1
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Possenti L, Vitullo P, Cicchetti A, Zunino P, Rancati T. Modeling hypoxia-induced radiation resistance and the impact of radiation sources. Comput Biol Med 2024; 173:108334. [PMID: 38520919 DOI: 10.1016/j.compbiomed.2024.108334] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/12/2024] [Revised: 02/29/2024] [Accepted: 03/17/2024] [Indexed: 03/25/2024]
Abstract
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.
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Affiliation(s)
- Luca Possenti
- Data Science Unit, Fondazione IRCCS Istituto Nazionale dei Tumori, Via Venezian 1, Milan, 20133, Italy.
| | - Piermario Vitullo
- MOX, Department of Mathematics, Politecnico di Milano, P.zza Da Vinci 32, Milan, 20133, Italy
| | - Alessandro Cicchetti
- Data Science Unit, Fondazione IRCCS Istituto Nazionale dei Tumori, Via Venezian 1, Milan, 20133, Italy
| | - Paolo Zunino
- MOX, Department of Mathematics, Politecnico di Milano, P.zza Da Vinci 32, Milan, 20133, Italy
| | - Tiziana Rancati
- Data Science Unit, Fondazione IRCCS Istituto Nazionale dei Tumori, Via Venezian 1, Milan, 20133, Italy
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2
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Vitullo P, Cicci L, Possenti L, Coclite A, Costantino ML, Zunino P. Sensitivity analysis of a multi-physics model for the vascular microenvironment. Int J Numer Method Biomed Eng 2023; 39:e3752. [PMID: 37455669 DOI: 10.1002/cnm.3752] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/19/2023] [Revised: 04/17/2023] [Accepted: 06/25/2023] [Indexed: 07/18/2023]
Abstract
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.
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Affiliation(s)
| | - Ludovica Cicci
- MOX, Department of Mathematics, Politecnico di Milano, Milan, Italy
- School of Biomedical Engineering & Imaging Sciences, King's College, London, UK
| | - Luca Possenti
- Data Science Unit, Fondazione IRCCS, Istituto Nazionale dei Tumori, Milan, Italy
- Department of Chemistry, Materials and Chemical Engineering "Giulio Natta", Politecnico di Milano, Milan, Italy
| | - Alessandro Coclite
- Dipartimento di Ingegneria Elettrica e dell'Informazione, Politecnico di Bari, Bari, Italy
| | - Maria Laura Costantino
- Department of Chemistry, Materials and Chemical Engineering "Giulio Natta", Politecnico di Milano, Milan, Italy
| | - Paolo Zunino
- MOX, Department of Mathematics, Politecnico di Milano, Milan, Italy
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3
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Rota A, Possenti L, Offeddu GS, Senesi M, Stucchi A, Venturelli I, Rancati T, Zunino P, Kamm RD, Costantino ML. A three-dimensional method for morphological analysis and flow velocity estimation in microvasculature on-a-chip. Bioeng Transl Med 2023; 8:e10557. [PMID: 37693050 PMCID: PMC10487341 DOI: 10.1002/btm2.10557] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/05/2022] [Revised: 03/21/2023] [Accepted: 04/30/2023] [Indexed: 09/12/2023] Open
Abstract
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.
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Affiliation(s)
- Alberto Rota
- LaBS, Chemistry, Materials, and Chemical Engineering "Giulio Natta" DepartmentPolitecnico di MilanoMilanItaly
| | - Luca Possenti
- Data Science Unit, Department of Epidemiology and Data ScienceFondazione IRCCS Istituto Nazionale dei TumoriMilanItaly
| | - Giovanni S. Offeddu
- Department of Biological EngineeringMassachusetts Institute of TechnologyCambridgeMassachusettsUSA
| | - Martina Senesi
- LaBS, Chemistry, Materials, and Chemical Engineering "Giulio Natta" DepartmentPolitecnico di MilanoMilanItaly
| | - Adelaide Stucchi
- LaBS, Chemistry, Materials, and Chemical Engineering "Giulio Natta" DepartmentPolitecnico di MilanoMilanItaly
| | - Irene Venturelli
- LaBS, Chemistry, Materials, and Chemical Engineering "Giulio Natta" DepartmentPolitecnico di MilanoMilanItaly
| | - Tiziana Rancati
- Data Science Unit, Department of Epidemiology and Data ScienceFondazione IRCCS Istituto Nazionale dei TumoriMilanItaly
| | - Paolo Zunino
- MOX, Department of MathematicsPolitecnico di MilanoMilanItaly
| | - Roger D. Kamm
- Department of Biological EngineeringMassachusetts Institute of TechnologyCambridgeMassachusettsUSA
| | - Maria Laura Costantino
- LaBS, Chemistry, Materials, and Chemical Engineering "Giulio Natta" DepartmentPolitecnico di MilanoMilanItaly
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4
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Fritz M, Köppl T, Oden JT, Wagner A, Wohlmuth B, Wu C. A 1D-0D-3D coupled model for simulating blood flow and transport processes in breast tissue. Int J Numer Method Biomed Eng 2022; 38:e3612. [PMID: 35522186 DOI: 10.1002/cnm.3612] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/13/2022] [Revised: 03/30/2022] [Accepted: 04/27/2022] [Indexed: 06/14/2023]
Abstract
In this work, we present mixed dimensional models for simulating blood flow and transport processes in breast tissue and the vascular tree supplying it. These processes are considered, to start from the aortic inlet to the capillaries and tissue of the breast. Large variations in biophysical properties and flow conditions exist in this system necessitating the use of different flow models for different geometries and flow regimes. In total, we consider four different model types. First, a system of 1D nonlinear hyperbolic partial differential equations (PDEs) is considered to simulate blood flow in larger arteries with highly elastic vessel walls. Second, we assign 1D linearized hyperbolic PDEs to model the smaller arteries with stiffer vessel walls. The third model type consists of ODE systems (0D models). It is used to model the arterioles and peripheral circulation. Finally, homogenized 3D porous media models are considered to simulate flow and transport in capillaries and tissue within the breast volume. Sink terms are used to account for the influence of the venous and lymphatic systems. Combining the four model types, we obtain two different 1D-0D-3D coupled models for simulating blood flow and transport processes: The first model results in a fully coupled 1D-0D-3D model covering the complete path from the aorta to the breast combining a generic arterial network with a patient specific breast network and geometry. The second model is a reduced one based on the separation of the generic and patient specific parts. The information from a calibrated fully coupled model is used as inflow condition for the patient specific sub-model allowing a significant computational cost reduction. Several numerical experiments are conducted to calibrate the generic model parameters and to demonstrate realistic flow simulations compared to existing data on blood flow in the human breast and vascular system. Moreover, we use two different breast vasculature and tissue data sets to illustrate the robustness of our reduced sub-model approach.
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Affiliation(s)
- Marvin Fritz
- Department of Mathematics, Technical University of Munich, Garching, Germany
| | - Tobias Köppl
- Department of Mathematics, Technical University of Munich, Garching, Germany
| | - John Tinsley Oden
- Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, Texas, USA
| | - Andreas Wagner
- Department of Mathematics, Technical University of Munich, Garching, Germany
| | - Barbara Wohlmuth
- Department of Mathematics, Technical University of Munich, Garching, Germany
| | - Chengyue Wu
- Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, Texas, USA
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5
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Qohar UNA, Zanna Munthe-Kaas A, Nordbotten JM, Hanson EA. A nonlinear multi-scale model for blood circulation in a realistic vascular system. R Soc Open Sci 2021; 8:201949. [PMID: 34966547 PMCID: PMC8633777 DOI: 10.1098/rsos.201949] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/31/2020] [Accepted: 10/28/2021] [Indexed: 06/14/2023]
Abstract
In the last decade, numerical models have become an increasingly important tool in biological and medical science. Numerical simulations contribute to a deeper understanding of physiology and are a powerful tool for better diagnostics and treatment. In this paper, a nonlinear multi-scale model framework is developed for blood flow distribution in the full vascular system of an organ. We couple a quasi one-dimensional vascular graph model to represent blood flow in larger vessels and a porous media model to describe flow in smaller vessels and capillary bed. The vascular model is based on Poiseuille's Law, with pressure correction by elasticity and pressure drop estimation at vessels' junctions. The porous capillary bed is modelled as a two-compartment domain (artery and venous) using Darcy's Law. The fluid exchange between the artery and venous capillary bed compartments is defined as blood perfusion. The numerical experiments show that the proposed model for blood circulation: (i) is closely dependent on the structure and parameters of both the larger vessels and of the capillary bed, and (ii) provides a realistic blood circulation in the organ. The advantage of the proposed model is that it is complex enough to reliably capture the main underlying physiological function, yet highly flexible as it offers the possibility of incorporating various local effects. Furthermore, the numerical implementation of the model is straightforward and allows for simulations on a regular desktop computer.
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Affiliation(s)
- Ulin Nuha A. Qohar
- Department of Mathematics, University of Bergen, Allegaten 41, Bergen 5008, Norway
| | | | | | - Erik Andreas Hanson
- Department of Mathematics, University of Bergen, Allegaten 41, Bergen 5008, Norway
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6
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Possenti L, Cicchetti A, Rosati R, Cerroni D, Costantino ML, Rancati T, Zunino P. A Mesoscale Computational Model for Microvascular Oxygen Transfer. Ann Biomed Eng 2021. [PMID: 34184146 DOI: 10.1007/s10439-021-02807-x] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/17/2021] [Accepted: 06/01/2021] [Indexed: 01/06/2023]
Abstract
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.
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7
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Abstract
Skeletal muscle is the largest organ in humans. The viability and performance of this metabolically demanding organ are exquisitely dependent on the integrity of its microcirculation. The architectural and functional attributes of the skeletal muscle microvasculature are acquired during embryonic and early postnatal development. However, peripheral vascular disease in the adult can damage the distal microvasculature, together with damaging the skeletal myofibers. Importantly, adult skeletal muscle has the capacity to regenerate. Understanding the extent to which the microvascular network also reforms, and acquires structural and functional competence, will thus be critical to regenerative medicine efforts for those with peripheral artery disease (PAD). Herein, we discuss recent advances in studying the regenerating microvasculature in the mouse hindlimb following severe ischemic injury. We highlight new insights arising from real-time imaging of the microcirculation. This includes identifying otherwise hidden flaws in both network microarchitecture and function, deficiencies that could underlie the progressive nature of PAD and its refractoriness to therapy. Recognizing and overcoming these vulnerabilities in regenerative angiogenesis will be important for advancing treatment options for PAD.
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Affiliation(s)
- Hao Yin
- Robarts Research Institute, Western University, London, ON, Canada
| | | | - Jason J Lee
- Robarts Research Institute, Western University, London, ON, Canada.,Department of Medicine, Western University, London, ON, Canada
| | - J Geoffrey Pickering
- Robarts Research Institute, Western University, London, ON, Canada.,Department of Medicine, Western University, London, ON, Canada.,Department of Medical Biophysics, Western University, London, ON, Canada.,Department of Biochemistry, Western University, London, ON, Canada
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8
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Boissier N, Drasdo D, Vignon-Clementel IE. Simulation of a detoxifying organ function: Focus on hemodynamics modeling and convection-reaction numerical simulation in microcirculatory networks. Int J Numer Method Biomed Eng 2021; 37:e3422. [PMID: 33249746 DOI: 10.1002/cnm.3422] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/05/2019] [Revised: 10/09/2020] [Accepted: 11/09/2020] [Indexed: 06/12/2023]
Abstract
When modeling a detoxifying organ function, an important component is the impact of flow on the metabolism of a compound of interest carried by the blood. We here study the effects of red blood cells (such as the Fahraeus-Lindqvist effect and plasma skimming) on blood flow in typical microcirculatory components such as tubes, bifurcations and entire networks, with particular emphasis on the liver as important representative of detoxifying organs. In one of the plasma skimming models, under certain conditions, oscillations between states are found and analyzed in a methodical study to identify their causes and influencing parameters. The flow solution obtained is then used to define the velocity at which a compound would be transported. A convection-reaction equation is studied to simulate the transport of a compound in blood and its uptake by the surrounding cells. Different types of signal sharpness have to be handled depending on the application to address different temporal compound concentration profiles. To permit executing the studied models numerically stable and accurate, we here extend existing transport schemes to handle converging bifurcations, and more generally multi-furcations. We study the accuracy of different numerical schemes as well as the effect of reactions and of the network itself on the bolus shape. Even though this study is guided by applications in liver micro-architecture, the proposed methodology is general and can readily be applied to other capillary network geometries, hence to other organs or to bioengineered network designs.
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Affiliation(s)
- Noemie Boissier
- Inria, Paris, France
- Laboratoire Jacques-Louis Lions, Sorbonne Université, CNRS, Université de Paris, Paris, France
- IfADo - Leibniz Research Centre for Working Environment and Human Factors, Dortmund, Germany
| | - Dirk Drasdo
- Inria, Paris, France
- Laboratoire Jacques-Louis Lions, Sorbonne Université, CNRS, Université de Paris, Paris, France
- IfADo - Leibniz Research Centre for Working Environment and Human Factors, Dortmund, Germany
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9
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Hartung G, Badr S, Moeini M, Lesage F, Kleinfeld D, Alaraj A, Linninger A. Voxelized simulation of cerebral oxygen perfusion elucidates hypoxia in aged mouse cortex. PLoS Comput Biol 2021; 17:e1008584. [PMID: 33507970 PMCID: PMC7842915 DOI: 10.1371/journal.pcbi.1008584] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Grants] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/05/2020] [Accepted: 11/30/2020] [Indexed: 12/13/2022] Open
Abstract
Departures of normal blood flow and metabolite distribution from the cerebral microvasculature into neuronal tissue have been implicated with age-related neurodegeneration. Mathematical models informed by spatially and temporally distributed neuroimage data are becoming instrumental for reconstructing a coherent picture of normal and pathological oxygen delivery throughout the brain. Unfortunately, current mathematical models of cerebral blood flow and oxygen exchange become excessively large in size. They further suffer from boundary effects due to incomplete or physiologically inaccurate computational domains, numerical instabilities due to enormous length scale differences, and convergence problems associated with condition number deterioration at fine mesh resolutions. Our proposed simple finite volume discretization scheme for blood and oxygen microperfusion simulations does not require expensive mesh generation leading to the critical benefit that it drastically reduces matrix size and bandwidth of the coupled oxygen transfer problem. The compact problem formulation yields rapid and stable convergence. Moreover, boundary effects can effectively be suppressed by generating very large replica of the cortical microcirculation in silico using an image-based cerebrovascular network synthesis algorithm, so that boundaries of the perfusion simulations are far removed from the regions of interest. Massive simulations over sizeable portions of the cortex with feature resolution down to the micron scale become tractable with even modest computer resources. The feasibility and accuracy of the novel method is demonstrated and validated with in vivo oxygen perfusion data in cohorts of young and aged mice. Our oxygen exchange simulations quantify steep gradients near penetrating blood vessels and point towards pathological changes that might cause neurodegeneration in aged brains. This research aims to explain mechanistic interactions between anatomical structures and how they might change in diseases or with age. Rigorous quantification of age-related changes is of significant interest because it might aide in the search for imaging biomarkers for dementia and Alzheimer’s disease. Brain function critically depends on the maintenance of physiological blood supply and metabolism in the cortex. Disturbances to adequate perfusion have been linked to age-related neurodegeneration. However, the precise correlation between age-related hemodynamic changes and the resulting decline in oxygen delivery is not well understood and has not been quantified. Therefore, we introduce a new compact, and therefore highly scalable, computational method for predicting the physiological relationship between hemodynamics and cortical oxygen perfusion for large sections of the cortical microcirculation. We demonstrate the novel mesh generation-free (MGF), multi-scale simulation approach through realistic in vivo case studies of cortical microperfusion in the mouse brain. We further validate mechanistic correlations and a quantitative relationship between blood flow and brain oxygenation using experimental data from cohorts of young, middle aged and old mouse brains. Our computational approach overcomes size and performance limitations of previous unstructured meshing techniques to enable the prediction of oxygen tension with a spatial resolution of least two orders of magnitude higher than previously possible. Our simulation results support the hypothesis that structural changes in the microvasculature induce hypoxic pockets in the aged brain that are absent in the healthy, young mouse.
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Affiliation(s)
- Grant Hartung
- Department of Bioengineering, University of Illinois at Chicago, Chicago, Illinois, United States of America
| | - Shoale Badr
- Department of Bioengineering, University of Illinois at Chicago, Chicago, Illinois, United States of America
| | - Mohammad Moeini
- Polytechnique Montréal, Department of Electrical Engineering, Montreal, Canada
| | - Frédéric Lesage
- Polytechnique Montréal, Department of Electrical Engineering, Montreal, Canada
| | - David Kleinfeld
- Department of Physics, University of California San Diego, San Diego, California, United States of America
| | - Ali Alaraj
- Department of Neurosurgery, University of Illinois at Chicago, Chicago, Illinois, United States of America
| | - Andreas Linninger
- Department of Bioengineering, University of Illinois at Chicago, Chicago, Illinois, United States of America
- Department of Neurosurgery, University of Illinois at Chicago, Chicago, Illinois, United States of America
- * E-mail:
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10
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Possenti L, Di Gregorio S, Casagrande G, Costantino ML, Rancati T, Zunino P. A global sensitivity analysis approach applied to a multiscale model of microvascular flow. Comput Methods Biomech Biomed Engin 2020; 23:1215-1224. [DOI: 10.1080/10255842.2020.1793964] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
- L. Possenti
- LaBS, Department of Chemistry, Materials and Chemical Engineering ’Giulio Natta’, Politecnico di Milano, Milan, Italy
- Prostate Cancer Program, Fondazione IRCCS Istituto Nazionale dei Tumori, Milan, Italy
| | - S. Di Gregorio
- MOX, Department of Mathematics, Politecnico di Milano, Milan, Italy
| | - G. Casagrande
- LaBS, Department of Chemistry, Materials and Chemical Engineering ’Giulio Natta’, Politecnico di Milano, Milan, Italy
| | - M. L. Costantino
- LaBS, Department of Chemistry, Materials and Chemical Engineering ’Giulio Natta’, Politecnico di Milano, Milan, Italy
| | - T. Rancati
- Prostate Cancer Program, Fondazione IRCCS Istituto Nazionale dei Tumori, Milan, Italy
| | - P. Zunino
- MOX, Department of Mathematics, Politecnico di Milano, Milan, Italy
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11
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Köppl T, Vidotto E, Wohlmuth B. A 3D-1D coupled blood flow and oxygen transport model to generate microvascular networks. Int J Numer Method Biomed Eng 2020; 36:e3386. [PMID: 32659047 DOI: 10.1002/cnm.3386] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/20/2020] [Revised: 05/18/2020] [Accepted: 07/05/2020] [Indexed: 06/11/2023]
Abstract
In this work, we introduce an algorithmic approach to generate microvascular networks starting from larger vessels that can be reconstructed without noticeable segmentation errors. Contrary to larger vessels, the reconstruction of fine-scale components of microvascular networks shows significant segmentation errors, and an accurate mapping is time and cost intense. Thus there is a need for fast and reliable reconstruction algorithms yielding surrogate networks having similar stochastic properties as the original ones. The microvascular networks are constructed in a marching way by adding vessels to the outlets of the vascular tree from the previous step. To optimise the structure of the vascular trees, we use Murray's law to determine the radii of the vessels and bifurcation angles. In each step, we compute the local gradient of the partial pressure of oxygen and adapt the orientation of the new vessels to this gradient. At the same time, we use the partial pressure of oxygen to check whether the considered tissue block is supplied sufficiently with oxygen. Computing the partial pressure of oxygen, we use a 3D-1D coupled model for blood flow and oxygen transport. To decrease the complexity of a fully coupled 3D model, we reduce the blood vessel network to a 1D graph structure and use a bi-directional coupling with the tissue which is described by a 3D homogeneous porous medium. The resulting surrogate networks are analysed with respect to morphological and physiological aspects.
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Affiliation(s)
- Tobias Köppl
- Chair for Numerics, University of Technology Munich, Garching, Germany
| | - Ettore Vidotto
- Chair for Numerics, University of Technology Munich, Garching, Germany
| | - Barbara Wohlmuth
- Chair for Numerics, University of Technology Munich, Garching, Germany
- Department of Mathematics, University of Bergen, Allegaten 41, 5020 Bergen, Norway, Germany
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12
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Cicchetti A, Laurino F, Possenti L, Rancati T, Zunino P. In silico model of the early effects of radiation therapy on the microcirculation and the surrounding tissues. Phys Med 2020; 73:125-134. [DOI: 10.1016/j.ejmp.2020.04.006] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 11/11/2019] [Revised: 04/01/2020] [Accepted: 04/04/2020] [Indexed: 12/11/2022] Open
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13
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Koch T, Flemisch B, Helmig R, Wiest R, Obrist D. A multiscale subvoxel perfusion model to estimate diffusive capillary wall conductivity in multiple sclerosis lesions from perfusion MRI data. Int J Numer Method Biomed Eng 2020; 36:e3298. [PMID: 31883316 DOI: 10.1002/cnm.3298] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/17/2019] [Revised: 11/01/2019] [Accepted: 12/01/2019] [Indexed: 06/10/2023]
Abstract
We propose a new mathematical model to learn capillary leakage coefficients from dynamic susceptibility contrast MRI data. To this end, we derive an embedded mixed-dimension flow and transport model for brain tissue perfusion on a subvoxel scale. This model is used to obtain the contrast agent concentration distribution in a single MRI voxel during a perfusion MRI sequence. We further present a magnetic resonance signal model for the considered sequence including a model for local susceptibility effects. This allows modeling MR signal-time curves that can be compared with clinical MRI data. The proposed model can be used as a forward model in the inverse modeling problem of inferring model parameters such as the diffusive capillary wall conductivity. Acute multiple sclerosis lesions are associated with a breach in the integrity of the blood-brain barrier. Applying the model to perfusion MR data of a patient with acute multiple sclerosis lesions, we conclude that diffusive capillary wall conductivity is a good indicator for characterizing activity of lesions, even if other patient-specific model parameters are not well-known.
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Affiliation(s)
- Timo Koch
- Department of Hydromechanics and Modelling of Hydrosystems, University of Stuttgart, Stuttgart, Germany
| | - Bernd Flemisch
- Department of Hydromechanics and Modelling of Hydrosystems, University of Stuttgart, Stuttgart, Germany
| | - Rainer Helmig
- Department of Hydromechanics and Modelling of Hydrosystems, University of Stuttgart, Stuttgart, Germany
| | - Roland Wiest
- Support Center for Advanced Neuroimaging (SCAN), University Institute of Diagnostic and Interventional Neuroradiology, Inselspital, University of Bern, Bern, Switzerland
| | - Dominik Obrist
- ARTORG Center for Biomedical Engineering Research, University of Bern, Bern, Switzerland
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14
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Adjoua O, Pitre-Champagnat S, Lucor D. Reduced-order modeling of hemodynamics across macroscopic through mesoscopic circulation scales. Int J Numer Method Biomed Eng 2019; 35:e3274. [PMID: 31680447 DOI: 10.1002/cnm.3274] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/10/2019] [Accepted: 07/31/2019] [Indexed: 06/10/2023]
Abstract
We propose a hemodynamic reduced-order model bridging macroscopic and mesoscopic blood flow circulation scales from arteries to capillaries. In silico tree-like vascular geometries, mathematically described by graphs, are synthetically generated by means of stochastic growth algorithms constrained by statistical morphological and topological principles. Scale-specific pruning gradation of the tree is then proposed in order to fit computational budget requirement. Different compliant structural models with respect to pressure loads are used depending on vessel walls thicknesses and structures, which vary considerably from macroscopic to mesoscopic circulation scales. Nonlinear rheological properties of blood are also included, and microcirculation network responses are computed for different rheologies. Numerical results are in very good agreement with available experimental measurements. The computational model captures the dynamic transition between large- to small-scale flow pulsatility speeds and magnitudes and wall shear stresses, which have wide-ranging physiological influences.
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Affiliation(s)
- Olivier Adjoua
- ISCD, Sorbonne-Université, Paris, France
- LIMSI, CNRS, Université Paris-Saclay, Orsay, France
| | | | - Didier Lucor
- LIMSI, CNRS, Université Paris-Saclay, Orsay, France
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15
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Offeddu GS, Possenti L, Loessberg-Zahl JT, Zunino P, Roberts J, Han X, Hickman D, Knutson CG, Kamm RD. Application of Transmural Flow Across In Vitro Microvasculature Enables Direct Sampling of Interstitial Therapeutic Molecule Distribution. Small 2019; 15:e1902393. [PMID: 31497931 DOI: 10.1002/smll.201902393] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/11/2019] [Revised: 08/13/2019] [Indexed: 06/10/2023]
Abstract
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.
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Affiliation(s)
- Giovanni S Offeddu
- Department of Biological Engineering, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA
| | - Luca Possenti
- LaBS, Department of Chemistry, Materials and Chemical Engineering, Politecnico di Milano, Milan, 20133, Italy
| | | | - Paolo Zunino
- MOX, Department of Mathematics, Politecnico di Milano, Milan, 20133, Italy
| | - John Roberts
- Amgen Discovery Research, Amgen Inc., 360 Binney Street, Cambridge, MA, 02141, USA
| | - Xiaogang Han
- Amgen Discovery Research, Amgen Inc., 360 Binney Street, Cambridge, MA, 02141, USA
| | - Dean Hickman
- Amgen Discovery Research, Amgen Inc., 360 Binney Street, Cambridge, MA, 02141, USA
| | - Charles G Knutson
- Amgen Discovery Research, Amgen Inc., 360 Binney Street, Cambridge, MA, 02141, USA
| | - Roger D Kamm
- Department of Biological Engineering, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA
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16
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Possenti L, Casagrande G, Di Gregorio S, Zunino P, Costantino ML. Numerical simulations of the microvascular fluid balance with a non-linear model of the lymphatic system. Microvasc Res 2018; 122:101-110. [PMID: 30448400 DOI: 10.1016/j.mvr.2018.11.003] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/28/2018] [Revised: 11/08/2018] [Accepted: 11/08/2018] [Indexed: 02/03/2023]
Abstract
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.
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Affiliation(s)
- Luca Possenti
- LaBS, Chemistry, Material and Chemical Engineering Department "Giulio Natta", Politecnico di Milano, Italy.
| | - Giustina Casagrande
- LaBS, Chemistry, Material and Chemical Engineering Department "Giulio Natta", Politecnico di Milano, Italy
| | - Simone Di Gregorio
- LaBS, Chemistry, Material and Chemical Engineering Department "Giulio Natta", Politecnico di Milano, Italy; MOX, Department of Mathematics, Politecnico di Milano, Italy
| | - Paolo Zunino
- MOX, Department of Mathematics, Politecnico di Milano, Italy
| | - Maria Laura Costantino
- LaBS, Chemistry, Material and Chemical Engineering Department "Giulio Natta", Politecnico di Milano, Italy
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