ABSTRACT
CONTENTS 3.1 Scope ............................................................................................................. 68 3.2 Left Ventricular Shape Factor Based Contractility Index .................... 68
3.2.1 LV Model Geometry Development ............................................. 69 3.2.2 Determination of LV Model Wall Stress..................................... 70 3.2.3 Normalized Wall Stress based Shape Factor Index .................. 71 3.2.4 Optimal Left Ventricle Shape Factor and Corresponding
Shape Factor Index 2 ...................................................................... 73 3.2.5 Optimally Shaped LV(s) Compared to
Abnormally Shaped LV(s) for Different Age Groups .............. 77 3.2.6 Clinical Applications ...................................................................... 78
3.2.6.1 Measurements .................................................................. 78 3.2.6.2 Subjects .............................................................................. 78 3.2.6.3 Results ............................................................................... 78
3.2.7 Comparison with Traditional Invasive LV (dP=dt)max ............ 84 3.2.8 Discussion and Conclusion ........................................................... 84
3.3 Left Ventricular Sarcomere Contractile Characteristics and Associated Power Index .................................................................... 85 3.3.1 Left Ventricle Cylindrical Model (Incorporating the
Myocardial Fibers within Its Wall) .............................................. 85 3.3.2 Myocardial Structural Unit (MSU) Model ................................. 87 3.3.3 Determination of Fiber Density, Length, and Force;
Fiber Angle a and MSU Force (Ft); Torque Produced on the LV due to Fiber Activation ............................ 88 3.3.3.1 Fiber Density, Length, and Force .................................. 88 3.3.3.2 Determining the Fiber Pitch Angle a ........................... 90 3.3.3.3 Torque Imparted to the LV by Fiber Contraction ..... 91
3.3.4 Dynamics of a Myocardial Structural Unit ................................ 92 3.3.4.1 Governing Equation of MSU Dynamics
and Its Solution ................................................................ 92 3.3.4.2 Phase I: Solving Equation 3.31 for Isovolumic
Contraction Phase (during 0< t< tiso).......................... 95
3.3.4.3 Phase II: Expression for xT and Solving Equation 3.19 for the Ejection Phase to Determine Parameters xT0 and ze.................................. 96
3.3.4.4 Evaluating theModel Parameters (k,Bv, FCE0,vce, zce) ... 98 3.3.5 Sarcomere Force (FCE), Shortening Velocity (x˙2), and Power...... 98
3.3.5.1 Determining Sarcomere Contractile FCE and x2, and Their Physiological Implications ........................... 98
3.3.5.2 Power Generated by the Sarcomere Contractile-Element ......................................................... 99
3.3.5.3 Defining a Contractile Power Index ........................... 100 3.3.6 Clinical Application and Results ............................................... 100
3.3.6.1 Evaluation of the Model Parameters .......................... 101 3.3.6.2 Determination of CE Force FCE and
Shortening x2 Characteristics, with Determination of the LV Suction Effect ..................... 103
3.3.6.3 Computing TMSP and MSPI (Equations 3.52 and 3.53) ............................................. 104
3.3.7 Discussion: Comparison of CE Performance Characteristics for Three Patients, and Correlation of MSPI with (dP=dt)max ............................................................. 105 3.3.7.1 Computation of CE Performance
Characteristics for Other Subjects ............................... 105 3.3.7.2 Computation of MSPI, in Comparison
with (dP=dt)max ............................................................. 106 3.3.8 Highlights ...................................................................................... 107
References ........................................................................................................... 110
Contractility is the key mechanism of left ventricular pumping role. Hence, indices of contractility are important for differentiating poorly contracting left ventricles (LVs) from normally contracting LVs. In this chapter, we provide the theory and application of contractility indices based on (1) the left ventricular shape factor, in terms of the LV wall stress normalized with respect to the LV internal pressure, and (2) the spirally wound myocardial fiber’s sarcomere characteristics of contractile element force versus shortening velocity. These contractility indices values are compared to the values of the traditional contractility index of (dP=dt)max, and good correlations are observed between our new indices and the traditional index of (dP=dt)max.
