Parameter estimation in a crossbridge muscle model

Selecting Sensitive Parameter Subsets in Dynamical Models With Application to Biomechanical System Identification

Estimating many parameters of biomechanical systems with limited data may achieve good fit but may also increase 95% confidence intervals in parameter estimates. This results in poor identifiability in the estimation problem. Therefore, we propose a novel method to select sensitive biomechanical model parameters that should be estimated, while fixing the remaining parameters to values obtained from preliminary estimation. Our method relies on identifying the parameters to which the measurement output is most sensitive. The proposed method is based on the Fisher information matrix (FIM). It was compared against the nonlinear least absolute shrinkage and selection operator (LASSO) method to guide modelers on the pros and cons of our FIM method. We present an application identifying a biomechanical parametric model of a head position-tracking task for ten human subjects. Using measured data, our method (1) reduced model complexity by only requiring five out of twelve parameters to be estimated, (2) significantly reduced parameter 95% confidence intervals by up to 89% of the original confidence interval, (3) maintained goodness of fit measured by variance accounted for (VAF) at 82%, (4) reduced computation time, where our FIM method was 164 times faster than the LASSO method, and (5) selected similar sensitive parameters to the LASSO method, where three out of five selected sensitive parameters were shared by FIM and LASSO methods.

The N-terminal extension of cardiac troponin T stabilizes the blocked state of cardiac thin filament

Cardiac troponin T (cTnT) is a key component of contractile regulatory proteins. cTnT is characterized by a ∼32 amino acid N-terminal extension (NTE), the function of which remains unknown. To understand its function, we generated a transgenic (TG) mouse line that expressed a recombinant chimeric cTnT in which the NTE of mouse cTnT was removed by replacing its 1-73 residues with the corresponding 1-41 residues of mouse fast skeletal TnT. Detergent-skinned papillary muscle fibers from non-TG (NTG) and TG mouse hearts were used to measure tension, ATPase activity, Ca(2+) sensitivity (pCa(50)) of tension, rate of tension redevelopment, dynamic muscle fiber stiffness, and maximal fiber shortening velocity at sarcomere lengths (SLs) of 1.9 and 2.3 μm. Ca(2+) sensitivity increased significantly in TG fibers at both short SL (pCa(50) of 5.96 vs. 5.62 in NTG fibers) and long SL (pCa(50) of 6.10 vs. 5.76 in NTG fibers). Maximal cross-bridge turnover and detachment kinetics were unaltered in TG fibers. Our data suggest that the NTE constrains cardiac thin filament activation such that the transition of the thin filament from the blocked to the closed state becomes less responsive to Ca(2+). Our finding has implications regarding the effect of tissue- and disease-related changes in cTnT isoforms on cardiac muscle function.

Alanine or aspartic acid substitutions at serine23/24 of cardiac troponin I decrease thin filament activation, with no effect on crossbridge detachment kinetics

Ala/Asp substitutions at Ser23/24 have been employed to investigate the functional impact of cardiac troponin I (cTnI) phosphorylation by protein kinase A (PKA). Some limitations of previous studies include the use of heterologous proteins and confounding effects arising from phosphorylation of cardiac myosin binding protein-C. Our goal was to probe the effects of cTnI phosphorylation using a homologous assay, so that altered function could be solely attributed to changes in cTnI. We reconstituted detergent-skinned rat cardiac papillary fibers with homologous rat cardiac troponin subunits to study the impact of Ala and Asp substitutions at Ser23/24 of rat cTnI (RcTnI S23A/24A and RcTnI S23D/24D). Both RcTnI S23A/24A and RcTnI S23D/24D showed a ~36% decrease in Ca(2+)-activated maximal tension. Both RcTnI S23A/24A and RcTnI S23D/24D showed a ~18% decrease in ATPase activity. Muscle fiber stiffness measurements suggested that the decrease in thin filament activation observed in RcTnI S23A/24A and RcTnI S23D/24D was due to a decrease in the number of strongly-bound crossbridges. Another major finding was that Ala and Asp substitutions in cTnI did not affect crossbridge detachment kinetics.

MUSCULOSKELETAL STABILIZATION OF THE ELBOW — COMPLEX OR REAL

Both sensory information and mechanical properties of the musculoskeletal system are necessary for fast and appropriate reactions of humans and animals to environmental perturbations. In this paper, we focus on the musculoskeletal system and study the stability of a human elbow in an equilibrium state. We derive a biomechanical model of the human elbow, including an antagonistic pair of muscles, and investigate the stability analytically based on the theory of Ljapunov. Depending on the elbow angle and the level of coactivation, we obtain the following three qualitatively different behaviors: unstable, stable with real eigenvalues, and stable with complex eigenvalues. If the eigenvalues are real, then the system is critically damped; for complex eigenvalues, solutions near the equilibrium are oscillating. Based on experimental data, we found that in principle real and complex behaviors may occur in human arm movements. The experiments support the analytical predictions. Furthermore, in agreement with the simulations, we found differences in the experimental results among the subjects. The results of this study support the assumption that arm movements around an equilibrium point may be self-stabilized without sensory feedback or motor control, based only on mechanical properties of musculoskeletal systems.

An improved method to determine neuromuscular properties using force laws - From single muscle to applications in human movements

We evaluate an improved method for individually determining neuromuscular properties in vivo. The method is based on Hill's equation used as a force law combined with Newton's equation of motion. To ensure the range of validity of Hill's equation, we first perform detailed investigations on in vitro single muscles. The force-velocity relation determined with the model coincides well with results obtained by standard methods (r=.99) above 20% of the isometric force. In addition, the model-predicted force curves during work loop contractions very well agree with measurements (mean difference: 2-3%). Subsequently, we deduce theoretically under which conditions it is possible to combine several muscles of the human body to model muscles. This leads to a model equation for human leg extension movements containing parameters for the muscle properties and for the activation. To numerically determine these invariant neuromuscular properties we devise an experimental method based on concentric and isometric leg extensions. With this method we determine individual muscle parameters from experiments such that the simulated curves agree well with experiments (r=.99). A reliability test with 12 participants revealed correlations r=.72-.91 for the neuromuscular parameters (p<.01). Predictions of similar movements under different conditions show mean errors of about 5%. In addition, we present applications in sports practise and theory.

Derivation and Left Ventricular Pressure Phase Plane Based Validation of a Time Dependent Isometric Crossbridge Attachment Model

Huxley's crossbridge attachment model predicts tension (contractile force) development in isometric (fixed length) cells using constant attachment and detachment rates. Alternative models incorporating time-varying calcium concentrations are complex (coupled linear differential equations) and use time-dependent inputs (calcium, elastance, etc.) to model multiple states. We hypothesize that by incorporating the known significant rise and fall in intracellular calcium, via either an asymmetric damped function or a symmetric Gaussian function, into a time-varying, rather than constant, attachment rate function, the Huxley model prediction for tension (i.e., chamber pressure) in isovolumic (isometric) non-ejecting beats will improve. To test the hypothesis that the time-dependent model-predicted (TDM) pressure fits the in vivo isometric (isovolumic) LV pressure phase-plane (PPP) contour better than the constant attachment rate predicted pressure, we used the TDM to fit non-ejecting, premature ventricular contraction (PVC) PPP contours in 6 subjects. Conventional model fit was poor (relative error 74.0%+/-12.5%), while the asymmetric damped TDM rate function provided slight improvement relative to the conventional time-independent model (relative error 55.4%+/-9.8%). The symmetric Gaussian rate function TDM provided the best PPP fit to all non-ejecting beats tested (relative error 19.8%+/-4.8%). We conclude that approximating the lumped attachment rate via a time-varying, rather than constant, rate function generates a physiologically viable model of crossbridge behavior. The PPP provides the optimal arena for alternate mathematical formulation assessment of LVP contour prediction by time-dependent attachment rate functions and facilitates modeling of cardiac contraction and relaxation.

Cross-bridge mechanisms underlying the history-dependent properties of muscle spindles and stretch reflexes

The effects of prior movement on the force responses of skeletal muscle are compared with the effects of movement history on the changes in firing rate of muscle spindle receptors. Prior release results in the linearization of the mechanical properties of skeletal muscles, which can be provisionally explained by cross-bridge models of muscular contraction. The history-dependence of responses of muscle spindle receptors in unanesthetized decerebrate preparations appears to result from the kinetics of cycling and noncycling cross-bridges. The results of this comparison indicate that the integration of mechanical properties of muscle and spindle receptor promotes stiffness regulation.Key words: predictive control, muscular stiffness, muscle receptors, reflex compensation, cross-bridge cycling, nonlinear mechanical properties, feline motor control.