Research Papers

Finite-Element Extrapolation of Myocardial Structure Alterations Across the Cardiac Cycle in Rats

[+] Author and Article Information
Arnold David Gomez

Bioengineering Department,
University of Utah,
SMBB Room 1037,
36 S. Wasatch Drive,
Salt Lake City, UT 84112
e-mail: arnold.david.gomez@utah.edu

David A. Bull

Cardiothoracic Division,
Surgery Department,
University of Utah,
30 N 1900 E RM 3B205,
Salt Lake City, UT 84132-2101
e-mail: david.bull@hsc.utah.edu

Edward W. Hsu

Bioengineering Department,
University of Utah,
SMBB Room 1242,
36 S. Wasatch Drive,
Salt Lake City, UT 84112
e-mail: edward.hsu@utah.edu

Manuscript received April 28, 2015; final manuscript received August 17, 2015; published online September 7, 2015. Assoc. Editor: Kristen Billiar.

J Biomech Eng 137(10), 101010 (Sep 07, 2015) (11 pages) Paper No: BIO-15-1207; doi: 10.1115/1.4031419 History: Received April 28, 2015; Revised August 17, 2015

Myocardial microstructures are responsible for key aspects of cardiac mechanical function. Natural myocardial deformation across the cardiac cycle induces measurable structural alteration, which varies across disease states. Diffusion tensor magnetic resonance imaging (DT-MRI) has become the tool of choice for myocardial structural analysis. Yet, obtaining the comprehensive structural information of the whole organ, in 3D and time, for subject-specific examination is fundamentally limited by scan time. Therefore, subject-specific finite-element (FE) analysis of a group of rat hearts was implemented for extrapolating a set of initial DT-MRI to the rest of the cardiac cycle. The effect of material symmetry (isotropy, transverse isotropy, and orthotropy), structural input, and warping approach was observed by comparing simulated predictions against in vivo MRI displacement measurements and DT-MRI of an isolated heart preparation at relaxed, inflated, and contracture states. Overall, the results indicate that, while ventricular volume and circumferential strain are largely independent of the simulation strategy, structural alteration predictions are generally improved with the sophistication of the material model, which also enhances torsion and radial strain predictions. Moreover, whereas subject-specific transversely isotropic models produced the most accurate descriptions of fiber structural alterations, the orthotropic models best captured changes in sheet structure. These findings underscore the need for subject-specific input data, including structure, to extrapolate DT-MRI measurements across the cardiac cycle.

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Grahic Jump Location
Fig. 1

Angular quantification of fiber and sheet structures in the LV. The local fiber (f̂) or sheet direction (ŝ) can be expressed numerically as rotations about a coordinate system defined by the local circumferential, radial, and longitudinal direction (θ, r, and l, respectively). The fiber orientation is described by the helix α (which takes on negative values on the epicardium) and transverse α′ angles. A similar approach can be used to express sheet orientation (β and β′). The idealized imaging planes (long and short axes) approximately coincide with the longitudinal–radial plane and circumferential–radial plane near the midventricle.

Grahic Jump Location
Fig. 2

Representative FE model of the LV wall. The myocardium was represented as a mesh extracted from anatomical imaging embedded in a support block. LV mechanics were represented by a Fung-type constitutive model, and the surroundings were composed of a compliant and compressible material. The boundary conditions included the displacement constraints shown and a hydrostatic pressure in the endocardial surface.

Grahic Jump Location
Fig. 3

Material symmetry assumptions. The simulation cases included three material behavior models: isotropic (a), transverse isotropic (b), where the fiber (F) and cross-fiber (C) directions exhibit different responses, and orthotropic (c), where shear response was defined in terms in the local fiber (F), sheet (S), and sheet-normal (N) directions.

Grahic Jump Location
Fig. 4

Gross morphology of an isolated arrested heart. Long and short axes MRI of the LV (top two rows, see also Fig. 1) revealed morphological alterations consistent with the targeted cardiac states. Compared to EAD, balloon inflation at ED produced volume increase and wall thinning, whereas deflation at ES caused volume decrease and wall thickening. The volumes of the isolated perfused hearts were quantitatively similar to those seen in vivo.

Grahic Jump Location
Fig. 5

Histogram representation of structural angles populations at ED and ES from ex vivo DT-MRI (n = 3). Compared to ED, systolic helix angle population is more concentrated at higher angles, which indicates longitudinal alignment. During diastole, the transverse fiber angle population increases near 0 deg, which indicates alignment in the circumferential direction. Sheet angle distribution is markedly different between both states and tends to concentrate about zero at ES in comparison to ED, which has a different concavity.

Grahic Jump Location
Fig. 6

Averaged histograms of structural angle populations (n = 3) using the rotation-only approach to transform DTI data from an initial time point to ED and ES. The deformation results from case (i) (top row) do not show any difference between states, i.e., overlapping lines, constituting a poor prediction with respect to the experimental observations in Fig. 5. Cases (ii)–(iv) (rows 2–4, left column) produced similar helix angle distribution alterations that suggest longitudinal alignment at ES. Transverse angle alterations (middle column) are more realistic in cases (iii) and (iv). The rotation-only approach produced no visible differences in sheet angle distributions (right column).

Grahic Jump Location
Fig. 7

Averaged histograms of structural angle populations (n = 3) using the full-deformation approach to transform DTI data from an initial time point to ED and ES. Helix angle populations (left column) varied depending on the simulation strategy with (ii) and (iii) appearing to be closer to the experimental measurements in Fig. 5. Transverse angle populations (middle column) appeared to be identical regardless of the simulation approach. Sheet angle populations (right column) improved with the sophistication of the material model with (i) being the poorest (no difference between ED and ES) and (iv) being the best (largest change in concavity).

Grahic Jump Location
Fig. 8

Warping DTI data across the cardiac cycle. The FE model (a) was used to generate deformation estimates at times beyond the validation points (ED and ES) using simulation approach (iii). The modeling approach follows a realistic temporal representation of pressure, volume, and contractility via FE modeling by using an image-based, subject-specific transversely isotropic material model. The warped image slices showing helical angle maps (b) show contraction-induced shortening and some angle variation indicative of longitudinal alignment.

Grahic Jump Location
Fig. 9

Deformed tracts of a collection of fibers in a longitudinal isocline along the radial direction. Comparing the local inclination of an epicardial fiber tract at ED (black line, left), with respect to its warping configuration at ES (right) showed longitudinal alignment typical of systolic structural state.



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