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

A three-dimensional, discrete-continuum model of blood pressure in microvascular networks

We present a 3D discrete-continuum model to simulate blood pressure in large microvascular tissues in the absence of known capillary network architecture. Our hybrid approach combines a 1D Poiseuille flow description for large, discrete arteriolar and venular networks coupled to a continuum-based Darcy model, point sources of flux, for transport in the capillary bed. We evaluate our hybrid approach using a vascular network imaged from the mouse brain medulla/pons using multi-fluorescence high-resolution episcopic microscopy (MF-HREM). We use the fully-resolved vascular network to predict the hydraulic conductivity of the capillary network and generate a fully-discrete pressure solution to benchmark against. Our results demonstrate that the discrete-continuum methodology is a computationally feasible and effective tool for predicting blood pressure in real-world microvascular tissues when capillary microvessels are poorly defined.

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.

Modeling oxygen transport in the brain: An efficient coarse-grid approach to capture perivascular gradients in the parenchyma

Recent progresses in intravital imaging have enabled highly-resolved measurements of periarteriolar oxygen gradients (POGs) within the brain parenchyma. POGs are increasingly used as proxies to estimate the local baseline oxygen consumption, which is a hallmark of cell activity. However, the oxygen profile around a given arteriole arises from an interplay between oxygen consumption and delivery, not only by this arteriole but also by distant capillaries. Integrating such interactions across scales while accounting for the complex architecture of the microvascular network remains a challenge from a modelling perspective. This limits our ability to interpret the experimental oxygen maps and constitutes a key bottleneck toward the inverse determination of metabolic rates of oxygen. We revisit the problem of parenchymal oxygen transport and metabolism and introduce a simple, conservative, accurate and scalable direct numerical method going beyond canonical Krogh-type models and their associated geometrical simplifications. We focus on a two-dimensional formulation, and introduce the concepts needed to combine an operator-splitting and a Green's function approach. Oxygen concentration is decomposed into a slowly-varying contribution, discretized by Finite Volumes over a coarse cartesian grid, and a rapidly-varying contribution, approximated analytically in grid-cells surrounding each vessel. Starting with simple test cases, we thoroughly analyze the resulting errors by comparison with highly-resolved simulations of the original transport problem, showing considerable improvement of the computational-cost/accuracy balance compared to previous work. We then demonstrate the model ability to flexibly generate synthetic data reproducing the spatial dynamics of oxygen in the brain parenchyma, with sub-grid resolution. Based on these synthetic data, we show that capillaries distant from the arteriole cannot be overlooked when interpreting POGs, thus reconciling recent measurements of POGs across cortical layers with the fundamental idea that variations of vascular density within the depth of the cortex may reveal underlying differences in neuronal organization and metabolic load.

Enhanced perfusion following exposure to radiotherapy: A theoretical investigation

Tumour angiogenesis leads to the formation of blood vessels that are structurally and spatially heterogeneous. Poor blood perfusion, in conjunction with increased hypoxia and oxygen heterogeneity, impairs a tumour's response to radiotherapy. The optimal strategy for enhancing tumour perfusion remains unclear, preventing its regular deployment in combination therapies. In this work, we first identify vascular architectural features that correlate with enhanced perfusion following radiotherapy, using in vivo imaging data from vascular tumours. Then, we present a novel computational model to determine the relationship between these architectural features and blood perfusion in silico. If perfusion is defined to be the proportion of vessels that support blood flow, we find that vascular networks with small mean diameters and large numbers of angiogenic sprouts show the largest increases in perfusion post-irradiation for both biological and synthetic tumours. We also identify cases where perfusion increases due to the pruning of hypoperfused vessels, rather than blood being rerouted. These results indicate the importance of considering network composition when determining the optimal irradiation strategy. In the future, we aim to use our findings to identify tumours that are good candidates for perfusion enhancement and to improve the efficacy of combination therapies.

Drug transport modeling in solid tumors: A computational exploration of spatial heterogeneity of biophysical properties

Inadequate uptake of therapeutic agents by tumor cells is still a major barrier in clinical cancer therapy. Mathematical modeling is a powerful tool to describe and investigate the transport phenomena involved. However, current models for interstitial flow and drug delivery in solid tumors have not yet embedded the existing heterogeneity of tumor biomechanical properties. The purpose of this study is to introduce a novel and more realistic methodology for computational models of solid tumor perfusion and drug delivery accounting for these regional heterogeneities as well as lymphatic drainage effects. Several tumor geometries were studied using an advanced computational fluid dynamics (CFD) modeling approach of intratumor interstitial fluid flow and drug transport. Hereby, the following novelties were implemented: (i) the heterogeneity of tumor-specific hydraulic conductivity and capillary permeability; (ii) the effect of lymphatic drainage on interstitial fluid flow and drug penetration. Tumor size and shape both have a crucial role on the interstitial fluid flow regime as well as drug transport illustrating a direct correlation with interstitial fluid pressure (IFP) and an inverse correlation with drug penetration, except for large tumors having a diameter larger than 50 mm. The results also suggest that the interstitial fluid flow and drug penetration in small tumors depend on tumor shape. A parameter study on the necrotic core size illustrated that the core effect (i.e. fluid flow and drug penetration alteration) was only profound in small tumors. Interestingly, the impact of a necrotic core on drug penetration differs depending on the tumor shape from having no effect in ideally spherical tumors to a clear effect in elliptical tumors with a necrotic core. A realistic presence of lymphatic vessels only slightly affected tumor perfusion, having no substantial effect on drug delivery. In conclusion, our findings illustrated that our novel parametric CFD modeling strategy in combination with accurate profiling of heterogeneous tumor biophysical properties can provide a powerful tool for better insights into tumor perfusion and drug transport, enabling effective therapy planning.

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

OBJECTIVE

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

METHODS

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

RESULTS

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

CONCLUSIONS

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

Optimal heat transport induced by magnetic nanoparticle delivery in vascularised tumours

We describe a novel mathematical model for blood flow, delivery of nanoparticles, and heat transport in vascularised tumour tissue. The model, which is derived via the asymptotic homogenisation technique, provides a link between the macroscale behaviour of the system and its underlying, tortuous micro-structure, as parametrised in Penta and Ambrosi (2015). It consists of a double Darcy's law, coupled with a double advection-diffusion-reaction system describing heat transport, and an advection-diffusion-reaction equation for transport and adhesion of particles. Particles are assumed sufficiently large and do not extravasate to the tumour interstitial space but blood and heat can be exchanged between the two compartments. Numerical simulations of the model are performed using a finite element method to investigate cancer hyperthermia induced by the application of magnetic field applied to injected iron oxide nanoparticles. Since tumour microvasculature is more tortuous than that of healthy tissue and thus suboptimal in terms of fluid and drug transport, we study the influence of the vessels' geometry on tumour temperature. Effective and safe hyperthermia treatment requires tumour temperature within certain target range, generally estimated between 42 °C and 46 °C, for a certain target duration, typically 0.5h to 2h. As temperature is difficult to measure in situ, we use our model to determine the ranges of tortuosity of the microvessels, magnetic intensity, injection time, wall shear stress rate, and concentration of nanoparticles required to achieve given target conditions.

Perspectives on optimizing local delivery of drugs to peripheral nerves using mathematical models

Drug therapies for treating peripheral nerve injury repair have shown significant promise in preclinical studies. Despite this, drug treatments are not used routinely clinically to treat patients with peripheral nerve injuries. Drugs delivered systemically are often associated with adverse effects to other tissues and organs; it remains challenging to predict the effective concentration needed at an injured nerve and the appropriate delivery strategy. Local drug delivery approaches are being developed to mitigate this, for example via injections or biomaterial-mediated release. We propose the integration of mathematical modeling into the development of local drug delivery protocols for peripheral nerve injury repair. Mathematical models have the potential to inform understanding of the different transport mechanisms at play, as well as quantitative predictions around the efficacy of individual local delivery protocols. We discuss existing approaches in the literature, including drawing from other research fields, and present a process for taking forward an integrated mathematical-experimental approach to accelerate local drug delivery approaches for peripheral nerve injury repair. This article is categorized under: Neurological Diseases > Molecular and Cellular Physiology Neurological Diseases > Computational Models Neurological Diseases > Biomedical Engineering.

A physiologically based pharmacokinetic model for [68Ga]Ga-(HA-)DOTATATE to predict whole-body distribution and tumor sink effects in GEP-NET patients

BACKGROUND

Little is known about parameters that have a relevant impact on (dis)similarities in biodistribution between various ⁶⁸Ga-labeled somatostatin analogues. Additionally, the effect of tumor burden on organ uptake remains unclear. Therefore, the aim of this study was to describe and compare organ and tumor distribution of [⁶⁸Ga]Ga-DOTATATE and [⁶⁸Ga]Ga-HA-DOTATATE using a physiologically based pharmacokinetic (PBPK) model and to identify factors that might cause biodistribution and tumor uptake differences between both peptides. In addition, the effect of tumor burden on peptide biodistribution in gastroenteropancreatic (GEP) neuroendocrine tumor (NET) patients was assessed.

METHODS

A PBPK model was developed for [⁶⁸Ga]Ga-(HA-)DOTATATE in GEP-NET patients. Three tumor compartments were added, representing primary tumor, liver metastases and other metastases. Furthermore, reactions describing receptor binding, internalization and recycling, renal clearance and intracellular degradation were added to the model. Scan data from GEP-NET patients were used for evaluation of model predictions. Simulations with increasing tumor volumes were performed to assess the tumor sink effect.

RESULTS

Data of 39 and 59 patients receiving [⁶⁸Ga]Ga-DOTATATE and [⁶⁸Ga]Ga-HA-DOTATATE, respectively, were included. Evaluations showed that the model adequately described image-based patient data and that different receptor affinities caused organ uptake dissimilarities between both peptides. Sensitivity analysis indicated that tumor blood flow and blood volume impacted tumor distribution most. Tumor sink predictions showed a decrease in spleen uptake with increasing tumor volume, which seemed clinically relevant for patients with total tumor volumes higher than ~ 550 mL.

CONCLUSION

The developed PBPK model adequately predicted tumor and organ uptake for this GEP-NET population. Relevant organ uptake differences between [⁶⁸Ga]Ga-DOTATATE and [⁶⁸Ga]Ga-HA-DOTATATE were caused by different affinity profiles, while tumor uptake was mainly affected by tumor blood flow and blood volume. Furthermore, tumor sink predictions showed that for the majority of patients a tumor sink effect is not expected to be clinically relevant.

Investigation of the evolution of tumor-induced microvascular network under the inhibitory effect of anti-angiogenic factor, angiostatin: A mathematical study

Anti-angiogenesis as a treatment strategy for normalizing the microvascular network of tumors is of great interest among researchers, especially in combination with chemotherapy or radiotherapy. According to the vital role that angiogenesis plays in tumor growth and in exposing the tumor to therapeutic agents, this work develops a mathematical framework to study the influence of angiostatin, a plasminogen fragment that shows the anti-angiogenic function, in the evolutionary behavior of tumor-induced angiogenesis. Angiostatin-induced microvascular network reformation is investigated in a two-dimensional space by considering two parent vessels around a circular tumor by a modified discrete angiogenesis model in different tumor sizes. The effects of imposing modifications on the existing model, i.e., the matrix-degrading enzyme effect, proliferation and death of endothelial cells, matrix density function, and a more realistic chemotactic function, are investigated in this study. Results show a decrease in microvascular density in response to the angiostatin. A functional relationship exists between angiostatin's ability to normalize the capillary network and tumor size or progression stage, such that capillary density decreases by 55%, 41%, 24%, and 13% in tumors with a non-dimensional radius of 0.4, 0.3, 0.2, and 0.1, respectively, after angiostatin administration.

Red blood cell dynamics in extravascular biological tissues modelled as canonical disordered porous media

The dynamics of blood flow in the smallest vessels and passages of the human body, where the cellular character of blood becomes prominent, plays a dominant role in the transport and exchange of solutes. Recent studies have revealed that the microhaemodynamics of a vascular network is underpinned by its interconnected structure, and certain structural alterations such as capillary dilation and blockage can substantially change blood flow patterns. However, for extravascular media with disordered microstructure (e.g. the porous intervillous space in the placenta), it remains unclear how the medium's structure affects the haemodynamics. Here, we simulate cellular blood flow in simple models of canonical porous media representative of extravascular biological tissue, with corroborative microfluidic experiments performed for validation purposes. For the media considered here, we observe three main effects: first, the relative apparent viscosity of blood increases with the structural disorder of the medium; second, the presence of red blood cells (RBCs) dynamically alters the flow distribution in the medium; third, symmetry breaking introduced by moderate structural disorder can promote more homogeneous distribution of RBCs. Our findings contribute to a better understanding of the cell-scale haemodynamics that mediates the relationship linking the function of certain biological tissues to their microstructure.

Interstitial fluid pressure as an emerging biomarker in solid tumors

The physical microenvironment of cancer is characterized by elevated stiffness and tissue pressure, the main component of which is the interstitial fluid pressure (IFP). Elevated IFP is an established negative predictive and prognostic parameter, directly affecting malignant behavior and therapy response. As such, measurement of the IFP would allow to develop strategies aimed at engineering the physical microenvironment of cancer. Traditionally, IFP measurement required the use of invasive methods. Recent progress in dynamic and functional imaging methods such as dynamic contrast enhanced (DCE) magnetic resonance imaging and elastography, combined with numerical models and simulation, allows to comprehensively assess the biomechanical landscape of cancer, and may help to overcome physical barriers to drug delivery and immune cell infiltration. Here, we provide a comprehensive overview of the origin of elevated IFP, and its role in the malignant phenotype. Also, we review the methods used to measure IFP using invasive and imaging based methods, and highlight remaining obstacles and potential areas of progress in order to implement IFP measurement in clinical practice.

Modeling a 3-D multiscale blood-flow and heat-transfer framework for realistic vascular systems

Modeling of biological domains and simulation of biophysical processes occurring in them can help inform medical procedures. However, when considering complex domains such as large regions of the human body, the complexities of blood vessel branching and variation of blood vessel dimensions present a major modeling challenge. Here, we present a Voxelized Multi-Physics Simulation (VoM-PhyS) framework to simulate coupled heat transfer and fluid flow using a multi-scale voxel mesh on a biological domain obtained. In this framework, flow in larger blood vessels is modeled using the Hagen–Poiseuille equation for a one-dimensional flow coupled with a three-dimensional two-compartment porous media model for capillary circulation in tissue. The Dirac distribution function is used as Sphere of Influence (SoI) parameter to couple the one-dimensional and three-dimensional flow. This blood flow system is coupled with a heat transfer solver to provide a complete thermo-physiological simulation. The framework is demonstrated on a frog tongue and further analysis is conducted to study the effect of convective heat exchange between blood vessels and tissue, and the effect of SoI on simulation results.

Challenges and opportunities of integrating imaging and mathematical modelling to interrogate biological processes

Advances in biological imaging have accelerated our understanding of human physiology in both health and disease. As these advances have developed, the opportunities gained by integrating with cutting-edge mathematical models have become apparent yet remain challenging. Combined imaging-modelling approaches provide unprecedented opportunity to correlate data on tissue architecture and function, across length and time scales, to better understand the mechanisms that underpin fundamental biology and also to inform clinical decisions. Here we discuss the opportunities and challenges of such approaches, providing literature examples across a range of organ systems. Given the breadth of the field we focus on the intersection of continuum modelling and in vivo imaging applied to the vasculature and blood flow, though our rationale and conclusions extend widely. We propose three key research pillars (image acquisition, image processing, mathematical modelling) and present their respective advances as well as future opportunity via better integration. Multidisciplinary efforts that develop imaging and modelling tools concurrently, and share them open-source with the research community, provide exciting opportunity for advancing these fields.

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.

Numerical Investigation on the Anti-Angiogenic Therapy-Induced Normalization in Solid Tumors

This study numerically analyzes the fluid flow and solute transport in a solid tumor to comprehensively examine the consequence of normalization induced by anti-angiogenic therapy on drug delivery. The current study leads to a more accurate model in comparison to previous research, as it incorporates a non-homogeneous real-human solid tumor including necrotic, semi-necrotic, and well-vascularized regions. Additionally, the model considers the effects of concurrently chemotherapeutic agents (three macromolecules of IgG, F(ab')2, and F(ab')) and different normalization intensities in various tumor sizes. Examining the long-term influence of normalization on the quality of drug uptake by necrotic area is another contribution of the present study. Results show that normalization decreases the interstitial fluid pressure (IFP) and spreads the pressure gradient and non-zero interstitial fluid velocity (IFV) into inner areas. Subsequently, wash-out of the drug from the tumor periphery is decreased. It is also demonstrated that normalization can improve the distribution of solute concentration in the interstitium. The efficiency of normalization is introduced as a function of the time course of perfusion, which depends on the tumor size, drug type, as well as normalization intensity, and consequently on the dominant mechanism of drug delivery. It is suggested to accompany anti-angiogenic therapy by F(ab') in large tumor size (Req=2.79  cm) to improve reservoir behavior benefit from normalization. However, IgG is proposed as the better option in the small tumor (Req=0.46  cm), in which normalization finds the opportunity of enhancing uniformity of IgG average exposure by 22%. This study could provide a perspective for preclinical and clinical trials on how to take advantage of normalization, as an adjuvant treatment, in improving drug delivery into a non-homogeneous solid tumor.

Deep GRU-CNN Model for COVID-19 Detection From Chest X-Rays Data

In the current era, data is growing exponentially due to advancements in smart devices. Data scientists apply a variety of learning-based techniques to identify underlying patterns in the medical data to address various health-related issues. In this context, automated disease detection has now become a central concern in medical science. Such approaches can reduce the mortality rate through accurate and timely diagnosis. COVID-19 is a modern virus that has spread all over the world and is affecting millions of people. Many countries are facing a shortage of testing kits, vaccines, and other resources due to significant and rapid growth in cases. In order to accelerate the testing process, scientists around the world have sought to create novel methods for the detection of the virus. In this paper, we propose a hybrid deep learning model based on a convolutional neural network (CNN) and gated recurrent unit (GRU) to detect the viral disease from chest X-rays (CXRs). In the proposed model, a CNN is used to extract features, and a GRU is used as a classifier. The model has been trained on 424 CXR images with 3 classes (COVID-19, Pneumonia, and Normal). The proposed model achieves encouraging results of 0.96, 0.96, and 0.95 in terms of precision, recall, and f1-score, respectively. These findings indicate how deep learning can significantly contribute to the early detection of COVID-19 in patients through the analysis of X-ray scans. Such indications can pave the way to mitigate the impact of the disease. We believe that this model can be an effective tool for medical practitioners for early diagnosis.

Vincristine-doxorubicin co-loaded artificial low-density lipoproteins towards solid tumours

To construct an artificial low-density lipoprotein (aLDL) that highly mimics low-density lipoprotein (LDL) in vivo, and deliver vincristine (VCR) - doxorubicin (DOX) simultaneously, the 100 nm and 35 nm DOX-VCR-aLDLs (DV-aLDLs) were constructed, then the physicochemical characteristics were evaluated. Through in vitro inverse gravity diffusion experiment, the tumour cake and sphere model experiment, draw a conclusion that the diffusion of 35 nm DV-aLDLs was stronger than 100 nm DV-aLDLs, and the tumour retention of 35 nm DV-aLDLs was better than the DV-solution. In addition, the three-dimension (3D) in vivo distribution imaging of aLDLs was performed on HepG-2 tumour-bearing nude mice, followed by the biodistribution and therapeutic efficacy on these xenograft models. Taking advantage of better diffusion capacity in tumour tissue, as well as the synergistic effect of VCR and DOX, the 35 nm DV-aLDL had the strongest efficacy and the lowest toxicity. High entrapment efficiency and stability, both active and passive targeting, making aLDL a potential carrier for tumour-targeted therapy at the same time.

Validation and parameter optimization of a hybrid embedded/homogenized solid tumor perfusion model

The goal of this paper is to investigate the validity of a hybrid embedded/homogenized in-silico approach for modeling perfusion through solid tumors. The rationale behind this novel idea is that only the larger blood vessels have to be explicitly resolved while the smaller scales of the vasculature are homogenized. As opposed to typical discrete or fully resolved 1D-3D models, the required data can be obtained with in-vivo imaging techniques since the morphology of the smaller vessels is not necessary. By contrast, the larger vessels, whose topology and structure is attainable noninvasively, are resolved and embedded as one-dimensional inclusions into the three-dimensional tissue domain which is modeled as a porous medium. A sound mortar-type formulation is employed to couple the two representations of the vasculature. We validate the hybrid model and optimize its parameters by comparing its results to a corresponding fully resolved model based on several well-defined metrics. These tests are performed on a complex data set of three different tumor types with heterogeneous vascular architectures. The correspondence of the hybrid model in terms of mean representative elementary volume blood and interstitial fluid pressures is excellent with relative errors of less than 4%. Larger, but less important and explicable errors are present in terms of blood flow in the smaller, homogenized vessels. We finally discuss and demonstrate how the hybrid model can be further improved to apply it for studies on tumor perfusion and the efficacy of drug delivery.

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.

Vessel network extraction and analysis of mouse pulmonary vasculature via X-ray micro-computed tomographic imaging

In this work, non-invasive high-spatial resolution three-dimensional (3D) X-ray micro-computed tomography (μCT) of healthy mouse lung vasculature is performed. Methodologies are presented for filtering, segmenting, and skeletonizing the collected 3D images. Novel methods for the removal of spurious branch artefacts from the skeletonized 3D image are introduced, and these novel methods involve a combination of distance transform gradients, diameter-length ratios, and the fast marching method (FMM). These new techniques of spurious branch removal result in the consistent removal of spurious branches without compromising the connectivity of the pulmonary circuit. Analysis of the filtered, skeletonized, and segmented 3D images is performed using a newly developed Vessel Network Extraction algorithm to fully characterize the morphology of the mouse pulmonary circuit. The removal of spurious branches from the skeletonized image results in an accurate representation of the pulmonary circuit with significantly less variability in vessel diameter and vessel length in each generation. The branching morphology of a full pulmonary circuit is characterized by the mean diameter per generation and number of vessels per generation. The methods presented in this paper lead to a significant improvement in the characterization of 3D vasculature imaging, allow for automatic separation of arteries and veins, and for the characterization of generations containing capillaries and intrapulmonary arteriovenous anastomoses (IPAVA).

Image-guided thermosensitive liposomes for focused ultrasound enhanced co-delivery of carboplatin and SN-38 against triple negative breast cancer in mice

Triggerable nanocarriers have the potential to significantly improve the therapeutic index of existing anticancer agents. They allow for highly localised delivery and release of therapeutic cargos, reducing off-target toxicity and increasing anti-tumour activity. Liposomes may be engineered to respond to an externally applied stimulus such as focused ultrasound (FUS). Here, we report the first co-delivery of SN-38 (irinotecan's super-active metabolite) and carboplatin, using an MRI-visible thermosensitive liposome (iTSL). MR contrast enhancement was achieved by the incorporation of a gadolinium lipid conjugate in the liposome bilayer along with a dye-labelled lipid for near infrared fluorescence bioimaging. The resulting iTSL were successfully loaded with SN-38 in the lipid bilayer and carboplatin in the aqueous core - allowing co-delivery of both. The iTSL demonstrated both thermosensitivity and MR-imageability. In addition, they showed effective local targeted co-delivery of carboplatin and SN-38 after triggered release with brief FUS treatments. A single dosage induced significant improvement of anti-tumour activity (over either the free drugs or the iTSL without FUS-activation) in triple negative breast cancer xenografts tumours in mice.

A four-compartment multiscale model of fluid and drug distribution in vascular tumours

The subtle relationship between vascular network structure and mass transport is vital to predict and improve the efficacy of anticancer treatments. Here, mathematical homogenisation is used to derive a new multiscale continuum model of blood and chemotherapy transport in the vasculature and interstitium of a vascular tumour. This framework enables information at a range of vascular hierarchies to be fed into an effective description on the length scale of the tumour. The model behaviour is explored through a demonstrative case study of a simplified representation of a dorsal skinfold chamber, to examine the role of vascular network architecture in influencing fluid and drug perfusion on the length scale of the chamber. A single parameter, P, is identified that relates tumour-scale fluid perfusion to the permeability and density of the capillary bed. By fixing the topological and physiological properties of the arteriole and venule networks, an optimal value for P is identified, which maximises tumour fluid transport and is thus hypothesised to benefit chemotherapy delivery. We calculate the values for P for eight explicit network structures; in each case, vascular intervention by either decreasing the permeability or increasing the density of the capillary network would increase fluid perfusion through the cancerous tissue. Chemotherapeutic strategies are compared and indicate that single injection is consistently more successful compared with constant perfusion, and the model predicts optimal timing of a second dose. These results highlight the potential of computational modelling to elucidate the link between vascular architecture and fluid, drug distribution in tumours.