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.

A three-dimensional method for morphological analysis and flow velocity estimation in microvasculature on-a-chip.

Three-dimensional (3D) imaging techniques (e.g., confocal microscopy) are commonly used to visualize in vitro models, especially microvasculature on-a-chip. Conversely, 3D analysis is not the standard method to extract quantitative information from those models. We developed the µVES algorithm to analyze vascularized in vitro models leveraging 3D data. It computes morphological parameters (geometry, diameter, length, tortuosity, eccentricity) and intravascular flow velocity. µVES application to microfluidic vascularized in vitro models shows that they successfully replicate functional features of the microvasculature in vivo in terms of intravascular fluid flow velocity. However, wall shear stress is lower compared to in vivo references. The morphological analysis also highlights the model's physiological similarities (vessel length and tortuosity) and shortcomings (vessel radius and surface-over-volume ratio). The addition of the third dimension in our analysis produced significant differences in the metrics assessed compared to 2D estimations. It enabled the computation of new indices, such as vessel eccentricity. These µVES capabilities can find application in analyses of different in vitro vascular models, as well as in vivo and ex vivo microvasculature.

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

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

Approximation bounds for convolutional neural networks in operator learning.

Recently, deep Convolutional Neural Networks (CNNs) have proven to be successful when employed in areas such as reduced order modeling of parametrized PDEs. Despite their accuracy and efficiency, the approaches available in the literature still lack a rigorous justification on their mathematical foundations. Motivated by this fact, in this paper we derive rigorous error bounds for the approximation of nonlinear operators by means of CNN models. More precisely, we address the case in which an operator maps a finite dimensional input µ∈Rp onto a functional output uµ:[0,1]d→R, and a neural network model is used to approximate a discretized version of the input-to-output map. The resulting error estimates provide a clear interpretation of the hyperparameters defining the neural network architecture. All the proofs are constructive, and they ultimately reveal a deep connection between CNNs and the Fourier transform. Finally, we complement the derived error bounds by numerical experiments that illustrate their application.

Learning high-order interactions for polygenic risk prediction.

Within the framework of precision medicine, the stratification of individual genetic susceptibility based on inherited DNA variation has paramount relevance. However, one of the most relevant pitfalls of traditional Polygenic Risk Scores (PRS) approaches is their inability to model complex high-order non-linear SNP-SNP interactions and their effect on the phenotype (e.g. epistasis). Indeed, they incur in a computational challenge as the number of possible interactions grows exponentially with the number of SNPs considered, affecting the statistical reliability of the model parameters as well. In this work, we address this issue by proposing a novel PRS approach, called High-order Interactions-aware Polygenic Risk Score (hiPRS), that incorporates high-order interactions in modeling polygenic risk. The latter combines an interaction search routine based on frequent itemsets mining and a novel interaction selection algorithm based on Mutual Information, to construct a simple and interpretable weighted model of user-specified dimensionality that can predict a given binary phenotype. Compared to traditional PRSs methods, hiPRS does not rely on GWAS summary statistics nor any external information. Moreover, hiPRS differs from Machine Learning-based approaches that can include complex interactions in that it provides a readable and interpretable model and it is able to control overfitting, even on small samples. In the present work we demonstrate through a comprehensive simulation study the superior performance of hiPRS w.r.t. state of the art methods, both in terms of scoring performance and interpretability of the resulting model. We also test hiPRS against small sample size, class imbalance and the presence of noise, showcasing its robustness to extreme experimental settings. Finally, we apply hiPRS to a case study on real data from DACHS cohort, defining an interaction-aware scoring model to predict mortality of stage II-III Colon-Rectal Cancer patients treated with oxaliplatin.

Prediction of myocardial blood flow under stress conditions by means of a computational model.

PURPOSE: Quantification of myocardial blood flow (MBF) and functional assessment of coronary artery disease (CAD) can be achieved through stress myocardial computed tomography perfusion (stress-CTP). This requires an additional scan after the resting coronary computed tomography angiography (cCTA) and administration of an intravenous stressor. This complex protocol has limited reproducibility and non-negligible side effects for the patient. We aim to mitigate these drawbacks by proposing a computational model able to reproduce MBF maps. METHODS: A computational perfusion model was used to reproduce MBF maps. The model parameters were estimated by using information from cCTA and MBF measured from stress-CTP (MBFCTP) maps. The relative error between the computational MBF under stress conditions (MBFCOMP) and MBFCTP was evaluated to assess the accuracy of the proposed computational model. RESULTS: Applying our method to 9 patients (4 control subjects without ischemia vs 5 patients with myocardial ischemia), we found an excellent agreement between the values of MBFCOMP and MBFCTP. In all patients, the relative error was below 8% over all the myocardium, with an average-in-space value below 4%. CONCLUSION: The results of this pilot work demonstrate the accuracy and reliability of the proposed computational model in reproducing MBF under stress conditions. This consistency test is a preliminary step in the framework of a more ambitious project which is currently under investigation, i.e., the construction of a computational tool able to predict MBF avoiding the stress protocol and potential side effects while reducing radiation exposure.

Modeling the cardiac response to hemodynamic changes associated with COVID-19: a computational study.

Emerging studies address how COVID-19 infection can impact the human cardiovascular system. This relates particularly to the development of myocardial injury, acute coronary syndrome, myocarditis, arrhythmia, and heart failure. Prospective treatment approach is advised for these patients. To study the interplay between local changes (reduced contractility), global variables (peripheral resistances, heart rate) and the cardiac function, we considered a lumped parameters computational model of the cardiovascular system and a three-dimensional multiphysics model of cardiac electromechanics. Our mathematical model allows to simulate the systemic and pulmonary circulations, the four cardiac valves and the four heart chambers, through equations describing the underlying physical processes. By the assessment of conventionally relevant parameters of cardiac function obtained through our numerical simulations, we propose a computational model to effectively reveal the interactions between the cardiac and pulmonary functions in virtual subjects with normal and impaired cardiac function at baseline affected by mild or severe COVID-19.

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.

Development of a method for generating SNP interaction-aware polygenic risk scores for radiotherapy toxicity.

AIM: To identify the effect of single nucleotide polymorphism (SNP) interactions on the risk of toxicity following radiotherapy (RT) for prostate cancer (PCa) and propose a new method for polygenic risk score incorporating SNP-SNP interactions (PRSi). MATERIALS AND METHODS: Analysis included the REQUITE PCa cohort that received external beam RT and was followed for 2 years. Late toxicity endpoints were: rectal bleeding, urinary frequency, haematuria, nocturia, decreased urinary stream. Among 43 literature-identified SNPs, the 30% most strongly associated with each toxicity were tested. SNP-SNP combinations (named SNP-allele sets) seen in ≥10% of the cohort were condensed into risk (RS) and protection (PS) scores, respectively indicating increased or decreased toxicity risk. Performance of RS and PS was evaluated by logistic regression. RS and PS were then combined into a single PRSi evaluated by area under the receiver operating characteristic curve (AUC). RESULTS: Among 1,387 analysed patients, toxicity rates were 11.7% (rectal bleeding), 4.0% (urinary frequency), 5.5% (haematuria), 7.8% (nocturia) and 17.1% (decreased urinary stream). RS and PS combined 8 to 15 different SNP-allele sets, depending on the toxicity endpoint. Distributions of PRSi differed significantly in patients with/without toxicity with AUCs ranging from 0.61 to 0.78. PRSi was better than the classical summed PRS, particularly for the urinary frequency, haematuria and decreased urinary stream endpoints. CONCLUSIONS: Our method incorporates SNP-SNP interactions when calculating PRS for radiotherapy toxicity. Our approach is better than classical summation in discriminating patients with toxicity and should enable incorporating genetic information to improve normal tissue complication probability models.

A surrogate model for plaque modeling in carotids based on Robin conditions calibrated by cine MRI data.

We propose a surrogate model for the fluid-structure interaction (FSI) problem for the study of blood dynamics in carotid arteries in presence of plaque. This is based on the integration of a numerical model with subject-specific data and clinical imaging. We propose to model the plaque as part of the tissues surrounding the vessel wall through the application of an elastic support boundary condition. In order to characterize the plaque and other surrounding tissues, such as the close-by jugular vein, the elastic parameters of the boundary condition were spatially differentiated and their values were estimated by minimizing the discrepancies between computed vessel displacements and reference values obtained from CINE Magnetic Resonance Imaging data. We applied the model to three subjects with a degree of stenosis greater than 70%. We found that accounting for both plaque and jugular vein in the estimation of the elastic parameters increases the accuracy. In particular, in all patients, mismatches between computed and in vivo measured wall displacements were one to two orders of magnitude lower than the spatial resolution of the original MRI data. These results confirmed the validity of the proposed surrogate plaque model. We also compared fluid-dynamics results with those obtained in a fixed wall setting and in a full FSI model, used as gold standard, highlighting the better accordance of our results in comparison to the rigid ones.

A Deep Learning Approach Validates Genetic Risk Factors for Late Toxicity After Prostate Cancer Radiotherapy in a REQUITE Multi-National Cohort.

Background: REQUITE (validating pREdictive models and biomarkers of radiotherapy toxicity to reduce side effects and improve QUalITy of lifE in cancer survivors) is an international prospective cohort study. The purpose of this project was to analyse a cohort of patients recruited into REQUITE using a deep learning algorithm to identify patient-specific features associated with the development of toxicity, and test the approach by attempting to validate previously published genetic risk factors. Methods: The study involved REQUITE prostate cancer patients treated with external beam radiotherapy who had complete 2-year follow-up. We used five separate late toxicity endpoints: ≥grade 1 late rectal bleeding, ≥grade 2 urinary frequency, ≥grade 1 haematuria, ≥ grade 2 nocturia, ≥ grade 1 decreased urinary stream. Forty-three single nucleotide polymorphisms (SNPs) already reported in the literature to be associated with the toxicity endpoints were included in the analysis. No SNP had been studied before in the REQUITE cohort. Deep Sparse AutoEncoders (DSAE) were trained to recognize features (SNPs) identifying patients with no toxicity and tested on a different independent mixed population including patients without and with toxicity. Results: One thousand, four hundred and one patients were included, and toxicity rates were: rectal bleeding 11.7%, urinary frequency 4%, haematuria 5.5%, nocturia 7.8%, decreased urinary stream 17.1%. Twenty-four of the 43 SNPs that were associated with the toxicity endpoints were validated as identifying patients with toxicity. Twenty of the 24 SNPs were associated with the same toxicity endpoint as reported in the literature: 9 SNPs for urinary symptoms and 11 SNPs for overall toxicity. The other 4 SNPs were associated with a different endpoint. Conclusion: Deep learning algorithms can validate SNPs associated with toxicity after radiotherapy for prostate cancer. The method should be studied further to identify polygenic SNP risk signatures for radiotherapy toxicity. The signatures could then be included in integrated normal tissue complication probability models and tested for their ability to personalize radiotherapy treatment planning.

In silico model of the early effects of radiation therapy on the microcirculation and the surrounding tissues.

BACKGROUND: Radiation-induced organ dysfunction are frequently described by Normal Tissue Complication Probability models. The approximations of this radiobiological approach do not allow to consider the important role played by the microvasculature not only in the dose-response of the blood vessels but also of the organs where it is located. To this purpose, we presented a computational model that describes the fluid dynamics of microcirculation when the parameters of the network and the surrounding tissues are affected by radio-induced changes. MATERIALS AND METHODS: The effects of the ionizing radiation on the capillary bed are mediated by the inflammatory response. We derived from a literature search the possible morphological and functional variations of the network due to the process of the acute inflammation. Specifically, we considered vasodilation, increased membrane permeability with consequent fluid extravasation and increased wall elasticity. These perturbations to the system were included in a computational model, already able to describe the physics of the microcirculation and its exchanges with the surrounding tissues. RESULTS: Two computational descriptions were considered. In the first one, we changed a set of 4 parameters associated with the increased fluid exchange from the health scenario at the baseline to a seriously compromised scenario with the edema formation. The second study investigated the effect of a perturbation to the vessel wall elasticity. CONCLUSIONS: These simulations represent a first step towards the challenging objective of understanding and describing in a mechanistic way the effects of radiation on the vascular microenvironment.

Application of Transmural Flow Across In Vitro Microvasculature Enables Direct Sampling of Interstitial Therapeutic Molecule Distribution.

In vitro prediction of physiologically relevant transport of therapeutic molecules across the microcirculation represents an intriguing opportunity to predict efficacy in human populations. On-chip microvascular networks (MVNs) show physiologically relevant values of molecular permeability, yet like most systems, they lack an important contribution to transport: the ever-present fluid convection through the endothelium. Quantification of transport through the MVNs by current methods also requires confocal imaging and advanced analytical techniques, which can be a bottleneck in industry and academic laboratories. Here, it is shown that by recapitulating physiological transmural flow across the MVNs, the concentration of small and large molecule therapeutics can be directly sampled in the interstitial fluid and analyzed using standard analytical techniques. The magnitudes of transport measured in MVNs reveal trends with molecular size and type (protein versus nonprotein) that are expected in vivo, supporting the use of the MVNs platform as an in vitro tool to predict distribution of therapeutics in vivo.

A tissue chamber chip for assessing nanoparticle mobility in the extravascular space.

Although a plethora of nanoparticle configurations have been proposed over the past 10 years, the uniform and deep penetration of systemically injected nanomedicines into the diseased tissue stays as a major biological barrier. Here, a 'Tissue Chamber' chip is designed and fabricated to study the extravascular transport of small molecules and nanoparticles. The chamber comprises a collagen slab, deposited within a PDMS mold, and an 800 µm channel for the injection of the working solution. Through fluorescent microscopy, the dynamics of molecules and nanoparticles was estimated within the gel, under different operating conditions. Diffusion coefficients were derived from the analysis of the particle mean square displacements (MSD). For validating the experimental apparatus and the protocol for data analysis, the diffusion D of FITC-Dextran molecules of 4, 40 and 250 kDa was first quantified. As expected, D reduces with the molecular weight of the dextran molecules. The MSD-derived diffusion coefficients were in good agreement with values derived via fluorescence recovery after photobleaching (FRAP), an alternative technique that solely applies to small molecules. Then, the transport of six nanoparticles with similar hydrodynamic diameters (~ 200 nm) and different surface chemistries was quantified. Surface PEGylation was confirmed to favor the diffusion of nanoparticles within the collagen slab, whereas the surface decoration with hyaluronic acid (HA) chains reduced nanoparticle mobility in a way proportional to the HA molecular weight. To assess further the generality of the proposed approach, the diffusion of the six nanoparticles was also tested in freshly excised brain tissue slices. In these ex vivo experiments, the diffusion coefficients were 5-orders of magnitude smaller than for the Tissue Chamber chip. This was mostly ascribed to the lack of a cellular component in the chip. However, the trends documented for PEGylated and HA-coated nanoparticles in vitro were also confirmed ex vivo. This work demonstrates that the Tissue Chamber chip can be employed to effectively and efficiently test the extravascular transport of nanomedicines while minimizing the use of animals.

Numerical simulations of the microvascular fluid balance with a non-linear model of the lymphatic system.

Fluid homeostasis is required for life. Processes involved in fluid balance are strongly related to exchanges at the microvascular level. Computational models have been presented in the literature to analyze the microvascular-interstitial interactions. As far as we know, none of those models consider a physiological description for the lymphatic drainage-interstitial pressure relation. We develop a computational model that consists of a network of straight cylindrical vessels and an isotropic porous media with a uniformly distributed sink term acting as the lymphatic system. In order to describe the lymphatic flow rate, a non-linear function of the interstitial pressure is defined, based on literature data on the lymphatic system. The proposed model of lymphatic drainage is compared to a linear one, as is typically used in computational models. To evaluate the response of the model, the two are compared with reference to both physiological and pathological conditions. Differences in the local fluid dynamic description have been observed using the non-linear model. In particular, the distribution of interstitial pressure is heterogeneous in all the cases analyzed. The resulting averaged values of the interstitial pressure are also different, and they agree with literature data when using the non-linear model. This work highlights the key role of lymphatic drainage and its modeling when studying the fluid balance in microcirculation for both to physiological and pathological conditions, e.g. uremia.

A computational model for microcirculation including Fahraeus-Lindqvist effect, plasma skimming and fluid exchange with the tissue interstitium.

We present a two-phase model for microcirculation that describes the interaction of plasma with red blood cells. The model takes into account of typical effects characterizing the microcirculation, such as the Fahraeus-Lindqvist effect and plasma skimming. Besides these features, the model describes the interaction of capillaries with the surrounding tissue. More precisely, the model accounts for the interaction of capillary transmural flow with the surrounding interstitial pressure. Furthermore, the capillaries are represented as one-dimensional channels with arbitrary, possibly curved configuration. The latter two features rely on the unique ability of the model to account for variations of flow rate and pressure along the axis of the capillary, according to a local differential formulation of mass and momentum conservation. Indeed, the model stands on a solid mathematical foundation, which is also addressed in this work. In particular, we present the model derivation, the variational formulation, and its approximation using the finite element method. Finally, we conclude the work with a comparative computational study of the importance of the Fahraeus-Lindqvist, plasma skimming, and capillary leakage effects on the distribution of flow in a microvascular network.

Correction to: Design and validation of an osteochondral bioreactor for the screening of treatments for osteoarthritis.

The original version of this article unfortunately contained a mistake.

Design and validation of an osteochondral bioreactor for the screening of treatments for osteoarthritis.

Bioreactors are systems that can be used to monitor the response of tissues and cells to candidate drugs. Building on the experience developed in the creation of an osteochondral bioreactor, we have designed a new 3D printed system, which allows optical access to the cells throughout testing for in line monitoring. Because of the use of 3D printing, the fluidics could be developed in the third dimension, thus maintaining the footprint of a single well of a typical 96 well plate. This new design was optimized to achieve the maximum fluid transport through the central chamber, which corresponds to optimal nutrient or drug exposure. This optimization was achieved by altering each dimension of the bioreactor fluid path. A physical model for optimized drug exposure was then created and tested.

A computational study of cancer hyperthermia based on vascular magnetic nanoconstructs.

The application of hyperthermia to cancer treatment is studied using a novel model arising from the fundamental principles of flow, mass and heat transport in biological tissues. The model is defined at the scale of the tumour microenvironment and an advanced computational scheme called the embedded multiscale method is adopted to solve the governing equations. More precisely, this approach involves modelling capillaries as one-dimensional channels carrying flow, and special mathematical operators are used to model their interaction with the surrounding tissue. The proposed computational scheme is used to analyse hyperthermic treatment of cancer based on systemically injected vascular magnetic nanoconstructs carrying super-paramagnetic iron oxide nanoparticles. An alternating magnetic field is used to excite the nanoconstructs and generate localized heat within the tissue. The proposed model is particularly adequate for this application, since it has a unique capability of incorporating microvasculature configurations based on physiological data combined with coupled capillary flow, interstitial filtration and heat transfer. A virtual tumour model is initialized and the spatio-temporal distribution of nanoconstructs in the vascular network is analysed. In particular, for a reference iron oxide concentration, temperature maps of several different hypothesized treatments are generated in the virtual tumour model. The observations of the current study might in future guide the design of more efficient treatments for cancer hyperthermia.

Distributed and Lumped Parameter Models for the Characterization of High Throughput Bioreactors.

Next generation bioreactors are being developed to generate multiple human cell-based tissue analogs within the same fluidic system, to better recapitulate the complexity and interconnection of human physiology [1, 2]. The effective development of these devices requires a solid understanding of their interconnected fluidics, to predict the transport of nutrients and waste through the constructs and improve the design accordingly. In this work, we focus on a specific model of bioreactor, with multiple input/outputs, aimed at generating osteochondral constructs, i.e., a biphasic construct in which one side is cartilaginous in nature, while the other is osseous. We next develop a general computational approach to model the microfluidics of a multi-chamber, interconnected system that may be applied to human-on-chip devices. This objective requires overcoming several challenges at the level of computational modeling. The main one consists of addressing the multi-physics nature of the problem that combines free flow in channels with hindered flow in porous media. Fluid dynamics is also coupled with advection-diffusion-reaction equations that model the transport of biomolecules throughout the system and their interaction with living tissues and C constructs. Ultimately, we aim at providing a predictive approach useful for the general organ-on-chip community. To this end, we have developed a lumped parameter approach that allows us to analyze the behavior of multi-unit bioreactor systems with modest computational effort, provided that the behavior of a single unit can be fully characterized.