Left ventricular active strain energy density is a promising new measure of systolic function

The left ventricular ejection fraction does not accurately predict exercise capacity or symptom severity and has a limited role in predicting prognosis in heart failure. A better method of assessing ventricular performance is needed to aid understanding of the pathophysiological mechanisms and guide management in conditions such as heart failure. In this study, we propose two novel measures to quantify myocardial performance, the global longitudinal active strain energy (GLASE) and its density (GLASED) and compare them to existing measures in normal and diseased left ventricles. GLASED calculates the work done per unit volume of muscle (energy density) by combining information from myocardial strain and wall stress (contractile force per unit cross sectional area). Magnetic resonance images were obtained from 183 individuals forming four cohorts (normal, hypertension, dilated cardiomyopathy, and cardiac amyloidosis). GLASE and GLASED were compared with the standard ejection fraction, the corrected ejection fraction, myocardial strains, stroke work and myocardial forces. Myocardial shortening was decreased in all disease cohorts. Longitudinal stress was normal in hypertension, increased in dilated cardiomyopathy and severely decreased in amyloid heart disease. GLASE was increased in hypertension. GLASED was mildly reduced in hypertension (1.39 ± 0.65 kJ/m3), moderately reduced in dilated cardiomyopathy (0.86 ± 0.45 kJ/m3) and severely reduced in amyloid heart disease (0.42 ± 0.28 kJ/m3) compared to the control cohort (1.94 ± 0.49 kJ/m3). GLASED progressively decreased in the hypertension, dilated cardiomyopathy and cardiac amyloid cohorts indicating that mechanical work done and systolic performance is severely reduced in cardiac amyloid despite the relatively preserved ejection fraction. GLASED provides a new technique for assessing left ventricular myocardial health and contractile function.

Where D = LVIDd (mm), W=EDWT (mm),  = longitudinal shortening,  θ = midwall circumferential shortening. To calculate the EFc, we inputted D and W using the mean of the normal control cohort i.e. D = 52 mm, W = 7.6 mm and the longitudinal shortening ( ), midwall circumferential shortening ( θ ) and length (L) were inputted as the measured values in each individual.

Stresses
Longitudinal Lamé stress and since pericardial pressure is small the P o r o 2 term can be ignored, and the equation simplified to:

Laplace longitudinal stress
Laplace longitudianal stress = × 4 , (Eq 5) where P is systolic pressure, D is internal diameter, t is mean wall thickness.
Assuming a 10-shell model S=t/10 where t=end-diastolic wall thickness. Cardiomyocyte stress is then calculated so that total accumulative force for all the shells, calculated using numerical integration, is the same as that determined from longitudinal stress using the Lamé equation (Eq 3).

Stroke work
where MAP = (SBP + 2 × DBP)/3. SBP is peak systolic blood pressure and DBP is diastolic blood pressure measure in Pa.

LV pressure-strain loop (LV PSL) index
converted from mmHg% to mHg% by dividing by 1,000.

The Laplace stress-strain product (SSP)
Laplace longitudinal stress strain product was calculated as follows: where ε z is longitudinal shortening, P is systolic pressure, D is internal diameter, t is mean wall thickness.

Active strain energy density: comparison of non-linear and linear methods
A typical pressure-strain curve was derived from a study by Loncaric and colleagues ( Figure   A1). 44 The curve was divided into 13 points adjusting mural thickness and ventricular diameter between mitral valve closure (MVC) and aortic valve closure (AVC) and a stressstrain curve plotted ( Figure A2). The individual longitudinal stress for each of the 12 periods were calculated using the Lamé equation and the longitudinal ASED (GLASED) was calculated from the sum of the ASED for each period and giving the area under the curve between MVC and AVC ( Figure A3).

AVC MVC
In this example, the GLASED was 2.80 KPa/m 3 (non-linear method) and using Eq 8 was 2.71 KPa/m 3 (linear method -blue triangle A4) suggesting that using the ½ factor is a reasonable compromise for routine use in clinical practice. Geometrically, the ½ factor is half the area of the rectangle with height (σ z , peak stress based on SBP) and width (ε z , peak strain) with area of (σ z × ε z , dashed box). Note that this compromise is achieved because the vertical hatched area is similar to the horizontal hatched area in Figure A4.
A downloadable Excel spreadsheet to calculate MASED is available online.

Strain energy density proof
SED can be derived from the definition of Work i.e. F × l where F = force, l = displacement/distance, V=volume, A = cross sectional area, L, original length.