Calibration of parameters for cardiovascular models with application to arterial growth

Abstract

We present a computational framework for the calibration of parameters describing cardiovascular models with a focus on the application of growth of abdominal aortic aneurysms (AAA). The growth rate in this sort of pathology is considered a critical parameter in the risk management and is an essential indicator for the assessment of surveillance intervals. Parameters describing growth of AAAs are not measurable directly and need to be estimated from available data often given by medical imaging technologies. Registration procedures often applied in standard workflows of parameter identification to extract the image encoded information are a source of significant systematic error. The concept of surface currents provides means to effectively avoid this source of errors by establishing a mathematical framework to compare surface information, directly accessible from image data. By utilizing this concept it is possible to inversely estimate growth parameters using sophisticated numerical models of AAAs from measurements available as surface information. In this work we present a framework to obtain spatial distributions of parameters governing growth of arterial tissue, and we show how the use of surface currents can significantly improve the results. We further present the application to patient specific follow-up data resulting in a spatial map of volumetric growth rates enabling, for the first time, prediction of further AAA expansion.

Biomechanical rupture risk assessment of abdominal aortic aneurysms using clinical data: A patient-specific, probabilistic framework and comparative case-control study

“…Future work will also address how further model parameters such as the blood pressure influence the rupture risk index and whether this quantity should be treated probabilistically as well. Lastly, to be able to make predictions over time, it is required to incorporate AAA growth [ 46 , 47 ] into the framework and analyze its effect on the biomechanical rupture risk assessment.…”

Bayesian calibration of coupled computational mechanics models under uncertainty based on interface deformation

“…For the kernel we choose the radial basis function (RBF) in (10b) which takes the location vectors, respectively the function values f (s) as arguments and returns their correlation. The expression is also known under the term surface currents [23] and was already successfully applied for inverse analysis in [6,24]…”

“…In that case only information about the shape of a boundary or interface is reliably accessible, without further details on correspondence of material points in simulation and experimental data. For such scenarios that have been studied before [4] for, e.g., cardiac mechanics [5] or arterial growth [6], we want to investigate and discuss the effect of different definitions for discrepancy measures between simulated and observed interface deformations of objects. Especially regarding bio-materials the main interest is to determine material properties as they act in-situ, i.e., in the natural environment.…”

Inverse analysis of material parameters in coupled multi-physics biofilm models

“…Overall the presented measurement method is considered rather hands-on, as the observed interface location must only be determined for the measurement points. For our type of problems, this is also a clear advantage compared to the usage of global surface comparisons as for example the ones presented in [29] and [30]. For global approaches for surface comparison a full representation of the surface must be available and therefore must be constructed from the data.…”

“…In that case no parameter result can be found. The algorithm is terminated if a certain convergence criterion is met or if a maximum number of iterations is n max reached grad > err k grad (29) res > err k res (30) k > n max .…”