highlights a key driver for the growth of glioblastoma: IGFBP2-HIF1α feedback. This interaction provides a target that could open the door for new therapies in glioma and other solid tumors.

Unsupervised deconvolution of dynamic imaging reveals intratumor vascular heterogeneity and repopulation dynamics

With the existence of biologically distinctive malignant cells originated within the same tumor, intratumor functional heterogeneity is present in many cancers and is often manifested by the intermingled vascular compartments with distinct pharmacokinetics. However, intratumor vascular heterogeneity cannot be resolved directly by most in vivo dynamic imaging. We developed multi-tissue compartment modeling (MTCM), a completely unsupervised method of deconvoluting dynamic imaging series from heterogeneous tumors that can improve vascular characterization in many biological contexts. Applying MTCM to dynamic contrast-enhanced magnetic resonance imaging of breast cancers revealed characteristic intratumor vascular heterogeneity and therapeutic responses that were otherwise undetectable. MTCM is readily applicable to other dynamic imaging modalities for studying intratumor functional and phenotypic heterogeneity, together with a variety of foreseeable applications in the clinic.

Tuneable resolution as a systems biology approach for multi-scale, multi-compartment computational models

The use of multi-scale mathematical and computational models to study complex biological processes is becoming increasingly productive. Multi-scale models span a range of spatial and/or temporal scales and can encompass multi-compartment (e.g., multi-organ) models. Modeling advances are enabling virtual experiments to explore and answer questions that are problematic to address in the wet-lab. Wet-lab experimental technologies now allow scientists to observe, measure, record, and analyze experiments focusing on different system aspects at a variety of biological scales. We need the technical ability to mirror that same flexibility in virtual experiments using multi-scale models. Here we present a new approach, tuneable resolution, which can begin providing that flexibility. Tuneable resolution involves fine- or coarse-graining existing multi-scale models at the user's discretion, allowing adjustment of the level of resolution specific to a question, an experiment, or a scale of interest. Tuneable resolution expands options for revising and validating mechanistic multi-scale models, can extend the longevity of multi-scale models, and may increase computational efficiency. The tuneable resolution approach can be applied to many model types, including differential equation, agent-based, and hybrid models. We demonstrate our tuneable resolution ideas with examples relevant to infectious disease modeling, illustrating key principles at work. WIREs Syst Biol Med 2014, 6:225–245. doi:10.1002/wsbm.1270

How to cite this article:WIREs Syst Biol Med 2014, 6:289–309. doi:10.1002/wsbm.1270

3D tumor models: history, advances and future perspectives

ABSTRACT: 

Evaluation of cancer therapeutics by utilizing 3D tumor models, before clinical studies, could be more advantageous than conventional 2D tumor models (monolayer cultures). The 3D systems mimic the tumor microenvironment more closely than 2D systems. The following review discusses the various 3D tumor models present today with the advantages and limitations of each. 3D tumor models replicate the elements of a tumor microenvironment such as hypoxia, necrosis, angiogenesis and cell adhesion. The review introduces application of techniques such as microfluidics, imaging and tissue engineering to improve the 3D tumor models. Despite their tremendous potential to better screen chemotherapeutics, 3D tumor models still have a long way to go before they are used commonly as in vitro tumor models in pharmaceutical industrial research.

Multiscale and multi-modality visualization of angiogenesis in a human breast cancer model

Angiogenesis in breast cancer helps fulfill the metabolic demands of the progressing tumor and plays a critical role in tumor metastasis. Therefore, various imaging modalities have been used to characterize tumor angiogenesis. While micro-CT (μCT) is a powerful tool for analyzing the tumor microvascular architecture at micron-scale resolution, magnetic resonance imaging (MRI) with its sub-millimeter resolution is useful for obtaining in vivo vascular data (e.g. tumor blood volume and vessel size index). However, integration of these microscopic and macroscopic angiogenesis data across spatial resolutions remains challenging. Here we demonstrate the feasibility of 'multiscale' angiogenesis imaging in a human breast cancer model, wherein we bridge the resolution gap between ex vivo μCT and in vivo MRI using intermediate resolution ex vivo MR microscopy (μMRI). To achieve this integration, we developed suitable vessel segmentation techniques for the ex vivo imaging data and co-registered the vascular data from all three imaging modalities. We showcase two applications of this multiscale, multi-modality imaging approach: (1) creation of co-registered maps of vascular volume from three independent imaging modalities, and (2) visualization of differences in tumor vasculature between viable and necrotic tumor regions by integrating μCT vascular data with tumor cellularity data obtained using diffusion-weighted MRI. Collectively, these results demonstrate the utility of 'mesoscopic' resolution μMRI for integrating macroscopic in vivo MRI data and microscopic μCT data. Although focused on the breast tumor xenograft vasculature, our imaging platform could be extended to include additional data types for a detailed characterization of the tumor microenvironment and computational systems biology applications.

A bioimage informatics based reconstruction of breast tumor microvasculature with computational blood flow predictions

Induction of tumor angiogenesis is among the hallmarks of cancer and a driver of metastatic cascade initiation. Recent advances in high-resolution imaging enable highly detailed three-dimensional geometrical representation of the whole-tumor microvascular architecture. This enormous increase in complexity of image-based data necessitates the application of informatics methods for the analysis, mining and reconstruction of these spatial graph data structures. We present a novel methodology that combines ex-vivo high-resolution micro-computed tomography imaging data with a bioimage informatics algorithm to track and reconstruct the whole-tumor vasculature of a human breast cancer model. The reconstructed tumor vascular network is used as an input of a computational model that estimates blood flow in each segment of the tumor microvascular network. This formulation involves a well-established biophysical model and an optimization algorithm that ensures mass balance and detailed monitoring of all the vessels that feed and drain blood from the tumor microvascular network. Perfusion maps for the whole-tumor microvascular network are computed. Morphological and hemodynamic indices from different regions are compared to infer their role in overall tumor perfusion.

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 systems biology view of blood vessel growth and remodelling

Blood travels throughout the body in an extensive network of vessels – arteries, veins and capillaries. This vascular network is not static, but instead dynamically remodels in response to stimuli from cells in the nearby tissue. In particular, the smallest vessels – arterioles, venules and capillaries – can be extended, expanded or pruned, in response to exercise, ischaemic events, pharmacological interventions, or other physiological and pathophysiological events. In this review, we describe the multi-step morphogenic process of angiogenesis – the sprouting of new blood vessels – and the stability of vascular networks in vivo. In particular, we review the known interactions between endothelial cells and the various blood cells and plasma components they convey. We describe progress that has been made in applying computational modelling, quantitative biology and high-throughput experimentation to the angiogenesis process.

Compartment model predicts VEGF secretion and investigates the effects of VEGF trap in tumor-bearing mice

Angiogenesis, the formation of new blood vessels from existing vasculature, is important in tumor growth and metastasis. A key regulator of angiogenesis is vascular endothelial growth factor (VEGF), which has been targeted in numerous anti-angiogenic therapies aimed at inhibiting tumor angiogenesis. Systems biology approaches, including computational modeling, are useful for understanding this complex biological process and can aid in the development of novel and effective therapeutics that target the VEGF family of proteins and receptors. We have developed a computational model of VEGF transport and kinetics in the tumor-bearing mouse, which includes three-compartments: normal tissue, blood, and tumor. The model simulates human tumor xenografts and includes human (VEGF121 and VEGF165) and mouse (VEGF120 and VEGF164) isoforms. The model incorporates molecular interactions between these VEGF isoforms and receptors (VEGFR1 and VEGFR2), as well as co-receptors (NRP1 and NRP2). We also include important soluble factors: soluble VEGFR1 (sFlt-1) and α-2-macroglobulin. The model accounts for transport via macromolecular transendothelial permeability, lymphatic flow, and plasma clearance. We have fit the model to available in vivo experimental data on the plasma concentration of free VEGF Trap and VEGF Trap bound to mouse and human VEGF in order to estimate the rates at which parenchymal cells (myocytes and tumor cells) and endothelial cells secrete VEGF. Interestingly, the predicted tumor VEGF secretion rates are significantly lower (0.007-0.023 molecules/cell/s, depending on the tumor microenvironment) than most reported in vitro measurements (0.03-2.65 molecules/cell/s). The optimized model is used to investigate the interstitial and plasma VEGF concentrations and the effect of the VEGF-neutralizing agent, VEGF Trap (aflibercept). This work complements experimental studies performed in mice and provides a framework with which to examine the effects of anti-VEGF agents, aiding in the optimization of such anti-angiogenic therapeutics as well as analysis of clinical data. The model predictions also have implications for biomarker discovery with anti-angiogenic therapies.

Longitudinal in vivo monitoring of rodent glioma models through thinned skull using laser speckle contrast imaging

Laser speckle contrast imaging (LSCI) is a contrast agent free imaging technique suited for longitudinal assessment of vascular remodeling that accompanies brain tumor growth. We report the use of LSCI to monitor vascular changes in a rodent glioma model. Ten rats are inoculated with 9L gliosarcoma cells, and the angiogenic response is monitored five times over two weeks through a thinned skull imaging window. We are able to visualize neovascularization and measure the number of vessels per unit area to assess quantitatively the microvessel density (MVD). Spatial spread of MVD reveals regions of high MVD that may correspond to tumor location. Whole-field average MVD values increase with time in the tumor group but are fairly stable in the control groups. Statistical analysis shows significant differences in MVD values between the tumor group and both saline-receiving and unperturbed control groups over the two-week period (p<0.05). In conclusion, LSCI is suitable for investigation of tumor angiogenesis in rodent models. In addition, the statistical difference (p<0.02) between MVD values of the tumor (24.40 ± 1.41) and control groups (15.40 ± 1.60) on the 14th day after inoculation suggests a potential use of LSCI in the clinic in distinguishing tumor environments from normal vasculature.