Embodiments include a system for determining cardiovascular information for a patient. The system may include at least one computer system configured to receive patient-specific data regarding a geometry of the patient's heart, and create a three-dimensional model representing at least a portion of the patient's heart based on the patient-specific data. The at least one computer system may be further configured to create a physics-based model relating to a blood flow characteristic of the patient's heart and determine a fractional flow reserve within the patient's heart based on the three-dimensional model and the physics-based model.

Method and system for patient-specific modeling of blood flow

A modular numerical method for implicit 0D/3D coupling in cardiovascular finite element simulations

Aortic dissection is a disease whereby an injury in the wall of the aorta leads to the creation of a true lumen and a false lumen separated by an intimal flap which may contain multiple communicating tears between the lumina. It has a high associated morbidity and mortality, but at present, the timing of surgical intervention for stable type B dissections remains an area of debate. Detailed knowledge of haemodynamics may yield greater insight into the long-term outcomes for dissection patients by providing a greater understanding of pressures, wall shear stress and velocities in and around the dissection. In this paper, we aim to gather further insight into the complex haemodynamics in aortic dissection using medical imaging and computational fluid dynamics modelling. Towards this end, several computer models of the aorta of a patient presenting with an acute Stanford type B dissection were created whereby morphometric parameters related to the dissection septum were altered, such as removal of the septum, and the variation of the number of connecting tears between the lumina. Patient-specific flow data acquired using 2D PC-MRI in the ascending aorta were used to set the inflow boundary condition. Coupled zero-dimensional (Windkessel) models representing the distal vasculature were used to define the outlet boundary conditions and tuned to match 2D PC-MRI flow data acquired in the descending aorta. Haemodynamics in the dissected aorta were compared to those in an equivalent 'healthy aorta', created by virtually removing the intimal flap (septum). Local regions of increased velocity, pressure, wall shear stress and alterations in flow distribution were noted, particularly in the narrow true lumen and around the primary entry tear. The computed flow patterns compared favourably with those obtained using 4D PC-MRI. A lumped-parameter heart model was subsequently used to show that in this case there was an estimated 14 % increase in left ventricular stroke work with the onset of dissection. Finally, the effect of secondary connecting tears (i.e. those excluding the primary entry and exit tears) was also studied, revealing significant haemodynamic changes when no secondary tears are included in the model, particularly in the true lumen where increases in flow over [Formula: see text] and drops in peak pressure of 18 % were observed.

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Multi-modality image-based computational analysis of haemodynamics in aortic dissection

Mathematical models have long been used for prediction of dynamics in biological systems. Recently, several efforts have been made to render these models patient specific. One way to do so is to employ techniques to estimate parameters that enable model based prediction of observed quantities. Knowledge of variation in parameters within and between groups of subjects have potential to provide insight into biological function. Often it is not possible to estimate all parameters in a given model, in particular if the model is complex and the data is sparse. However, it may be possible to estimate a subset of model parameters reducing the complexity of the problem. In this study, we compare three methods that allow identification of parameter subsets that can be estimated given a model and a set of data. These methods will be used to estimate patient specific parameters in a model predicting baroreceptor feedback regulation of heart rate during head-up tilt. The three methods include: structured analysis of the correlation matrix, analysis via singular value decomposition followed by QR factorization, and identification of the subspace closest to the one spanned by eigenvectors of the model Hessian. Results showed that all three methods facilitate identification of a parameter subset. The “best” subset was obtained using the structured correlation method, though this method was also the most computationally intensive. Subsets obtained using the other two methods were easier to compute, but analysis revealed that the final subsets contained correlated parameters. In conclusion, to avoid lengthy computations, these three methods may be combined for efficient identification of parameter subsets.

A practical approach to parameter estimation applied to model predicting heart rate regulation

In recent years, considerable progress has been made in creating more realistic models of the cardiovascular system, often based on patient-specific anatomic data, whereas comparatively little progress has been made on incorporating measured physiological data. We have developed a method to systematically adjust the parameters of three-element windkessel outlet boundary conditions of three-dimensional blood flow models such that desired features of pressure and flow waveforms are achieved. This tuning method was formulated as the solution of a nonlinear system of equations and employed a quasi-Newton method that was informed by a reduced-order model. The three-dimensional hemodynamic models were solved using a stabilized finite-element method incorporating deformable vessel walls. The tuning method was applied to an idealized common carotid artery, an idealized iliac arterial bifurcation, and a patient-specific abdominal aorta. The objectives for the abdominal aortic model were values of the maximum and minimum of the pressure waveform, an indicator of the pressure waveform’s shape, and the mean, amplitude, and diastolic mean of the flow waveform for an infrarenal measurement plane. The hemodynamic models were automatically generated and tuned by custom software with minimal user input. This approach enables efficient development of cardiovascular models for applications including detailed evaluation of cardiovascular mechanics, simulation-based design of medical devices, and patient-specific treatment planning.

Tuning Multidomain Hemodynamic Simulations to Match Physiological Measurements

The complexity of mathematical models describing the cardiovascular system has grown in recent years to more accurately account for physiological dynamics. To aid in model validation and design, classical deterministic sensitivity analysis is performed on the cardiovascular model first presented by Olufsen, Tran, Ottesen, Ellwein, Lipsitz and Novak (J Appl Physiol 99(4):1523–1537, 2005). This model uses 11 differential state equations with 52 parameters to predict arterial blood flow and blood pressure. The relative sensitivity solutions of the model state equations with respect to each of the parameters is calculated and a sensitivity ranking is created for each parameter. Parameters are separated into two groups: sensitive and insensitive parameters. Small changes in sensitive parameters have a large effect on the model solution while changes in insensitive parameters have a negligible effect. This analysis was successfully used to reduce the effective parameter space by more than half and the computation time by two thirds. Additionally, a simpler model was designed that retained the necessary features of the original model but with two-thirds of the state equations and half of the model parameters.

Sensitivity analysis and model assessment: mathematical models for arterial blood flow and blood pressure.

This study shows how sensitivity analysis and subset selection can be employed
in a cardiovascular model to estimate total systemic resistance,
cerebrovascular resistance, arterial compliance, and time for peak systolic
ventricular pressure for healthy young and elderly subjects. These quantities
are parameters in a simple lumped parameter model that predicts pressure and
flow in the systemic circulation. The model is combined with experimental
measurements of blood flow velocity from the middle cerebral artery and
arterial finger blood pressure. To estimate the model parameters we use
nonlinear optimization combined with sensitivity analysis and subset selection.
Sensitivity analysis allows us to rank model parameters from the most to the
least sensitive with respect to the output states (cerebral blood flow
velocity and arterial blood pressure). Subset selection allows us to identify
a set of independent candidate parameters that can be estimated given limited
data. Analyses of output from both methods allow us to identify five
independent sensitive parameters that can be estimated given the data.
Results show that with the advance of age total systemic and cerebral
resistances increase, that time for peak systolic ventricular pressure is
increases, and that arterial compliance is reduced. Thus, the method discussed
in this study provides a new methodology to extract clinical markers that
cannot easily be assessed noninvasively.

https://www.aimsciences.org/article/exportPdf?id=16a59610-620c-4441-bb24-a161245ffbc5

Cheryl L. Zapata

Papers

Sensitivity analysis and model assessment: mathematical models for arterial blood flow and blood pressure.

Estimation and identification of parameters in a lumped cerebrovascular model.