Use of vascular adaptation in response to mechanical loading facilitates personalisation of a one-dimensional pulse wave propagation model

Abstract

BackgroundMathematical modelling of pressure and flow waveforms in blood vessels using pulse wave propagation (PWP) models could support clinical decision-making. For a personalised model outcome, measurements of all modelled vessel radii and wall thicknesses are required. In clinical practice, however, datasets are often incomplete. To overcome this problem, we hypothesised that the adaptive capacity of blood vessels in response to mechanical load can be utilised to fill in the gaps of incomplete patient-specific datasets.MethodsWe implemented homeostatic feedback loops in a validated PWP model [1] to allow adaptation of vessel geometry to maintain wall stress and wall shear stress. To evaluate our approach, we utilised complete datasets of 10 patients scheduled for vascular access surgery. Datasets comprised of wall thicknesses and radii of 7 central and 11 arm arterial segments. We simulated reference models (RefModel, n = 10) using complete data and adapted models (AdaptModel, n = 10) using data of one brachial artery segment only. The remaining AdaptModel geometries were estimated using adaptation. In both models, mean brachial pressure, brachial artery distensibility, heart rate and aortic inflow were prescribed. We evaluated agreement between RefModel and AdaptModel geometries, as well as between pressure and flow waveforms of both models.ResultsLimits of agreement (bias ± 1.96SD) between AdaptModel and RefModel radii and wall thicknesses were 0.029 ± 1.3mm and 28 ± 230µm, respectively. AdaptModel pressure and flow waveform characteristics across the proximal-to-distal arterial domain were within the uncertainty bounds of the RefModel (Fig. 1).Figure 1AdaptModel and RefModel pressure and flow waveforms at three arterial locations. For adequate comparison between the AdaptModel and the RefModel a total of 100 RefModel realisations were generated within the measurement uncertainty. The median RefModel is indicated by the blue dotted curves.ConclusionsOur adaptation-based PWP model enables personalisation even when not all required data is available.