  In this work we propose a mathematical model that describes the orientation
of ventricular cardiac fibers. These fibers are commonly computed as the
normalized gradient of certain harmonic potentials, so our work consisted in
finding the equations that such a vector field satisfies, considering the
unitary norm constraint. The resulting equations belong to the Frank-Oseen
theory of nematic liquid crystals, which yield a bulk of mathematical
properties to the cardiac fibers, such as the characterization of
singularities. The numerical methods available in literature are
computationally expensive and not sufficiently robust for the complex
geometries obtained from the human heart, so we also propose a preconditioned
projected gradient descent scheme that circumvents these difficulties in the
tested scenarios. The resulting model further confirms recent experimental
observations of liquid crystal behavior of soft tissue, and provides an
accurate mathematical description of such behavior.
