Left ventricular wall stress normalization in chronic pressure-overloaded heart: a mathematical model study
It is generally accepted that the left ventricle (LV) hypertrophies (LVH) to normalize systolic wall stress (sigma(s)) in chronic pressure overload. However, LV filling pressure (P(v)) may be elevated as well, supporting the alternative hypothesis of end-diastolic wall stress (sigma(d)) normalization in LVH. We used an LV time-varying elastance model coupled to an arterial four-element lumped-parameter model to study ventricular-arterial interaction in hypertension-induced LVH. We assessed model parameters for normotensive controls and applied arterial changes as observed in hypertensive patients with LVH (resistance +40%, compliance -25%) and assumed 1) no cardiac adaptation, 2) normalization of sigma(s) by LVH, and 3) normalization of sigma(s) by LVH and increase in P(v), such that sigma(d) is normalized as well. In patients, systolic and diastolic blood pressures increase by approximately 40%, cardiac output (CO) is constant, and wall thickness increases by 30-55%. In scenarios 1 and 2, blood pressure increased by only 10% while CO dropped by 20%. In scenario 2, LV wall thickness increased by only 10%. The predictions of scenario 3 were in qualitative and quantitative agreement with in vivo human data. LVH thus contributes to the elevated blood pressure in hypertension, and cardiac adaptations include an increase in P(v), normalization of sigma(s), and preservation of CO in the presence of an impaired diastolic function.