Filler flocculation in polymers - a simplified model derived from thermodynamics and game theory.

The performance of elastomeric materials, i.e. in car tires, is substantially determined by the used reinforcing filler system. In particular, the flocculation tendency of filler particles to form clusters and even network-like structures significantly determines the mechanical properties of these elastomer materials and enhances especially their energy dissipation under periodic mechanical deformations. In a simplified thermodynamic model, inspired by a segregation model from game theory, we describe fundamental mechanisms of filler structure formation. As the final goal of this paper we want to demonstrate how similar structures in society, nature or materials like rubbers emerge when supposing obvious cardinal mechanisms of structure formation in complex systems.

Shortening versus isometric contractions in isolated human failing and non-failing left ventricular myocardium: dependency of external work and force on muscle length, heart rate and inotropic stimulation.

BACKGROUND: For reasons of simplicity, studies on isolated human myocardium have been conducted using exclusively isometric contractions, although positive inotropic interventions may differently influence force development, extent of shortening and myocardial work performance. We investigated human left ventricular failing and non-failing preparations comparing isometric versus isotonic, i.e., shortening contractions. RESULTS: (1) When muscle length is increased from 90% to 100% lMAX, peak developed force increases by 36% and 43% (p < 0.05) in non-failing and failing human left ventricular myocardium, respectively. Maximum performed work increases similarly in non-failing but decreases in failing myocardium. It can be shown that this discrepancy is due to significantly higher resting tension and does not present an insufficient intrinsic shortening capacity in failing myocardium. (2) When stimulation rate is increased from 0.5 to 2.0 Hz, isometric force increases significantly by 59% in non-failing and decreases by 27% in failing myocardium, whereas maximum performed work increases by 98% and decreases by 46%, respectively. (3) Pharmacological positive inotropic interventions by 7.2 mM calcium (n = 9), 3 x 10(-8) M isoproterenol (n = 7), 3 x 10(-8) M ouabain (n = 5), and 10(-5) M EMD 57033 (n = 3) equally increased force development and extent of shortening: When the fractional effect on shortening (y) was correlated to the fractional effect on force (x), the following linear regression equation was obtained: y = 0.91x + 0.26 (r = 0.86; p < 0.001). CONCLUSIONS: The data presented are of clinical and pharmacological importance: (1) The Frank-Starling mechanism is demonstrated to be existent in the failing human myocardium regarding both isometric force developed and maximum work performed. (2) Both force-frequency relations and--to a greater extent--work-frequency relations are reversed in failing human myocardium. (3) Independent of the pharmacological mode of action, positive inotropic compounds increase developed isometric force to the same extent as isotonic shortening and therefore potentiate maximum performed work.