Muscle Force-velocity Relationship Research Articles

Four phases of a force transient emerge from a binary mechanical system.

Accurate models of muscle contraction are important for understanding both muscle performance and the therapeutics that enhance physiological function. However, models are only accurate and meaningful if they are consistent with physical laws. A single muscle fiber contains billions of randomly fluctuating atoms that on the spatial scale of a muscle fiber generate unidirectional force and power output. This thermal system is formally constrained by the laws of thermodynamics, and a recently developed thermodynamic model of muscle force generation provides qualitative descriptions of the muscle force-velocity relationship, muscle force generation, muscle force transients, and the thermodynamic work loop of muscle with a thermodynamic (not molecular) power stroke mechanism. To demonstrate the accuracy of this model requires that its outputs be quantitatively compared with experimentally observed muscle function. Here I show that a two-state thermodynamic model accurately describes the experimentally observed four-phase force transient response to both mechanical and chemical perturbations. This is the simplest possible model of one of the most complex characteristic signatures of muscle mechanics.

Changes in the Force-Velocity Relationship of Knee Muscles After Anterior Cruciate Ligament Reconstruction Using the Isokinetic 2-Point Model.

After anterior cruciate ligament reconstruction (ACL-R), knee muscle strength symmetry is used as part of the return-to-sport criteria. However, little is known about the changes in the force-velocity (F-V) relationship, which could affect athletic performance. This study investigated the F-V relationship of knee muscles at 4 and 8months after ACL-R, using the 2-point method tested by isokinetic dynamometry. A total of 103 physically trained individuals (24.6 [9.3]y, 59.2% male) who underwent primary ACL-R were included. Demographic information and surgery characteristics were collected at 6weeks postoperatively. Isokinetic knee flexors' and extensors' peak torques were measured at 60° and 240° per second in the concentric mode at 4 and 8 monthspostoperative. Peak torques and angular velocities were converted to force and linear velocity for calculating maximum isometric force (F0) and the slope of the regression line (F-V slope). At 4 and 8 months postoperative, F0 was significantly lower and F-V slope was significantly less steep (less negative) on the operated leg compared with the nonoperated leg for knee extensors (P < .001) and flexors (P < .001-.002). The limb symmetry index calculated using F0 was lower than the limb symmetry indexes assessed at 60° and 240° per second, especially for knee flexors (P < .001). The use of patellar tendon grafts was associated with lower F0 and a less steep F-V slope compared with hamstring tendon grafts (P < .010). The isokinetic 2-point model assessing the F-V relationship provides additional and relevant insight for evaluating knee muscle strength after ACL-R.

The Problem with Inventing Molecular Mechanisms to Fit Thermodynamic Equations of Muscle.

Almost every model of muscle contraction in the literature to date is a molecular power stroke model, even though this corpuscular mechanism is opposed by centuries of science, by 85 years of unrefuted evidence that muscle is a thermodynamic system, and by a quarter century of direct observations that the molecular mechanism of muscle contraction is a molecular switch, not a molecular power stroke. An ensemble of molecular switches is a binary mechanical thermodynamic system from which A.V. Hill's muscle force-velocity relationship is directly derived, where Hill's parameter a is the internal force against which unloaded muscle shortens, and Hill's parameter b is the product of the switch displacement, d, and the actin-myosin ATPase rate. Ignoring this model and the centuries of thermodynamics that preceded it, corpuscularians continue to develop molecular power stroke models, adding to their 65-year jumble of "new", "innovative", and "unconventional" molecular mechanisms for Hill's a and b parameters, none of which resemble the underlying physical chemistry. Remarkably, the corpuscularian community holds the thermodynamicist to account for these discrepancies, which, as outlined here, I have done for 25 years. It is long past time for corpuscularians to be held accountable for their mechanisms, which by all accounts have no foundation in science. The stakes are high. Molecular power stroke models are widely used in research and in clinical decision-making and have, for over half a century, muddied our understanding of the inner workings of one of the most efficient and clean-burning machines on the planet. It is problematic that corpuscularians present these models to stakeholders as science when in fact corpuscularians have been actively defending these models against science for decades. The path forward for scientists is to stop baseless rejections of muscle thermodynamics and to begin testing corpuscular and thermodynamic mechanisms with the goal of disproving one or the other of these hypotheses.

Thermodynamics and Kinetics of a Binary Mechanical System: Mechanisms of Muscle Contraction

Biological motors function at the interface of biology, physics, and chemistry, and it remains unsettled what rules from which disciplines account for how these motors work. Myosin motors are enzymes that catalyze the hydrolysis of ATP through a mechanism involving a switch-like myosin structural change (a lever arm rotation) induced by actin binding that generates a small displacement of an actin filament. In muscle, individual myosin motors are widely assumed to function as molecular machines having mechanical properties that resemble those of muscle. In a fundamental departure from this perspective, here, I show that muscle more closely resembles a heat engine with mechanical properties that emerge from the thermodynamics of a myosin motor ensemble. The transformative impact of thermodynamics on our understanding of how a heat engine works guides a parallel transformation in our understanding of how muscle works. I consider the simplest possible model of force generation: a binary mechanical system. I develop the mechanics, energetics, and kinetics of this system and show that a single binding reaction generates force when muscle is held at a fixed length and performs work when muscle is allowed to shorten. This creates a network of thermodynamic binding pathways that resembles many of the characteristic mechanical and energetic behaviors of muscle including the muscle force-velocity relationship, heat output by shortening muscle, four phases of a muscle tension transient, spontaneous oscillatory contractions, and force redevelopment. Analogous to the thermodynamic (Carnot) cycle for a heat engine, isothermal and adiabatic binding and detachment reactions create a thermodynamic cycle for muscle that resembles cardiac pressure-volume loops (i.e., how the heart works). This paper provides an outline for how to re-interpret muscle mechanic data using thermodynamics - an ongoing effort that will continue providing novel insights into how muscle and molecular motors work.

Molecular Events of the Crossbridge Cycle Reflected in the Force-Velocity Relationship of Activated Muscle.

Muscles convert chemical energy to mechanical work. Mechanical performance of a muscle is often assessed by the muscle’s ability to shorten and generate power over a range of loads or forces, characterized by the force–velocity and force–power relationships. The hyperbolic force–velocity relationship of muscle, for a long time, has been regarded as a pure empirical description of the force–velocity data. Connections between mechanical manifestation in terms of force–velocity properties and the kinetics of the crossbridge cycle have only been established recently. In this review, we describe how the model of Huxley’s crossbridge kinetics can be transformed to the hyperbolic Hill equation, and link the changes in force–velocity properties to molecular events within the crossbridge cycle driven by ATP hydrolysis. This allows us to reinterpret some findings from previous studies on experimental interventions that altered the force–velocity relationship and gain further insight into the molecular mechanisms of muscle contraction under physiological and pathophysiological conditions.

The load dependence of muscle's force-velocity curve is modulated by alternative myosin converter domains.

The hyperbolic shape of the muscle force-velocity relationship (FVR) is characteristic of all muscle fiber types. The degree of curvature of the hyperbola varies between muscle fiber types and is thought to be set by force-dependent properties of different myosin isoforms. However, the structural elements in myosin and the mechanism that determines force dependence are unresolved. We tested our hypothesis that the myosin converter domain plays a critical role in the force-velocity relationship (FVR) mechanism. Drosophila contains a single myosin heavy chain gene with five converters encoded by alternative exons. We measured FVR properties of Drosophila jump muscle fibers from five transgenic lines each expressing a single converter. Consistent with our hypothesis, we observed up to 2.4-fold alterations in FVR curvature. Maximum shortening velocity (v0) and optimal velocity for maximum power generation were also altered, but isometric tension and maximum power generation were unaltered. Converter 11a, normally found in the indirect flight muscle (IFM), imparted the highest FVR curvature and v0, whereas converter 11d, found in larval body wall muscle, imparted the most linear FVR and slowest v0. Jump distance strongly correlated with increasing FVR curvature and v0, meaning flies expressing the converter from the IFM jumped farther than flies expressing the native jump muscle converter. Fitting our data with Huxley's two-state model and a biophysically based four-state model suggest a testable hypothesis that the converter sets muscle type FVR curvature by influencing the detachment rate of negatively strained myosin via changes in the force dependence of product release.

Muscle Force-Velocity Relationships Observed in Four Different Functional Tests.

The aims of the present study were to investigate the shape and strength of the force-velocity relationships observed in different functional movement tests and explore the parameters depicting force, velocity and power producing capacities of the tested muscles. Twelve subjects were tested on maximum performance in vertical jumps, cycling, bench press throws, and bench pulls performed against different loads. Thereafter, both the averaged and maximum force and velocity variables recorded from individual trials were used for force–velocity relationship modeling. The observed individual force-velocity relationships were exceptionally strong (median correlation coefficients ranged from r = 0.930 to r = 0.995) and approximately linear independently of the test and variable type. Most of the relationship parameters observed from the averaged and maximum force and velocity variable types were strongly related in all tests (r = 0.789-0.991), except for those in vertical jumps (r = 0.485-0.930). However, the generalizability of the force-velocity relationship parameters depicting maximum force, velocity and power of the tested muscles across different tests was inconsistent and on average moderate. We concluded that the linear force-velocity relationship model based on either maximum or averaged force-velocity data could provide the outcomes depicting force, velocity and power generating capacity of the tested muscles, although such outcomes can only be partially generalized across different muscles.

Force-velocity Relationship of Muscles Performing Multi-joint Maximum Performance Tasks

Manipulation of external loads typically provides a range of force, velocity, and power data that allows for modeling muscle mechanical characteristics. While a typical force-velocity relationship obtained from either in vitro muscles or isolated muscle groups can be described by a hyperbolic equation, the present review paper reveals the evidence that the same relationship obtained from maximum-performance multi-joint movements could be approximately linear. As a consequence, this pattern also results in a relatively simple shape of the power-velocity relationship. The parameters of the linear force-velocity relationship reveal the maximum force, velocity and power. Recent studies conducted on various functional movement tasks reveal that these parameters could be reliable, on average moderately valid, and typically sensitive enough to detect differences among populations of different physical abilities. Therefore, the linear force-velocity relationship together with the associated parabolic power-velocity relationship could provide both a new and simplified approach to studies of the design and function of human muscular system and its modeling. Regarding the practical applications, the reviewed findings also suggest that the loaded multi-joint movements could be developed into relatively simple routine tests of the force-, velocity- and power-generating capacity of the neuromuscular system.

Inherent Force-Dependent Properties of β Cardiac Myosin Contribute to the Force-Velocity Relationship of Cardiac Muscle

The cardiac cycle is a tightly regulated process in which the heart generates power during systole and relaxes during diastole. Appropriate power must be generated to effectively pump blood against cardiac afterload. Dysfunction of this cycle has devastating consequences for affected individuals. Cardiac power output is regulated by several feedback mechanisms (e.g. neuronal, hormonal, mechanical) which ultimately lead to changes in the force and power output of the molecular motor, β-cardiac myosin (βCM). Despite its importance in driving and regulating cardiac power output, the effect of force on the contractility of a single βCM has not been measured at physiological [ATP]. Using optical trapping techniques, we found that similar to some other myosins, βCM has a two-substep working stroke where the second mechanical substep is associated with ADP release. At saturating [ATP] (4 mM), forces that resist the power stroke slow myosin-driven contraction, suggesting that the inherent properties of myosin contribute to the force-velocity relationship in muscle and play an important role in the regulation of cardiac power output. Based on our results and kinetic modeling, we propose that force inhibits the mechanical transition associated with ADP release, leading to slowing of the rate of ADP release, the same kinetic step that limits muscle shortening. These results have important implications for cardiac diseases which affect power output, such as heart failure and cardiomyopathies. This work was supported by the American Heart Association (14SDG18850009 to M.J.G.) and National Institutes of Health (R01GM057247 to E.M.O. and K99HL123623 to M.J.G.).

Effects of Isometric Scaling on Vertical Jumping Performance

Jump height, defined as vertical displacement in the airborne phase, depends on vertical takeoff velocity. For centuries, researchers have speculated on how jump height is affected by body size and many have adhered to what has come to be known as Borelli’s law, which states that jump height does not depend on body size per se. The underlying assumption is that the amount of work produced per kg body mass during the push-off is independent of size. However, if a big body is isometrically downscaled to a small body, the latter requires higher joint angular velocities to achieve a given takeoff velocity and work production will be more impaired by the force-velocity relationship of muscle. In the present study, the effects of pure isometric scaling on vertical jumping performance were investigated using a biologically realistic model of the human musculoskeletal system. The input of the model, muscle stimulation over time, was optimized using jump height as criterion. It was found that when the human model was miniaturized to the size of a mouse lemur, with a mass of about one-thousandth that of a human, jump height dropped from 40 cm to only 6 cm, mainly because of the force-velocity relationship. In reality, mouse lemurs achieve jump heights of about 33 cm. By implication, the unfavourable effects of the small body size of mouse lemurs on jumping performance must be counteracted by favourable effects of morphological and physiological adaptations. The same holds true for other small jumping animals. The simulations for the first time expose and explain the sheer magnitude of the isolated effects of isometric downscaling on jumping performance, to be counteracted by morphological and physiological adaptations.

Predictor-Based Compensation for Electromechanical Delay During Neuromuscular Electrical Stimulation

Electromechanical delay (EMD) is a biological artifact that arises due to a time lag between electrical excitation and tension development in a muscle. EMD is known to cause degraded performance and instability during neuromuscular electrical stimulation (NMES). Compensating for such input delay is complicated by the unknown nonlinear muscle force-length and muscle force-velocity relationships. This paper provides control development and a mathematical stability analysis of a NMES controller with a predictive term that actively accounts for EMD. The results are obtained through the development of a novel predictor-type method to address the delay in the voltage input to the muscle. Lyapunov-Krasovskii functionals are used within a Lyapunov-based stability analysis to prove semi-global uniformly ultimately bounded tracking. Experiments on able-bodied volunteers illustrate the performance and robustness of the developed controller during a leg extension trajectory following task.

Caffeine improves neuromuscular function during maximal dynamic exercise

In this study we tested the hypothesis that caffeine supplementation improves neuromuscular function, which has both nutritional and clinical relevance. Fourteen male subjects (mean ± SD: 23.8 ± 2.8 years) volunteered in a double-blind, repeated-measures study with placebo (PLA) or caffeine (CAFF) (6 mg kg(-1)). Maximal voluntary isometric contractions (MVCs), evoked maximal twitch, and maximal isokinetic contractions during elbow flexion were assessed. Mechanical and electromyographic (EMG) signals from the biceps brachii muscle were recorded, and muscle fiber conduction velocity (CV) was calculated to evaluate changes in the muscle force-velocity relationship and muscle fiber recruitment. The torque-angular velocity curve was enhanced after CAFF supplementation. This was supported by a concomitant increase of CV values (8.7% higher in CAFF). Caffeine improves muscle performance during short-duration maximal dynamic contractions. The concomitant improvement of mean fiber CV supports the hypothesis of an effect of caffeine on motor unit recruitment.

Bilateral deficit and EMG activity during explosive lower limb contractions against different overloads

We investigated whether bilateral deficit (BLD): (1) is observed during explosive lower limb contractions; (2) can be attributed to a reduction of neural drive and/or (3) to a different muscle coordination, and/or (4) to changes of the muscle force-velocity (F-v) relationship. Ten volunteers performed maximal explosive efforts of approximately 450 ms on a sledge ergometer, with both lower limbs (BL), with the right and left limb separately (ML), against different overloads. Peak-force (F, N), peak-power (w, W), sledge peak-velocity (v, m/s) and electromyography (EMG) of vastus lateralis (VL), rectus femoris (RF), biceps femoris (BF) and gastrocnemius medialis (GM) were recorded. Average values over the six overloads of F and w, developed by right or left limb during BL, were significantly lower (883 +/- 200 and 918 +/- 141 N; 1089 +/- 407 and 1099 +/- 325 W) than those developed during ML contractions (1285 +/- 177 and 1306 +/- 147 N; 1536 +/- 408 and 1497 +/- 392 W). VL and RF iEMGs were lower in BL than in ML (74 +/- 28 vs. 91 +/- 21% MVC and 39 +/- 21 vs. 56 +/- 28% MVC). The coordination among the four muscles, as determined from an analysis of the time course of iEMG, expressed as percentage of that attained at the end of the push, was poorer in BL, as compared to ML. BL F-v curves were different as compared to the ML ones, the force and power developed, at a given v, being significantly larger in ML. It is concluded that BLD occurs also during explosive pushes with the lower limbs, and that it is mainly due to different muscle coordination.

A case study of the effect of skill training on the pitching motions of collegiate baseball pitchers

A three-dimensional (3D) videography study was performed to clarify the mechanical effects of a change of pitching motion from an overhand throw (OH style) to a three-quarter throw (TQ style). Two collegiate pitchers (subjects A and B) who normally used the OH style participated. They were requested to change their original OH style into the TQ style. To do this, they were subjected to a one-year skill training program based on biomechanical principles and on knowledge such as the stretch-shortening cycle theory, muscle force-velocity relationship, and the motions of skilled pitchers (e.g., shoulder positioning at 90 degrees of abduction-adduction during the acceleration phase). Four pitches for subject A (two in pre-training, one during training and one in post-training), and three for subject B (one each in pre-training, training and post-training) were videotaped with the 3D DLT procedure using two high-speed cameras, and then analyzed. We then examined the mechanical differences between pre- and post-training. The speed of the ball at release increased progressively with every successive pitch for both subjects (Subject A : 1st : 130.3km/h ; 2nd : 133.2km/h ; 3rd : 135.7km/h ; 4th : 142.2km/h. Subject B : 1st : 131.0km/h ; 2nd : 135.0km/h ; 3rd : 139.3km/h). The pitching styles of both subjects changed from their original OH style to the TQ style, both qualitatively and quantitatively. The time-dependent patterns and peak values of the angular velocities of shoulder internal-external rotation and elbow flexion-extension of the throwing arm did not change very much. However, the peak value of the angular velocity of shoulder internal rotation occurred immediately after ball release for the OH style, while for the TQ style it occurred at ball release. As a result, the angular velocity of elbow extension at ball release was larger in the OH style than in the TQ style. On the other hand, the angular velocity of shoulder internal rotation at ball release was larger in the TQ style than in the OH style. These findings suggest that the increase in the speed of the ball is dominated by elbow extension in the OH style, and by shoulder internal rotation in the TQ style.

Changes in the human muscle force-velocity relationship in response to resistance training and subsequent detraining

Previous studies show that cessation of resistance training, commonly known as "detraining," is associated with strength loss, decreased neural drive, and muscular atrophy. Detraining may also increase the expression of fast muscle myosin heavy chain (MHC) isoforms. The present study examined the effect of detraining subsequent to resistance training on contractile performance during slow-to-medium velocity isokinetic muscle contraction vs. performance of maximal velocity "unloaded" limb movement (i.e., no external loading of the limb). Maximal knee extensor strength was measured in an isokinetic dynamometer at 30 and 240 degrees/s, and performance of maximal velocity limb movement was measured with a goniometer during maximal unloaded knee extension. Muscle cross-sectional area was determined with MRI. Electromyographic signals were measured in the quadriceps and hamstring muscles. Twitch contractions were evoked in the passive vastus lateralis muscle. MHC isoform composition was determined with SDS-PAGE. Isokinetic muscle strength increased 18% (P < 0.01) and 10% (P < 0.05) at slow and medium velocities, respectively, along with gains in muscle cross-sectional area and increased electromyogram in response to 3 mo of resistance training. After 3 mo of detraining these gains were lost, whereas in contrast maximal unloaded knee extension velocity and power increased 14% (P < 0.05) and 44% (P < 0.05), respectively. Additionally, faster muscle twitch contractile properties along with an increased and decreased amount of MHC type II and MHC type I isoforms, respectively, were observed. In conclusion, detraining subsequent to resistance training increases maximal unloaded movement speed and power in previously untrained subjects. A phenotypic shift toward faster muscle MHC isoforms (I --> IIA --> IIX) and faster electrically evoked muscle contractile properties in response to detraining may explain the present results.

The adaptive intracellular control of cardiac muscle function.

This study explores the mechanisms dominating the regulation of the biochemical energy consumption and the mechanical output of the actin-myosin motor units, the crossbridges (Xbs), in the cardiac sarcomere. Our analytical model, which couples Xbs cycling dynamics with the kinetics of the free Ca(2+) binding to troponin-C (Tn-C), includes two feedback mechanisms: (1) a cooperativity mechanism, whereby the amount of force generating Xbs determines the affinity of calcium binding to the regulatory protein and the force-length relationship (FLR); and (2) a mechanical (negative) feedback, whereby the filament shortening velocity affects the rate of Xb turnover from the force- to the nonforce-generating state, allows the analytical solution for the muscle force-velocity relationship (FVR), and the linear relation between energy consumption and the generated mechanical energy. Our experimental and analytical studies of the force response to large-amplitude sarcomere length (SL) oscillations at various frequencies and constant [Ca(2+)] in the isolated tetanized rat trabeculae reveal that the generated force depends on the history of contraction and establishes the validity of these two feedbacks. The cooperativity mechanism generates counterclockwise (CCW) hystereses, where the muscle generates external work; while at higher frequencies the mechanical feedback produces clockwise (CW) hystereses, where the muscle behaves as a damper. The cooperativity provides the adaptive control of the cardiac response to short-term changes in the load by modulating Xb recruitment. The cardiac efficiency, defined as the ratio of the generated mechanical energy (i.e., external work and pseudo-potential energy) to the sarcomere energy consumption, is determined by the mechanical feedback, reflecting an inherent property of the single Xb. The efficiency is thus independent of the number of strong Xbs and is constant and load independent.

Mechano-chemical model describing the force-velocity relationship in muscle

Performance of the muscle is examined employing the self-excited oscillation analysis, which is useful to express the force-velocity relationship in muscle. What the present formula suggests is that when a muscle is activated, mechanical myoplasmic resistance initially drops, and then part of the contractile elements build up a tensile stress equal to tensile strain (load, p) while the rest part of these elements draw the load and shorten the muscle. The new formula is mathematically identical with Hill's equation, but utilizes only a single constant (β), which implies an important intrinsic property of muscle and is deserving of further investigation.

SCALING PEAK POWER OUTPUT FOR DIFFERENCES IN BODY SIZE IN WOMEN 301

There has been a revival of interest in how physiological and performance variables should be scaled for differences in the size of the body or its exercising segments and it has been demonstrated that non-linear allometric modelling can be used to scale peak power output in men. The purpose of this study was to evaluate the use of such modelling in women. Fifteen women age 22.7 ± 1.6 years, stature 164.3 ± 5.5 cm and body mass 61.8± 5.5 kg (mean ± S.D.) who were fully accustomed to the procedures provided written informed consent and were recruited. Optimised peak power output (OPP) was determined on a friction braked cycle ergometer(Monark 814E) in a procedure that accounts for muscle force-velocity relationships. Lean leg volume (LLV) and lean upper leg volume (LULV) were determined anthropometrically. The OPP was 618 ± 98 W, LLV 4.96± 0.68 l and LULV 3.12 ± 0.48 l. Logarithmic transformations of the measures were used to identify the allometric relationships between OPP and the anthropometric variables. The resulting power functions were: 207.5LLV0.68 (r = 0.585, P = 0.022) and 334.6LULV0.53 (r = 0.514, P = 0.050). Standard errors of the exponents were 0.261 and 0.247 respectively. Neither of the measures satisfied the criterion for the use of simple ratio standards. Both variables were raised to the surface law's exponent of 0.67 and then divided into OPP to produce power function ratios. These were: 211 ± 26 W·l-0.67 for LLV and 289 ± 38 W·l-0.67 for LULV. The results suggest that non-linear allometric modelling can be used to scale peak power output for differences in body size in women.

Architecture-based force-velocity models of load-moving skeletal muscles

A predictive model of muscle force-velocity relationships is presented based on functional architectural variables. The parameters of Hill's equation describing muscle force-velocity relationship of nine muscles were estimated by their relationships with variables extracted from the whole-muscle length-force relationship and the percentage of slow-twitch fibres. Specifically, the maximal unloaded velocity (Vo) was estimated through multiple linear regression, from each muscle's fibre composition and the shortening range through which each muscle could produce active force. The maximal isometric force (Po) was also extracted from each muscle's length-force relationship. The ratio of Hill's dynamic constant a to Po and b to Vo, which determines the degree of curvature of the relation, was determined solely by the percent of slow-twitch fibres. This model was verified by fitting it to experimental force-velocity curves of nine different muscles in the cat's hindlimb. It was found that reasonable fits of force-velocity curves would be obtained with correlation coefficient in the range of 0.61 to 0.92, with an average of 0.82. The model predicted that muscles with relatively long shortening ranges would achieve higher maximal velocity, and that muscles with higher percentage of slow-twitch fibres had less pronounced curvature and lower maximal velocity in their force-velocity relationships.

Determining ideal baseball bat weights using muscle force-velocity relationships

The equations of physics for bat-ball collisions were coupled to the physiology of the muscle force-velocity relationship to compute the ideal bat weight for individual baseball players. The results of this coupling suggest that some batters use bats that are too heavy for them, and some batters use bats that are too light, but most experienced batters use bats that are just right. However, ideal bat weight is not correlated with height, weight, or age. Decades of prior physiological research on force-velocity relationships of isolated muscle have shown that hyperbolic curves usually fit the data best. However, for the present data, the hyperbolic curves fit only one class of subjects best: for the others a straight line provides the best fit. We hypothesize that these two classes of players use different control strategies.