Integrative models of vascular remodeling during tumor growth

Computational modeling of angiogenesis: The importance of cell rearrangements during vascular growth

Angiogenesis is the process wherein endothelial cells (ECs) form sprouts that elongate from the pre-existing vasculature to create new vascular networks. In addition to its essential role in normal development, angiogenesis plays a vital role in pathologies such as cancer, diabetes and atherosclerosis. Mathematical and computational modeling has contributed to unraveling its complexity. Many existing theoretical models of angiogenic sprouting are based on the "snail-trail" hypothesis. This framework assumes that leading ECs positioned at sprout tips migrate toward low-oxygen regions while other ECs in the sprout passively follow the leaders' trails and proliferate to maintain sprout integrity. However, experimental results indicate that, contrary to the snail-trail assumption, ECs exchange positions within developing vessels, and the elongation of sprouts is primarily driven by directed migration of ECs. The functional role of cell rearrangements remains unclear. This review of the theoretical modeling of angiogenesis is the first to focus on the phenomenon of cell mixing during early sprouting. We start by describing the biological processes that occur during early angiogenesis, such as phenotype specification, cell rearrangements and cell interactions with the microenvironment. Next, we provide an overview of various theoretical approaches that have been employed to model angiogenesis, with particular emphasis on recent in silico models that account for the phenomenon of cell mixing. Finally, we discuss when cell mixing should be incorporated into theoretical models and what essential modeling components such models should include in order to investigate its functional role. This article is categorized under: Cardiovascular Diseases > Computational Models Cancer > Computational Models.

CT-Based Radiomics Analysis of Different Machine Learning Models for Discriminating the Risk Stratification of Pheochromocytoma and Paraganglioma: A Multicenter Study

RATIONALE AND OBJECTIVES

Using different machine learning models CT-based radiomics to integrate clinical radiological features to discriminating the risk stratification of pheochromocytoma/paragangliomas (PPGLs).

MATERIALS AND METHODS

The present study included 201 patients with PPGLs from three hospitals (training set: n = 125; external validation set: n = 45; external test set: n = 31). Patients were divided into low-risk and high-risk groups using a staging system for adrenal pheochromocytoma and paraganglioma (GAPP). We extracted and selected CT radiomics features, and built radiomics models using support vector machines (SVM), k-nearest neighbors, random forests, and multilayer perceptrons. Using receiver operating characteristic curve analysis to select the optimal radiomics model, a combined model was built using the output of the optimal radiomics model and clinical radiological features, and its accuracy and clinical applicability were evaluated using calibration curves and clinical decision curve analysis (DCA).

RESULTS

Finally, 13 radiomics features were selected to construct machine learning models. In the radiomics model, the SVM model demonstrated higher accuracy and stability, with an AUC value of 0.915 in the training set, 0.846 in external validation set, and 0.857 in external test set. Combining the outputs of SVM models with two clinical radiological features, a combined model constructed has demonstrated optimal risk stratification ability for PPGLs with an AUC of 0.926 for the training set, 0.883 for the external validation set, and 0.899 for the external test set. The calibration curve and DCA show good calibration accuracy and clinical effectiveness for the combined model.

CONCLUSION

Combined model that integrates radiomics and clinical radiological features can discriminate the risk stratification of PPGLs.

Clinical Trials for Oral, Inhaled and Intravenous Drug Delivery System for Lung Cancer and Emerging Nanomedicine-Based Approaches

Lung cancer is one of the most common malignant tumors worldwide and is characterized by high morbidity and mortality rates and a poor prognosis. It is the leading cause of cancer-related death in the United States and worldwide. Most patients with lung cancer are treated with chemotherapy, radiotherapy, or surgery; however, effective treatment options remain limited. In this review, we aim to provide an overview of clinical trials, ranging from Phase I to III, conducted on drug delivery systems for lung cancer treatment. The trials included oral, inhaled, and intravenous administration of therapeutics. Furthermore, the study also talks about the evolving paradigm of targeted therapy and immunotherapy providing promising directions for personalized treatment. In addition, we summarize the best results and limitations of these drug delivery systems and discuss the potential capacity of nanomedicine.

RGS5 maintaining vascular homeostasis is altered by the tumor microenvironment

BACKGROUND

Regulator of G protein signaling 5 (RGS5), as a negative regulator of G protein-coupled receptor (GPCR) signaling, is highly expressed in arterial VSMCs and pericytes, which is involved in VSMC phenotypic heterogeneity and vascular remodeling in tumors. However, its role in normal and tumor vascular remodeling is controversial.

METHODS

RGS5 knockout (Rgs5-KO) mice and RGS5 overexpression or knockdown in VSMCs in vivo by adeno-associated virus type 9 (AAV) carrying RGS5 cDNA or small hairpin RNA (shRNA) targeting RGS5 were used to determine the functional significance of RGS5 in vascular inflammation. RGS5 expression in the triple-negative (TNBCs) and non-triple-negative breast cancers (Non-TNBCs) was determined by immunofluorescent and immunohistochemical staining. The effect of breast cancer cell-conditioned media (BC-CM) on the pro-inflammatory phenotype of VSMCs was measured by phagocytic activity assays, adhesion assay and Western blot.

RESULTS

We identified that knockout and VSMC-specific knockdown of RGS5 exacerbated accumulation and pyroptosis of pro-inflammatory VSMCs, resulting in vascular remodeling, which was negated by VSMC-specific RGS5 overexpression. In contrast, in the context of breast cancer tissues, the role of RGS5 was completely disrupted. RGS5 expression was increased in the triple-negative breast cancer (TNBC) tissues and in the tumor blood vessels, accompanied with an extensive vascular network. VSMCs treated with BC-CM displayed enhanced pro-inflammatory phenotype and higher adherent with macrophages. Furthermore, tumor-derived RGS5 could be transferred into VSMCs.

CONCLUSIONS

These findings suggest that tumor microenvironment shifts the function of RGS5 from anti-inflammation to pro-inflammation and induces the pro-inflammatory phenotype of VSMCs that is favorable for tumor metastasis.

Mechanobiology in oncology: basic concepts and clinical prospects

The interplay between genetic transformations, biochemical communications, and physical interactions is crucial in cancer progression. Metastasis, a leading cause of cancer-related deaths, involves a series of steps, including invasion, intravasation, circulation survival, and extravasation. Mechanical alterations, such as changes in stiffness and morphology, play a significant role in all stages of cancer initiation and dissemination. Accordingly, a better understanding of cancer mechanobiology can help in the development of novel therapeutic strategies. Targeting the physical properties of tumours and their microenvironment presents opportunities for intervention. Advancements in imaging techniques and lab-on-a-chip systems enable personalized investigations of tumor biomechanics and drug screening. Investigation of the interplay between genetic, biochemical, and mechanical factors, which is of crucial importance in cancer progression, offers insights for personalized medicine and innovative treatment strategies.

Approaches to vascular network, blood flow, and metabolite distribution modeling in brain tissue

The cardiovascular system plays a key role in the transport of nutrients, ensuring a continuous supply of all cells of the body with the metabolites necessary for life. The blood supply to the brain is carried out by the large arteries located on its surface, which branch into smaller arterioles that penetrate the cerebral cortex and feed the capillary bed, thereby forming an extensive branching network. The formation of blood vessels is carried out via vasculogenesis and angiogenesis, which play an important role in both embryo and adult life. The review presents approaches to modeling various aspects of both the formation of vascular networks and the construction of the formed arterial tree. In addition, a brief description of models that allows one to study the blood flow in various parts of the circulatory system and the spatiotemporal metabolite distribution in brain tissues is given. Experimental study of these issues is not always possible due to both the complexity of the cardiovascular system and the mechanisms through which the perfusion of all body cells is carried out. In this regard, mathematical models are a good tool for studying hemodynamics and can be used in clinical practice to diagnose vascular diseases and assess the need for treatment.

A Simulation of the Effects of Diffusion on Hyperpolarized [1-13C]-Pyruvate Signal Evolution

OBJECTIVE

Hyperpolarized [1-13C]-pyruvate magnetic resonance imaging is an emerging metabolic imaging method that offers unprecedented spatiotemporal resolution for monitoring tumor metabolism in vivo. To establish robust imaging biomarkers of metabolism, we must characterize phenomena that may modulate the apparent pyruvate-to-lactate conversion rate (kPL). Here, we investigate the potential effect of diffusion on pyruvate-to-lactate conversion, as failure to account for diffusion in pharmacokinetic analysis may obscure true intracellular chemical conversion rates.

METHODS

Changes in hyperpolarized pyruvate and lactate signal were calculated using a finite-difference time domain simulation of a two-dimensional tissue model. Signal evolution curves with intracellular kPL values from 0.02 to 1.00 s-1 were analyzed using spatially invariant one-compartment and two-compartment pharmacokinetic models. A second spatially variant simulation incorporating compartmental instantaneous mixing was fit with the same one-compartment model.

RESULTS

When fitting with the one-compartment model, apparent kPL underestimated intracellular kPL by approximately 50% at an intracellular kPL of 0.02 s-1. This underestimation increased for larger kPL values. However, fitting the instantaneous mixing curves showed that diffusion accounted for only a small part of this underestimation. Fitting with the two-compartment model yielded more accurate intracellular kPL values.

SIGNIFICANCE

This work suggests diffusion is not a significant rate-limiting factor in pyruvate-to-lactate conversion given that our model assumptions hold true. In higher order models, diffusion effects may be accounted for by a term characterizing metabolite transport. Pharmacokinetic models used to analyze hyperpolarized pyruvate signal evolution should focus on carefully selecting the analytical model for fitting rather than accounting for diffusion effects.

Computational models for generating microvascular structures: Investigations beyond medical imaging resolution

Angiogenesis, arteriogenesis, and pruning are revascularization processes essential to our natural vascular development and adaptation, as well as central players in the onset and development of pathologies such as tumoral growth and stroke recovery. Computational modeling allows for repeatable experimentation and exploration of these complex biological processes. In this review, we provide an introduction to the biological understanding of the vascular adaptation processes of sprouting angiogenesis, intussusceptive angiogenesis, anastomosis, pruning, and arteriogenesis, discussing some of the more significant contributions made to the computational modeling of these processes. Each computational model represents a theoretical framework for how biology functions, and with rises in computing power and study of the problem these frameworks become more accurate and complete. We highlight physiological, pathological, and technological applications that can be benefit from the advances performed by these models, and we also identify which elements of the biology are underexplored in the current state-of-the-art computational models. This article is categorized under: Cancer > Computational Models Cardiovascular Diseases > Computational Models.

A proof-of-concept pipeline to guide evaluation of tumor tissue perfusion by dynamic contrast-agent imaging: Direct simulation and inverse tracer-kinetic procedures

Dynamic contrast-enhanced (DCE) perfusion imaging has shown great potential to non-invasively assess cancer development and its treatment by their characteristic tissue signatures. Different tracer kinetics models are being applied to estimate tissue and tumor perfusion parameters from DCE perfusion imaging. The goal of this work is to provide an in silico model-based pipeline to evaluate how these DCE imaging parameters may relate to the true tissue parameters. As histology data provides detailed microstructural but not functional parameters, this work can also help to better interpret such data. To this aim in silico vasculatures are constructed and the spread of contrast agent in the tissue is simulated. As a proof of principle we show the evaluation procedure of two tracer kinetic models from in silico contrast-agent perfusion data after a bolus injection. Representative microvascular arterial and venous trees are constructed in silico. Blood flow is computed in the different vessels. Contrast-agent input in the feeding artery, intra-vascular transport, intra-extravascular exchange and diffusion within the interstitial space are modeled. From this spatiotemporal model, intensity maps are computed leading to in silico dynamic perfusion images. Various tumor vascularizations (architecture and function) are studied and show spatiotemporal contrast imaging dynamics characteristic of in vivo tumor morphotypes. The Brix II also called 2CXM, and extended Tofts tracer-kinetics models common in DCE imaging are then applied to recover perfusion parameters that are compared with the ground truth parameters of the in silico spatiotemporal models. The results show that tumor features can be well identified for a certain permeability range. The simulation results in this work indicate that taking into account space explicitly to estimate perfusion parameters may lead to significant improvements in the perfusion interpretation of the current tracer-kinetics models.

Effect of Hypertension on EPR effect Induced by Polymer Nanomicelles in Renal Cell Carcinoma in vitro

Objective

To investigate the effect of hypertension on the (enhanced permeability and retention, EPR) effect induced by polymer nanomicelles in renal cell carcinoma in vitro.

Methods

A total of 80 patients with renal cell carcinoma treated at the Department of Urology Surgery in the Dept. of Urology of the Affiliated Hospital of Hebei University from Oct. 2019 to Oct. 2020, were analyzed retrospectively. The hypertension group (experimental group) included 40 patients, and the normal blood pressure group (control group) included 40 patients. The diagnosis of renal clear cell carcinoma was confirmed by preoperative auxiliary examinations, such as ultrasonography and CT combined with postoperative pathological analysis. All patients underwent laparoscopic radical nephrectomy for renal cell carcinoma. Polymer nanomicelles (loaded with prolonium iodide) were perfused into the resected kidney specimens within the specified time. The iodine enrichment of polymer nanomicelles in renal tumors was assessed by CT scanning. The peak EPR effect and the time to the peak were statistically compared between the two groups.

Results

No significant differences were found in age, sex, location of kidney disease, tumor location or tumor size between the two groups (p> 0.05). The peak (χ̄±S) of the EPR effect in experimental group was 3.60±0.95 ug/cm3 and 3.01±0.96 ug/cm3 in control group, respectively. There was significant difference between the two groups (p< 0.05). The time to the peak of the EPR effect was 3.76±0.75 h in experimental group and 3.82±0.93 hour in control group, respectively. No statistically significant difference was found in the time to the peak of the EPR effect between the two groups (p> 0.05).

Conclusion

Hypertension has a certain effect on the EPR effect induced by polymer nanomicelles in renal cell carcinoma in vitro.

Tension-Relaxation In Vivo Computing Principle for Tumor Sensitization and Targeting

By modeling the tumor sensitization and targeting (TST) as a natural computational process, we have proposed the framework of nanorobots-assisted in vivo computation. The externally manipulable nanorobots are steered to detect the tumor in the high-risk tissue, which is analogous to the process of searching for the optimal solution by the computing agents in the search space. To overcome the constraint of a nanorobotic platform that can only generate a uniform magnetic field to actuate the nanorobots, we have proposed the weak priority evolution strategy (WP-ES) in our previous works. However, these works do not consider the proportions of the nanorobot control and tracking operations, which are part and parcel of in vivo computation as the control operation aims at searching for the tumor effectively while the tracking mode is used for gathering information about the biological gradient function (BGF). Careful planning about the durations spent in these operations is needed for optimal performance of the TST strategy. To account for this issue, in the current article, we propose a novel computational principle, called the tension-relaxation (T-R) principle, to balance the displacements of nanorobots during each control and tracking cycle. Furthermore, we build three tumor vascular models with different sizes to represent three different targeting regions as the morphology of tumor vasculature determined by the tumor growth process is an important factor affecting TST. We carry out the computational experiments for tumors with three different sizes for several representative landscapes by introducing the T-R principle into the WP-ES-based swarm intelligence algorithms and considering the realistic internal constraints. The experimental outcomes demonstrate the effectiveness of the proposed TST strategy.

An Updated Review on EPR-Based Solid Tumor Targeting Nanocarriers for Cancer Treatment

Simple Summary

One of the important efforts in the treatment of cancers is to achieve targeted drug delivery by nanocarriers to be more effective and reduce adverse effects. However, due to the adverse responses of nanocarriers in clinical trials due to the very weak EPR effects, doubts have been raised in this regard. In this study, an attempt has been made to take a critical look at EPR approaches to enable the convergence of previous papers and the EPR critics to reach an appropriate therapeutic path. Although the effectiveness of EPR is highly variable due to the complex microenvironment of the tumor, there is high hope for cancer treatment by describing new strategies to overcome the challenges of EPR effect. Furthermore, in this paper an attempt was made to provide a reliable path for future to develop cancer therapeutics based on EPR effect.

Abstract

The enhanced permeability and retention (EPR) effect in cancer treatment is one of the key mechanisms that enables drug accumulation at the tumor site. However, despite a plethora of virus/inorganic/organic-based nanocarriers designed to rely on the EPR effect to effectively target tumors, most have failed in the clinic. It seems that the non-compliance of research activities with clinical trials, goals unrelated to the EPR effect, and lack of awareness of the impact of solid tumor structure and interactions on the performance of drug nanocarriers have intensified this dissatisfaction. As such, the asymmetric growth and structural complexity of solid tumors, physicochemical properties of drug nanocarriers, EPR analytical combination tools, and EPR description goals should be considered to improve EPR-based cancer therapeutics. This review provides valuable insights into the limitations of the EPR effect in therapeutic efficacy and reports crucial perspectives on how the EPR effect can be modulated to improve the therapeutic effects of nanomedicine.

NGA-Inspired Nanorobots-Assisted Detection of Multifocal Cancer

We propose a new framework of computing-inspired multifocal cancer detection procedure (MCDP). Under the rubric of MCDP, the tumor foci to be detected are regarded as solutions of the objective function, the tissue region around the cancer areas represents the parameter space, and the nanorobots loaded with contrast medium molecules for cancer detection correspond to the optimization agents. The process that the nanorobots detect tumors by swimming in the high-risk tissue region can be regarded as the process that the agents search for the solutions of an objective function in the parameter space with some constraints. For multimodal optimization (MMO) aiming to locate multiple optimal solutions in a single simulation run, the niche technology has been widely used. Specifically, the niche genetic algorithm (NGA) has been shown to be particularly effective in solving MMO. It can be used to identify the global optima of multiple hump functions in a running, effectively keep the diversity of the population, and prematurely avoid the genetic algorithm. Learning from the optimization procedure of NGA, we propose the NGA-inspired MCDP in order to locate the tumor targets efficiently while taking into account realistic in vivo propagation and controlling of nanorobots, which is different from the use scenario of the standard NGA. To improve the performance of the MCDP, we also modify the crossover operator of the original NGA from crossing within a population to crossing between two populations. Finally, we present comprehensive numerical examples to demonstrate the effectiveness of the NGA-inspired MCDP when the biological objective function is associated with the blood flow velocity profile caused by tumor-induced angiogenesis.

Brain tumor classification of virtual NMR voxels based on realistic blood vessel-induced spin dephasing using support vector machines

Remodeling of tissue microvasculature commonly promotes neoplastic growth; however, there is no imaging modality in oncology yet that noninvasively quantifies microvascular changes in clinical routine. Although blood capillaries cannot be resolved in typical magnetic resonance imaging (MRI) measurements, their geometry and distribution influence the integral nuclear magnetic resonance (NMR) signal from each macroscopic MRI voxel. We have numerically simulated the expected transverse relaxation in NMR voxels with different dimensions based on the realistic microvasculature in healthy and tumor-bearing mouse brains (U87 and GL261 glioblastoma). The 3D capillary structure in entire, undissected brains was acquired using light sheet fluorescence microscopy to produce large datasets of the highly resolved cerebrovasculature. Using this data, we trained support vector machines to classify virtual NMR voxels with different dimensions based on the simulated spin dephasing accountable to field inhomogeneities caused by the underlying vasculature. In prediction tests with previously blinded virtual voxels from healthy brain tissue and GL261 tumors, stable classification accuracies above 95% were reached. Our results indicate that high classification accuracies can be stably attained with achievable training set sizes and that larger MRI voxels facilitated increasingly successful classifications, even with small training datasets. We were able to prove that, theoretically, the transverse relaxation process can be harnessed to learn endogenous contrasts for single voxel tissue type classifications on tailored MRI acquisitions. If translatable to experimental MRI, this may augment diagnostic imaging in oncology with automated voxel-by-voxel signal interpretation to detect vascular pathologies.

A Fokker-Planck feedback control framework for optimal personalized therapies in colon cancer-induced angiogenesis

In this paper, a new framework for obtaining personalized optimal treatment strategies in colon cancer-induced angiogenesis is presented. The dynamics of colon cancer is given by a Itó stochastic process, which helps in modeling the randomness present in the system. The stochastic dynamics is then represented by the Fokker-Planck (FP) partial differential equation that governs the evolution of the associated probability density function. The optimal therapies are obtained using a three step procedure. First, a finite dimensional FP-constrained optimization problem is formulated that takes input individual noisy patient data, and is solved to obtain the unknown parameters corresponding to the individual tumor characteristics. Next, a sensitivity analysis of the optimal parameter set is used to determine the parameters to be controlled, thus, helping in assessing the types of treatment therapies. Finally, a feedback FP control problem is solved to determine the optimal combination therapies. Numerical results with the combination drug, comprising of Bevacizumab and Capecitabine, demonstrate the efficiency of the proposed framework.

LINC01615 activates ZEB2 through competitively binding with miR-3653-3p to promote the carcinogenesis of colon cancer cells

As a newly discovered cancer-related molecule, we explored the unreported mechanism of LINC01615 intervention in colon cancer.LINC01615 expression in clinical samples and cells were detected. Effects of LINC01615 silencing/overexpression on the malignant development of colon cancer cells were analyzed through cell function experiments. Changes at the level of molecular biology were detected by quantitative real-time polymerase chain reaction and Western blot. Bioinformatics analysis and dual luciferase reporter assay were involved in the display and verification of targeted binding sequences. The rescue tests and correlation analysis examined the relationship among LINC01615, miR-3653-3p and zinc finger E-box binding homeobox 2 (ZEB2) in colon cancer cells. The xenograft experiment and immunohistochemistry were performed to verify these results.TCGA suggested that LINC01615 was high-expressed in colon cancer, as verified in clinical and cell samples, and patients with LINC01615 overexpression suffered from a poor prognosis. Silent LINC01615 blocked the malignant development of colon cancer cells through regulating related genes expressions, while overexpressed LINC01615 had the opposite effect. LINC01615, which was targeted by miR-3653-3p, partially offset the inhibitory effect of miR-3653-3p on colon cancer cells. The downstream target gene ZEB2 of miR-3653-3p was high-expressed in colon cancer. MiR-3653-3p was negatively correlated with LINC01615 or ZEB2, while LINC01615 was positively correlated with ZEB2. Therefore, LINC01615 induced ZEB2 up-regulation, while miR-3653-3p reduced ZEB2 level. The results of in vivo studies were consistent with cell experiments.LINC01615 competitively binds with miR-3653-3p to regulate ZEB2 and promote canceration of colon cancer cells.

Systems biology of angiogenesis signaling: Computational models and omics

Angiogenesis is a highly regulated multiscale process that involves a plethora of cells, their cellular signal transduction, activation, proliferation, differentiation, as well as their intercellular communication. The coordinated execution and integration of such complex signaling programs is critical for physiological angiogenesis to take place in normal growth, development, exercise, and wound healing, while its dysregulation is critically linked to many major human diseases such as cancer, cardiovascular diseases, and ocular disorders; it is also crucial in regenerative medicine. Although huge efforts have been devoted to drug development for these diseases by investigation of angiogenesis‐targeted therapies, only a few therapeutics and targets have proved effective in humans due to the innate multiscale complexity and nonlinearity in the process of angiogenic signaling. As a promising approach that can help better address this challenge, systems biology modeling allows the integration of knowledge across studies and scales and provides a powerful means to mechanistically elucidate and connect the individual molecular and cellular signaling components that function in concert to regulate angiogenesis. In this review, we summarize and discuss how systems biology modeling studies, at the pathway‐, cell‐, tissue‐, and whole body‐levels, have advanced our understanding of signaling in angiogenesis and thereby delivered new translational insights for human diseases.

This article is categorized under:

Cardiovascular Diseases > Computational Models

Cancer > Computational Models

Superlinear growth reveals the Allee effect in tumors

Integrating experimental data into ecological models plays a central role in understanding biological mechanisms that drive tumor progression where such knowledge can be used to develop new therapeutic strategies. While the current studies emphasize the role of competition among tumor cells, they fail to explain recently observed superlinear growth dynamics across human tumors. Here we study tumor growth dynamics by developing a model that incorporates evolutionary dynamics inside tumors with tumor-microenvironment interactions. Our results reveal that tumor cells' ability to manipulate the environment and induce angiogenesis drives superlinear growth-a process compatible with the Allee effect. In light of this understanding, our model suggests that, for high-risk tumors that have a higher growth rate, suppressing angiogenesis can be the appropriate therapeutic intervention.

Nanorobots-Assisted Natural Computation for Multifocal Tumor Sensitization and Targeting

We have proposed a new tumor sensitization and targeting (TST) framework, named in vivo computation, in our previous investigations. The problem of TST for an early and microscopic tumor is interpreted from the computational perspective with nanorobots being the "natural" computing agents, the high-risk tissue being the search space, the tumor targeted being the global optimal solution, and the tumor-triggered biological gradient field (BGF) providing the aided knowledge for fitness evaluation of nanorobots. This natural computation process can be seen as on-the-fly path planning for nanorobot swarms with an unknown target position, which is different from the traditional path planning methods. Our previous works are focusing on the TST for a solitary lesion, where we proposed the weak priority evolution strategy (WP-ES) to adapt to the actuating mode of the homogeneous magnetic field used in the state-of-the-art nanorobotic platforms, and some in vitro validations were performed. In this paper, we focus on the problem of TST for multifocal tumors, which can be seen as a multimodal optimization problem for the "natural" computation. To overcome this issue, we propose a sequential targeting strategy (Se-TS) to complete TST for the multiple lesions with the assistance of nanorobot swarms, which are maneuvered by the external actuating and tracking devices according to the WP-ES. The Se-TS is used to modify the BGF landscape after a tumor is detected by a nanorobot swarm with the gathered BGF information around the detected tumor. Next, another nanorobot swarm will be employed to find the second tumor according to the modified BGF landscape without being misguided to the previous one. In this way, all the tumor lesions will be detected one by one. In other words, the paths of nanorobots to find the targets can be generated successively with the sequential modification of the BGF landscape. To demonstrate the effectiveness of the proposed Se-TS, we perform comprehensive simulation studies by enhancing the WP-ES based swarm intelligence algorithms using this strategy considering the realistic in-body constraints. The performance is compared against that of the "brute-force" search, which corresponds to the traditional systemic tumor targeting, and also against that of the standard swarm intelligence algorithms from the algorithmic perspective. Furthermore, some in vitro experiments are performed by using Janus microparticles as magnetic nanorobots, a two-dimensional microchannel network as the human vasculature, and a magnetic nanorobotic control system as the external actuating and tracking system. Results from the in silico simulations and in vitro experiments verify the effectiveness of the proposed Se-TS for two representative BGF landscapes.

Crosstalk between HER2 and PD-1/PD-L1 in Breast Cancer: From Clinical Applications to Mathematical Models

Breast cancer is one of the major causes of mortality in women worldwide. The most aggressive breast cancer subtypes are human epidermal growth factor receptor-positive (HER2+) and triple-negative breast cancers. Therapies targeting HER2 receptors have significantly improved HER2+ breast cancer patient outcomes. However, several recent studies have pointed out the deficiency of existing treatment protocols in combatting disease relapse and improving response rates to treatment. Overriding the inherent actions of the immune system to detect and annihilate cancer via the immune checkpoint pathways is one of the important hallmarks of cancer. Thus, restoration of these pathways by various means of immunomodulation has shown beneficial effects in the management of various types of cancers, including breast. We herein review the recent progress in the management of HER2+ breast cancer via HER2-targeted therapies, and its association with the programmed death receptor-1 (PD-1)/programmed death ligand-1 (PD-L1) axis. In order to link research in the areas of medicine and mathematics and point out specific opportunities for providing efficient theoretical analysis related to HER2+ breast cancer management, we also review mathematical models pertaining to the dynamics of HER2+ breast cancer and immune checkpoint inhibitors.

Gibbs point field model quantifies disorder in microvasculature of U87-glioblastoma

Microvascular proliferation in glioblastoma multiforme is a biological key mechanism to facilitate tumor growth and infiltration and a main target for treatment interventions. The vascular architecture can be obtained by Single Plane Illumination Microscopy (SPIM) to evaluate vascular heterogeneity in tumorous tissue. We make use of the Gibbs point field model to quantify the order of regularity in capillary distributions found in the U87 glioblastoma model in a murine model and to compare tumorous and healthy brain tissue. A single model parameter Γ was assigned that is linked to tissue-specific vascular topology through Monte-Carlo simulations. Distributions of the model parameter Γ differ significantly between glioblastoma tissue with mean 〈Γ_G〉=2.1±0.4, as compared to healthy brain tissue with mean 〈Γ_H〉=4.9±0.4, suggesting that the average Γ-value allows for tissue differentiation. These results may be used for diagnostic magnetic resonance imaging, where it has been shown recently that Γ is linked to tissue-inherent relaxation parameters.

Necrosis in the Tumor Microenvironment and Its Role in Cancer Recurrence

Cancer recurrence is one of the most imminent problems in the current world of medicine, and it is responsible for most of the cancer-related death rates worldwide. Long-term administration of anticancer cytotoxic drugs may act as a double-edged sword, as necrosis may lead to renewed cancer progression and treatment resistance. The lack of nutrients, coupled with the induced hypoxia, triggers cell death and secretion of signals that affect the tumor niche. Many efforts have been made to better understand the contribution of hypoxia and metabolic stress to cancer progression and resistance, but mostly with respect to inflammation. Here we provide an overview of the direct anticancer effects of necrotic signals, which are not necessarily mediated by inflammation and the role of DAMPs (damage-associated molecular patterns) on the formation of a pro-cancerous environment.

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.

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.

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.

Engineered Models of Metastasis with Application to Study Cancer Biomechanics

Three-dimensional complex biomechanical interactions occur from the initial steps of tumor formation to the later phases of cancer metastasis. Conventional monolayer cultures cannot recapitulate the complex microenvironment and chemical and mechanical cues that tumor cells experience during their metastatic journey, nor the complexity of their interactions with other, noncancerous cells. As alternative approaches, various engineered models have been developed to recapitulate specific features of each step of metastasis with tunable microenvironments to test a variety of mechanistic hypotheses. Here the main recent advances in the technologies that provide deeper insight into the process of cancer dissemination are discussed, with an emphasis on three-dimensional and mechanical factors as well as interactions between multiple cell types.

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.

Eco-evolutionary causes and consequences of temporal changes in intratumoural blood flow

Temporal changes in blood flow are commonly observed in malignant tumours, but the evolutionary causes and consequences are rarely considered. We propose that stochastic temporal variations in blood flow and microenvironmental conditions arise from the eco-evolutionary dynamics of tumour angiogenesis in which cancer cells, as individual units of selection, can influence and respond only to local environmental conditions. This leads to new vessels arising from the closest available vascular structure regardless of the size or capacity of this parental vessel. These dynamics produce unstable vascular networks with unpredictable spatial and temporal variations in blood flow and microenvironmental conditions. Adaptations of evolving populations to temporally varying environments in nature include increased diversity, greater motility and invasiveness, and highly plastic phenotypes, allowing for broad metabolic adaptability and rapid shifts to high rates of proliferation and profound quiescence. These adaptive strategies, when adopted in cancer cells, promote many commonly observed phenotypic properties including those found in the stem phenotype and in epithelial-to-mesenchymal transition. Temporal variations in intratumoural blood flow, which occur through the promotion of cancer cell phenotypes that facilitate both metastatic spread and resistance to therapy, may have substantial clinical consequences.

The importance of geometry in the corneal micropocket angiogenesis assay

The corneal micropocket angiogenesis assay is an experimental protocol for studying vessel network formation, or neovascularization, in vivo. The assay is attractive due to the ease with which the developing vessel network can be observed in the same animal over time. Measurements from the assay have been used in combination with mathematical modeling to gain insights into the mechanisms of angiogenesis. While previous modeling studies have adopted planar domains to represent the assay, the hemispherical shape of the cornea and asymmetric positioning of the angiogenic source can be seen to affect vascular patterning in experimental images. As such, we aim to better understand: i) how the geometry of the assay influences vessel network formation and ii) how to relate observations from planar domains to those in the hemispherical cornea. To do so, we develop a three-dimensional, off-lattice mathematical model of neovascularization in the cornea, using a spatially resolved representation of the assay for the first time. Relative to the detailed model, we predict that the adoption of planar geometries has a noticeable impact on vascular patterning, leading to increased vessel 'merging', or anastomosis, in particular when circular geometries are adopted. Significant differences in the dynamics of diffusible aniogenesis simulators are also predicted between different domains. In terms of comparing predictions across domains, the 'distance of the vascular front to the limbus' metric is found to have low sensitivity to domain choice, while metrics such as densities of tip cells and vessels and 'vascularized fraction' are sensitive to domain choice. Given the widespread adoption and attractive simplicity of planar tissue domains, both in silico and in vitro, the differences identified in the present study should prove useful in relating the results of previous and future theoretical studies of neovascularization to in vivo observations in the cornea.

Hyalomma dromedarii (Acari: Ixodidae) Salivary Gland Extract Inhibits Angiogenesis and Exhibits In Vitro Antitumor Effects

Hard ticks (Acari: Ixodidae) are blood-sucking ectoparasites characterized by the extended period of their attachment to their host. To access their bloodmeal, ticks secrete saliva containing a range of molecules that target the host's inflammation, immune system, and hemostatic components. Some of these molecules reportedly possess antiangiogenic and antitumor properties. The present study describes our investigation, the first of its kind, of the antiangiogenic and antitumoral effects of the Hyalomma dromedarii Koch, 1844 (Acari: Ixodidae), salivary gland extract (SGE), which inhibited the adhesion and migration of Human Umbilical Vein Endothelial Cells (HUVECs) in a dose-dependent manner, as well as angiogenesis in the Chick Chorioallantoic Membrane model. Interestingly, H. dromedarii SGE exerted an antiproliferative effect on U87 glioblastoma cells and inhibited their adhesion and migration to fibrinogen. These results open up new possibilities for characterizing and developing new molecules involved in the key steps of tumor progression.

A mathematical model of tumour angiogenesis: growth, regression and regrowth

Cancerous tumours have the ability to recruit new blood vessels through a process called angiogenesis. By stimulating vascular growth, tumours get connected to the circulatory system, receive nutrients and open a way to colonize distant organs. Tumour-induced vascular networks become unstable in the absence of tumour angiogenic factors (TAFs). They may undergo alternating stages of growth, regression and regrowth. Following a phase-field methodology, we propose a model of tumour angiogenesis that reproduces the aforementioned features and highlights the importance of vascular regression and regrowth. In contrast with previous theories which focus on vessel remodelling due to the absence of flow, we model an alternative regression mechanism based on the dependency of tumour-induced vascular networks on TAFs. The model captures capillaries at full scale, the plastic dynamics of tumour-induced vessel networks at long time scales, and shows the key role played by filopodia during angiogenesis. The predictions of our model are in agreement with in vivo experiments and may prove useful for the design of antiangiogenic therapies.

Microvessel Chaste: An Open Library for Spatial Modeling of Vascularized Tissues

Spatial models of vascularized tissues are widely used in computational physiology. We introduce a software library for composing multiscale, multiphysics models for applications including tumor growth, angiogenesis, osteogenesis, coronary perfusion, and oxygen delivery. Composition of such models is time consuming, with many researchers writing custom software. Recent advances in imaging have produced detailed three-dimensional (3D) datasets of vascularized tissues at the scale of individual cells. To fully exploit such data there is an increasing need for software that allows user-friendly composition of efficient, 3D models of vascularized tissues, and comparison of predictions with in vivo or in vitro experiments and alternative computational formulations. Microvessel Chaste can be used to build simulations of vessel growth and adaptation in response to mechanical and chemical stimuli; intra- and extravascular transport of nutrients, growth factors and drugs; and cell proliferation in complex 3D geometries. In addition, it can be used to develop custom software for integrating modeling with experimental data processing workflows, facilitated by a comprehensive Python interface to solvers implemented in C++. This article links to two reproducible example problems, showing how the library can be used to build simulations of tumor growth and angiogenesis with realistic vessel networks.

MR Vascular Fingerprinting in Stroke and Brain Tumors Models

In this study, we evaluated an MRI fingerprinting approach (MRvF) designed to provide high-resolution parametric maps of the microvascular architecture (i.e., blood volume fraction, vessel diameter) and function (blood oxygenation) simultaneously. The method was tested in rats (n = 115), divided in 3 models: brain tumors (9 L, C6, F98), permanent stroke, and a control group of healthy animals. We showed that fingerprinting can robustly distinguish between healthy and pathological brain tissues with different behaviors in tumor and stroke models. In particular, fingerprinting revealed that C6 and F98 glioma models have similar signatures while 9 L present a distinct evolution. We also showed that it is possible to improve the results of MRvF and obtain supplemental information by changing the numerical representation of the vascular network. Finally, good agreement was found between MRvF and conventional MR approaches in healthy tissues and in the C6, F98, and permanent stroke models. For the 9 L glioma model, fingerprinting showed blood oxygenation measurements that contradict results obtained with a quantitative BOLD approach. In conclusion, MR vascular fingerprinting seems to be an efficient technique to study microvascular properties in vivo. Multiple technical improvements are feasible and might improve diagnosis and management of brain diseases.

Coupled Hybrid Continuum-Discrete Model of Tumor Angiogenesis and Growth

The processes governing tumor growth and angiogenesis are codependent. To study the relationship between them, we proposed a coupled hybrid continuum-discrete model. In this model, tumor cells, their microenvironment (extracellular matrixes, matrix-degrading enzymes, and tumor angiogenic factors), and their network of blood vessels, described by a series of discrete points, were considered. The results of numerical simulation reveal the process of tumor growth and the change in microenvironment from avascular to vascular stage, indicating that the network of blood vessels develops gradually as the tumor grows. Our findings also reveal that a tumor is divided into three regions: necrotic, semi-necrotic, and well-vascularized. The results agree well with the previous relevant studies and physiological facts, and this model represents a platform for further investigations of tumor therapy.

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.

Computer Simulations of the Tumor Vasculature: Applications to Interstitial Fluid Flow, Drug Delivery, and Oxygen Supply

Tumor vasculature, the blood vessel network supplying a growing tumor with nutrients such as oxygen or glucose, is in many respects different from the hierarchically organized arterio-venous blood vessel network in normal tissues. Angiogenesis (the formation of new blood vessels), vessel cooption (the integration of existing blood vessels into the tumor vasculature), and vessel regression remodel the healthy vascular network into a tumor-specific vasculature. Integrative models, based on detailed experimental data and physical laws, implement, in silico, the complex interplay of molecular pathways, cell proliferation, migration, and death, tissue microenvironment, mechanical and hydrodynamic forces, and the fine structure of the host tissue vasculature. With the help of computer simulations high-precision information about blood flow patterns, interstitial fluid flow, drug distribution, oxygen and nutrient distribution can be obtained and a plethora of therapeutic protocols can be tested before clinical trials. This chapter provides an overview over the current status of computer simulations of vascular remodeling during tumor growth including interstitial fluid flow, drug delivery, and oxygen supply within the tumor. The model predictions are compared with experimental and clinical data and a number of longstanding physiological paradigms about tumor vasculature and intratumoral solute transport are critically scrutinized.

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.