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. 2015 Apr;14(2):217-29.
doi: 10.1007/s10237-014-0598-0. Epub 2014 Jun 3.

A computational model that predicts reverse growth in response to mechanical unloading

L C Lee  1 , M Genet, G Acevedo-Bolton, K Ordovas, J M Guccione, E Kuhl
Affiliations

A computational model that predicts reverse growth in response to mechanical unloading

L C Lee et al. Biomech Model Mechanobiol. 2015 Apr.

Abstract

Ventricular growth is widely considered to be an important feature in the adverse progression of heart diseases, whereas reverse ventricular growth (or reverse remodeling) is often considered to be a favorable response to clinical intervention. In recent years, a number of theoretical models have been proposed to model the process of ventricular growth while little has been done to model its reverse. Based on the framework of volumetric strain-driven finite growth with a homeostatic equilibrium range for the elastic myofiber stretch, we propose here a reversible growth model capable of describing both ventricular growth and its reversal. We used this model to construct a semi-analytical solution based on an idealized cylindrical tube model, as well as numerical solutions based on a truncated ellipsoidal model and a human left ventricular model that was reconstructed from magnetic resonance images. We show that our model is able to predict key features in the end-diastolic pressure-volume relationship that were observed experimentally and clinically during ventricular growth and reverse growth. We also show that the residual stress fields generated as a result of differential growth in the cylindrical tube model are similar to those in other nonidentical models utilizing the same geometry.

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Figures

Fig. 1
Fig. 1. Inflation of cylindrical tube. The base vectors ez and eZ point out of the page
Fig. 2
Fig. 2. Prescribed cyclical hemodynamics load pi of the cylindrical tube model
Fig. 3
Fig. 3
Construction of the HUMAN finite element model: (a) segmentation of the MRI, (b) reconstruction the endocardial (red) and epicardial (green), (c) construction of the finite element mesh and (d) assignment of rule-based myofiber orientation—streamlines follow fiber direction and are color coded with fiber helix angle
Fig. 4
Fig. 4
Cyclical loading in the ELLISPOID and HUMAN models consisting of five high pressure cycles and five low pressure cycles. Every growth step lasts one characteristic time of the growth model
Fig. 5
Fig. 5
Growth multiplier θ at the inner and outer surfaces as a function of the cycle number. Cross section of the unloaded cylindrical tube are shown in the inset at cycles 0, 200 and 400. Color denotes growth multiplier θ in cycles 200 and 400
Fig. 6
Fig. 6
Internal pressure pi versus inner radius ri at every 10th cycle in (a): cycles 1–200 during growth (inset: unloaded cylindrical cross section at cycles 1, 20, 200) and (b) cycles 200–400 during reverse growth (inset: unloaded cylindrical cross section at cycles 200, 220, 400). Dotted line: pi versus ri at first cycle
Fig. 7
Fig. 7
Residual normal stresses in the circumferential (σϕϕ), radial (σrr) and longitudinal (σzz) directions versus referential radial position R at the beginning of (a) cycle 201 and (b) cycle 400 with pi = 0
Fig. 8
Fig. 8
Evolution of the pressure–volume relationship of the HUMAN model during (a) growth and (b) reverse growth. The first and last cycle of the pressure–volume relationship in (a) is also shown in (b) as solid and dotted lines, respectively. Refer to text for definition of P̄−, P̄ and P̄+
Fig. 9
Fig. 9
Evolution of the unloaded geometry and growth multiplier θ field of the ELLIPSOID (top) and HUMAN (bottom) models as a result of growth and reverse growth. Geometries are of the same scale in each model. Black and red line in (a) correspond to the geometry outline of (b) and (d), respectively. Note (b) and (c) are identical since no growth or reverse growth occurred between these 2 time points. a Before growth (Cycle 1). b After growth (Cycle 5). c Before reverse growth (Cycle 6). d After reverse growth (Cycle 10)
Fig. 10
Fig. 10
Evolution of elastic myofiber stretch λe in the ELLIPSOID (top) and HUMAN (bottom) models as a result of growth and its reversal. Geometries are of the same scale in each model. a Before growth (Cycle 1). b After growth (Cycle 5). c Before reverse growth (Cycle 6). d After reverse growth (Cycle 10)
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