Background: Although electrophysiology may serve as a cardiac function surrogate, it does not provide a direct measure of the cardiac biomechanical function, such as contractility, or active stress. Hence, active stress quantification from tissue displacement data acquired using medical imaging is critical for assessing direct, cardiac biomechanical function.
Methods: We describe a framework to reconstruct active stresses from displacement data by solving the three-dimensional force-balance equation constrained by tissue incompressibility. To prove this concept, we implemented this method using a synthetic tissue sample of isotropic (100 x 100 x 100 nodes) resolution featuring a realistically defined fiber architecture that rotates smoothly about the vertical axis from apex to base, mimicking cardiac transverse isotropy. The solution to the forward problem yielded synthetic tissue deformation data in response to several prescribed active stress wave patterns. The displacement data was subsequently used as input into the inverse problem, which we solved using a low-order finite element method on the same transverse isotropic synthetic tissue geometry, and yielded the active stress wave.
Results: We conducted numerical experiments to evaluate the capability of the inverse model to reconstruct the active stress wave pattern under different conditions, including noise-free displacement, 15% uncertainty in fiber direction, 1% noise in displacement field, presence of limited active stress wave intensity regions mimicking infarcted myocardium, and tissue displacement noise coupled with sub-contractile regions. Our proposed method yielded error-free reconstruction of active stress in presence of no noise, yielded less than 10% active stress reconstruction error given uncertainty /noise in fiber direction or displacement data, and enabled clear identification of tissue regions featuring compromised contractility.
Conclusion: We described a method for reconstructing active stress wave patterns from displacement data and demonstrated the proposed framework enables sufficiently accurate quantification of the active stress waves and clear visualization of sub-contractile, malfunctioning tissue regions.