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

Deciphering oxygen distribution and hypoxia profiles in the tumor microenvironment: a data-driven mechanistic modeling approach

Objective. The distribution of hypoxia within tissues plays a critical role in tumor diagnosis and prognosis. Recognizing the significance of tumor oxygenation and hypoxia gradients, we introduce mathematical frameworks grounded in mechanistic modeling approaches for their quantitative assessment within a tumor microenvironment. By utilizing known blood vasculature, we aim to predict hypoxia levels across different tumor types.Approach. Our approach offers a computational method to measure and predict hypoxia using known blood vasculature. By formulating a reaction-diffusion model for oxygen distribution, we derive the corresponding hypoxia profile.Main results. The framework successfully replicates observed inter- and intra-tumor heterogeneity in experimentally obtained hypoxia profiles across various tumor types (breast, ovarian, pancreatic). Additionally, we propose a data-driven method to deduce partial differential equation models with spatially dependent parameters, which allows us to comprehend the variability of hypoxia profiles within tissues. The versatility of our framework lies in capturing diverse and dynamic behaviors of tumor oxygenation, as well as categorizing states of vascularization based on the dynamics of oxygen molecules, as identified by the model parameters.Significance. The proposed data-informed mechanistic method quantitatively assesses hypoxia in the tumor microenvironment by integrating diverse histopathological data and making predictions across different types of data. The framework provides valuable insights from both modeling and biological perspectives, advancing our comprehension of spatio-temporal dynamics of tumor oxygenation.

Modeling hypoxia-induced radiation resistance and the impact of radiation sources

Hypoxia contributes significantly to resistance in radiotherapy. Our research rigorously examines the influence of microvascular morphology on radiotherapy outcome, specifically focusing on how microvasculature shapes hypoxia within the microenvironment and affects resistance to a standard treatment regimen (30×2GyRBE). Our computational modeling extends to the effects of different radiation sources. For photons and protons, our analysis establishes a clear correlation between hypoxic volume distribution and treatment effectiveness, with vascular density and regularity playing a crucial role in treatment success. On the contrary, carbon ions exhibit distinct effectiveness, even in areas of intense hypoxia and poor vascularization. This finding points to the potential of carbon-based hadron therapy in overcoming hypoxia-induced resistance to RT. Considering that the spatial scale analyzed in this study is closely aligned with that of imaging data voxels, we also address the implications of these findings in a clinical context envisioning the possibility of detecting subvoxel hypoxia.

Sensitivity analysis of a multi-physics model for the vascular microenvironment

The vascular microenvironment is the scale at which microvascular transport, interstitial tissue properties and cell metabolism interact. The vascular microenvironment has been widely studied by means of quantitative approaches, including multi-physics mathematical models as it is a central system for the pathophysiology of many diseases, such as cancer. The microvascular architecture is a key factor for fluid balance and mass transfer in the vascular microenvironment, together with the physical parameters characterizing the vascular wall and the interstitial tissue. The scientific literature of this field has witnessed a long debate about which factor of this multifaceted system is the most relevant. The purpose of this work is to combine the interpretative power of an advanced multi-physics model of the vascular microenvironment with state of the art and robust sensitivity analysis methods, in order to determine the factors that most significantly impact quantities of interest, related in particular to cancer treatment. We are particularly interested in comparing the factors related to the microvascular architecture with the ones affecting the physics of microvascular transport. Ultimately, this work will provide further insight into how the vascular microenvironment affects cancer therapies, such as chemotherapy, radiotherapy or immunotherapy.

Water and lipid content of breast tissue measured by six-wavelength time-domain diffuse optical spectroscopy

SIGNIFICANCE

The water and lipid content of normal breast tissue showed mammary gland characteristics with less influence from the chest wall using six-wavelength time-domain diffuse optical spectroscopy (TD-DOS) in a reflectance geometry.

AIM

To determine the depth sensitivity of a six-wavelength TD-DOS system and evaluate whether the optical parameters in normal breast tissue can distinguish dense breasts from non-dense breasts.

APPROACH

Measurements were performed in normal breast tissue of 37 breast cancer patients. We employed a six-wavelength TD-DOS system to measure the water and lipid content in addition to the hemoglobin concentration. The breast density in mammography and optical parameters were then compared.

RESULTS

The depth sensitivity of the system for water and lipid content was estimated to be ∼15 mm. Our findings suggest that the influence of the chest wall on the water content is weaker than that on the total hemoglobin concentration. In data with evaluation conditions, the water content was significantly higher (p < 0.001) and the lipid content was significantly lower (p < 0.001) in dense breast tissue. The water and lipid content exhibited a high sensitivity and specificity to distinguish dense from non-dense breasts in receiver-operating-characteristic curve analysis.

CONCLUSIONS

With less influence from the chest wall, the water and lipid content of normal breast tissue measured by a reflectance six-wavelength TD-DOS system, together with ultrasonography, can be applied to distinguish dense from non-dense breasts.

Modeling the Effect of Hyperoxia on the Spin-Lattice Relaxation Rate R1 of Tissues

PURPOSE

Inducing hyperoxia in tissues is common practice in several areas of research, including oxygen-enhanced MRI (OE-MRI), which attempts to use the resulting signal changes to detect regions of tumor hypoxia or pulmonary disease. The linear relationship between PO₂ and R1 has been reproduced in phantom solutions and body fluids such as vitreous fluid; however, in tissue and blood experiments, factors such as changes in deoxyhemoglobin levels can also affect the ΔR1.

THEORY AND METHODS

This manuscript proposes a three-compartment model for estimating the hyperoxia-induced changes in R1 of tissues depending on B0, SO₂ , blood volume, hematocrit, oxygen extraction fraction, and changes in blood and tissue PO₂ . The model contains two blood compartments (arterial and venous) and a tissue compartment. This model has been designed to be easy for researchers to tailor to their tissue of interest by substituting their preferred model for tissue oxygen diffusion and consumption. A specific application of the model is demonstrated by calculating the resulting ΔR1 expected in healthy, hypoxic and necrotic tumor tissues. In addition, the effect of sex-based hematocrit differences on ΔR1 is assessed.

RESULTS

The ΔR1 values predicted by the model are consistent with reported literature OE-MRI results: with larger positive changes in the vascular periphery than hypoxic and necrotic regions. The observed sex-based differences in ΔR1 agree with findings by Kindvall et al. suggesting that differences in hematocrit levels may sometimes be a confounding factor in ΔR1.

CONCLUSION

This model can be used to estimate the expected tissue ΔR1 in oxygen-enhanced MRI experiments.

Recent Strategies to Address Hypoxic Tumor Environments in Photodynamic Therapy

Photodynamic therapy (PDT) has become a promising method of cancer treatment due to its unique properties, such as noninvasiveness and low toxicity. The efficacy of PDT is, however, significantly reduced by the hypoxia tumor environments, because PDT involves the generation of reactive oxygen species (ROS), which requires the great consumption of oxygen. Moreover, the consumption of oxygen caused by PDT would further exacerbate the hypoxia condition, which leads to angiogenesis, invasion of tumors to other parts, and metastasis. Therefore, many research studies have been conducted to design nanoplatforms that can alleviate tumor hypoxia and enhance PDT. Herein, the recent progress on strategies for overcoming tumor hypoxia is reviewed, including the direct transport of oxygen to the tumor site by O₂ carriers, the in situ generation of oxygen by decomposition of oxygen-containing compounds, reduced O₂ consumption, as well as the regulation of tumor microenvironments. Limitations and future perspectives of these technologies to improve PDT are also discussed.

Regulating Acidosis and Relieving Hypoxia by Platelet Membrane-Coated Nanoparticle for Enhancing Tumor Chemotherapy

Acidosis and hypoxia of tumor remain a great challenge for cancer therapy. Herein, we developed Hb-LOX-DOX-ZIF8@platelet membrane nanoparticles (H-L-D-Z@PM NPs) to address this problem. Lactate oxidase (LOX) could deplete intratumoral lactate adequately and amplify oxidative stress efficiently. In the meantime, hemoglobin (Hb) was intended to deliver oxygen, relieve hypoxia, and boost the catalytic activity of LOX. The coated PM bestowed active tumor-targeting ability and good biocompatibility to these nanoparticles. Moreover, the encapsulation of zeolitic imidazolate framework-8 (ZIF8) offered the acid response capacity to nanoparticles. With the synergism of chemotherapy drug doxorubicin (DOX), these H-L-D-Z@PM NPs appeared to have excellent antitumor competence. Collectively, this study offered a new strategy for enhancing tumor chemotherapy by regulating acidosis and relieving hypoxia.

A multiscale cell-based model of tumor growth for chemotherapy assessment and tumor-targeted therapy through a 3D computational approach

OBJECTIVES

Computational modeling of biological systems is a powerful tool to clarify diverse processes contributing to cancer. The aim is to clarify the complex biochemical and mechanical interactions between cells, the relevance of intracellular signaling pathways in tumor progression and related events to the cancer treatments, which are largely ignored in previous studies.

MATERIALS AND METHODS

A three-dimensional multiscale cell-based model is developed, covering multiple time and spatial scales, including intracellular, cellular, and extracellular processes. The model generates a realistic representation of the processes involved from an implementation of the signaling transduction network.

RESULTS

Considering a benign tumor development, results are in good agreement with the experimental ones, which identify three different phases in tumor growth. Simulating tumor vascular growth, results predict a highly vascularized tumor morphology in a lobulated form, a consequence of cells' motile behavior. A novel systematic study of chemotherapy intervention, in combination with targeted therapy, is presented to address the capability of the model to evaluate typical clinical protocols. The model also performs a dose comparison study in order to optimize treatment efficacy and surveys the effect of chemotherapy initiation delays and different regimens.

CONCLUSIONS

Results not only provide detailed insights into tumor progression, but also support suggestions for clinical implementation. This is a major step toward the goal of predicting the effects of not only traditional chemotherapy but also tumor-targeted therapies.

Improving cancer treatments via dynamical biophysical models

Despite significant advances in oncological research, cancer nowadays remains one of the main causes of mortality and morbidity worldwide. New treatment techniques, as a rule, have limited efficacy, target only a narrow range of oncological diseases, and have limited availability to the general public due their high cost. An important goal in oncology is thus the modification of the types of antitumor therapy and their combinations, that are already introduced into clinical practice, with the goal of increasing the overall treatment efficacy. One option to achieve this goal is optimization of the schedules of drugs administration or performing other medical actions. Several factors complicate such tasks: the adverse effects of treatments on healthy cell populations, which must be kept tolerable; the emergence of drug resistance due to the intrinsic plasticity of heterogeneous cancer cell populations; the interplay between different types of therapies administered simultaneously. Mathematical modeling, in which a tumor and its microenvironment are considered as a single complex system, can address this complexity and can indicate potentially effective protocols, that would require experimental verification. In this review, we consider classical methods, current trends and future prospects in the field of mathematical modeling of tumor growth and treatment. In particular, methods of treatment optimization are discussed with several examples of specific problems related to different types of treatment.

A Mesoscale Computational Model for Microvascular Oxygen Transfer

We address a mathematical model for oxygen transfer in the microcirculation. The model includes blood flow and hematocrit transport coupled with the interstitial flow, oxygen transport in the blood and the tissue, including capillary-tissue exchange effects. Moreover, the model is suited to handle arbitrarily complex vascular geometries. The purpose of this study is the validation of the model with respect to classical solutions and the further demonstration of its adequacy to describe the heterogeneity of oxygenation in the tissue microenvironment. Finally, we discuss the importance of these effects in the treatment of cancer using radiotherapy.

Modular microenvironment components reproduce vascular dynamics de novo in a multi-scale agent-based model

Cells do not exist in isolation; they continuously act within and react to their environment. And this environment is not static; it continuously adapts and responds to cells. Here, we investigate how vascular structure and function impact emergent cell population behavior using an agent-based model (ABM). Our ABM enables researchers to "mix and match" cell agents, subcellular modules, and microenvironment components ranging from simple nutrient sources to complex, realistic vascular architectures that accurately capture hemodynamics. We use this ABM to highlight the bilateral relationship between cells and nearby vasculature, demonstrate the effect of vascular structure on environmental heterogeneity, and emphasize the non-linear, non-intuitive relationship between vascular function and the behavior of cell populations over time. Our ABM is well suited to characterizing in vitro and in vivo studies, with applications from basic science to translational synthetic biology and medicine. The model is freely available at https://github.com/bagherilab/ARCADE. A record of this paper's transparent peer review process is included in the supplemental information.

Photoacoustic dual-scan mammoscope: results from 38 patients

We have developed a photoacoustics-based imaging system, the dual-scan mammoscope (DSM), that combines optical contrasts with acoustic detection, to obtain the angiographic features in human breast. In this study, we investigated whether the system can differentiate malignant tumor and healthy breast. We have imaged 38 patients with various tumor types and compared results of tumor-bearing breast with healthy breast for each patient. We also compared the photoacoustic and ultrasound imaging results with clinical US. Vascular features in and around the tumor mass were visualized. We found that tumor-bearing breast contained vessels of larger caliber and exhibited stronger variations in the background signals than those in the contralateral healthy breasts. Preliminary data on photoacoustic and ultrasound images also indicate that the technique has potential in differentiating different tumor types. Overall, our results indicate that combining photoacoustic and ultrasound images can improve breast cancer screening.

A fast numerical method for oxygen supply in tissue with complex blood vessel network

Angiogenesis plays an essential role in many pathological processes such as tumor growth, wound healing, and keloid development. Low oxygen level is the main driving stimulus for angiogenesis. In an animal tissue, the oxygen level is mainly determined by three effects—the oxygen delivery through blood flow in a refined vessel network, the oxygen diffusion from blood to tissue, and the oxygen consumption in cells. Evaluation of the oxygen field is usually the bottleneck in large scale modeling and simulation of angiogenesis and related physiological processes. In this work, a fast numerical method is developed for the simulation of oxygen supply in tissue with a large-scale complex vessel network. This method employs an implicit finite-difference scheme to compute the oxygen field. By virtue of an oxygen source distribution technique from vessel center lines to mesh points and a corresponding post-processing technique that eliminate the local numerical error induced by source distribution, square mesh with relatively large mesh sizes can be applied while sufficient numerical accuracy is maintained. The new method has computational complexity which is slightly higher than linear with respect to the number of mesh points and has a convergence order which is slightly lower than second order with respect to the mesh size. With this new method, accurate evaluation of the oxygen field in a fully vascularized tissue on the scale of centimeter becomes possible.

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.

Au-Hemoglobin Loaded Platelet Alleviating Tumor Hypoxia and Enhancing the Radiotherapy Effect with Low-Dose X-ray

Radiotherapy (RT) is a widely explored clinical modality to combat cancer. However, its therapeutic efficacy is not always satisfied because of the severe hypoxic microenvironment in solid tumors and the high dosage of radiation harmful to the adjacent healthy tissue. Herein, Au nanoparticle-hemoglobin complex nanoparticle loaded platelets (Au-Hb@PLT) were fabricated. These Au-Hb@PLT would be activated by tumor cells, and the formed platelet-derivate particles (PM) could deliver Au nanoparticle-hemoglobin complex deeply into tumor tissue because of their small size and tumor homing ability. Hemoglobin acts as an oxygen carrier to relieve the hypoxia and gold nanoparticles work as radiosensitizers to potentiate the sensitivity of tumor cells to X-ray, thus, enhancing the in vivo therapeutic outcome even under a low-dose RT in tumor bearing mice. The enhanced antitumor effect and survival benefits endowed by the Au-Hb@PLT were confirmed in vitro and in vivo. These results demonstrate that these Au-Hb@PLT can work as an oxygen vehicle, offer a promising approach to mitigate hypoxia and improve RT efficacy with a low RT dosage.

Tumor vascular status controls oxygen delivery facilitated by infused polymerized hemoglobins with varying oxygen affinity

Oxygen (O₂) delivery facilitated by hemoglobin (Hb)-based O₂ carriers (HBOCs) is a promising strategy to increase the effectiveness of chemotherapeutics for treatment of solid tumors. However, the heterogeneous vascular structures present within tumors complicates evaluating the oxygenation potential of HBOCs within the tumor microenvironment. To account for spatial variations in the vasculature and tumor tissue that occur during tumor growth, we used a computational model to develop artificial tumor constructs. With these simulated tumors, we performed a polymerized human hemoglobin (hHb) (PolyhHb) enhanced oxygenation simulation accounting for differences in the physiologic characteristics of human and mouse blood. The results from this model were used to determine the potential effectiveness of different treatment options including a top load (low volume) and exchange (large volume) infusion of a tense quaternary state (T-State) PolyhHb, relaxed quaternary state (R-State) PolyhHb, and a non O₂ carrying control. Principal component analysis (PCA) revealed correlations between the different regimes of effectiveness within the different simulated dosage options. In general, we found that infusion of T-State PolyhHb is more likely to decrease tissue hypoxia and modulate the metabolic rate of O₂ consumption. Though the developed models are not a definitive descriptor of O₂ carrier interaction in tumor capillary networks, we accounted for factors such as non-uniform vascular density and permeability that limit the applicability of O₂ carriers during infusion. Finally, we have used these validated computational models to establish potential benchmarks to guide tumor treatment during translation of PolyhHb mediated therapies into clinical applications.

High rates of oxygen consumption and abnormal vascularization lead to low oxygen levels within solid tumors. The lack of oxygen results in resistance to chemotherapies and increased rates of cancer progression. Hemoglobin-based oxygen carriers have the potential to increase the amount of oxygen delivered to tumors, which may make chemotherapies more effective. Unfortunately, translating experimental results from mice to humans is complicated by allometric scaling between mice and humans. To predict how these therapies may perform differently between human and murine systems, we computationally predicted how hemoglobin-based oxygen delivery varies between the two organisms. Our model accounts for how variations in the tumor vascular network impact the performance of hemoglobin-based oxygen carriers. This model also allows us to assess how the oxygen affinity of hemoglobin-based oxygen carriers affects the oxygenation of hypoxic tissue. The results of these models help us predict how results from murine models may translate to humans. Also, our models help to highlight what clinically-measurable tumor properties should be measured to predict the effectiveness of hemoglobin-based oxygen carriers in biological systems.

Breast cancer models: Engineering the tumor microenvironment

The mechanisms behind cancer initiation and progression are not clear. Therefore, development of clinically relevant models to study cancer biology and drug response in tumors is essential. In vivo models are very valuable tools for studying cancer biology and for testing drugs; however, they often suffer from not accurately representing the clinical scenario because they lack either human cells or a functional immune system. On the other hand, two-dimensional (2D) in vitro models lack the three-dimensional (3D) network of cells and extracellular matrix (ECM) and thus do not represent the tumor microenvironment (TME). As an alternative approach, 3D models have started to gain more attention, as such models offer a platform with the ability to study cell-cell and cell-material interactions parametrically, and possibly include all the components present in the TME. Here, we first give an overview of the breast cancer TME, and then discuss the current state of the pre-clinical breast cancer models, with a focus on the engineered 3D tissue models. We also highlight two engineering approaches that we think are promising in constructing models representative of human tumors: 3D printing and microfluidics. In addition to giving basic information about the TME in the breast tissue, this review article presents the state-of-the-art tissue engineered breast cancer models. STATEMENT OF SIGNIFICANCE: Involvement of biomaterials and tissue engineering fields in cancer research enables realistic mimicry of the cell-cell and cell-extracellular matrix (ECM) interactions in the tumor microenvironment (TME), and thus creation of better models that reflect the tumor response against drugs. Engineering the 3D in vitro models also requires a good understanding of the TME. Here, an overview of the breast cancer TME is given, and the current state of the pre-clinical breast cancer models, with a focus on the engineered 3D tissue models is discussed. This review article is useful not only for biomaterials scientists aiming to engineer 3D in vitro TME models, but also for cancer researchers willing to use these models for studying cancer biology and drug testing.

Oxygen in the Tumor Microenvironment: Mathematical and Numerical Modeling

There are many reasons to try to achieve a good grasp of the distribution of oxygen in the tumor microenvironment. The lack of oxygen - hypoxia - is a main actor in the evolution of tumors and in their growth and appears to be just as important in tumor invasion and metastasis. Mathematical models of the distribution of oxygen in tumors which are based on reaction-diffusion equations provide partial but qualitatively significant descriptions of the measured oxygen concentrations in the tumor microenvironment, especially when they incorporate important elements of the blood vessel network such as the blood vessel size and spatial distribution and the pulsation of local pressure due to blood circulation. Here, we review our mathematical and numerical approaches to the distribution of oxygen that yield insights both on the role of the distribution of blood vessel density and size and on the fluctuations of blood pressure.

An approach for vascular tumor growth based on a hybrid embedded/homogenized treatment of the vasculature within a multiphase porous medium model

The aim of this work is to develop a novel computational approach to facilitate the modeling of angiogenesis during tumor growth. The preexisting vasculature is modeled as a 1D inclusion and embedded into the 3D tissue through a suitable coupling method, which allows for nonmatching meshes in 1D and 3D domain. The neovasculature, which is formed during angiogenesis, is represented in a homogenized way as a phase in our multiphase porous medium system. This splitting of models is motivated by the highly complex morphology, physiology, and flow patterns in the neovasculature, which are challenging and computationally expensive to resolve with a discrete, 1D angiogenesis and blood flow model. Moreover, it is questionable if a discrete representation generates any useful additional insight. By contrast, our model may be classified as a hybrid vascular multiphase tumor growth model in the sense that a discrete, 1D representation of the preexisting vasculature is coupled with a continuum model describing angiogenesis. It is based on an originally avascular model which has been derived via the thermodynamically constrained averaging theory. The new model enables us to study mass transport from the preexisting vasculature into the neovasculature and tumor tissue. We show by means of several illustrative examples that it is indeed capable of reproducing important aspects of vascular tumor growth phenomenologically.

Dynamic vessel adaptation in synthetic arteriovenous networks

Blood vessel networks of living organisms continuously adapt their structure under the influence of hemodynamic and metabolic stimuli. For a fixed vessel arrangement, blood flow characteristics still depend crucially on the morphology of each vessel. Vessel diameters adapt dynamically according to internal and external stimuli: Endothelial wall shear stress, intravascular pressure, flow-dependent metabolic stimuli, and electrical stimuli conducted from distal to proximal segments along vascular walls. Pries et al. formulated a theoretical model involving these four local stimuli to simulate long-term changes of vessel diameters during structural adaption of microvascular networks. Here we apply this vessel adaptation algorithm to synthetic arteriovenous blood vessel networks generated by our simulation framework "Tumorcode". We fixed the free model parameters by an optimization method combined with the requirement of homogeneous flow in the capillary bed. We find that the local blood volume, surface to volume ratio and branching ratio differs from networks with radii fulfilling Murray's law exactly to networks with radii obtained by the adaptation algorithm although their relation is close to Murray's law.

Fine-grained simulations of the microenvironment of vascularized tumours

One of many important features of the tumour microenvironment is that it is a place of active Darwinian selection where different tumour clones become adapted to the variety of ecological niches that make up the microenvironment. These evolutionary processes turn the microenvironment into a powerful source of tumour heterogeneity and contribute to the development of drug resistance in cancer. Here, we describe a computational tool to study the ecology of the microenvironment and report results about the ecology of the tumour microenvironment and its evolutionary dynamics.

Hybrid modeling frameworks of tumor development and treatment

Tumors are complex multicellular heterogeneous systems comprised of components that interact with and modify one another. Tumor development depends on multiple factors: intrinsic, such as genetic mutations, altered signaling pathways, or variable receptor expression; and extrinsic, such as differences in nutrient supply, crosstalk with stromal or immune cells, or variable composition of the surrounding extracellular matrix. Tumors are also characterized by high cellular heterogeneity and dynamically changing tumor microenvironments. The complexity increases when this multiscale, multicomponent system is perturbed by anticancer treatments. Modeling such complex systems and predicting how tumors will respond to therapies require mathematical models that can handle various types of information and combine diverse theoretical methods on multiple temporal and spatial scales, that is, hybrid models. In this update, we discuss the progress that has been achieved during the last 10 years in the area of the hybrid modeling of tumors. The classical definition of hybrid models refers to the coupling of discrete descriptions of cells with continuous descriptions of microenvironmental factors. To reflect on the direction that the modeling field has taken, we propose extending the definition of hybrid models to include of coupling two or more different mathematical frameworks. Thus, in addition to discussing recent advances in discrete/continuous modeling, we also discuss how these two mathematical descriptions can be coupled with theoretical frameworks of optimal control, optimization, fluid dynamics, game theory, and machine learning. All these methods will be illustrated with applications to tumor development and various anticancer treatments.

This article is characterized under:

Analytical and Computational Methods > Computational Methods

Translational, Genomic, and Systems Medicine > Therapeutic Methods

Models of Systems Properties and Processes > Organ, Tissue, and Physiological Models

Towards personalized computational oncology: from spatial models of tumour spheroids, to organoids, to tissues

A main goal of mathematical and computational oncology is to develop quantitative tools to determine the most effective therapies for each individual patient. This involves predicting the right drug to be administered at the right time and at the right dose. Such an approach is known as precision medicine. Mathematical modelling can play an invaluable role in the development of such therapeutic strategies, since it allows for relatively fast, efficient and inexpensive simulations of a large number of treatment schedules in order to find the most effective. This review is a survey of mathematical models that explicitly take into account the spatial architecture of three-dimensional tumours and address tumour development, progression and response to treatments. In particular, we discuss models of epithelial acini, multicellular spheroids, normal and tumour spheroids and organoids, and multi-component tissues. Our intent is to showcase how these in silico models can be applied to patient-specific data to assess which therapeutic strategies will be the most efficient. We also present the concept of virtual clinical trials that integrate standard-of-care patient data, medical imaging, organ-on-chip experiments and computational models to determine personalized medical treatment strategies.

Tumorcode : A framework to simulate vascularized tumors

During the past years our group published several articles using computer simulations to address the complex interaction of tumors and the vasculature as underlying transport network. Advances in imaging and lab techniques pushed in vitro research of tumor spheroids forward and animal models as well as clinical studies provided more insights to single processes taking part in tumor growth, however, an overall picture is still missing. Computer simulations are a non-invasive option to cumulate current knowledge and form a quasi in vivo system. In our software, several known models were assembled into a multi-scale approach which allows to study length scales relevant for clinical applications. We release our code to the public domain, together with a detailed description of the implementation and several examples, with the hope of usage and futher development by the community. A justification for the included algorithms and the biological models was obtained in previous publications, here we summarize the technical aspects following the workflow of a typical simulation procedure.

Adaptation to Stochastic Temporal Variations in Intratumoral Blood Flow: The Warburg Effect as a Bet Hedging Strategy

While most cancers promote ingrowth of host blood vessels, the resulting vascular network usually fails to develop a mature organization, resulting in abnormal vascular dynamics with stochastic variations that include slowing, cessation, and even reversal of flow. Thus, substantial spatial and temporal variations in oxygen concentration are commonly observed in most cancers. Cancer cells, like all living systems, are subject to Darwinian dynamics such that their survival and proliferation are dependent on developing optimal phenotypic adaptations to local environmental conditions. Here, we consider the environmental stresses placed on tumors subject to profound, frequent, but stochastic variations in oxygen concentration as a result of temporal variations in blood flow. While vascular fluctuations will undoubtedly affect local concentrations of a wide range of molecules including growth factors (e.g., estrogen), substrate (oxygen, glucose, etc.), and metabolites ([Formula: see text], we focus on the selection forces that result solely from stochastic fluctuations in oxygen concentration. The glucose metabolism of cancer cells has been investigated for decades following observations that malignant cells ferment glucose regardless of oxygen concentration, a condition termed the Warburg effect. In contrast, normal cells cease fermentation under aerobic conditions and this physiological response is termed the Pasteur effect. Fermentation is markedly inefficient compared to cellular respiration in terms of adenosine triphosphate (ATP) production, generating just 2 ATP/glucose, whereas respiration generates 38 ATP/glucose. This inefficiency requires cancer cells to increase glycolytic flux, which subsequently increases acid production and can significantly acidify local tissue. Hence, it initially appears that cancer cells adopt a disadvantageous metabolic phenotype. Indeed, this metabolic "hallmark" of cancer is termed "energy dysregulation." However, if cancers arise through an evolutionary optimization process, any common observed property must confer an adaptive advantage. In the present work, we investigate the hypothesis that aerobic glycolysis represents an adaptation to stochastic variations in oxygen concentration stemming from disordered intratumoral blood flow. Using mathematical models, we demonstrate that the Warburg effect evolves as a conservative metabolic bet hedging strategy in response to stochastic fluctuations of oxygen. Specifically, the Warburg effect sacrifices fitness in physoxia by diverting resources from the more efficient process of respiration, but preemptively adapts cells to hypoxia because fermentation produces ATP anaerobically. An environment with sufficiently stochastic fluctuations of oxygen will select for the bet hedging (Warburg) phenotype since it is modestly successful irrespective of oxygen concentration.

How tumour-induced vascular changes alter angiogenesis: Insights from a computational model

A computational model was developed to describe experimentally observed vascular changes induced by the introduction of a tumour on a mouse equipped with a dorsal skinfold chamber. The vascular structure of the host tissue was segmented from in vivo images and transposed into the computational framework. Simulations of tumour-induced vascular changes were performed and include the destabilizing effects of the growth factor VEGF on the integrity of the vessels walls. The integration of those effects, that include alteration of the vessel wall elasticity and wall breaching, were required to realistically reproduce the experimental observations. The model was then used to investigate the importance of the vascular changes for oxygen delivery and tumour development. To that end, we compared simulations obtained with a dynamic vasculature with those obtained with a static one. The results showed that the tumour growth was strongly impeded by the constant vascular changes. More precisely, it is the angiogenic process itself that was affected by vascular changes occurring in bigger upstream vessels and resulting in a less efficient angiogenic network for oxygen delivery. As a consequence, tumour cells are mostly kept in a non-proliferative hypoxic state. Tumour dormancy thus appears as one potential consequence of the intense vascular changes in the host tissue.