1
|
Menon K, Khan MO, Sexton ZA, Richter J, Nguyen PK, Malik SB, Boyd J, Nieman K, Marsden AL. Personalized coronary and myocardial blood flow models incorporating CT perfusion imaging and synthetic vascular trees. NPJ IMAGING 2024; 2:9. [PMID: 38706558 PMCID: PMC11062925 DOI: 10.1038/s44303-024-00014-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 08/22/2023] [Accepted: 02/25/2024] [Indexed: 05/07/2024]
Abstract
Computational simulations of coronary artery blood flow, using anatomical models based on clinical imaging, are an emerging non-invasive tool for personalized treatment planning. However, current simulations contend with two related challenges - incomplete anatomies in image-based models due to the exclusion of arteries smaller than the imaging resolution, and the lack of personalized flow distributions informed by patient-specific imaging. We introduce a data-enabled, personalized and multi-scale flow simulation framework spanning large coronary arteries to myocardial microvasculature. It includes image-based coronary anatomies combined with synthetic vasculature for arteries below the imaging resolution, myocardial blood flow simulated using Darcy models, and systemic circulation represented as lumped-parameter networks. We propose an optimization-based method to personalize multiscale coronary flow simulations by assimilating clinical CT myocardial perfusion imaging and cardiac function measurements to yield patient-specific flow distributions and model parameters. Using this proof-of-concept study on a cohort of six patients, we reveal substantial differences in flow distributions and clinical diagnosis metrics between the proposed personalized framework and empirical methods based purely on anatomy; these errors cannot be predicted a priori. This suggests virtual treatment planning tools would benefit from increased personalization informed by emerging imaging methods.
Collapse
Affiliation(s)
- Karthik Menon
- Department of Pediatrics (Cardiology), Stanford School of Medicine, Stanford, CA USA
- Institute for Computational and Mathematical Engineering, Stanford University, Stanford, CA USA
| | - Muhammed Owais Khan
- Department of Electrical, Computer, and Biomedical Engineering, Toronto Metropolitan University, Toronto, ON Canada
| | | | - Jakob Richter
- Department of Pediatrics (Cardiology), Stanford School of Medicine, Stanford, CA USA
| | - Patricia K. Nguyen
- VA Palo Alto Healthcare System, Palo Alto, CA USA
- Division of Cardiovascular Medicine, Stanford School of Medicine, Stanford, CA USA
| | | | - Jack Boyd
- Department of Cardiothoracic Surgery, Stanford School of Medicine, Stanford, CA USA
| | - Koen Nieman
- Division of Cardiovascular Medicine, Stanford School of Medicine, Stanford, CA USA
- Department of Radiology, Stanford School of Medicine, Stanford, CA USA
| | - Alison L. Marsden
- Department of Pediatrics (Cardiology), Stanford School of Medicine, Stanford, CA USA
- Institute for Computational and Mathematical Engineering, Stanford University, Stanford, CA USA
- Department of Bioengineering, Stanford University, Stanford, CA USA
| |
Collapse
|
2
|
Kojic M, Milosevic M, Simic V, Milicevic B, Terracciano R, Filgueira CS. On the generality of the finite element modeling physical fields in biological systems by the multiscale smeared concept (Kojic transport model). Heliyon 2024; 10:e26354. [PMID: 38434281 PMCID: PMC10907537 DOI: 10.1016/j.heliyon.2024.e26354] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/17/2023] [Revised: 02/09/2024] [Accepted: 02/12/2024] [Indexed: 03/05/2024] Open
Abstract
The biomechanical and biochemical processes in the biological systems of living organisms are extremely complex. Advances in understanding these processes are mainly achieved by laboratory and clinical investigations, but in recent decades they are supported by computational modeling. Besides enormous efforts and achievements in this modeling, there still is a need for new methods that can be used in everyday research and medical practice. In this report, we give a view of the generality of the finite element methodology introduced by the first author and supported by his collaborators. It is based on the multiscale smeared physical fields, termed as Kojic Transport Model (KTM), published in several journal papers and summarized in a recent book (Kojic et al., 2022) [1]. We review relevant literature to demonstrate the distinctions and advantages of our methodology and indicate possible further applications. We refer to our published results by a selection of a few examples which include modeling of partitioning, blood flow, molecular transport within the pancreas, multiscale-multiphysics model of coupling electrical field and ion concentration, and a model of convective-diffusive transport within the lung parenchyma. Two new examples include a model of convective-diffusive transport within a growing tumor, and drug release from nanofibers with fiber degradation.
Collapse
Affiliation(s)
- Milos Kojic
- Houston Methodist Research Institute, The Department of Nanomedicine, 6670 Bertner Ave., R7 117, Houston, TX, 77030, USA
- Bioengineering Research and Development Center BioIRC Kragujevac, Prvoslava Stojanovica 6, 3400, Kragujevac, Serbia
- Serbian Academy of Sciences and Arts, Knez Mihailova 35, 11000, Belgrade, Serbia
| | - Miljan Milosevic
- Bioengineering Research and Development Center BioIRC Kragujevac, Prvoslava Stojanovica 6, 3400, Kragujevac, Serbia
- Institute of Information Technologies, University of Kragujevac, Department of Technical- Technological Sciences, Jovana Cvijica bb, 34000, Kragujevac, Serbia
- Belgrade Metropolitan University, Tadeusa Koscuska 63, 11000, Belgrade, Serbia
| | - Vladimir Simic
- Bioengineering Research and Development Center BioIRC Kragujevac, Prvoslava Stojanovica 6, 3400, Kragujevac, Serbia
- Institute of Information Technologies, University of Kragujevac, Department of Technical- Technological Sciences, Jovana Cvijica bb, 34000, Kragujevac, Serbia
| | - Bogdan Milicevic
- Bioengineering Research and Development Center BioIRC Kragujevac, Prvoslava Stojanovica 6, 3400, Kragujevac, Serbia
- Faculty of Engineering, University of Kragujevac, Kragujevac, 34000, Serbia
| | - Rossana Terracciano
- Houston Methodist Research Institute, The Department of Nanomedicine, 6670 Bertner Ave., R7 117, Houston, TX, 77030, USA
- Department of Electronics and Telecommunications, Politecnico di Torino, Torino, Italy
| | - Carly S. Filgueira
- Houston Methodist Research Institute, The Department of Nanomedicine, 6670 Bertner Ave., R7 117, Houston, TX, 77030, USA
- Department of Cardiovascular Surgery, Houston Methodist Research Institute, Houston, TX, 77030, USA
| |
Collapse
|
3
|
Zingaro A, Vergara C, Dede' L, Regazzoni F, Quarteroni A. A comprehensive mathematical model for cardiac perfusion. Sci Rep 2023; 13:14220. [PMID: 37648701 PMCID: PMC10469210 DOI: 10.1038/s41598-023-41312-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/10/2023] [Accepted: 08/24/2023] [Indexed: 09/01/2023] Open
Abstract
The aim of this paper is to introduce a new mathematical model that simulates myocardial blood perfusion that accounts for multiscale and multiphysics features. Our model incorporates cardiac electrophysiology, active and passive mechanics, hemodynamics, valve modeling, and a multicompartment Darcy model of perfusion. We consider a fully coupled electromechanical model of the left heart that provides input for a fully coupled Navier-Stokes-Darcy Model for myocardial perfusion. The fluid dynamics problem is modeled in a left heart geometry that includes large epicardial coronaries, while the multicompartment Darcy model is set in a biventricular myocardium. Using a realistic and detailed cardiac geometry, our simulations demonstrate the biophysical fidelity of our model in describing cardiac perfusion. Specifically, we successfully validate the model reliability by comparing in-silico coronary flow rates and average myocardial blood flow with clinically established values ranges reported in relevant literature. Additionally, we investigate the impact of a regurgitant aortic valve on myocardial perfusion, and our results indicate a reduction in myocardial perfusion due to blood flow taken away by the left ventricle during diastole. To the best of our knowledge, our work represents the first instance where electromechanics, hemodynamics, and perfusion are integrated into a single computational framework.
Collapse
Affiliation(s)
- Alberto Zingaro
- MOX, Laboratory of Modeling and Scientific Computing, Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133, Milano, Italy.
- ELEM Biotech S.L., Pier01, Palau de Mar, Plaça Pau Vila, 1, 08003, Barcelona, Spain.
| | - Christian Vergara
- LaBS, Dipartimento di Chimica, Materiali e Ingegneria Chimica "Giulio Natta", Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133, Milano, Italy
| | - Luca Dede'
- MOX, Laboratory of Modeling and Scientific Computing, Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133, Milano, Italy
| | - Francesco Regazzoni
- MOX, Laboratory of Modeling and Scientific Computing, Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133, Milano, Italy
| | - Alfio Quarteroni
- MOX, Laboratory of Modeling and Scientific Computing, Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133, Milano, Italy
- Institute of Mathematics, École Polytechnique Fédérale de Lausanne, Station 8, Av. Piccard, CH-1015, Lausanne, Switzerland
| |
Collapse
|
4
|
Menon K, Khan MO, Sexton ZA, Richter J, Nieman K, Marsden AL. Personalized coronary and myocardial blood flow models incorporating CT perfusion imaging and synthetic vascular trees. MEDRXIV : THE PREPRINT SERVER FOR HEALTH SCIENCES 2023:2023.08.17.23294242. [PMID: 37645850 PMCID: PMC10462196 DOI: 10.1101/2023.08.17.23294242] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 08/31/2023]
Abstract
Computational simulations of coronary artery blood flow, using anatomical models based on clinical imaging, are an emerging non-invasive tool for personalized treatment planning. However, current simulations contend with two related challenges - incomplete anatomies in image-based models due to the exclusion of arteries smaller than the imaging resolution, and the lack of personalized flow distributions informed by patient-specific imaging. We introduce a data-enabled, personalized and multi-scale flow simulation framework spanning large coronary arteries to myocardial microvasculature. It includes image-based coronary models combined with synthetic vasculature for arteries below the imaging resolution, myocardial blood flow simulated using Darcy models, and systemic circulation represented as lumped-parameter networks. Personalized flow distributions and model parameters are informed by clinical CT myocardial perfusion imaging and cardiac function using surrogate-based optimization. We reveal substantial differences in flow distributions and clinical diagnosis metrics between the proposed personalized framework and empirical methods based on anatomy; these errors cannot be predicted a priori. This suggests virtual treatment planning tools would benefit from increased personalization informed by emerging imaging methods.
Collapse
Affiliation(s)
- Karthik Menon
- Department of Pediatrics (Cardiology), Stanford School of Medicine, Stanford, CA, USA
- Institute for Computational and Mathematical Engineering, Stanford University, Stanford, CA, USA
| | - Muhammed Owais Khan
- Department of Electrical, Computer, and Biomedical Engineering, Toronto Metropolitan University, Toronto, Ontario, Canada
| | - Zachary A Sexton
- Department of Bioengineering, Stanford University, Stanford, CA, USA
| | - Jakob Richter
- Department of Pediatrics (Cardiology), Stanford School of Medicine, Stanford, CA, USA
| | - Koen Nieman
- Departments of Radiology and Medicine (Cardiovascular Medicine), Stanford School of Medicine, Stanford, CA, USA
| | - Alison L Marsden
- Department of Pediatrics (Cardiology), Stanford School of Medicine, Stanford, CA, USA
- Institute for Computational and Mathematical Engineering, Stanford University, Stanford, CA, USA
- Department of Bioengineering, Stanford University, Stanford, CA, USA
| |
Collapse
|
5
|
Kim HJ, Rundfeldt HC, Lee I, Lee S. Tissue-growth-based synthetic tree generation and perfusion simulation. Biomech Model Mechanobiol 2023; 22:1095-1112. [PMID: 36869925 PMCID: PMC10167159 DOI: 10.1007/s10237-023-01703-8] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/05/2022] [Accepted: 02/10/2023] [Indexed: 03/05/2023]
Abstract
Biological tissues receive oxygen and nutrients from blood vessels by developing an indispensable supply and demand relationship with the blood vessels. We implemented a synthetic tree generation algorithm by considering the interactions between the tissues and blood vessels. We first segment major arteries using medical image data and synthetic trees are generated originating from these segmented arteries. They grow into extensive networks of small vessels to fill the supplied tissues and satisfy the metabolic demand of them. Further, the algorithm is optimized to be executed in parallel without affecting the generated tree volumes. The generated vascular trees are used to simulate blood perfusion in the tissues by performing multiscale blood flow simulations. One-dimensional blood flow equations were used to solve for blood flow and pressure in the generated vascular trees and Darcy flow equations were solved for blood perfusion in the tissues using a porous model assumption. Both equations are coupled at terminal segments explicitly. The proposed methods were applied to idealized models with different tree resolutions and metabolic demands for validation. The methods demonstrated that realistic synthetic trees were generated with significantly less computational expense compared to that of a constrained constructive optimization method. The methods were then applied to cerebrovascular arteries supplying a human brain and coronary arteries supplying the left and right ventricles to demonstrate the capabilities of the proposed methods. The proposed methods can be utilized to quantify tissue perfusion and predict areas prone to ischemia in patient-specific geometries.
Collapse
Affiliation(s)
- Hyun Jin Kim
- Mechanical Engineering, Korea Advanced Institute of Science and Technology, 291 Daehak-ro, Yuseong-gu, Daejeon, 34141, Republic of Korea.
| | - Hans Christian Rundfeldt
- Mechanical Engineering, Korea Advanced Institute of Science and Technology, 291 Daehak-ro, Yuseong-gu, Daejeon, 34141, Republic of Korea
- Mechanical Engineering, Kalsruhe Institute of Technology, Kaiserstraße 12, Karlsruhe, 76131, Germany
| | - Inpyo Lee
- Mechanical Engineering, Korea Advanced Institute of Science and Technology, 291 Daehak-ro, Yuseong-gu, Daejeon, 34141, Republic of Korea
| | - Seungmin Lee
- Mechanical Engineering, Korea Advanced Institute of Science and Technology, 291 Daehak-ro, Yuseong-gu, Daejeon, 34141, Republic of Korea
| |
Collapse
|
6
|
Warne CM, Essajee SI, Tucker SM, Figueroa CA, Beard DA, Dick GM, Tune JD. Oxygen-sensing pathways below autoregulatory threshold act to sustain myocardial oxygen delivery during reductions in perfusion pressure. Basic Res Cardiol 2023; 118:12. [PMID: 36988670 PMCID: PMC10797605 DOI: 10.1007/s00395-023-00985-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 11/17/2022] [Revised: 03/13/2023] [Accepted: 03/17/2023] [Indexed: 03/30/2023]
Abstract
The coronary circulation has an innate ability to maintain constant blood flow over a wide range of perfusion pressures. However, the mechanisms responsible for coronary autoregulation remain a fundamental and highly contested question. This study interrogated the local metabolic hypothesis of autoregulation by testing the hypothesis that hypoxemia-induced exaggeration of the metabolic error signal improves the autoregulatory response. Experiments were performed on open-chest anesthetized swine during stepwise changes in coronary perfusion pressure (CPP) from 140 to 40 mmHg under normoxic (n = 15) and hypoxemic (n = 8) conditions, in the absence and presence of dobutamine-induced increases in myocardial oxygen consumption (MVO2) (n = 5-7). Hypoxemia (PaO2 < 40 mmHg) decreased coronary venous PO2 (CvPO2) ~ 30% (P < 0.001) and increased coronary blood flow ~ 100% (P < 0.001), sufficient to maintain myocardial oxygen delivery (P = 0.14) over a wide range of CPPs. Autoregulatory responsiveness during hypoxemia-induced reductions in CvPO2 were associated with increases of autoregulatory gain (Gc; P = 0.033) but not slope (P = 0.585) over a CPP range of 120 to 60 mmHg. Preservation of autoregulatory Gc (P = 0.069) and slope (P = 0.264) was observed during dobutamine administration ± hypoxemia. Reductions in coronary resistance in response to decreases in CPP predominantly occurred below CvPO2 values of ~ 25 mmHg, irrespective of underlying vasomotor reserve. These findings support the presence of an autoregulatory threshold under which oxygen-sensing pathway(s) act to preserve sufficient myocardial oxygen delivery as CPP is reduced during increases in MVO2 and/or reductions in arterial oxygen content.
Collapse
Affiliation(s)
- Cooper M Warne
- Department of Physiology and Anatomy, University of North Texas Health Science Center, 3500 Camp Bowie Blvd., TX, 76107, Fort Worth, USA
| | - Salman I Essajee
- Department of Physiology and Anatomy, University of North Texas Health Science Center, 3500 Camp Bowie Blvd., TX, 76107, Fort Worth, USA
| | - Selina M Tucker
- Department of Physiology and Anatomy, University of North Texas Health Science Center, 3500 Camp Bowie Blvd., TX, 76107, Fort Worth, USA
| | - C Alberto Figueroa
- Section of Vascular Surgery, Department of Surgery, University of Michigan, Ann Arbor, USA
- Department of Biomedical Engineering, University of Michigan, Ann Arbor, USA
| | - Daniel A Beard
- Department of Molecular and Integrative Physiology, University of Michigan, Ann Arbor, USA
| | - Gregory M Dick
- Department of Physiology and Anatomy, University of North Texas Health Science Center, 3500 Camp Bowie Blvd., TX, 76107, Fort Worth, USA
| | - Johnathan D Tune
- Department of Physiology and Anatomy, University of North Texas Health Science Center, 3500 Camp Bowie Blvd., TX, 76107, Fort Worth, USA.
| |
Collapse
|
7
|
Di Gregorio S, Vergara C, Pelagi GM, Baggiano A, Zunino P, Guglielmo M, Fusini L, Muscogiuri G, Rossi A, Rabbat MG, Quarteroni A, Pontone G. Prediction of myocardial blood flow under stress conditions by means of a computational model. Eur J Nucl Med Mol Imaging 2022; 49:1894-1905. [PMID: 34984502 DOI: 10.1007/s00259-021-05667-8] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/11/2021] [Accepted: 12/18/2021] [Indexed: 12/30/2022]
Abstract
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.
Collapse
Affiliation(s)
| | - Christian Vergara
- LABS, Dipartimento Di Chimica, Materiali E Ingegneria Chimica, Politecnico Di Milano, Milan, Italy
| | | | - Andrea Baggiano
- Cardiovascular Imaging Department, Centro Cardiologico Monzino IRCSS, Via C. Parea 4, 20138, Milan, Italy
- Department of Clinical Science and Community Health, University of Milan, Milan, Italy
| | - Paolo Zunino
- Dipartimento Di Matematica, MOX, Politecnico Di Milano, Milan, Italy
| | - Marco Guglielmo
- Cardiovascular Imaging Department, Centro Cardiologico Monzino IRCSS, Via C. Parea 4, 20138, Milan, Italy
| | - Laura Fusini
- Cardiovascular Imaging Department, Centro Cardiologico Monzino IRCSS, Via C. Parea 4, 20138, Milan, Italy
- Department of Electronics, Information and Bioengineering, Politecnico di Milano, Milan, Italy
| | - Giuseppe Muscogiuri
- Cardiovascular Imaging Department, Centro Cardiologico Monzino IRCSS, Via C. Parea 4, 20138, Milan, Italy
| | - Alexia Rossi
- Department of Nuclear Medicine, University Hospital, Zurich, Switzerland
- Center for Molecular Cardiology, University of Zurich, Zurich, Switzerland
| | - Mark G Rabbat
- Loyola University of Chicago, Chicago, IL, USA
- Edward Hines Jr. VA Hospital, Hines, IL, USA
| | - Alfio Quarteroni
- Dipartimento Di Matematica, MOX, Politecnico Di Milano, Milan, Italy
- Institute of Mathematics, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland
| | - Gianluca Pontone
- Cardiovascular Imaging Department, Centro Cardiologico Monzino IRCSS, Via C. Parea 4, 20138, Milan, Italy.
| |
Collapse
|
8
|
In silico trials for treatment of acute ischemic stroke: Design and implementation. Comput Biol Med 2021; 137:104802. [PMID: 34520989 DOI: 10.1016/j.compbiomed.2021.104802] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/19/2021] [Revised: 07/30/2021] [Accepted: 08/17/2021] [Indexed: 01/21/2023]
Abstract
An in silico trial simulates a disease and its corresponding therapies on a cohort of virtual patients to support the development and evaluation of medical devices, drugs, and treatment. In silico trials have the potential to refine, reduce cost, and partially replace current in vivo studies, namely clinical trials and animal testing. We present the design and implementation of an in silico trial for treatment of acute ischemic stroke. We propose an event-based modelling approach for the simulation of a disease and injury, where changes to the state of the system (the events) are assumed to be instantaneous. Using this approach we are able to combine a diverse set of models, spanning multiple time scales, to model acute ischemic stroke, treatment, and resulting brain tissue injury. The in silico trial is designed to be modular to aid development and reproducibility. It provides a comprehensive framework for application to any potential in silico trial. A statistical population model is used to generate cohorts of virtual patients. Patient functional outcomes are also predicted with a statistical model, using treatment and injury results and the patient's clinical parameters. We demonstrate the functionality of the event-based modelling approach and trial framework by running proof of concept in silico trials. The proof of concept trials simulate the same cohort of patients twice: once with successful treatment (successful recanalisation) and once with unsuccessful treatment (unsuccessful treatment). Ways to overcome some of the challenges and difficulties in setting up such an in silico trial are discussed, such as validation and computational limitations.
Collapse
|
9
|
Józsa TI, Padmos RM, El-Bouri WK, Hoekstra AG, Payne SJ. On the Sensitivity Analysis of Porous Finite Element Models for Cerebral Perfusion Estimation. Ann Biomed Eng 2021; 49:3647-3665. [PMID: 34155569 PMCID: PMC8671295 DOI: 10.1007/s10439-021-02808-w] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/15/2021] [Accepted: 06/01/2021] [Indexed: 11/08/2022]
Abstract
Computational physiological models are promising tools to enhance the design of clinical trials and to assist in decision making. Organ-scale haemodynamic models are gaining popularity to evaluate perfusion in a virtual environment both in healthy and diseased patients. Recently, the principles of verification, validation, and uncertainty quantification of such physiological models have been laid down to ensure safe applications of engineering software in the medical device industry. The present study sets out to establish guidelines for the usage of a three-dimensional steady state porous cerebral perfusion model of the human brain following principles detailed in the verification and validation (V&V 40) standard of the American Society of Mechanical Engineers. The model relies on the finite element method and has been developed specifically to estimate how brain perfusion is altered in ischaemic stroke patients before, during, and after treatments. Simulations are compared with exact analytical solutions and a thorough sensitivity analysis is presented covering every numerical and physiological model parameter. The results suggest that such porous models can approximate blood pressure and perfusion distributions reliably even on a coarse grid with first order elements. On the other hand, higher order elements are essential to mitigate errors in volumetric blood flow rate estimation through cortical surface regions. Matching the volumetric flow rate corresponding to major cerebral arteries is identified as a validation milestone. It is found that inlet velocity boundary conditions are hard to obtain and that constant pressure inlet boundary conditions are feasible alternatives. A one-dimensional model is presented which can serve as a computationally inexpensive replacement of the three-dimensional brain model to ease parameter optimisation, sensitivity analyses and uncertainty quantification. The findings of the present study can be generalised to organ-scale porous perfusion models. The results increase the applicability of computational tools regarding treatment development for stroke and other cerebrovascular conditions.
Collapse
Affiliation(s)
- T I Józsa
- Institute of Biomedical Engineering, Department of Engineering Science, University of Oxford, Parks Road, Oxford, OX1 3PJ, UK.
| | - R M Padmos
- Computational Science Laboratory, Institute for Informatics, Faculty of Science, University of Amsterdam, Science Park 904, Amsterdam, 1098 XH, The Netherlands
| | - W K El-Bouri
- Institute of Biomedical Engineering, Department of Engineering Science, University of Oxford, Parks Road, Oxford, OX1 3PJ, UK.,Liverpool Centre for Cardiovascular Science, Department of Cardiovascular and Metabolic Medicine, University of Liverpool, Thomas Drive, Liverpool, L14 3PE, UK
| | - A G Hoekstra
- Computational Science Laboratory, Institute for Informatics, Faculty of Science, University of Amsterdam, Science Park 904, Amsterdam, 1098 XH, The Netherlands
| | - S J Payne
- Institute of Biomedical Engineering, Department of Engineering Science, University of Oxford, Parks Road, Oxford, OX1 3PJ, UK
| |
Collapse
|
10
|
Richardson SIH, Gao H, Cox J, Janiczek R, Griffith BE, Berry C, Luo X. A poroelastic immersed finite element framework for modelling cardiac perfusion and fluid-structure interaction. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2021; 37:e3446. [PMID: 33559359 PMCID: PMC8274593 DOI: 10.1002/cnm.3446] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/17/2020] [Revised: 12/22/2020] [Accepted: 01/20/2021] [Indexed: 05/11/2023]
Abstract
Modern approaches to modelling cardiac perfusion now commonly describe the myocardium using the framework of poroelasticity. Cardiac tissue can be described as a saturated porous medium composed of the pore fluid (blood) and the skeleton (myocytes and collagen scaffold). In previous studies fluid-structure interaction in the heart has been treated in a variety of ways, but in most cases, the myocardium is assumed to be a hyperelastic fibre-reinforced material. Conversely, models that treat the myocardium as a poroelastic material typically neglect interactions between the myocardium and intracardiac blood flow. This work presents a poroelastic immersed finite element framework to model left ventricular dynamics in a three-phase poroelastic system composed of the pore blood fluid, the skeleton, and the chamber fluid. We benchmark our approach by examining a pair of prototypical poroelastic formations using a simple cubic geometry considered in the prior work by Chapelle et al (2010). This cubic model also enables us to compare the differences between system behaviour when using isotropic and anisotropic material models for the skeleton. With this framework, we also simulate the poroelastic dynamics of a three-dimensional left ventricle, in which the myocardium is described by the Holzapfel-Ogden law. Results obtained using the poroelastic model are compared to those of a corresponding hyperelastic model studied previously. We find that the poroelastic LV behaves differently from the hyperelastic LV model. For example, accounting for perfusion results in a smaller diastolic chamber volume, agreeing well with the well-known wall-stiffening effect under perfusion reported previously. Meanwhile differences in systolic function, such as fibre strain in the basal and middle ventricle, are found to be comparatively minor.
Collapse
Affiliation(s)
| | - Hao Gao
- School of Mathematics and Statistics, University of
Glasgow, Glasgow, UK
| | | | | | - Boyce E. Griffith
- Departments of Mathematics, Applied Physical Sciences, and
Biomedical Engineering, University of North Carolina, Chapel Hill, North Carolina,
USA
| | - Colin Berry
- British Heart Foundation Glasgow Cardiovascular Research
Centre, University of Glasgow, Glasgow, UK
| | - Xiaoyu Luo
- School of Mathematics and Statistics, University of
Glasgow, Glasgow, UK
| |
Collapse
|
11
|
Józsa TI, Padmos RM, Samuels N, El-Bouri WK, Hoekstra AG, Payne SJ. A porous circulation model of the human brain for in silico clinical trials in ischaemic stroke. Interface Focus 2021; 11:20190127. [PMID: 33343874 PMCID: PMC7739914 DOI: 10.1098/rsfs.2019.0127] [Citation(s) in RCA: 20] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 09/23/2020] [Indexed: 12/30/2022] Open
Abstract
The advancement of ischaemic stroke treatment relies on resource-intensive experiments and clinical trials. In order to improve ischaemic stroke treatments, such as thrombolysis and thrombectomy, we target the development of computational tools for in silico trials which can partially replace these animal and human experiments with fast simulations. This study proposes a model that will serve as part of a predictive unit within an in silico clinical trial estimating patient outcome as a function of treatment. In particular, the present work aims at the development and evaluation of an organ-scale microcirculation model of the human brain for perfusion prediction. The model relies on a three-compartment porous continuum approach. Firstly, a fast and robust method is established to compute the anisotropic permeability tensors representing arterioles and venules. Secondly, vessel encoded arterial spin labelling magnetic resonance imaging and clustering are employed to create an anatomically accurate mapping between the microcirculation and large arteries by identifying superficial perfusion territories. Thirdly, the parameter space of the problem is reduced by analysing the governing equations and experimental data. Fourthly, a parameter optimization is conducted. Finally, simulations are performed with the tuned model to obtain perfusion maps corresponding to an open and an occluded (ischaemic stroke) scenario. The perfusion map in the occluded vessel scenario shows promising qualitative agreement with computed tomography images of a patient with ischaemic stroke caused by large vessel occlusion. The results highlight that in the case of vessel occlusion (i) identifying perfusion territories is essential to capture the location and extent of underperfused regions and (ii) anisotropic permeability tensors are required to give quantitatively realistic estimation of perfusion change. In the future, the model will be thoroughly validated against experiments.
Collapse
Affiliation(s)
- T. I. Józsa
- Institute of Biomedical Engineering, Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, UK
| | - R. M. Padmos
- Computational Science Laboratory, Institute for Informatics, Faculty of Science, University of Amsterdam, Science Park 904, Amsterdam 1098 XH, The Netherlands
| | - N. Samuels
- Department of Radiology and Nuclear Medicine, Erasmus MC, University Medical Center, Rotterdam 3015 GD, The Netherlands
| | - W. K. El-Bouri
- Institute of Biomedical Engineering, Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, UK
| | - A. G. Hoekstra
- Computational Science Laboratory, Institute for Informatics, Faculty of Science, University of Amsterdam, Science Park 904, Amsterdam 1098 XH, The Netherlands
| | - S. J. Payne
- Institute of Biomedical Engineering, Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, UK
| |
Collapse
|
12
|
Coccarelli A, Saha S, Purushotham T, Arul Prakash K, Nithiarasu P. On the poro-elastic models for microvascular blood flow resistance: An in vitro validation. J Biomech 2021; 117:110241. [PMID: 33486261 DOI: 10.1016/j.jbiomech.2021.110241] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/11/2020] [Revised: 11/11/2020] [Accepted: 01/04/2021] [Indexed: 10/22/2022]
Abstract
Nowadays, adequate and accurate representation of the microvascular flow resistance constitutes one of the major challenges in computational haemodynamic studies. In this work, a theoretical, porous media framework, ultimately designed for representing downstream resistance, is presented and compared against an in vitro experimental results. The resistor consists of a poro-elastic tube, with either a constant or variable porosity profile in space. The underlying physics, characterizing the fluid flow through the porous media, is analysed by considering flow variables at different network locations. Backward reflections, originated in the reservoir of the in vitro model, are accounted for through a reflection coefficient imposed as an outflow network condition. The simulation results are in good agreement with the measurements for both the homogenous and heterogeneous porosity conditions. In addition, the comparison allows identification of the range of values representing experimental reservoir reflection coefficients. The pressure drops across the heterogeneous porous media increases with respect to the simpler configuration, whilst flow remains almost unchanged. The effect of some fluid network features, such as tube Young's modulus and fluid viscosity, on the theoretical results is also elucidated, providing a reference for the invitro and insilico simulation of different microvascular conditions.
Collapse
Affiliation(s)
- Alberto Coccarelli
- Biomedical Engineering Group, Zienkiewicz Centre for Computational Engineering, College of Engineering, Swansea University, UK
| | - Supratim Saha
- Department of Applied Mechanics, Indian Institute of Technology Madras, India
| | - Tanjeri Purushotham
- Department of Applied Mechanics, Indian Institute of Technology Madras, India
| | - K Arul Prakash
- Department of Applied Mechanics, Indian Institute of Technology Madras, India
| | - Perumal Nithiarasu
- Biomedical Engineering Group, Zienkiewicz Centre for Computational Engineering, College of Engineering, Swansea University, UK; VAJRA Adjunct Professor, Indian Institute of Technology Madras, India.
| |
Collapse
|
13
|
Myocardial Perfusion Simulation for Coronary Artery Disease: A Coupled Patient-Specific Multiscale Model. Ann Biomed Eng 2020; 49:1432-1447. [PMID: 33263155 PMCID: PMC8057976 DOI: 10.1007/s10439-020-02681-z] [Citation(s) in RCA: 21] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/07/2020] [Accepted: 10/25/2020] [Indexed: 11/26/2022]
Abstract
Patient-specific models of blood flow are being used clinically to diagnose and plan treatment for coronary artery disease. A remaining challenge is bridging scales from flow in arteries to the micro-circulation supplying the myocardium. Previously proposed models are descriptive rather than predictive and have not been applied to human data. The goal here is to develop a multiscale patient-specific model enabling blood flow simulation from large coronary arteries to myocardial tissue. Patient vasculatures are segmented from coronary computed tomography angiography data and extended from the image-based model down to the arteriole level using a space-filling forest of synthetic trees. Blood flow is modeled by coupling a 1D model of the coronary arteries to a single-compartment Darcy myocardium model. Simulated results on five patients with non-obstructive coronary artery disease compare overall well to [\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$^{15}$$\end{document}15O]\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$\text {H}_{{2}}$$\end{document}H2O PET exam data for both resting and hyperemic conditions. Results on a patient with severe obstructive disease link coronary artery narrowing with impaired myocardial blood flow, demonstrating the model’s ability to predict myocardial regions with perfusion deficit. This is the first report of a computational model for simulating blood flow from the epicardial coronary arteries to the left ventricle myocardium applied to and validated on human data.
Collapse
|
14
|
Papamanolis L, Kim HJ, Jaquet C, Sinclair M, Schaap M, Danad I, van Diemen P, Knaapen P, Najman L, Talbot H, Taylor CA, Vignon-Clementel IE. Patient-specific, multiscale, myocardial blood flow simulation for coronary artery disease. Comput Methods Biomech Biomed Engin 2020. [DOI: 10.1080/10255842.2020.1813433] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
| | | | - C. Jaquet
- LIGM, Univ Gustave Eiffel, CNRS, ESIEE Paris, Marne-la-Vallée, France
| | - M. Sinclair
- HeartFlow Inc., Redwood City, USA
- Biomedical Image Analysis Group, Department of Computing, Imperial College London, UK
| | - M. Schaap
- HeartFlow Inc., Redwood City, USA
- Biomedical Image Analysis Group, Department of Computing, Imperial College London, UK
| | - I. Danad
- Department of Cardiology, Amsterdam UMC, Vrije Universiteit Amsterdam, Amsterdam, The Netherlands
| | - P. van Diemen
- Department of Cardiology, Amsterdam UMC, Vrije Universiteit Amsterdam, Amsterdam, The Netherlands
| | - P. Knaapen
- Department of Cardiology, Amsterdam UMC, Vrije Universiteit Amsterdam, Amsterdam, The Netherlands
| | - L. Najman
- LIGM, Univ Gustave Eiffel, CNRS, ESIEE Paris, Marne-la-Vallée, France
| | - H. Talbot
- Inria, Paris, France
- LIGM, Univ Gustave Eiffel, CNRS, ESIEE Paris, Marne-la-Vallée, France
- Center for Visual Computing, Université Paris-Saclay, CentraleSupélec, Inria, Gif-sur-Yvette, France
| | | | | |
Collapse
|
15
|
Donahue WP, Newhauser WD, Wong H, Moreno J, Dey J, Wilson VL. Computational feasibility of calculating the steady-state blood flow rate through the vasculature of the entire human body. Biomed Phys Eng Express 2020; 6:055026. [PMID: 33444257 DOI: 10.1088/2057-1976/abaf5d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Abstract
The human body contains approximately 20 billion individual blood vessels that deliver nutrients and oxygen to tissues. While blood flow is a well-developed field of research, no previous studies have calculated the blood flow rates through more than 5 million connected vessels. The goal of this study was to test if it is computationally feasible to calculate the blood flow rates through a vasculature equal in size to that of the human body. We designed and implemented a two-step algorithm to calculate the blood flow rates using principles of steady-state fluid dynamics. Steady-state fluid dynamics is an accurate approximation for the microvascular and venous structures in the human body. To determine the computational feasibility, we measured and evaluated the execution time, scalability, and memory usage to quantify the computational requirements. We demonstrated that it is computationally feasible to calculate the blood flow rate through 17 billion vessels in 6.5 hours using 256 compute nodes. The computational modeling of blood flow rate in entire organisms may find application in research on drug delivery, treatment of cancer metastases, and modulation of physiological performance.
Collapse
Affiliation(s)
- William P Donahue
- Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA, United States of America
| | | | | | | | | | | |
Collapse
|
16
|
Diem AK, Valen-Sendstad K. Time-Lapsing Perfusion: Proof of Concept of a Novel Method to Study Drug Delivery in Whole Organs. Biophys J 2019; 117:2316-2323. [PMID: 31648790 DOI: 10.1016/j.bpj.2019.09.029] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/21/2019] [Revised: 08/29/2019] [Accepted: 09/23/2019] [Indexed: 11/18/2022] Open
Abstract
Perfusion is one of the most important processes maintaining organ health. From a computational perspective, however, perfusion is among the least-studied physiological processes of the heart. The recent development of novel nanoparticle-based targeted cardiac therapy calls for novel simulation methods that can provide insights into the distribution patterns of therapeutic agents within the heart tissue. Additionally, resolving the distribution patterns of perfusion is crucial for gaining a full understanding of the long-term impacts of cardiovascular diseases that can lead to adverse remodeling such as myocardial ischemia and heart failure. In this study, we have developed and used a, to our knowledge, novel particle-tracking-based method to simulate the perfusion-mediated distribution of nanoparticles or other solutes. To model blood flow through perfused tissue, we follow the approach of others and treat the tissue as a porous medium in a continuum model. Classically, solutes are modeled using reaction-advection-diffusion kinetics. However, because of the discrepancy of scales between advection and diffusion in blood vessels, this method becomes practically numerically unstable. Instead, we track a bolus of solutes or nanoparticles using particle tracking based purely on advection in arteries. In capillaries, we employ diffusion kinetics, using an effective diffusion coefficient to mimic capillary blood flow. We first demonstrate the numerical validity and computational efficiency of this method on a two-dimensional benchmark problem. Finally, we demonstrate how the method is used to visualize perfusion patterns of a healthy and ischemic human left ventricle geometry. The efficiency of the method allows for nanoparticle tracking over multiple cardiac cycles using a conventional laptop, providing a framework for the simulation of experimentally relevant timeframes to advance preclinical research.
Collapse
Affiliation(s)
- Alexandra K Diem
- Department of Computational Physiology, Simula Research Laboratory, Fornebu, Norway.
| | | |
Collapse
|
17
|
Gkontra P, El‐Bouri WK, Norton K, Santos A, Popel AS, Payne SJ, Arroyo AG. Dynamic Changes in Microvascular Flow Conductivity and Perfusion After Myocardial Infarction Shown by Image-Based Modeling. J Am Heart Assoc 2019; 8:e011058. [PMID: 30897998 PMCID: PMC6509718 DOI: 10.1161/jaha.118.011058] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 09/25/2018] [Accepted: 02/19/2019] [Indexed: 12/26/2022]
Abstract
Background Microcirculation is a decisive factor in tissue reperfusion inadequacy following myocardial infarction ( MI ). Nonetheless, experimental assessment of blood flow in microcirculation remains a bottleneck. We sought to model blood flow properties in coronary microcirculation at different time points after MI and to compare them with healthy conditions to obtain insights into alterations in cardiac tissue perfusion. Methods and Results We developed an image-based modeling framework that permitted feeding a continuum flow model with anatomical data previously obtained from the pig coronary microvasculature to calculate physiologically meaningful permeability tensors. The tensors encompassed the microvascular conductivity and were also used to estimate the arteriole-venule drop in pressure and myocardial blood flow. Our results indicate that the tensors increased in a bimodal pattern at infarcted areas on days 1 and 7 after MI while a nonphysiological decrease in arteriole-venule drop in pressure was observed; contrary, the tensors and the arteriole-venule drop in pressure on day 3 after MI , and in remote areas, were closer to values for healthy tissue. Myocardial blood flow calculated using the condition-dependent arteriole-venule drop in pressure decreased in infarcted areas. Last, we simulated specific modes of vascular remodeling, such as vasodilation, vasoconstriction, or pruning, and quantified their distinct impact on microvascular conductivity. Conclusions Our study unravels time- and region-dependent alterations of tissue perfusion related to the structural changes occurring in the coronary microvasculature due to MI . It also paves the way for conducting simulations in new therapeutic interventions in MI and for image-based microvascular modeling by applying continuum flow models in other biomedical scenarios.
Collapse
Affiliation(s)
- Polyxeni Gkontra
- Centro Nacional de Investigaciones Cardiovasculares (CNIC)MadridSpain
- Biomedical Image Technologies (BIT), ETSI Telecomunicación,Universidad Politécnica de MadridMadridSpain
| | - Wahbi K. El‐Bouri
- Institute of Biomedical EngineeringDepartment of Engineering ScienceUniversity of OxfordUnited Kingdom
| | - Kerri‐Ann Norton
- Division of Science, Mathematics, and ComputingBard CollegeAnnandale‐on‐HudsonNY
| | - Andrés Santos
- Biomedical Image Technologies (BIT), ETSI Telecomunicación,Universidad Politécnica de MadridMadridSpain
- Centro de Investigación Biomédica en Red de BioingenieríaBiomateriales y Nanomedicina (CIBERBBN)MadridSpain
| | - Aleksander S. Popel
- Department of Biomedical EngineeringSchool of MedicineJohns Hopkins UniversityBaltimoreMD
| | - Stephen J. Payne
- Institute of Biomedical EngineeringDepartment of Engineering ScienceUniversity of OxfordUnited Kingdom
| | - Alicia G. Arroyo
- Centro Nacional de Investigaciones Cardiovasculares (CNIC)MadridSpain
- Centro de Investigaciones Biológicas (CIB‐CSIC)MadridSpain
| |
Collapse
|
18
|
El-Bouri WK, Payne SJ. Investigating the effects of a penetrating vessel occlusion with a multi-scale microvasculature model of the human cerebral cortex. Neuroimage 2018; 172:94-106. [PMID: 29360574 DOI: 10.1016/j.neuroimage.2018.01.049] [Citation(s) in RCA: 20] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/14/2017] [Revised: 01/12/2018] [Accepted: 01/18/2018] [Indexed: 01/20/2023] Open
Abstract
The effect of the microvasculature on observed clinical parameters, such as cerebral blood flow, is poorly understood. This is partly due to the gap between the vessels that can be individually imaged in humans and the microvasculature, meaning that mathematical models are required to understand the role of the microvasculature. As a result, a multi-scale model based on morphological data was developed here that is able to model large regions of the human microvasculature. From this model, a clear layering of flow (and 1-dimensional depth profiles) was observed within a voxel, with the flow in the microvasculature being driven predominantly by the geometry of the penetrating vessels. It also appears that the pressure and flow are decoupled, both in healthy vasculatures and in those where occlusions have occurred, again due to the topology of the penetrating vessels shunting flow between them. Occlusion of a penetrating arteriole resulted in a very high degree of overlap of blood pressure drop with experimentally observed cell death. However, drops in blood flow were far more widespread, providing additional support for the theory that pericyte controlled regulation on the capillary scale likely plays a large part in the perfusion of tissue post-occlusion.
Collapse
Affiliation(s)
- Wahbi K El-Bouri
- Institute of Biomedical Engineering, Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, UK.
| | - Stephen J Payne
- Institute of Biomedical Engineering, Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, UK
| |
Collapse
|
19
|
Peyrounette M, Davit Y, Quintard M, Lorthois S. Multiscale modelling of blood flow in cerebral microcirculation: Details at capillary scale control accuracy at the level of the cortex. PLoS One 2018; 13:e0189474. [PMID: 29324784 PMCID: PMC5764267 DOI: 10.1371/journal.pone.0189474] [Citation(s) in RCA: 56] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/03/2017] [Accepted: 11/28/2017] [Indexed: 11/19/2022] Open
Abstract
Aging or cerebral diseases may induce architectural modifications in human brain microvascular networks, such as capillary rarefaction. Such modifications limit blood and oxygen supply to the cortex, possibly resulting in energy failure and neuronal death. Modelling is key in understanding how these architectural modifications affect blood flow and mass transfers in such complex networks. However, the huge number of vessels in the human brain—tens of billions—prevents any modelling approach with an explicit architectural representation down to the scale of the capillaries. Here, we introduce a hybrid approach to model blood flow at larger scale in the brain microcirculation, based on its multiscale architecture. The capillary bed, which is a space-filling network, is treated as a porous medium and modelled using a homogenized continuum approach. The larger arteriolar and venular trees, which cannot be homogenized because of their fractal-like nature, are treated as a network of interconnected tubes with a detailed representation of their spatial organization. The main contribution of this work is to devise a proper coupling model at the interface between these two components. This model is based on analytical approximations of the pressure field that capture the strong pressure gradients building up in the capillaries connected to arterioles or venules. We evaluate the accuracy of this model for both very simple architectures with one arteriole and/or one venule and for more complex ones, with anatomically realistic tree-like vessels displaying a large number of coupling sites. We show that the hybrid model is very accurate in describing blood flow at large scales and further yields a significant computational gain by comparison with a classical network approach. It is therefore an important step towards large scale simulations of cerebral blood flow and lays the groundwork for introducing additional levels of complexity in the future.
Collapse
Affiliation(s)
- Myriam Peyrounette
- Institut de Mécanique des Fluides de Toulouse, IMFT, Université de Toulouse, CNRS - Toulouse, France
| | - Yohan Davit
- Institut de Mécanique des Fluides de Toulouse, IMFT, Université de Toulouse, CNRS - Toulouse, France
| | - Michel Quintard
- Institut de Mécanique des Fluides de Toulouse, IMFT, Université de Toulouse, CNRS - Toulouse, France
| | - Sylvie Lorthois
- Institut de Mécanique des Fluides de Toulouse, IMFT, Université de Toulouse, CNRS - Toulouse, France
- Nancy E. and Peter C. Meinig School of Biomedical Engineering, Cornell University, Ithaca, NY, United States of America
- * E-mail:
| |
Collapse
|
20
|
Rivolo S, Hadjilucas L, Sinclair M, van Horssen P, van den Wijngaard J, Wesolowski R, Chiribiri A, Siebes M, Smith NP, Lee J. Impact of coronary bifurcation morphology on wave propagation. Am J Physiol Heart Circ Physiol 2016; 311:H855-H870. [PMID: 27402665 PMCID: PMC5114464 DOI: 10.1152/ajpheart.00130.2016] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 02/09/2016] [Accepted: 07/05/2016] [Indexed: 01/09/2023]
Abstract
The branching pattern of the coronary vasculature is a key determinant of its function and plays a crucial role in shaping the pressure and velocity wave forms measured for clinical diagnosis. However, although multiple scaling laws have been proposed to characterize the branching pattern, the implications they have on wave propagation remain unassessed to date. To bridge this gap, we have developed a new theoretical framework by combining the mathematical formulation of scaling laws with the wave propagation theory in the pulsatile flow regime. This framework was then validated in multiple species using high-resolution cryomicrotome images of porcine, canine, and human coronary networks. Results demonstrate that the forward well-matchedness (no reflection for pressure/flow waves traveling from the coronary stem toward the microcirculation) is a salient feature in the coronary vasculature, and this result remains robust under many scenarios of the underlying pulse wave speed distribution assumed in the network. This result also implies a significant damping of the backward traveling waves, especially for smaller vessels (radius, <0.3 mm). Furthermore, the theoretical prediction of increasing area ratios (ratio between the area of the mother and daughter vessels) in more symmetric bifurcations found in the distal circulation was confirmed by experimental measurements. No differences were observed by clustering the vessel segments in terms of transmurality (from epicardium to endocardium) or perfusion territories (left anterior descending, left circumflex, and right coronary artery).
Collapse
Affiliation(s)
- Simone Rivolo
- Department of Biomedical Engineering, Division of Imaging Sciences and Biomedical Engineering, King's College London, London, United Kingdom, European Union
| | - Lucas Hadjilucas
- Department of Biomedical Engineering, Division of Imaging Sciences and Biomedical Engineering, King's College London, London, United Kingdom, European Union
| | - Matthew Sinclair
- Department of Biomedical Engineering, Division of Imaging Sciences and Biomedical Engineering, King's College London, London, United Kingdom, European Union
| | - Pepijn van Horssen
- Department of Biomedical Engineering and Physics, Academic Medical Center, University of Amsterdam, Amsterdam, The Netherlands
| | - Jeroen van den Wijngaard
- Department of Biomedical Engineering and Physics, Academic Medical Center, University of Amsterdam, Amsterdam, The Netherlands
| | - Roman Wesolowski
- Department of Cardiovascular Imaging, Division of Imaging Sciences and Biomedical Engineering, King's College London, London, United Kingdom, European Union; and
| | - Amedeo Chiribiri
- Department of Cardiovascular Imaging, Division of Imaging Sciences and Biomedical Engineering, King's College London, London, United Kingdom, European Union; and
| | - Maria Siebes
- Department of Biomedical Engineering and Physics, Academic Medical Center, University of Amsterdam, Amsterdam, The Netherlands
| | - Nicolas P Smith
- Faculty of Engineering, The University of Auckland, Auckland, New Zealand
| | - Jack Lee
- Department of Biomedical Engineering, Division of Imaging Sciences and Biomedical Engineering, King's College London, London, United Kingdom, European Union;
| |
Collapse
|
21
|
Chabiniok R, Wang VY, Hadjicharalambous M, Asner L, Lee J, Sermesant M, Kuhl E, Young AA, Moireau P, Nash MP, Chapelle D, Nordsletten DA. Multiphysics and multiscale modelling, data-model fusion and integration of organ physiology in the clinic: ventricular cardiac mechanics. Interface Focus 2016; 6:20150083. [PMID: 27051509 PMCID: PMC4759748 DOI: 10.1098/rsfs.2015.0083] [Citation(s) in RCA: 139] [Impact Index Per Article: 17.4] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
With heart and cardiovascular diseases continually challenging healthcare systems worldwide, translating basic research on cardiac (patho)physiology into clinical care is essential. Exacerbating this already extensive challenge is the complexity of the heart, relying on its hierarchical structure and function to maintain cardiovascular flow. Computational modelling has been proposed and actively pursued as a tool for accelerating research and translation. Allowing exploration of the relationships between physics, multiscale mechanisms and function, computational modelling provides a platform for improving our understanding of the heart. Further integration of experimental and clinical data through data assimilation and parameter estimation techniques is bringing computational models closer to use in routine clinical practice. This article reviews developments in computational cardiac modelling and how their integration with medical imaging data is providing new pathways for translational cardiac modelling.
Collapse
Affiliation(s)
- Radomir Chabiniok
- Division of Imaging Sciences and Biomedical Engineering, King's College London, St Thomas’ Hospital, London SE1 7EH, UK
- Inria and Paris-Saclay University, Bâtiment Alan Turing, 1 rue Honoré d'Estienne d'Orves, Campus de l'Ecole Polytechnique, Palaiseau 91120, France
| | - Vicky Y. Wang
- Auckland Bioengineering Institute, University of Auckland, 70 Symonds Street, Auckland, New Zealand
| | - Myrianthi Hadjicharalambous
- Division of Imaging Sciences and Biomedical Engineering, King's College London, St Thomas’ Hospital, London SE1 7EH, UK
| | - Liya Asner
- Division of Imaging Sciences and Biomedical Engineering, King's College London, St Thomas’ Hospital, London SE1 7EH, UK
| | - Jack Lee
- Division of Imaging Sciences and Biomedical Engineering, King's College London, St Thomas’ Hospital, London SE1 7EH, UK
| | - Maxime Sermesant
- Inria, Asclepios team, 2004 route des Lucioles BP 93, Sophia Antipolis Cedex 06902, France
| | - Ellen Kuhl
- Departments of Mechanical Engineering, Bioengineering, and Cardiothoracic Surgery, Stanford University, 496 Lomita Mall, Durand 217, Stanford, CA 94306, USA
| | - Alistair A. Young
- Auckland Bioengineering Institute, University of Auckland, 70 Symonds Street, Auckland, New Zealand
| | - Philippe Moireau
- Inria and Paris-Saclay University, Bâtiment Alan Turing, 1 rue Honoré d'Estienne d'Orves, Campus de l'Ecole Polytechnique, Palaiseau 91120, France
| | - Martyn P. Nash
- Auckland Bioengineering Institute, University of Auckland, 70 Symonds Street, Auckland, New Zealand
- Department of Engineering Science, University of Auckland, 70 Symonds Street, Auckland, New Zealand
| | - Dominique Chapelle
- Inria and Paris-Saclay University, Bâtiment Alan Turing, 1 rue Honoré d'Estienne d'Orves, Campus de l'Ecole Polytechnique, Palaiseau 91120, France
| | - David A. Nordsletten
- Division of Imaging Sciences and Biomedical Engineering, King's College London, St Thomas’ Hospital, London SE1 7EH, UK
| |
Collapse
|
22
|
Lee J, Nordsletten D, Cookson A, Rivolo S, Smith N. In silico coronary wave intensity analysis: application of an integrated one-dimensional and poromechanical model of cardiac perfusion. Biomech Model Mechanobiol 2016; 15:1535-1555. [PMID: 27008197 PMCID: PMC5106513 DOI: 10.1007/s10237-016-0782-5] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/05/2015] [Accepted: 03/08/2016] [Indexed: 01/09/2023]
Abstract
Coronary wave intensity analysis (cWIA) is a diagnostic technique based on invasive measurement of coronary pressure and velocity waveforms. The theory of WIA allows the forward- and backward-propagating coronary waves to be separated and attributed to their origin and timing, thus serving as a sensitive and specific cardiac functional indicator. In recent years, an increasing number of clinical studies have begun to establish associations between changes in specific waves and various diseases of myocardium and perfusion. These studies are, however, currently confined to a trial-and-error approach and are subject to technological limitations which may confound accurate interpretations. In this work, we have developed a biophysically based cardiac perfusion model which incorporates full ventricular–aortic–coronary coupling. This was achieved by integrating our previous work on one-dimensional modelling of vascular flow and poroelastic perfusion within an active myocardial mechanics framework. Extensive parameterisation was performed, yielding a close agreement with physiological levels of global coronary and myocardial function as well as experimentally observed cumulative wave intensity magnitudes. Results indicate a strong dependence of the backward suction wave on QRS duration and vascular resistance, the forward pushing wave on the rate of myocyte tension development, and the late forward pushing wave on the aortic valve dynamics. These findings are not only consistent with experimental observations, but offer a greater specificity to the wave-originating mechanisms, thus demonstrating the value of the integrated model as a tool for clinical investigation.
Collapse
Affiliation(s)
- Jack Lee
- Department of Biomedical Engineering, King's College London, 3rd Floor, Lambeth Wing, St Thomas' Hospital, London, UK.
| | - David Nordsletten
- Department of Biomedical Engineering, King's College London, 3rd Floor, Lambeth Wing, St Thomas' Hospital, London, UK
| | - Andrew Cookson
- Department of Biomedical Engineering, King's College London, 3rd Floor, Lambeth Wing, St Thomas' Hospital, London, UK
| | - Simone Rivolo
- Department of Biomedical Engineering, King's College London, 3rd Floor, Lambeth Wing, St Thomas' Hospital, London, UK
| | - Nicolas Smith
- Department of Biomedical Engineering, King's College London, 3rd Floor, Lambeth Wing, St Thomas' Hospital, London, UK
| |
Collapse
|
23
|
Clinical Diagnostic Biomarkers from the Personalization of Computational Models of Cardiac Physiology. Ann Biomed Eng 2015; 44:46-57. [PMID: 26399986 DOI: 10.1007/s10439-015-1439-8] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/06/2015] [Accepted: 08/25/2015] [Indexed: 10/23/2022]
Abstract
Computational modelling of the heart is rapidly advancing to the point of clinical utility. However, the difficulty of parameterizing and validating models from clinical data indicates that the routine application of truly predictive models remains a significant challenge. We argue there is significant value in an intermediate step towards prediction. This step is the use of biophysically based models to extract clinically useful information from existing patient data. Specifically in this paper we review methodologies for applying modelling frameworks for this goal in the areas of quantifying cardiac anatomy, estimating myocardial stiffness and optimizing measurements of coronary perfusion. Using these indicative examples of the general overarching approach, we finally discuss the value, ongoing challenges and future potential for applying biophysically based modelling in the clinical context.
Collapse
|
24
|
Sinclair MD, Lee J, Cookson AN, Rivolo S, Hyde ER, Smith NP. Measurement and modeling of coronary blood flow. WILEY INTERDISCIPLINARY REVIEWS-SYSTEMS BIOLOGY AND MEDICINE 2015; 7:335-56. [PMID: 26123867 DOI: 10.1002/wsbm.1309] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/18/2015] [Revised: 05/19/2015] [Accepted: 05/21/2015] [Indexed: 01/10/2023]
Abstract
Ischemic heart disease that comprises both coronary artery disease and microvascular disease is the single greatest cause of death globally. In this context, enhancing our understanding of the interaction of coronary structure and function is not only fundamental for advancing basic physiology but also crucial for identifying new targets for treating these diseases. A central challenge for understanding coronary blood flow is that coronary structure and function exhibit different behaviors across a range of spatial and temporal scales. While experimental studies have sought to understand this feature by isolating specific mechanisms, in tandem, computational modeling is increasingly also providing a unique framework to integrate mechanistic behaviors across different scales. In addition, clinical methods for assessing coronary disease severity are continuously being informed and updated by findings in basic physiology. Coupling these technologies, computational modeling of the coronary circulation is emerging as a bridge between the experimental and clinical domains, providing a framework to integrate imaging and measurements from multiple sources with mathematical descriptions of governing physical laws. State-of-the-art computational modeling is being used to combine mechanistic models with data to provide new insight into coronary physiology, optimization of medical technologies, and new applications to guide clinical practice.
Collapse
Affiliation(s)
- Matthew D Sinclair
- Division of Imaging Sciences and Biomedical Engineering, British Heart Foundation (BHF) Centre of Excellence, King's College London, London, UK
| | - Jack Lee
- Division of Imaging Sciences and Biomedical Engineering, British Heart Foundation (BHF) Centre of Excellence, King's College London, London, UK
| | - Andrew N Cookson
- Division of Imaging Sciences and Biomedical Engineering, British Heart Foundation (BHF) Centre of Excellence, King's College London, London, UK
| | - Simone Rivolo
- Division of Imaging Sciences and Biomedical Engineering, British Heart Foundation (BHF) Centre of Excellence, King's College London, London, UK
| | - Eoin R Hyde
- Division of Imaging Sciences and Biomedical Engineering, British Heart Foundation (BHF) Centre of Excellence, King's College London, London, UK
| | - Nicolas P Smith
- Division of Imaging Sciences and Biomedical Engineering, British Heart Foundation (BHF) Centre of Excellence, King's College London, London, UK.,Department of Engineering, University of Auckland, Auckland, New Zealand
| |
Collapse
|
25
|
Sinclair M, Lee J, Schuster A, Chiribiri A, van den Wijngaard J, van Horssen P, Siebes M, Spaan JAE, Nagel E, Smith NP. Microsphere skimming in the porcine coronary arteries: Implications for flow quantification. Microvasc Res 2015; 100:59-70. [PMID: 25963318 DOI: 10.1016/j.mvr.2015.04.005] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/02/2015] [Revised: 03/28/2015] [Accepted: 04/17/2015] [Indexed: 11/25/2022]
Abstract
Particle skimming is a phenomenon where particles suspended in fluid flowing through vessels distribute disproportionately to bulk fluid volume at junctions. Microspheres are considered a gold standard of intra-organ perfusion measurements and are used widely in studies of flow distribution and quantification. It has previously been hypothesised that skimming at arterial junctions is responsible for a systematic over-estimation of myocardial perfusion from microspheres at the subendocardium. Our objective is to integrate coronary arterial structure and microsphere distribution, imaged at high resolution, to test the hypothesis of microsphere skimming in a porcine left coronary arterial (LCA) network. A detailed network was reconstructed from cryomicrotome imaging data and a Poiseuille flow model was used to simulate flow. A statistical approach using Clopper-Pearson confidence intervals was applied to determine the prevalence of skimming at bifurcations in the LCA. Results reveal that microsphere skimming is most prevalent at bifurcations in the larger coronary arteries, namely the epicardial and transmural arteries. Bifurcations at which skimming was identified have significantly more asymmetric branching parameters. This finding suggests that when using thin transmural segments to quantify flow from microspheres, a skimming-related deposition bias may result in underestimation of perfusion in the subepicardium, and overestimation in the subendocardium.
Collapse
Affiliation(s)
- Matthew Sinclair
- Division of Imaging Sciences and Biomedical Engineering, King's College London, British Heart Foundation (BHF) Centre of Excellence, UK; National Institute of Heath Research (NIHR) Biomedical Research Centre at Guy's and St. Thomas' NHS Foundation Trust, Lambeth Wing, St. Thomas' Hospital, UK; Wellcome Trust and Engineering and Physical Sciences Research Council (EPSRC) Medical Engineering Centre, Lambeth Wing, St. Thomas' Hospital, London, UK
| | - Jack Lee
- Division of Imaging Sciences and Biomedical Engineering, King's College London, British Heart Foundation (BHF) Centre of Excellence, UK; National Institute of Heath Research (NIHR) Biomedical Research Centre at Guy's and St. Thomas' NHS Foundation Trust, Lambeth Wing, St. Thomas' Hospital, UK; Wellcome Trust and Engineering and Physical Sciences Research Council (EPSRC) Medical Engineering Centre, Lambeth Wing, St. Thomas' Hospital, London, UK
| | - Andreas Schuster
- Division of Imaging Sciences and Biomedical Engineering, King's College London, British Heart Foundation (BHF) Centre of Excellence, UK; National Institute of Heath Research (NIHR) Biomedical Research Centre at Guy's and St. Thomas' NHS Foundation Trust, Lambeth Wing, St. Thomas' Hospital, UK; Wellcome Trust and Engineering and Physical Sciences Research Council (EPSRC) Medical Engineering Centre, Lambeth Wing, St. Thomas' Hospital, London, UK; Department of Cardiology and Pneumology, Georg-August-University, Göttingen, Germany; German Centre for Cardiovascular Research (DZHK, Partner Site Göttingen), Göttingen, Germany
| | - Amedeo Chiribiri
- Division of Imaging Sciences and Biomedical Engineering, King's College London, British Heart Foundation (BHF) Centre of Excellence, UK; National Institute of Heath Research (NIHR) Biomedical Research Centre at Guy's and St. Thomas' NHS Foundation Trust, Lambeth Wing, St. Thomas' Hospital, UK; Wellcome Trust and Engineering and Physical Sciences Research Council (EPSRC) Medical Engineering Centre, Lambeth Wing, St. Thomas' Hospital, London, UK
| | - Jeroen van den Wijngaard
- Department of Biomedical Engineering & Physics, Academic Medical Centre, Amsterdam, The Netherlands
| | - Pepijn van Horssen
- Department of Biomedical Engineering & Physics, Academic Medical Centre, Amsterdam, The Netherlands
| | - Maria Siebes
- Department of Biomedical Engineering & Physics, Academic Medical Centre, Amsterdam, The Netherlands
| | - Jos A E Spaan
- Department of Biomedical Engineering & Physics, Academic Medical Centre, Amsterdam, The Netherlands
| | - Eike Nagel
- Division of Imaging Sciences and Biomedical Engineering, King's College London, British Heart Foundation (BHF) Centre of Excellence, UK; National Institute of Heath Research (NIHR) Biomedical Research Centre at Guy's and St. Thomas' NHS Foundation Trust, Lambeth Wing, St. Thomas' Hospital, UK; Wellcome Trust and Engineering and Physical Sciences Research Council (EPSRC) Medical Engineering Centre, Lambeth Wing, St. Thomas' Hospital, London, UK
| | - Nicolas P Smith
- Division of Imaging Sciences and Biomedical Engineering, King's College London, British Heart Foundation (BHF) Centre of Excellence, UK; National Institute of Heath Research (NIHR) Biomedical Research Centre at Guy's and St. Thomas' NHS Foundation Trust, Lambeth Wing, St. Thomas' Hospital, UK; Wellcome Trust and Engineering and Physical Sciences Research Council (EPSRC) Medical Engineering Centre, Lambeth Wing, St. Thomas' Hospital, London, UK; Department of Engineering, University of Auckland, Auckland, New Zealand.
| |
Collapse
|
26
|
Cookson AN, Lee J, Michler C, Chabiniok R, Hyde E, Nordsletten D, Smith NP. A spatially-distributed computational model to quantify behaviour of contrast agents in MR perfusion imaging. Med Image Anal 2014; 18:1200-16. [PMID: 25103922 PMCID: PMC4156310 DOI: 10.1016/j.media.2014.07.002] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/21/2013] [Revised: 07/07/2014] [Accepted: 07/08/2014] [Indexed: 10/30/2022]
Abstract
Contrast agent enhanced magnetic resonance (MR) perfusion imaging provides an early, non-invasive indication of defects in the coronary circulation. However, the large variation of contrast agent properties, physiological state and imaging protocols means that optimisation of image acquisition is difficult to achieve. This situation motivates the development of a computational framework that, in turn, enables the efficient mapping of this parameter space to provide valuable information for optimisation of perfusion imaging in the clinical context. For this purpose a single-compartment porous medium model of capillary blood flow is developed which is coupled with a scalar transport model, to characterise the behaviour of both blood-pool and freely-diffusive contrast agents characterised by their ability to diffuse through the capillary wall into the extra-cellular space. A parameter space study is performed on the nondimensionalised equations using a 2D model for both healthy and diseased myocardium, examining the sensitivity of system behaviour to Peclet number, Damköhler number (Da), diffusivity ratio and fluid porosity. Assuming a linear MR signal response model, sample concentration time series data are calculated, and the sensitivity of clinically-relevant properties of these signals to the model parameters is quantified. Both upslope and peak values display significant non-monotonic behaviour with regard to the Damköhler number, with these properties showing a high degree of sensitivity in the parameter range relevant to contrast agents currently in use. However, the results suggest that signal upslope is the more robust and discerning metric for perfusion quantification, in particular for correlating with perfusion defect size. Finally, the results were examined in the context of nonlinear signal response, flow quantification via Fermi deconvolution and perfusion reserve index, which demonstrated that there is no single best set of contrast agent parameters, instead the contrast agents should be tailored to the specific imaging protocol and post-processing method to be used.
Collapse
Affiliation(s)
- A N Cookson
- Department of Biomedical Engineering, Division of Imaging Sciences & Biomedical Engineering, St. Thomas' Hospital, King's College London, London SE1 7EH, UK
| | - J Lee
- Department of Biomedical Engineering, Division of Imaging Sciences & Biomedical Engineering, St. Thomas' Hospital, King's College London, London SE1 7EH, UK
| | - C Michler
- Department of Biomedical Engineering, Division of Imaging Sciences & Biomedical Engineering, St. Thomas' Hospital, King's College London, London SE1 7EH, UK
| | - R Chabiniok
- Department of Biomedical Engineering, Division of Imaging Sciences & Biomedical Engineering, St. Thomas' Hospital, King's College London, London SE1 7EH, UK
| | - E Hyde
- Department of Computer Science, University of Oxford, Oxford OX1 3QD, UK
| | - D Nordsletten
- Department of Biomedical Engineering, Division of Imaging Sciences & Biomedical Engineering, St. Thomas' Hospital, King's College London, London SE1 7EH, UK
| | - N P Smith
- Department of Biomedical Engineering, Division of Imaging Sciences & Biomedical Engineering, St. Thomas' Hospital, King's College London, London SE1 7EH, UK.
| |
Collapse
|
27
|
Smith AF, Shipley RJ, Lee J, Sands GB, LeGrice IJ, Smith NP. Transmural variation and anisotropy of microvascular flow conductivity in the rat myocardium. Ann Biomed Eng 2014; 42:1966-77. [PMID: 24866569 DOI: 10.1007/s10439-014-1028-2] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/03/2014] [Accepted: 05/03/2014] [Indexed: 11/30/2022]
Abstract
Transmural variations in the relationship between structural and fluid transport properties of myocardial capillary networks are determined via continuum modeling approaches using recent three-dimensional (3D) data on the microvascular structure. Specifically, the permeability tensor, which quantifies the inverse of the blood flow resistivity of the capillary network, is computed by volume-averaging flow solutions in synthetic networks with geometrical and topological properties derived from an anatomically-detailed microvascular data set extracted from the rat myocardium. Results show that the permeability is approximately ten times higher in the principal direction of capillary alignment (the "longitudinal" direction) than perpendicular to this direction, reflecting the strong anisotropy of the microvascular network. Additionally, a 30% increase in capillary diameter from subepicardium to subendocardium is shown to translate to a 130% transmural rise in permeability in the longitudinal capillary direction. This result supports the hypothesis that perfusion is preferentially facilitated during diastole in the subendocardial microvasculature to compensate for the severely-reduced systolic perfusion in the subendocardium.
Collapse
Affiliation(s)
- Amy F Smith
- Oxford Centre for Collaborative Applied Mathematics, Mathematical Institute, University of Oxford, Woodstock Road, Oxford, OX2 6GG, UK
| | | | | | | | | | | |
Collapse
|