Raphael Sivan

Publications (2)6.08 Total impact

• Article: Stability, controllability, and observability of the "four state" model for the sarcomeric control of contraction.

  Yael Yaniv, Raphael Sivan, Amir Landesberg
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  ABSTRACT: A model of the sarcomeric control of contraction at various loading conditions has to maintain three cardinal features: stability, controllability (where the output can be controlled by the input), and observability (where the output reflects the effects of all the state variables). The suggested model of the sarcomere couples calcium kinetics with cross-bridge (XB) cycling and comprises two feedback mechanisms: (i) the cooperativity, whereby the number of force-generating (strong) XBs determines calcium affinity, regulates XB recruitment, and (ii) the mechanical feedback, whereby shortening velocity determines XBs cycling rate, controls the XBs contractile efficiency. The sarcomere is described by a set of four first-order nonlinear differential equations, utilizing the Matlab's Simulink software. Small oscillatory input was imposed when the state variables trajectories reached a steady state. The linearized state-space representations of the model were calculated for various initial sarcomere lengths. The analysis of the state-space representation validates the controllability and observability of the model. The model has four poles: three at the left side of the complex plane and one integrating pole at the origin. Therefore, the system is marginally stable. The Laplace transform confirms that the state representation is minimal and is therefore observable and controllable. The extension of the model to a multi-sarcomere lattice was explored, and the effects of inhomogeneity and nonuniform activation were described.
  Annals of Biomedical Engineering 06/2006; 34(5):778-89. · 2.37 Impact Factor
• Article: Analysis of hystereses in force length and force calcium relations.

  Yael Yaniv, Raphael Sivan, Amir Landesberg
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  ABSTRACT: Analysis of the hystereses in the force-length relationship at constant Ca(2+) concentration and in the force-calcium relationship at constant sarcomere length (SL) provides insight into the mechanisms that control cross-bridge (XB) recruitment. The hystereses are related here to two mechanisms that regulate the number of strong XBs: the cooperativity, whereby the number of strong XBs determines calcium affinity, and the mechanical feedback, whereby the shortening velocity determines the duration for which the XBs are in the strong state. The study simulates the phenomena and defines the role of these feedbacks. The model that couples calcium kinetics with XB cycling was built on Simulink software (Matlab). Counterclockwise (CCW) hysteresis, wherein the force response lags behind the SL oscillations, at a constant calcium level, is obtained in the force-length plane when neglecting the mechanical feedback and accounting only for the cooperativity mechanism. Conversely, the force response precedes the SL oscillations, yielding a clockwise (CW) hysteresis when only the mechanical feedback is allowed to exist. In agreement with experimental observations, either CW or CCW hysteresis is obtained when both feedbacks coexist: CCW hystereses are obtained at low frequencies (<3 Hz), and the direction is reversed to CW at higher frequencies (>3 Hz). The cooperativity dominates at low frequencies and allows the muscle to adapt XB recruitment to slow changes in the loading conditions. The changeover frequency from CCW to CW hysteresis defines the velocity limit above which the muscle absorbs rather than generates energy. The hysteresis in the force-calcium relation is conveniently explained by the same cooperativity mechanism. We propose that a single cooperativity mechanism that depends on the number of strong XBs can explain the hystereses in the force-length as well as in the force-calcium relationships.
  AJP Heart and Circulatory Physiology 01/2005; 288(1):H389-99. · 3.71 Impact Factor