Colebank, Mitchel J

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VCU Scholars Compass

Virginia Commonwealth UniversityVCU Scholars CompassBiology and Medicine Through MathematicsConference 2017May 18th, 12:00 PM - 12:30 PMUncertainty of 1-D Fluid Models in Patients withPulmonary HypertensionMitchel J. ColebankNorth Carolina State University, mjcoleba@ncsu.eduFollow this and additional works at: http://scholarscompass.vcu.edu/bammPart of the Cardiovascular Diseases Commons, Life Sciences Commons, MedicalBiomathematics and Biometrics Commons, and the Physical Sciences and Mathematics CommonsThis Event is brought to you for free and open access by the Dept. of Mathematics and Applied Mathematics at VCU Scholars Compass. It has beenaccepted for inclusion in Biology and Medicine Through Mathematics Conference by an authorized administrator of VCU Scholars Compass. Formore information, please contact libcompass@vcu.edu.http://scholarscompass.vcu.edu/bamm/2017/thursday/3 Pulmonary Arterial Hypertension (PAH) is defined as abnormally high mean blood pressure (> 25mmHg) in the proximal pulmonary artery. This is coupled with remodeling of arterial walls, involving changes in arterial wall cellular composition, and the distal vascular network, such as microvascular rarefaction. A lumped effect of vascular remodeling can be characterized as an increase in arterial stiffness and the total pulmonary vascular resistance (>3 HRU). This leads to changes in the mean and pulsatile components of the arterial blood pressure, which in turn determine the right ventricular afterload. Our current work is based on a 1-D fluid dynamical network model that uses either Windkessel or structure tree models to represent the vascular beds. We also believe that arterial viscoelastic behavior can be accurately identified, though currently we have assumed a linear elastic model.  The model is capable of simulating the physiological pressure and flow, which can be validated using real patient data, available from our clinical collaborators at Golden Jubilee National Hospital, Glasgow. However, the clinical data are subject to inaccuracies in measurements due to invasive and non-invasive techniques, e.g. catheterization, MRI, and CT scans. This leads to uncertainties in pressure and flow recordings, and the geometric measurements of large vessels. Since both construction of the model and its validation are based on real data, the measurement errors which propagate throughout the model may lead to an augmented effect on the model output. This makes the process of validation a challenging task, which can only be dealt by quantifying the uncertainty in model simulations in a systematic way involving methods of error propagation. Thus, the focus of this work is prediction as well as uncertainty quantification of physiological parameters that have strong influence on blood pressure, flow, and vessel cross-sectional area in the pulmonary vasculature. This will be done by extending common physiological and mathematical relationships, such as Poiseuille’s, Murray’s, and Stoke’s law, to obtain nominal parameter values corresponding to error bounds around measurements of fundamental quantities, such as vascular dimensions and pulse pressure. Since these mathematical relationships explicitly depend on these fundamental quantities, their values can become highly variable if appropriate bounds are not set on measurement errors. This approach would allow us to determine the sensitivity of simulated blood pressure and flow in the main pulmonary artery to the inaccuracies in the geometric and hemodynamic data. Finally, this will also increase our understanding of the processes involved in cardiovascular modeling when there is a relatively high error propagation.     

Uncertainty of 1-D Fluid Models in Patients with Pulmonary Hypertension

Virginia Commonwealth University
VCU Scholars Compass
Biology and Medicine Through Mathematics
Conference 2017
May 18th, 12:00 PM - 12:30 PM
Uncertainty of 1-D Fluid Models in Patients with
Pulmonary Hypertension
Mitchel J. Colebank
North Carolina State University, mjcoleba@ncsu.edu
Follow this and additional works at: http://scholarscompass.vcu.edu/bamm
Part of the Cardiovascular Diseases Commons, Life Sciences Commons, Medical
Biomathematics and Biometrics Commons, and the Physical Sciences and Mathematics Commons
This Event is brought to you for free and open access by the Dept. of Mathematics and Applied Mathematics at VCU Scholars Compass. It has been
accepted for inclusion in Biology and Medicine Through Mathematics Conference by an authorized administrator of VCU Scholars Compass. For
more information, please contact libcompass@vcu.edu.
http://scholarscompass.vcu.edu/bamm/2017/thursday/3
 Pulmonary Arterial Hypertension (PAH) is defined as abnormally high mean blood 
pressure (> 25mmHg) in the proximal pulmonary artery. This is coupled with remodeling 
of arterial walls, involving changes in arterial wall cellular composition, and the distal 
vascular network, such as microvascular rarefaction. A lumped effect of vascular 
remodeling can be characterized as an increase in arterial stiffness and the total pulmonary 
vascular resistance (>3 HRU). This leads to changes in the mean and pulsatile components 
of the arterial blood pressure, which in turn determine the right ventricular afterload. 
Our current work is based on a 1-D fluid dynamical network model that uses either 
Windkessel or structure tree models to represent the vascular beds. We also believe that 
arterial viscoelastic behavior can be accurately identified, though currently we have 
assumed a linear elastic model.  The model is capable of simulating the physiological 
pressure and flow, which can be validated using real patient data, available from our 
clinical collaborators at Golden Jubilee National Hospital, Glasgow. However, the clinical 
data are subject to inaccuracies in measurements due to invasive and non-invasive 
techniques, e.g. catheterization, MRI, and CT scans. This leads to uncertainties in pressure 
and flow recordings, and the geometric measurements of large vessels. Since both 
construction of the model and its validation are based on real data, the measurement 
errors which propagate throughout the model may lead to an augmented effect on the 
model output. This makes the process of validation a challenging task, which can only be 
dealt by quantifying the uncertainty in model simulations in a systematic way involving 
methods of error propagation. Thus, the focus of this work is prediction as well as 
uncertainty quantification of physiological parameters that have strong influence on blood 
pressure, flow, and vessel cross-sectional area in the pulmonary vasculature. This will be 
done by extending common physiological and mathematical relationships, such as 
Poiseuille’s, Murray’s, and Stoke’s law, to obtain nominal parameter values corresponding 
to error bounds around measurements of fundamental quantities, such as vascular 
dimensions and pulse pressure. Since these mathematical relationships explicitly depend 
on these fundamental quantities, their values can become highly variable if appropriate 
bounds are not set on measurement errors. This approach would allow us to determine the 
sensitivity of simulated blood pressure and flow in the main pulmonary artery to the 
inaccuracies in the geometric and hemodynamic data. Finally, this will also increase our 
understanding of the processes involved in cardiovascular modeling when there is a 
relatively high error propagation. 
 
 
 
 


https://scholarscompass.vcu.edu/cgi/viewcontent.cgi?article=1147&amp;context=bamm

Uncertainty of 1-D Fluid Models in Patients with Pulmonary Hypertension

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