Parametric Modeling of the Mouse Left Ventricular Myocardial Fiber Structure

Abstract

Magnetic resonance diffusion tensor imaging (DTI) has greatly facilitated detailed quantifications of myocardial structures. However, structural patterns, such as the distinctive transmural rotation of the fibers, remain incompletely described. To investigate the validity and practicality of pattern-based analysis, 3D DTI was performed on 13 fixed mouse hearts and fiber angles in the left ventricle were transformed and fitted to parametric expressions constructed from elementary functions of the prolate spheroidal spatial variables. It was found that, on average, the myocardial fiber helix angle could be represented to 6.5° accuracy by the equivalence of a product of 10th-order polynomials of the radial and longitudinal variables, and 17th-order Fourier series of the circumferential variable. Similarly, the fiber imbrication angle could be described by 10th-order polynomials and 24th-order Fourier series, to 5.6° accuracy. The representations, while relatively concise, did not adversely affect the information commonly derived from DTI datasets including the whole-ventricle mean fiber helix angle transmural span and atlases constructed for the group. The unique ability of parametric models for predicting the 3D myocardial fiber structure from finite number of 2D slices was also demonstrated. These findings strongly support the principle of parametric modeling for characterizing myocardial structures in the mouse and beyond.

A Mathematical Spline-Based Model of Cardiac Left Ventricle Anatomy and Morphology

“…Yet, that method usually requires about 10 parameters for each algebraic and 10-40 for trigonometric polynomials, whereas our technique uses only three parameters. Furthermore, the parameters in [72] have unclear geometrical or physical meaning, unlike ours. Moreover, the numbers of those parameters for different hearts vary, so the coefficients cannot be averaged to obtain recommended species-level parameter sets.…”

“…Fiber directions can also be fitted through widely-used fitting functions with many more parameters, as was done in [72]. In that work, fiber direction field in mice was approximated in spheroidal coordinates by a product of two algebraic and one trigonometric polynomials.…”

Imaging technologies for cardiac fiber and heart failure: a review

“…Some animal models that have been used with these imaging protocols for HF studies are rat [76, 77], canine [2, 10, 50, 78, 79], rabbit [12, 80], pig [81], sheep [56, 80, 82], and mice [14, 83]. Figure 3 shows representative DT-MRI images of hearts from a mouse, a rabbit, and a sheep.…”

“…In order to investigate the validity and practicality of pattern-based analysis, Merchant et al used 3D MR-DTI on 13 fixed mouse hearts [83]. Fiber angles in the LV were set to parametric expressions constructed from elementary functions of the prolate spheroidal spatial variables.…”

“…Fiber angles in the LV were set to parametric expressions constructed from elementary functions of the prolate spheroidal spatial variables. It was determined that on average, the myocardial fiber helix angle can be represented to 6.5° accuracy by the equivalence of a product of 10th-order polynomials of the radial and longitudinal variables and 17th-order Fourier series of the circumferential variable [83]. Similarly, the fiber imbrication angle was described by 10th-order polynomials and 24th-order Fourier series to 5.6° accuracy.…”