Diastolic function: modeling left ventricular untwisting as a damped harmonic oscillator

Objective.We developed a method using cardiovascular magnetic resonance imaging to model the untwisting of the left ventricle (LV) as a damped torsional harmonic oscillator to estimate shear modulus (intrinsic myocardial stiffness) and frictional damping, then applied this method to evaluate the torsional stiffness of patients with resistant hypertension (RHTN) compared to a control group.Approach.The angular displacement of the LV during diastole was measured. Myocardial shear modulus and damping constant were determined by solving a system of equations modeling the diastolic untwisting as a damped, unforced harmonic oscillator, in 100 subjects with RHTN and 36 control subjects.Main Results.Though overall torsional stiffness was increased in RHTN (41.7 (27.1-60.7) versus 29.6 (17.3-35.7) kdyn*cm;p = 0.001), myocardial shear modulus was not different between RHTN and control subjects (0.34 (0.23-0.50) versus 0.33 (0.22-0.46) kPa;p= 0.758). RHTN demonstrated an increase in overall diastolic frictional damping (6.13 ± 3.77 versus 3.35 ± 1.70 kdyn*cm*s;p< 0.001), but no difference in damping when corrected for the overlap factor (74.3 ± 25.9 versus 68.0 ± 24.0 dyn*s/cm³;p = 0.201). There was an increase in the polar moment (geometric component of stiffness; 11.47 ± 6.95 versus 7.58 ± 3.28 cm⁴;p<0.001).Significance.We have developed a phenomenological method, estimating the intrinsic stiffness and relaxation properties of the LV based on restorative diastolic untwisting. This model finds increased overall stiffness in RHTN and points to hypertrophy, rather than tissue- level changes, as the major factor leading to increased stiffness.