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Colunga A, Carlson BE, Olufsen MS. The importance of incorporating ventricular-ventricular interaction (VVI) in the study of pulmonary hypertension. Math Biosci 2024; 375:109242. [PMID: 38944112 DOI: 10.1016/j.mbs.2024.109242] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2024] [Revised: 06/18/2024] [Accepted: 06/22/2024] [Indexed: 07/01/2024]
Abstract
Ventricular ventricular interaction (VVI) affects blood volume and pressure in the right and left ventricles of the heart due to the location and balance of forces on the septal wall separating the ventricles. In healthy patients, the pressure of the left ventricle is considerably higher than the right, resulting in a septal wall that bows into the right ventricle. However, in patients with pulmonary hypertension, the pressure in the right ventricle increases significantly to a point where the pressure is similar to or surpasses that of the left ventricle during portions of the cardiac cycle. For these patients, the septal wall deviates towards the left ventricle, impacting its function. It is possible to study this effect using mathematical modeling, but existing models are nonlinear, leading to a system of algebraic differential equations that can be challenging to solve in patient-specific optimizations of clinical data. This study demonstrates that a simplified linearized model is sufficient to account for the effect of VVI and that, as expected, the impact is significantly more pronounced in patients with pulmonary hypertension.
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Affiliation(s)
- Amanda Colunga
- North Carolina State University, 2311 Stinson Drive, Raleigh, 27695, NC, USA
| | - Brian E Carlson
- University of Michigan, 2800 Plymouth Rd, Ann Arbor, 48105, MI, USA
| | - Mette S Olufsen
- North Carolina State University, 2311 Stinson Drive, Raleigh, 27695, NC, USA.
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2
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Colebank MJ, Oomen PA, Witzenburg CM, Grosberg A, Beard DA, Husmeier D, Olufsen MS, Chesler NC. Guidelines for mechanistic modeling and analysis in cardiovascular research. Am J Physiol Heart Circ Physiol 2024; 327:H473-H503. [PMID: 38904851 DOI: 10.1152/ajpheart.00766.2023] [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: 12/11/2023] [Revised: 06/07/2024] [Accepted: 06/16/2024] [Indexed: 06/22/2024]
Abstract
Computational, or in silico, models are an effective, noninvasive tool for investigating cardiovascular function. These models can be used in the analysis of experimental and clinical data to identify possible mechanisms of (ab)normal cardiovascular physiology. Recent advances in computing power and data management have led to innovative and complex modeling frameworks that simulate cardiovascular function across multiple scales. While commonly used in multiple disciplines, there is a lack of concise guidelines for the implementation of computer models in cardiovascular research. In line with recent calls for more reproducible research, it is imperative that scientists adhere to credible practices when developing and applying computational models to their research. The goal of this manuscript is to provide a consensus document that identifies best practices for in silico computational modeling in cardiovascular research. These guidelines provide the necessary methods for mechanistic model development, model analysis, and formal model calibration using fundamentals from statistics. We outline rigorous practices for computational, mechanistic modeling in cardiovascular research and discuss its synergistic value to experimental and clinical data.
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Affiliation(s)
- Mitchel J Colebank
- Edwards Lifesciences Foundation Cardiovascular Innovation and Research Center, Department of Biomedical Engineering, University of California, Irvine, Irvine, California, United States
| | - Pim A Oomen
- Edwards Lifesciences Foundation Cardiovascular Innovation and Research Center, Department of Biomedical Engineering, University of California, Irvine, Irvine, California, United States
| | - Colleen M Witzenburg
- Department of Biomedical Engineering, University of Wisconsin-Madison, Madison, Wisconsin, United States
| | - Anna Grosberg
- Edwards Lifesciences Foundation Cardiovascular Innovation and Research Center, Department of Biomedical Engineering, University of California, Irvine, Irvine, California, United States
| | - Daniel A Beard
- Department of Molecular and Integrative Physiology, University of Michigan, Ann Arbor, Michigan, United States
| | - Dirk Husmeier
- School of Mathematics and Statistics, University of Glasgow, Glasgow, United Kingdom
| | - Mette S Olufsen
- Department of Mathematics, North Carolina State University, Raleigh, North Carolina, United States
| | - Naomi C Chesler
- Edwards Lifesciences Foundation Cardiovascular Innovation and Research Center, Department of Biomedical Engineering, University of California, Irvine, Irvine, California, United States
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3
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Saxton H, Xu X, Schenkel T, Clayton RH, Halliday I. Convergence, sampling and total order estimator effects on parameter orthogonality in global sensitivity analysis. PLoS Comput Biol 2024; 20:e1011946. [PMID: 39018334 DOI: 10.1371/journal.pcbi.1011946] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/23/2024] [Revised: 07/29/2024] [Accepted: 06/13/2024] [Indexed: 07/19/2024] Open
Abstract
Dynamical system models typically involve numerous input parameters whose "effects" and orthogonality need to be quantified through sensitivity analysis, to identify inputs contributing the greatest uncertainty. Whilst prior art has compared total-order estimators' role in recovering "true" effects, assessing their ability to recover robust parameter orthogonality for use in identifiability metrics has not been investigated. In this paper, we perform: (i) an assessment using a different class of numerical models representing the cardiovascular system, (ii) a wider evaluation of sampling methodologies and their interactions with estimators, (iii) an investigation of the consequences of permuting estimators and sampling methodologies on input parameter orthogonality, (iv) a study of sample convergence through resampling, and (v) an assessment of whether positive outcomes are sustained when model input dimensionality increases. Our results indicate that Jansen or Janon estimators display efficient convergence with minimum uncertainty when coupled with Sobol and the lattice rule sampling methods, making them prime choices for calculating parameter orthogonality and influence. This study reveals that global sensitivity analysis is convergence driven. Unconverged indices are subject to error and therefore the true influence or orthogonality of the input parameters are not recovered. This investigation importantly clarifies the interactions of the estimator and the sampling methodology by reducing the associated ambiguities, defining novel practices for modelling in the life sciences.
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Affiliation(s)
- Harry Saxton
- Materials & Engineering Research Institute, Sheffield Hallam University, Sheffield, United Kingdom
| | - Xu Xu
- Department of Computer Science, Faculty of Engineering, University of Sheffield, Sheffield, United Kingdom
- Insigneo Institute for in silico Medicine, University of Sheffield, Sheffield, United Kingdom
| | - Torsten Schenkel
- Department of Engineering and Mathematics, Sheffield Hallam University, Sheffield, United Kingdom
| | - Richard H Clayton
- Department of Computer Science, Faculty of Engineering, University of Sheffield, Sheffield, United Kingdom
- Insigneo Institute for in silico Medicine, University of Sheffield, Sheffield, United Kingdom
| | - Ian Halliday
- Insigneo Institute for in silico Medicine, University of Sheffield, Sheffield, United Kingdom
- Clinical Medicine, School of Medicine and Population Health, University of Sheffield, Sheffield, United Kingdom
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Haider MA, Pearce KJ, Chesler NC, Hill NA, Olufsen MS. Application and reduction of a nonlinear hyperelastic wall model capturing ex vivo relationships between fluid pressure, area, and wall thickness in normal and hypertensive murine left pulmonary arteries. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2024; 40:e3798. [PMID: 38214099 DOI: 10.1002/cnm.3798] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/02/2022] [Revised: 08/10/2023] [Accepted: 11/26/2023] [Indexed: 01/13/2024]
Abstract
Pulmonary hypertension is a cardiovascular disorder manifested by elevated mean arterial blood pressure (>20 mmHg) together with vessel wall stiffening and thickening due to alterations in collagen, elastin, and smooth muscle cells. Hypoxia-induced (type 3) pulmonary hypertension can be studied in animals exposed to a low oxygen environment for prolonged time periods leading to biomechanical alterations in vessel wall structure. This study introduces a novel approach to formulating a reduced order nonlinear elastic structural wall model for a large pulmonary artery. The model relating blood pressure and area is calibrated using ex vivo measurements of vessel diameter and wall thickness changes, under controlled pressure conditions, in left pulmonary arteries isolated from control and hypertensive mice. A two-layer, hyperelastic, and anisotropic model incorporating residual stresses is formulated using the Holzapfel-Gasser-Ogden model. Complex relations predicting vessel area and wall thickness with increasing blood pressure are derived and calibrated using the data. Sensitivity analysis, parameter estimation, subset selection, and physical plausibility arguments are used to systematically reduce the 16-parameter model to one in which a much smaller subset of identifiable parameters is estimated via solution of an inverse problem. Our final reduced one layer model includes a single set of three elastic moduli. Estimated ranges of these parameters demonstrate that nonlinear stiffening is dominated by elastin in the control animals and by collagen in the hypertensive animals. The pressure-area relation developed in this novel manner has potential impact on one-dimensional fluids network models of vessel wall remodeling in the presence of cardiovascular disease.
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Affiliation(s)
- Mansoor A Haider
- Department of Mathematics, North Carolina State University, Raleigh, North Carolina, USA
| | - Katherine J Pearce
- Department of Mathematics, North Carolina State University, Raleigh, North Carolina, USA
| | - Naomi C Chesler
- Edwards Lifesciences Foundation Cardiovascular Innovation and Research Center & Department of Biomedical Engineering, University of California, Irvine (UCI), Irvine, California, USA
| | - Nicholas A Hill
- School of Mathematics and Statistics, University of Glasgow, Glasgow, UK
| | - Mette S Olufsen
- Department of Mathematics, North Carolina State University, Raleigh, North Carolina, USA
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5
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Lu L, Zhu T, Morelli D, Creagh A, Liu Z, Yang J, Liu F, Zhang YT, Clifton DA. Uncertainties in the Analysis of Heart Rate Variability: A Systematic Review. IEEE Rev Biomed Eng 2024; 17:180-196. [PMID: 37186539 DOI: 10.1109/rbme.2023.3271595] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/17/2023]
Abstract
Heart rate variability (HRV) is an important metric with a variety of applications in clinical situations such as cardiovascular diseases, diabetes mellitus, and mental health. HRV data can be potentially obtained from electrocardiography and photoplethysmography signals, then computational techniques such as signal filtering and data segmentation are used to process the sampled data for calculating HRV measures. However, uncertainties arising from data acquisition, computational models, and physiological factors can lead to degraded signal quality and affect HRV analysis. Therefore, it is crucial to address these uncertainties and develop advanced models for HRV analysis. Although several reviews of HRV analysis exist, they primarily focus on clinical applications, trends in HRV methods, or specific aspects of uncertainties such as measurement noise. This paper provides a comprehensive review of uncertainties in HRV analysis, quantifies their impacts, and outlines potential solutions. To the best of our knowledge, this is the first study that presents a holistic review of uncertainties in HRV methods and quantifies their impacts on HRV measures from an engineer's perspective. This review is essential for developing robust and reliable models, and could serve as a valuable future reference in the field, particularly for dealing with uncertainties in HRV analysis.
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Colebank MJ, Taylor R, Hacker TA, Chesler NC. Biventricular Interaction During Acute Left Ventricular Ischemia in Mice: A Combined In-Vivo and In-Silico Approach. Ann Biomed Eng 2023; 51:2528-2543. [PMID: 37453977 PMCID: PMC10598180 DOI: 10.1007/s10439-023-03293-z] [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: 01/27/2023] [Accepted: 06/17/2023] [Indexed: 07/18/2023]
Abstract
Computational models provide an efficient paradigm for integrating and linking multiple spatial and temporal scales. However, these models are difficult to parameterize and match to experimental data. Recent advances in both data collection and model analyses have helped overcome this limitation. Here, we combine a multiscale, biventricular interaction model with mouse data before and after left ventricular (LV) ischemia. Sensitivity analyses are used to identify the most influential parameters on pressure and volume predictions. The subset of influential model parameters are calibrated to biventricular pressure-volume loop data (n = 3) at baseline. Each mouse underwent left anterior descending coronary artery ligation, during which changes in fractional shortening and RV pressure-volume dynamics were recorded. Using the calibrated model, we simulate acute LV ischemia and contrast outputs at baseline and in simulated ischemia. Our baseline simulations align with the LV and RV data, and our predictions during ischemia complement recorded RV data and prior studies on LV function during myocardial infarction. We show that a model with both biventricular mechanical interaction and systems-level cardiovascular dynamics can quantitatively reproduce in-vivo data and qualitatively match prior findings from animal studies on LV ischemia.
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Affiliation(s)
- M J Colebank
- Edwards Lifesciences Foundation Cardiovascular Innovation and Research Center, and Department of Biomedical Engineering, University of California, Irvine, Irvine, CA, USA
| | - R Taylor
- Cardiovascular Research Center, University of Wisconsin-Madison, Madison, WI, USA
| | - T A Hacker
- Cardiovascular Research Center, University of Wisconsin-Madison, Madison, WI, USA
| | - N C Chesler
- Edwards Lifesciences Foundation Cardiovascular Innovation and Research Center, and Department of Biomedical Engineering, University of California, Irvine, Irvine, CA, USA.
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Kim SM, Randall EB, Jezek F, Beard DA, Chesler NC. Computational modeling of ventricular-ventricular interactions suggest a role in clinical conditions involving heart failure. Front Physiol 2023; 14:1231688. [PMID: 37745253 PMCID: PMC10512181 DOI: 10.3389/fphys.2023.1231688] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/30/2023] [Accepted: 08/09/2023] [Indexed: 09/26/2023] Open
Abstract
Introduction: The left (LV) and right (RV) ventricles are linked biologically, hemodynamically, and mechanically, a phenomenon known as ventricular interdependence. While LV function has long been known to impact RV function, the reverse is increasingly being realized to have clinical importance. Investigating ventricular interdependence clinically is challenging given the invasive measurements required, including biventricular catheterization, and confounding factors such as comorbidities, volume status, and other aspects of subject variability. Methods: Computational modeling allows investigation of mechanical and hemodynamic interactions in the absence of these confounding factors. Here, we use a threesegment biventricular heart model and simple circulatory system to investigate ventricular interdependence under conditions of systolic and diastolic dysfunction of the LV and RV in the presence of compensatory volume loading. We use the end-diastolic pressure-volume relationship, end-systolic pressure-volume relationship, Frank Starling curves, and cardiac power output as metrics. Results: The results demonstrate that LV systolic and diastolic dysfunction lead to RV compensation as indicated by increases in RV power. Additionally, RV systolic and diastolic dysfunction lead to impaired LV filling, interpretable as LV stiffening especially with volume loading to maintain systemic pressure. Discussion: These results suggest that a subset of patients with intact LV systolic function and diagnosed to have impaired LV diastolic function, categorized as heart failure with preserved ejection fraction (HFpEF), may in fact have primary RV failure. Application of this computational approach to clinical data sets, especially for HFpEF, may lead to improved diagnosis and treatment strategies and consequently improved outcomes.
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Affiliation(s)
- Salla M. Kim
- Department of Biomedical Engineering, Edwards Lifesciences Foundation Cardiovascular Innovation and Research Center, University of California Irvine, Irvine, CA, United States
| | - E. Benjamin Randall
- Department of Molecular and Integrative Physiology, University of Michigan, Ann Arbor, MI, United States
| | - Filip Jezek
- Department of Molecular and Integrative Physiology, University of Michigan, Ann Arbor, MI, United States
- Department of Pathological Physiology, First Faculty of Medicine, Charles University, Prague, Czechia
| | - Daniel A. Beard
- Department of Molecular and Integrative Physiology, University of Michigan, Ann Arbor, MI, United States
| | - Naomi C. Chesler
- Department of Biomedical Engineering, Edwards Lifesciences Foundation Cardiovascular Innovation and Research Center, University of California Irvine, Irvine, CA, United States
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Zhang D, Lindsey SE. Recasting Current Knowledge of Human Fetal Circulation: The Importance of Computational Models. J Cardiovasc Dev Dis 2023; 10:240. [PMID: 37367405 PMCID: PMC10299027 DOI: 10.3390/jcdd10060240] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/15/2023] [Revised: 05/16/2023] [Accepted: 05/23/2023] [Indexed: 06/28/2023] Open
Abstract
Computational hemodynamic simulations are becoming increasingly important for cardiovascular research and clinical practice, yet incorporating numerical simulations of human fetal circulation is relatively underutilized and underdeveloped. The fetus possesses unique vascular shunts to appropriately distribute oxygen and nutrients acquired from the placenta, adding complexity and adaptability to blood flow patterns within the fetal vascular network. Perturbations to fetal circulation compromise fetal growth and trigger the abnormal cardiovascular remodeling that underlies congenital heart defects. Computational modeling can be used to elucidate complex blood flow patterns in the fetal circulatory system for normal versus abnormal development. We present an overview of fetal cardiovascular physiology and its evolution from being investigated with invasive experiments and primitive imaging techniques to advanced imaging (4D MRI and ultrasound) and computational modeling. We introduce the theoretical backgrounds of both lumped-parameter networks and three-dimensional computational fluid dynamic simulations of the cardiovascular system. We subsequently summarize existing modeling studies of human fetal circulation along with their limitations and challenges. Finally, we highlight opportunities for improved fetal circulation models.
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Affiliation(s)
| | - Stephanie E. Lindsey
- Department of Mechanical and Aerospace Engineering, University of California, San Diego, CA 92093, USA;
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9
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Masud MA, Kim JY, Kim E. Effective dose window for containing tumor burden under tolerable level. NPJ Syst Biol Appl 2023; 9:17. [PMID: 37221258 DOI: 10.1038/s41540-023-00279-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/14/2022] [Accepted: 05/05/2023] [Indexed: 05/25/2023] Open
Abstract
A maximum-tolerated dose (MTD) reduces the drug-sensitive cell population, though it may result in the competitive release of drug resistance. Alternative treatment strategies such as adaptive therapy (AT) or dose modulation aim to impose competitive stress on drug-resistant cell populations by maintaining a sufficient number of drug-sensitive cells. However, given the heterogeneous treatment response and tolerable tumor burden level of individual patients, determining an effective dose that can fine-tune competitive stress remains challenging. This study presents a mathematical model-driven approach that determines the plausible existence of an effective dose window (EDW) as a range of doses that conserve sufficient sensitive cells while maintaining the tumor volume below a threshold tolerable tumor volume (TTV). We use a mathematical model that explains intratumor cell competition. Analyzing the model, we derive an EDW determined by TTV and the competitive strength. By applying a fixed endpoint optimal control model, we determine the minimal dose to contain cancer at a TTV. As a proof of concept, we study the existence of EDW for a small cohort of melanoma patients by fitting the model to longitudinal tumor response data. We performed identifiability analysis, and for the patients with uniquely identifiable parameters, we deduced patient-specific EDW and minimal dose. The tumor volume for a patient could be theoretically contained at the TTV either using continuous dose or AT strategy with doses belonging to EDW. Further, we conclude that the lower bound of the EDW approximates the minimum effective dose (MED) for containing tumor volume at the TTV.
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Affiliation(s)
- M A Masud
- Natural Product Informatics Research Center, Korea Institute of Science and Technology (KIST), Gangneung, 25451, Republic of Korea
| | - Jae-Young Kim
- Graduate School of Analytical Science and Technology (GRAST), Chungnam National University, Daejeon, 34134, Republic of Korea
| | - Eunjung Kim
- Natural Product Informatics Research Center, Korea Institute of Science and Technology (KIST), Gangneung, 25451, Republic of Korea.
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Bjørdalsbakke NL, Sturdy J, Ingeström EML, Hellevik LR. Monitoring variability in parameter estimates for lumped parameter models of the systemic circulation using longitudinal hemodynamic measurements. Biomed Eng Online 2023; 22:34. [PMID: 37055807 PMCID: PMC10099701 DOI: 10.1186/s12938-023-01086-y] [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: 08/16/2022] [Accepted: 02/23/2023] [Indexed: 04/15/2023] Open
Abstract
BACKGROUND Physics-based cardiovascular models are only recently being considered for disease diagnosis or prognosis in clinical settings. These models depend on parameters representing the physical and physiological properties of the modeled system. Personalizing these parameters may give insight into the specific state of the individual and etiology of disease. We applied a relatively fast model optimization scheme based on common local optimization methods to two model formulations of the left ventricle and systemic circulation. One closed-loop model and one open-loop model were applied. Intermittently collected hemodynamic data from an exercise motivation study were used to personalize these models for data from 25 participants. The hemodynamic data were collected for each participant at the start, middle and end of the trial. We constructed two data sets for the participants, both consisting of systolic and diastolic brachial pressure, stroke volume, and left-ventricular outflow tract velocity traces paired with either the finger arterial pressure waveform or the carotid pressure waveform. RESULTS We examined the feasibility of separating parameter estimates for the individual from population estimates by assessing the variability of estimates using the interquartile range. We found that the estimated parameter values were similar for the two model formulations, but that the systemic arterial compliance was significantly different ([Formula: see text]) depending on choice of pressure waveform. The estimates of systemic arterial compliance were on average higher when using the finger artery pressure waveform as compared to the carotid waveform. CONCLUSIONS We found that for the majority of participants, the variability of parameter estimates for a given participant on any measurement day was lower than the variability both across all measurement days combined for one participant, and for the population. This indicates that it is possible to identify individuals from the population, and that we can distinguish different measurement days for the individual participant by parameter values using the presented optimization method.
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Affiliation(s)
- Nikolai L Bjørdalsbakke
- Department of Structural Engineering, Norwegian University of Science and Technology (NTNU), Richard Birkelandsvei 1a, Trondheim, Norway.
| | - Jacob Sturdy
- Department of Structural Engineering, Norwegian University of Science and Technology (NTNU), Richard Birkelandsvei 1a, Trondheim, Norway
| | - Emma M L Ingeström
- Department of Circulation and Medical Imaging, Norwegian University of Science and Technology (NTNU), Prinsesse Kristinas gt. 3, Trondheim, Norway
| | - Leif R Hellevik
- Department of Structural Engineering, Norwegian University of Science and Technology (NTNU), Richard Birkelandsvei 1a, Trondheim, Norway
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11
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Colunga AL, Colebank MJ, Olufsen MS. Parameter inference in a computational model of haemodynamics in pulmonary hypertension. J R Soc Interface 2023; 20:20220735. [PMID: 36854380 PMCID: PMC9974303 DOI: 10.1098/rsif.2022.0735] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/08/2022] [Accepted: 01/31/2023] [Indexed: 03/02/2023] Open
Abstract
Pulmonary hypertension (PH), defined by a mean pulmonary arterial pressure (mPAP) greater than 20 mmHg, is characterized by increased pulmonary vascular resistance and decreased pulmonary arterial compliance. There are few measurable biomarkers of PH progression, but a conclusive diagnosis of the disease requires invasive right heart catheterization (RHC). Patient-specific cardiovascular systems-level computational models provide a potential non-invasive tool for determining additional indicators of disease severity. Using computational modelling, this study quantifies physiological parameters indicative of disease severity in nine PH patients. The model includes all four heart chambers, the pulmonary and systemic circulations. We consider two sets of calibration data: static (systolic and diastolic values) RHC data and a combination of static and continuous, time-series waveform data. We determine a subset of identifiable parameters for model calibration using sensitivity analyses and multi-start inference and perform posterior uncertainty quantification. Results show that additional waveform data enables accurate calibration of the right atrial reservoir and pump function across the PH cohort. Model outcomes, including stroke work and pulmonary resistance-compliance relations, reflect typical right heart dynamics in PH phenotypes. Lastly, we show that estimated parameters agree with previous, non-modelling studies, supporting this type of analysis in translational PH research.
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Affiliation(s)
- Amanda L. Colunga
- Department of Mathematics, North Carolina State University, Raleigh, NC, USA
| | - Mitchel J. Colebank
- Department of Mathematics, North Carolina State University, Raleigh, NC, USA
- University of California, Irvine—Edwards Lifesciences Foundation Cardiovascular Innovation and Research Center, and Department of Biomedical Engineering, University of California, Irvine, CA, USA
| | - REU Program
- Department of Mathematics, North Carolina State University, Raleigh, NC, USA
| | - Mette S. Olufsen
- Department of Mathematics, North Carolina State University, Raleigh, NC, USA
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12
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Colebank MJ, Taylor R, Hacker TA, Chesler N. Biventricular interaction during acute left ventricular ischemia in mice: a combined in-vivo and in-silico approach. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2023:2023.01.26.525736. [PMID: 36747704 PMCID: PMC9900958 DOI: 10.1101/2023.01.26.525736] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Indexed: 01/29/2023]
Abstract
Computational models provide an efficient paradigm for integrating and linking multiple spatial and temporal scales. However, these models are difficult to parameterize and match to experimental data. Recent advances in both data collection and model analyses have helped overcome this limitation. Here, we combine a multiscale, biventricular interaction model with mouse data before and after left ventricular (LV) ischemia. Sensitivity analyses are used to identify the most influential parameters on pressure and volume predictions. The subset of influential model parameters are calibrated to biventricular pressure-volume loop data (n=3) at baseline. Each mouse underwent left anterior descending coronary artery ligation, during which changes in fractional shortening and RV pressure-volume dynamics were recorded. Using the calibrated model, we simulate acute LV ischemia and contrast outputs at baseline and in simulated ischemia. Our baseline simulations align with the LV and RV data, and our predictions during ischemia complement recorded RV data and prior studies on LV function during myocardial infarction. We show that a model with both biventricular mechanical interaction and systems level cardiovascular dynamics can quantitatively reproduce in-vivo data and qualitatively match prior findings from animal studies on LV ischemia.
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Affiliation(s)
- M. J. Colebank
- Edwards Lifesciences Foundation Cardiovascular Innovation and Research Center, and Department of Biomedical Engineering, University of California, Irvine, Irvine, CA, USA
| | - R. Taylor
- Cardiovascular Research Center, University of Wisconsin-Madison, Madison, WI, USA
| | - T. A. Hacker
- Cardiovascular Research Center, University of Wisconsin-Madison, Madison, WI, USA
| | - N.C. Chesler
- Edwards Lifesciences Foundation Cardiovascular Innovation and Research Center, and Department of Biomedical Engineering, University of California, Irvine, Irvine, CA, USA
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13
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Sala L, Golse N, Joosten A, Vibert E, Vignon-Clementel I. Sensitivity Analysis of a Mathematical Model Simulating the Post-Hepatectomy Hemodynamics Response. Ann Biomed Eng 2023; 51:270-289. [PMID: 36326994 PMCID: PMC9832106 DOI: 10.1007/s10439-022-03098-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/13/2022] [Accepted: 09/30/2022] [Indexed: 11/06/2022]
Abstract
Recently a lumped-parameter model of the cardiovascular system was proposed to simulate the hemodynamics response to partial hepatectomy and evaluate the risk of portal hypertension (PHT) due to this surgery. Model parameters are tuned based on each patient data. This work focuses on a global sensitivity analysis (SA) study of such model to better understand the main drivers of the clinical outputs of interest. The analysis suggests which parameters should be considered patient-specific and which can be assumed constant without losing in accuracy in the predictions. While performing the SA, model outputs need to be constrained to physiological ranges. An innovative approach exploits the features of the polynomial chaos expansion method to reduce the overall computational cost. The computed results give new insights on how to improve the calibration of some model parameters. Moreover the final parameter distributions enable the creation of a virtual population available for future works. Although this work is focused on partial hepatectomy, the pipeline can be applied to other cardiovascular hemodynamics models to gain insights for patient-specific parameterization and to define a physiologically relevant virtual population.
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Affiliation(s)
- Lorenzo Sala
- Inria Saclay Ile-de-France, 91120 Palaiseau, France
| | - Nicolas Golse
- Université Paris-Saclay, Inserm Physiopathogénèse et traitement des maladie du foie, UMR-S 1193, 94800 Villejuif, France
| | - Alexandre Joosten
- Université Paris-Saclay, Inserm Physiopathogénèse et traitement des maladie du foie, UMR-S 1193, 94800 Villejuif, France
| | - Eric Vibert
- Université Paris-Saclay, Inserm Physiopathogénèse et traitement des maladie du foie, UMR-S 1193, 94800 Villejuif, France
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14
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Colebank MJ, Chesler NC. An in-silico analysis of experimental designs to study ventricular function: A focus on the right ventricle. PLoS Comput Biol 2022; 18:e1010017. [PMID: 36126091 PMCID: PMC9524687 DOI: 10.1371/journal.pcbi.1010017] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/14/2022] [Revised: 09/30/2022] [Accepted: 09/07/2022] [Indexed: 11/19/2022] Open
Abstract
In-vivo studies of pulmonary vascular disease and pulmonary hypertension (PH) have provided key insight into the progression of right ventricular (RV) dysfunction. Additional in-silico experiments using multiscale computational models have provided further details into biventricular mechanics and hemodynamic function in the presence of PH, yet few have assessed whether model parameters are practically identifiable prior to data collection. Moreover, none have used modeling to devise synergistic experimental designs. To address this knowledge gap, we conduct a practical identifiability analysis of a multiscale cardiovascular model across four simulated experimental designs. We determine a set of parameters using a combination of Morris screening and local sensitivity analysis, and test for practical identifiability using profile likelihood-based confidence intervals. We employ Markov chain Monte Carlo (MCMC) techniques to quantify parameter and model forecast uncertainty in the presence of noise corrupted data. Our results show that model calibration to only RV pressure suffers from practical identifiability issues and suffers from large forecast uncertainty in output space. In contrast, parameter and model forecast uncertainty is substantially reduced once additional left ventricular (LV) pressure and volume data is included. A comparison between single point systolic and diastolic LV data and continuous, time-dependent LV pressure-volume data reveals that at least some quantitative data from both ventricles should be included for future experimental studies.
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Affiliation(s)
- Mitchel J. Colebank
- University of California, Irvine–Edwards Lifesciences Foundation Cardiovascular Innovation and Research Center, and Department of Biomedical Engineering, University of California, Irvine, Irvine, California, United States of America
| | - Naomi C. Chesler
- University of California, Irvine–Edwards Lifesciences Foundation Cardiovascular Innovation and Research Center, and Department of Biomedical Engineering, University of California, Irvine, Irvine, California, United States of America
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15
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Geddes JR, Ottesen JT, Mehlsen J, Olufsen MS. Postural orthostatic tachycardia syndrome explained using a baroreflex response model. J R Soc Interface 2022; 19:20220220. [PMID: 36000360 PMCID: PMC9399868 DOI: 10.1098/rsif.2022.0220] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Patients with postural orthostatic tachycardia syndrome (POTS) experience an excessive increase in heart rate (HR) and low-frequency (∼0.1 Hz) blood pressure (BP) and HR oscillations upon head-up tilt (HUT). These responses are attributed to increased baroreflex (BR) responses modulating sympathetic and parasympathetic signalling. This study uses a closed-loop cardiovascular compartment model controlled by the BR to predict BP and HR dynamics in response to HUT. The cardiovascular model predicts these quantities in the left ventricle, upper and lower body arteries and veins. HUT is simulated by letting gravity shift blood volume (BV) from the upper to the lower body compartments, and the BR control is modelled using set-point functions modulating peripheral vascular resistance, compliance, and cardiac contractility in response to changes in mean carotid BP. We demonstrate that modulation of parameters characterizing BR sensitivity allows us to predict the persistent increase in HR and the low-frequency BP and HR oscillations observed in POTS patients. Moreover, by increasing BR sensitivity, inhibiting BR control of the lower body vasculature, and decreasing central BV, we demonstrate that it is possible to simulate patients with neuropathic and hyperadrenergic POTS.
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Affiliation(s)
- Justen R. Geddes
- Department of Mathematics, North Carolina State University, Raleigh, NC 27695, USA
| | - Johnny T. Ottesen
- Department of Science and Environment and Centre for Mathematical Modeling – Human Health and Disease, Roskilde University, Roskilde, Denmark
| | - Jesper Mehlsen
- Section for Surgical Pathophysiology, Rigshospitalet, Copenhagen, Denmark
| | - Mette S. Olufsen
- Department of Mathematics, North Carolina State University, Raleigh, NC 27695, USA
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16
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Lazarus A, Dalton D, Husmeier D, Gao H. Sensitivity analysis and inverse uncertainty quantification for the left ventricular passive mechanics. Biomech Model Mechanobiol 2022; 21:953-982. [PMID: 35377030 PMCID: PMC9132878 DOI: 10.1007/s10237-022-01571-8] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/27/2021] [Accepted: 02/28/2022] [Indexed: 01/08/2023]
Abstract
Personalized computational cardiac models are considered to be a unique and powerful tool in modern cardiology, integrating the knowledge of physiology, pathology and fundamental laws of mechanics in one framework. They have the potential to improve risk prediction in cardiac patients and assist in the development of new treatments. However, in order to use these models for clinical decision support, it is important that both the impact of model parameter perturbations on the predicted quantities of interest as well as the uncertainty of parameter estimation are properly quantified, where the first task is a priori in nature (meaning independent of any specific clinical data), while the second task is carried out a posteriori (meaning after specific clinical data have been obtained). The present study addresses these challenges for a widely used constitutive law of passive myocardium (the Holzapfel-Ogden model), using global sensitivity analysis (SA) to address the first challenge, and inverse-uncertainty quantification (I-UQ) for the second challenge. The SA is carried out on a range of different input parameters to a left ventricle (LV) model, making use of computationally efficient Gaussian process (GP) surrogate models in place of the numerical forward simulator. The results of the SA are then used to inform a low-order reparametrization of the constitutive law for passive myocardium under consideration. The quality of this parameterization in the context of an inverse problem having observed noisy experimental data is then quantified with an I-UQ study, which again makes use of GP surrogate models. The I-UQ is carried out in a Bayesian manner using Markov Chain Monte Carlo, which allows for full uncertainty quantification of the material parameter estimates. Our study reveals insights into the relation between SA and I-UQ, elucidates the dependence of parameter sensitivity and estimation uncertainty on external factors, like LV cavity pressure, and sheds new light on cardio-mechanic model formulation, with particular focus on the Holzapfel-Ogden myocardial model.
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Affiliation(s)
- Alan Lazarus
- School of Mathematics and Statistics, University of Glasgow, Glasgow, UK
| | - David Dalton
- School of Mathematics and Statistics, University of Glasgow, Glasgow, UK
| | - Dirk Husmeier
- School of Mathematics and Statistics, University of Glasgow, Glasgow, UK
| | - Hao Gao
- School of Mathematics and Statistics, University of Glasgow, Glasgow, UK
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17
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Noreen S, Ben-Tal A, Elstad M, Sweatman WL, Ramchandra R, Paton J. Mathematical modelling of atrial and ventricular pressure-volume dynamics and their change with heart rate. Math Biosci 2021; 344:108766. [PMID: 34919936 DOI: 10.1016/j.mbs.2021.108766] [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: 01/01/2021] [Revised: 10/22/2021] [Accepted: 12/07/2021] [Indexed: 11/30/2022]
Abstract
This paper presents mathematical models that can simulate the cardiovascular system of a healthy sheep under normal resting conditions in which the heart rate changes significantly. The models include several new modelling features that are introduced progressively. The contraction of the cardiac chambers is modelled using a time-dependent muscle force with constant elasticity instead of time dependent elasticity. A new hypothesis about the mechanical contraction of the atria generates realistic pressure volume (PV) loops. The inter-ventricular interaction is modelled as well. Additionally, hysteresis is incorporated in the aortic valve to produce an end-systolic reverse (negative) flow. Most of the model parameter values are based on previous literature data while time periods of delay, atrial and ventricular contraction are derived using experimental data from 14 sheep. We provide new relationships between contraction time and delay as a function of heart period. The effects of different aspects of our modelling on the mean cardiac output, stroke volume, ejection time, ejection fraction and PV loops are studied. Model outputs are compared with published experimental results where possible, and are within a wide range of physiological observations.
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Affiliation(s)
- Shumaila Noreen
- School of Natural and Computational Sciences, Massey University, New Zealand
| | - Alona Ben-Tal
- School of Natural and Computational Sciences, Massey University, New Zealand.
| | - Maja Elstad
- Institute of Basic Medical Sciences, University of Oslo, Norway
| | - Winston L Sweatman
- School of Natural and Computational Sciences, Massey University, New Zealand
| | | | - Julian Paton
- Department of Physiology, University of Auckland, New Zealand
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18
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Parameter estimation for closed-loop lumped parameter models of the systemic circulation using synthetic data. Math Biosci 2021; 343:108731. [PMID: 34758345 DOI: 10.1016/j.mbs.2021.108731] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/28/2021] [Revised: 09/07/2021] [Accepted: 10/08/2021] [Indexed: 12/19/2022]
Abstract
Physics-based models can be applied to describe mechanisms in both health and disease, which has the potential to accelerate the development of personalized medicine. The aim of this study was to investigate the feasibility of personalizing a model of systemic hemodynamics by estimating model parameters. We investigated the feasibility of estimating model parameters for a closed-loop lumped parameter model of the left heart and systemic circulation using the step-wise subset reduction method. This proceeded by first investigating the structural identifiability of the model parameters. Secondly we performed sensitivity analysis to determine which parameters were most influential on the most relevant model outputs. Finally, we constructed a sequence of progressively smaller subsets including parameters based on their ranking by model output influence. The model was then optimized to data for each set of parameters to evaluate how well the parameters could be estimated for each subset. The subsequent results allowed assessment of how different data sets, and noise affected the parameter estimates. In the noiseless case, all parameters could be calibrated to less than 10-3% error using time series data, while errors using clinical index data could reach over 100%. With 5% normally distributed noise the accuracy was limited to be within 10% error for the five most sensitive parameters, while the four least sensitive parameters were unreliably estimated for waveform data. The three least sensitive parameters were particularly challenging to estimate so these should be prioritised for measurement. Cost functions based on time series such as pressure waveforms, were found to give better parameter estimates than cost functions based on standard indices used in clinical assessment of the cardiovascular system, for example stroke volume (SV) and pulse pressure (PP). Averaged parameter estimate errors were reduced by several orders of magnitude by choosing waveforms for noiseless synthetic data. Also when measurement data were noisy, the parameter estimation procedure based on continuous waveforms was more accurate than that based on clinical indices. By application of the step-wise subset reduction method we demonstrated that by the addition of venous pressure to the cost function, or conversely fixing the systemic venous compliance parameter at an accurate value improved all parameter estimates, especially the diastolic filling parameters which have least influence on the aortic pressure.
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19
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Colebank MJ, Umar Qureshi M, Olufsen MS. Sensitivity analysis and uncertainty quantification of 1-D models of pulmonary hemodynamics in mice under control and hypertensive conditions. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2021; 37:e3242. [PMID: 31355521 DOI: 10.1002/cnm.3242] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/01/2019] [Revised: 07/01/2019] [Accepted: 07/14/2019] [Indexed: 06/10/2023]
Abstract
Pulmonary hypertension (PH), defined as an elevated mean blood pressure in the main pulmonary artery (MPA) at rest, is associated with vascular remodeling of both large and small arteries. PH has several sub-types that are all linked to high mortality rates. In this study, we use a one-dimensional (1-D) fluid dynamics model driven by in vivo measurements of MPA flow to understand how model parameters and network size influence MPA pressure predictions in the presence of PH. We compare model predictions with in vivo MPA pressure measurements from a control and a hypertensive mouse and analyze results in three networks of increasing complexity, extracted from micro-computed tomography (micro-CT) images. We introduce global scaling factors for boundary condition parameters and perform local and global sensitivity analysis to calculate parameter influence on model predictions of MPA pressure and correlation analysis to determine a subset of identifiable parameters. These are inferred using frequentist optimization and Bayesian inference via the Delayed Rejection Adaptive Metropolis (DRAM) algorithm. Frequentist and Bayesian uncertainty is computed for model parameters and MPA pressure predictions. Results show that MPA pressure predictions are most sensitive to distal vascular resistance and that parameter influence changes with increasing network complexity. Our outcomes suggest that PH leads to increased vascular stiffness and decreased peripheral compliance, congruent with clinical observations.
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Affiliation(s)
- Mitchel J Colebank
- Department of Mathematics, North Carolina State University, Raleigh, North Carolina
| | - M Umar Qureshi
- Department of Mathematics, North Carolina State University, Raleigh, North Carolina
| | - Mette S Olufsen
- Department of Mathematics, North Carolina State University, Raleigh, North Carolina
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20
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Parvinian B, Bighamian R, Scully CG, Hahn JO, Pathmanathan P. Credibility Assessment of a Subject-Specific Mathematical Model of Blood Volume Kinetics for Prediction of Physiological Response to Hemorrhagic Shock and Fluid Resuscitation. Front Physiol 2021; 12:705222. [PMID: 34603074 PMCID: PMC8481867 DOI: 10.3389/fphys.2021.705222] [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: 05/04/2021] [Accepted: 08/23/2021] [Indexed: 11/30/2022] Open
Abstract
Subject-specific mathematical models for prediction of physiological parameters such as blood volume, cardiac output, and blood pressure in response to hemorrhage have been developed. In silico studies using these models may provide an effective tool to generate pre-clinical safety evidence for medical devices and help reduce the size and scope of animal studies that are performed prior to initiation of human trials. To achieve such a goal, the credibility of the mathematical model must be established for the purpose of pre-clinical in silico testing. In this work, the credibility of a subject-specific mathematical model of blood volume kinetics intended to predict blood volume response to hemorrhage and fluid resuscitation during fluid therapy was evaluated. A workflow was used in which: (i) the foundational properties of the mathematical model such as structural identifiability were evaluated; (ii) practical identifiability was evaluated both pre- and post-calibration, with the pre-calibration results used to determine an optimal splitting of experimental data into calibration and validation datasets; (iii) uncertainty in model parameters and the experimental uncertainty were quantified for each subject; and (iv) the uncertainty was propagated through the blood volume kinetics model and its predictive capability was evaluated via validation tests. The mathematical model was found to be structurally identifiable. Pre-calibration identifiability analysis led to splitting the 180 min of time series data per subject into 50 and 130 min calibration and validation windows, respectively. The average root mean squared error of the mathematical model was 12.6% using the calibration window of (0 min, 50 min). Practical identifiability was established post-calibration after fixing one of the parameters to a nominal value. In the validation tests, 82 and 75% of the subject-specific mathematical models were able to correctly predict blood volume response when predictive capability was evaluated at 180 min and at the time when amount of infused fluid equals fluid loss.
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Affiliation(s)
- Bahram Parvinian
- Department of Mechanical Engineering, University of Maryland College Park, College Park, MD, United States
| | - Ramin Bighamian
- Office of Science and Engineering Laboratories, Food and Drug Administration, Silver Spring, MD, United States
| | - Christopher George Scully
- Office of Science and Engineering Laboratories, Food and Drug Administration, Silver Spring, MD, United States
| | - Jin-Oh Hahn
- Department of Mechanical Engineering, University of Maryland College Park, College Park, MD, United States
| | - Pras Pathmanathan
- Office of Science and Engineering Laboratories, Food and Drug Administration, Silver Spring, MD, United States
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21
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Domogo AA, Ottesen JT. Patient-specific parameter estimation: Coupling a heart model and experimental data. J Theor Biol 2021; 526:110791. [PMID: 34087267 DOI: 10.1016/j.jtbi.2021.110791] [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: 12/01/2020] [Revised: 05/01/2021] [Accepted: 05/28/2021] [Indexed: 10/21/2022]
Abstract
This study develops a hemodynamic model involving the atrium, ventricle, veins, and arteries that can be calibrated to experimental results. It is a Windkessel model that incorporates an unsteady Bernoulli effect in the blood flow to the atrium. The model is represented by ordinary differential equations in terms of blood volumes in the compartments as state variables and it demonstrates the use of conductance instead of resistance to capture the effect of a non-leaking heart valve. The experimental results are blood volume data from 20 young (half of which are women) and 20 elderly (half of which are women) subjects during rest, inotropic stress (dobutamine), and chronotropic stress (glycopyrrolate). The model is calibrated to conform with data and physiological findings in 4 different levels. First, an optimization routine is devised to find model parameter values that give good fit between the model volume curves and blood volume data in the atrium and ventricle. Patient-specific information are used to get initial parameter values as a starting point of the optimization. Also, model pressure curves must show realistic behavior. Second, parametric bootstrapping is performed to establish the reliability of the optimal parameters. Third, statistical tests comparing mean optimal parameter values from young vs elderly subjects and women vs men are examined to support and present age and sex related differences in heart functions. Lastly, statistical tests comparing mean optimal parameter values from resting condition vs pharmacological stress are studied to verify and quantify the effects of dobutamine and glycopyrrolate to the cardiovascular system.
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Affiliation(s)
- Andrei A Domogo
- University of the Philippines Baguio, Baguio City, Philippines; Roskilde University, Roskilde, Denmark.
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22
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Randall EB, Randolph NZ, Alexanderian A, Olufsen MS. Global sensitivity analysis informed model reduction and selection applied to a Valsalva maneuver model. J Theor Biol 2021; 526:110759. [PMID: 33984355 DOI: 10.1016/j.jtbi.2021.110759] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/26/2020] [Revised: 05/03/2021] [Accepted: 05/04/2021] [Indexed: 12/30/2022]
Abstract
In this study, we develop a methodology for model reduction and selection informed by global sensitivity analysis (GSA) methods. We apply these techniques to a control model that takes systolic blood pressure and thoracic tissue pressure data as inputs and predicts heart rate in response to the Valsalva maneuver (VM). The study compares four GSA methods based on Sobol' indices (SIs) quantifying the parameter influence on the difference between the model output and the heart rate data. The GSA methods include standard scalar SIs determining the average parameter influence over the time interval studied and three time-varying methods analyzing how parameter influence changes over time. The time-varying methods include a new technique, termed limited-memory SIs, predicting parameter influence using a moving window approach. Using the limited-memory SIs, we perform model reduction and selection to analyze the necessity of modeling both the aortic and carotid baroreceptor regions in response to the VM. We compare the original model to systematically reduced models including (i) the aortic and carotid regions, (ii) the aortic region only, and (iii) the carotid region only. Model selection is done quantitatively using the Akaike and Bayesian Information Criteria and qualitatively by comparing the neurological predictions. Results show that it is necessary to incorporate both the aortic and carotid regions to model the VM.
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Affiliation(s)
- E Benjamin Randall
- Department of Molecular and Integrative Physiology, University of Michigan, Ann Arbor, MI, United States; Department of Mathematics, North Carolina State University, Raleigh, NC, United States.
| | - Nicholas Z Randolph
- Department of Bioinformatics and Computational Biology, University of North Carolina at Chapel Hill, Chapel Hill, NC, United States; Department of Mathematics, North Carolina State University, Raleigh, NC, United States.
| | - Alen Alexanderian
- Department of Mathematics, North Carolina State University, Raleigh, NC, United States.
| | - Mette S Olufsen
- Department of Mathematics, North Carolina State University, Raleigh, NC, United States.
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23
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Prud'homme C, Sala L, Szopos M. Uncertainty propagation and sensitivity analysis: results from the Ocular Mathematical Virtual Simulator. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2021; 18:2010-2032. [PMID: 33892535 DOI: 10.3934/mbe.2021105] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
We propose an uncertainty propagation study and a sensitivity analysis with the Ocular Mathematical Virtual Simulator, a computational and mathematical model that predicts the hemodynamics and biomechanics within the human eye. In this contribution, we focus on the effect of intraocular pressure, retrolaminar tissue pressure and systemic blood pressure on the ocular posterior tissue vasculature. The combination of a physically-based model with experiments-based stochastic input allows us to gain a better understanding of the physiological system, accounting both for the driving mechanisms and the data variability.
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Affiliation(s)
| | - Lorenzo Sala
- Centre de recherche INRIA de Paris, Paris 75012, France
| | - Marcela Szopos
- MAP5 UMR CNRS 8145, Université de Paris, Paris 75006, France
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24
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Chambers MJ, Colebank MJ, Qureshi MU, Clipp R, Olufsen MS. Structural and hemodynamic properties of murine pulmonary arterial networks under hypoxia-induced pulmonary hypertension. Proc Inst Mech Eng H 2020; 234:1312-1329. [DOI: 10.1177/0954411920944110] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
Detection and monitoring of patients with pulmonary hypertension, defined as a mean blood pressure in the main pulmonary artery above 25 mmHg, requires a combination of imaging and hemodynamic measurements. This study demonstrates how to combine imaging data from microcomputed tomography images with hemodynamic pressure and flow waveforms from control and hypertensive mice. Specific attention is devoted to developing a tool that processes computed tomography images, generating subject-specific arterial networks in which one-dimensional fluid dynamics modeling is used to predict blood pressure and flow. Each arterial network is modeled as a directed graph representing vessels along the principal pathway to ensure perfusion of all lobes. The one-dimensional model couples these networks with structured tree boundary conditions representing the small arteries and arterioles. Fluid dynamics equations are solved in this network and compared to measurements of pressure in the main pulmonary artery. Analysis of microcomputed tomography images reveals that the branching ratio is the same in the control and hypertensive animals, but that the vessel length-to-radius ratio is significantly lower in the hypertensive animals. Fluid dynamics predictions show that in addition to changed network geometry, vessel stiffness is higher in the hypertensive animal models than in the control models.
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Affiliation(s)
- Megan J Chambers
- Department of Mathematics, North Carolina State University, Raleigh, NC, USA
| | - Mitchel J Colebank
- Department of Mathematics, North Carolina State University, Raleigh, NC, USA
| | - M Umar Qureshi
- Department of Mathematics, North Carolina State University, Raleigh, NC, USA
- Kitware, Inc., Carrboro, NC, USA
| | | | - Mette S Olufsen
- Department of Mathematics, North Carolina State University, Raleigh, NC, USA
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25
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Fleeter CM, Geraci G, Schiavazzi DE, Kahn AM, Marsden AL. Multilevel and multifidelity uncertainty quantification for cardiovascular hemodynamics. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2020; 365:113030. [PMID: 32336811 PMCID: PMC7182133 DOI: 10.1016/j.cma.2020.113030] [Citation(s) in RCA: 34] [Impact Index Per Article: 8.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
Standard approaches for uncertainty quantification in cardiovascular modeling pose challenges due to the large number of uncertain inputs and the significant computational cost of realistic three-dimensional simulations. We propose an efficient uncertainty quantification framework utilizing a multilevel multifidelity Monte Carlo (MLMF) estimator to improve the accuracy of hemodynamic quantities of interest while maintaining reasonable computational cost. This is achieved by leveraging three cardiovascular model fidelities, each with varying spatial resolution to rigorously quantify the variability in hemodynamic outputs. We employ two low-fidelity models (zero- and one-dimensional) to construct several different estimators. Our goal is to investigate and compare the efficiency of estimators built from combinations of these two low-fidelity model alternatives and our high-fidelity three-dimensional models. We demonstrate this framework on healthy and diseased models of aortic and coronary anatomy, including uncertainties in material property and boundary condition parameters. Our goal is to demonstrate that for this application it is possible to accelerate the convergence of the estimators by utilizing a MLMF paradigm. Therefore, we compare our approach to single fidelity Monte Carlo estimators and to a multilevel Monte Carlo approach based only on three-dimensional simulations, but leveraging multiple spatial resolutions. We demonstrate significant, on the order of 10 to 100 times, reduction in total computational cost with the MLMF estimators. We also examine the differing properties of the MLMF estimators in healthy versus diseased models, as well as global versus local quantities of interest. As expected, global quantities such as outlet pressure and flow show larger reductions than local quantities, such as those relating to wall shear stress, as the latter rely more heavily on the highest fidelity model evaluations. Similarly, healthy models show larger reductions than diseased models. In all cases, our workflow coupling Dakota's MLMF estimators with the SimVascular cardiovascular modeling framework makes uncertainty quantification feasible for constrained computational budgets.
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Affiliation(s)
- Casey M. Fleeter
- Institute for Computational and Mathematical Engineering, Stanford University, Stanford, CA, USA
| | - Gianluca Geraci
- Center for Computing Research, Sandia National Laboratories, Albuquerque, NM, USA
| | - Daniele E. Schiavazzi
- Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, IN, USA
| | - Andrew M. Kahn
- Department of Medicine, University of California San Diego, La Jolla, CA, USA
| | - Alison L. Marsden
- Institute for Computational and Mathematical Engineering, Stanford University, Stanford, CA, USA
- Departments of Pediatrics and Bioengineering, Stanford University, Stanford, CA, USA
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26
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Tivay A, Jin X, Lo AKY, Scully CG, Hahn JO. Practical Use of Regularization in Individualizing a Mathematical Model of Cardiovascular Hemodynamics Using Scarce Data. Front Physiol 2020; 11:452. [PMID: 32528303 PMCID: PMC7264422 DOI: 10.3389/fphys.2020.00452] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/03/2020] [Accepted: 04/09/2020] [Indexed: 12/16/2022] Open
Abstract
Individualizing physiological models to a patient can enable patient-specific monitoring and treatment in critical care environments. However, this task often presents a unique "practical identifiability" challenge due to the conflict between model complexity and data scarcity. Regularization provides an established framework to cope with this conflict by compensating for data scarcity with prior knowledge. However, regularization has not been widely pursued in individualizing physiological models to facilitate patient-specific critical care. Thus, the goal of this work is to garner potentially generalizable insight into the practical use of regularization in individualizing a complex physiological model using scarce data by investigating its effect in a clinically significant critical care case study of blood volume kinetics and cardiovascular hemodynamics in hemorrhage and circulatory resuscitation. We construct a population-average model as prior knowledge and individualize the physiological model via regularization to illustrate that regularization can be effective in individualizing a physiological model to learn salient individual-specific characteristics (resulting in the goodness of fit to individual-specific data) while restricting unnecessary deviations from the population-average model (achieving practical identifiability). We also illustrate that regularization yields parsimonious individualization of only sensitive parameters as well as adequate physiological plausibility and relevance in predicting internal physiological states.
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Affiliation(s)
- Ali Tivay
- Department of Mechanical Engineering, University of Maryland, College Park, College Park, MD, United States
| | - Xin Jin
- Department of Mechanical Engineering, University of Maryland, College Park, College Park, MD, United States
| | - Alex Kai-Yuan Lo
- Department of Mechanical Engineering, University of Maryland, College Park, College Park, MD, United States
| | - Christopher G Scully
- Office of Science and Engineering Laboratories, Center for Devices and Radiological Health, U.S. Food and Drug Administration, Silver Spring, MD, United States
| | - Jin-Oh Hahn
- Department of Mechanical Engineering, University of Maryland, College Park, College Park, MD, United States
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27
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Colunga AL, Kim KG, Woodall NP, Dardas TF, Gennari JH, Olufsen MS, Carlson BE. Deep phenotyping of cardiac function in heart transplant patients using cardiovascular system models. J Physiol 2020; 598:3203-3222. [PMID: 32372434 DOI: 10.1113/jp279393] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/09/2019] [Accepted: 05/01/2020] [Indexed: 01/10/2023] Open
Abstract
KEY POINTS Right heart catheterization data from clinical records of heart transplant patients are used to identify patient-specific models of the cardiovascular system. These patient-specific cardiovascular models represent a snapshot of cardiovascular function at a given post-transplant recovery time point. This approach is used to describe cardiac function in 10 heart transplant patients, five of which had multiple right heart catheterizations allowing an assessment of cardiac function over time. These patient-specific models are used to predict cardiovascular function in the form of right and left ventricular pressure-volume loops and ventricular power, an important metric in the clinical assessment of cardiac function. Outcomes for the longitudinally tracked patients show that our approach was able to identify the one patient from the group of five that exhibited post-transplant cardiovascular complications. ABSTRACT Heart transplant patients are followed with periodic right heart catheterizations (RHCs) to identify post-transplant complications and guide treatment. Post-transplant positive outcomes are associated with a steady reduction of right ventricular and pulmonary arterial pressures, toward normal levels of right-side pressure (about 20 mmHg) measured by RHC. This study shows that more information about patient progression is obtained by combining standard RHC measures with mechanistic computational cardiovascular system models. The purpose of this study is twofold: to understand how cardiovascular system models can be used to represent a patient's cardiovascular state, and to use these models to track post-transplant recovery and outcome. To obtain reliable parameter estimates comparable within and across datasets, we use sensitivity analysis, parameter subset selection, and optimization to determine patient-specific mechanistic parameters that can be reliably extracted from the RHC data. Patient-specific models are identified for 10 patients from their first post-transplant RHC, and longitudinal analysis is carried out for five patients. Results of the sensitivity analysis and subset selection show that we can reliably estimate seven non-measurable quantities; namely, ventricular diastolic relaxation, systemic resistance, pulmonary venous elastance, pulmonary resistance, pulmonary arterial elastance, pulmonary valve resistance and systemic arterial elastance. Changes in parameters and predicted cardiovascular function post-transplant are used to evaluate the cardiovascular state during recovery of five patients. Of these five patients, only one showed inconsistent trends during recovery in ventricular pressure-volume relationships and power output. At the four-year post-transplant time point this patient exhibited biventricular failure along with graft dysfunction while the remaining four exhibited no cardiovascular complications.
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Affiliation(s)
- Amanda L Colunga
- North Carolina State University, Raleigh, North Carolina, United States
| | - Karam G Kim
- University of Washington, Seattle, Washington, United States
| | - N Payton Woodall
- North Carolina State University, Raleigh, North Carolina, United States
| | - Todd F Dardas
- University of Washington, Seattle, Washington, United States
| | - John H Gennari
- University of Washington, Seattle, Washington, United States
| | - Mette S Olufsen
- North Carolina State University, Raleigh, North Carolina, United States
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28
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Cardiovascular models for personalised medicine: Where now and where next? Med Eng Phys 2020; 72:38-48. [PMID: 31554575 DOI: 10.1016/j.medengphy.2019.08.007] [Citation(s) in RCA: 30] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/05/2019] [Accepted: 08/23/2019] [Indexed: 12/14/2022]
Abstract
The aim of this position paper is to provide a brief overview of the current status of cardiovascular modelling and of the processes required and some of the challenges to be addressed to see wider exploitation in both personal health management and clinical practice. In most branches of engineering the concept of the digital twin, informed by extensive and continuous monitoring and coupled with robust data assimilation and simulation techniques, is gaining traction: the Gartner Group listed it as one of the top ten digital trends in 2018. The cardiovascular modelling community is starting to develop a much more systematic approach to the combination of physics, mathematics, control theory, artificial intelligence, machine learning, computer science and advanced engineering methodology, as well as working more closely with the clinical community to better understand and exploit physiological measurements, and indeed to develop jointly better measurement protocols informed by model-based understanding. Developments in physiological modelling, model personalisation, model outcome uncertainty, and the role of models in clinical decision support are addressed and 'where-next' steps and challenges discussed.
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29
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Larson K, Bowman C, Papadimitriou C, Koumoutsakos P, Matzavinos A. Detection of arterial wall abnormalities via Bayesian model selection. ROYAL SOCIETY OPEN SCIENCE 2019; 6:182229. [PMID: 31824680 PMCID: PMC6837237 DOI: 10.1098/rsos.182229] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 03/13/2019] [Accepted: 09/17/2019] [Indexed: 06/10/2023]
Abstract
Patient-specific modelling of haemodynamics in arterial networks has so far relied on parameter estimation for inexpensive or small-scale models. We describe here a Bayesian uncertainty quantification framework which makes two major advances: an efficient parallel implementation, allowing parameter estimation for more complex forward models, and a system for practical model selection, allowing evidence-based comparison between distinct physical models. We demonstrate the proposed methodology by generating simulated noisy flow velocity data from a branching arterial tree model in which a structural defect is introduced at an unknown location; our approach is shown to accurately locate the abnormality and estimate its physical properties even in the presence of significant observational and systemic error. As the method readily admits real data, it shows great potential in patient-specific parameter fitting for haemodynamical flow models.
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Affiliation(s)
- Karen Larson
- Division of Applied Mathematics, Brown University, Providence, RI 02912, USA
| | - Clark Bowman
- Department of Mathematics and Statistics, Hamilton College, Clinton, NY 13323, USA
| | - Costas Papadimitriou
- Department of Mechanical Engineering, University of Thessaly, 38334 Volos, Greece
| | - Petros Koumoutsakos
- Computational Science and Engineering Laboratory, ETH Zürich CH-8092, Switzerland
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30
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Williams ND, Brady R, Gilmore S, Gremaud P, Tran HT, Ottesen JT, Mehlsen J, Olufsen MS. Cardiovascular dynamics during head-up tilt assessed via pulsatile and non-pulsatile models. J Math Biol 2019; 79:987-1014. [PMID: 31152210 DOI: 10.1007/s00285-019-01386-9] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/11/2018] [Revised: 05/09/2019] [Indexed: 11/28/2022]
Abstract
This study develops non-pulsatile and pulsatile models for the prediction of blood flow and pressure during head-up tilt. This test is used to diagnose potential pathologies within the autonomic control system, which acts to keep the cardiovascular system at homeostasis. We show that mathematical modeling can be used to predict changes in cardiac contractility, vascular resistance, and arterial compliance, quantities that cannot be measured but are useful to assess the system's state. These quantities are predicted as time-varying parameters modeled using piecewise linear splines. Having models with various levels of complexity formulated with a common set of parameters, allows us to combine long-term non-pulsatile simulations with pulsatile simulations on a shorter time-scale. We illustrate results for a representative subject tilted head-up from a supine position to a [Formula: see text] angle. The tilt is maintained for 5 min before the subject is tilted back down. Results show that if volume data is available for all vascular compartments three parameters can be identified, cardiovascular resistance, vascular compliance, and ventricular contractility, whereas if model predictions are made against arterial pressure and cardiac output data alone, only two parameters can be estimated either resistance and contractility or resistance and compliance.
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Affiliation(s)
- Nakeya D Williams
- Mathematical Sciences Department, United States Military Academy, West Point, NY, USA
| | - Renee Brady
- Department of Integrated Mathematical Oncology, H Lee Moffitt Cancer Center and Research Institute, Tampa, FL, USA
| | - Steven Gilmore
- Department of Mathematics, NC State University, Raleigh, NC, USA
| | - Pierre Gremaud
- Department of Mathematics, NC State University, Raleigh, NC, USA
| | - Hien T Tran
- Department of Mathematics, NC State University, Raleigh, NC, USA
| | - Johnny T Ottesen
- Department of Science and Environment, Roskilde University, Roskilde, Denmark
| | - Jesper Mehlsen
- Surgical Pathophysiology Unit, Rigshospitalet, Copenhagen, Denmark
| | - Mette S Olufsen
- Department of Mathematics, NC State University, Raleigh, NC, USA.
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31
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Ciocanel MV, Docken SS, Gasper RE, Dean C, Carlson BE, Olufsen MS. Cardiovascular regulation in response to multiple hemorrhages: analysis and parameter estimation. BIOLOGICAL CYBERNETICS 2019; 113:105-120. [PMID: 30209563 PMCID: PMC6414294 DOI: 10.1007/s00422-018-0781-y] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/05/2018] [Accepted: 09/02/2018] [Indexed: 05/22/2023]
Abstract
Mathematical models can provide useful insights explaining behavior observed in experimental data; however, rigorous analysis is needed to select a subset of model parameters that can be informed by available data. Here we present a method to estimate an identifiable set of parameters based on baseline left ventricular pressure and volume time series data. From this identifiable subset, we then select, based on current understanding of cardiovascular control, parameters that vary in time in response to blood withdrawal, and estimate these parameters over a series of blood withdrawals. These time-varying parameters are first estimated using piecewise linear splines minimizing the mean squared error between measured and computed left ventricular pressure and volume data over four consecutive blood withdrawals. As a final step, the trends in these splines are fit with empirical functional expressions selected to describe cardiovascular regulation during blood withdrawal. Our analysis at baseline found parameters representing timing of cardiac contraction, systemic vascular resistance, and cardiac contractility to be identifiable. Of these parameters, vascular resistance and cardiac contractility were varied in time. Data used for this study were measured in a control Sprague-Dawley rat. To our knowledge, this is the first study to analyze the response to multiple blood withdrawals both experimentally and theoretically, as most previous studies focus on analyzing the response to one large blood withdrawal. Results show that during each blood withdrawal both systemic vascular resistance and contractility decrease acutely and partially recover, and they decrease chronically across the series of blood withdrawals.
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Affiliation(s)
| | | | | | - Caron Dean
- Medical College of Wisconsin, Milwaukee, USA
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32
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Tran JS, Schiavazzi DE, Kahn AM, Marsden AL. Uncertainty quantification of simulated biomechanical stimuli in coronary artery bypass grafts. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2019; 345:402-428. [PMID: 31223175 PMCID: PMC6586227 DOI: 10.1016/j.cma.2018.10.024] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/25/2023]
Abstract
Coronary artery bypass graft surgery (CABG) is performed on more than 400,000 patients annually in the U.S. However, saphenous vein grafts (SVGs) implanted during CABG exhibit poor patency compared to arterial grafts, with failure rates up to 40% within 10 years after surgery. Differences in mechanical stimuli are known to play a role in driving maladaptation and have been correlated with endothelial damage and thrombus formation. As these quantities are difficult to measure in vivo, multi-scale coronary models offer a way to quantify them, while accounting for complex coronary physiology. However, prior studies have primarily focused on deterministic evaluations, without reporting variability in the model parameters due to uncertainty. This study aims to assess confidence in multi-scale predictions of wall shear stress and wall strain while accounting for uncertainty in peripheral hemodynamics and material properties. Boundary condition distributions are computed by assimilating uncertain clinical data, while spatial variations of vessel wall stiffness are obtained through approximation by a random field. We developed a stochastic submodeling approach to mitigate the computational burden of repeated multi-scale model evaluations to focus exclusively on the bypass grafts. This produces a two-level decomposition of quantities of interest into submodel contributions and full model/submodel discrepancies. We leverage these two levels in the context of forward uncertainty propagation using a previously proposed multi-resolution approach. The time- and space-averaged wall shear stress is well estimated with a coefficient of variation of <35%, but ignorance about the spatial distribution on the wall elastic modulus and thickness lead to large variations in an objective measure of wall strain, with coefficients of variation up to 100%. Sensitivity analysis reveals how the interactions between the flow and material parameters contribute to output variability.
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Affiliation(s)
- Justin S Tran
- Department of Mechanical Engineering, Stanford University, Stanford, CA, USA
| | | | - Andrew M Kahn
- Department of Medicine, University of California San Diego, La Jolla, CA, USA
| | - Alison L Marsden
- Department of Pediatrics (Cardiology), Bioengineering and ICME, Stanford University, Stanford, CA, USA
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