iandanforth
commented
6 years ago Supported Statements
Motor unit size and force generation relationship
https://www.ncbi.nlm.nih.gov/pubmed/10423192
Muscle models that incorperate motor units better predict in vivo measurements
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3386380/
Muscle fiber types don't seem to have different force-length curves
https://www.ncbi.nlm.nih.gov/pubmed/19647260 http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.843.2694&rep=rep1&type=pdf
Muscle fiber type may influence force velocity curves
"a fast muscle like extensor digitorum longus (EDL), compared with a slow one like soleus, not only shortens faster but also has greater power output because of less curvature in its force–velocity curve." https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3840917/
The standard model of force-length relationships is not perfect
https://www.ncbi.nlm.nih.gov/pubmed/19647260
Other models of motor unit activity, fatigue and recovery are available
https://www.sciencedirect.com/science/article/pii/S000634950275580X
The spring constant of muscle fibers (in rats) is near 1.71 N/mm
https://www.physiology.org/doi/full/10.1152/ajpregu.2000.278.6.r1661
Passive mechanical properties of muscle change over long timescales, partially by adding / removing sarcomeres in series
The slack length of human biceps brachii occurs when the arm is bent to ~95 degrees
http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0053159
Passive steady-state force–length curves showed large inter-animal variation
https://link.springer.com/article/10.1007/s00422-012-0530-6
The greatest contractile force (in frog sartorius muscle) is generated when the muscle is elongated beyond its 'natural length'
https://www.tandfonline.com/doi/abs/10.3109/13813455109145002
The method of measurement for maximum contraction velocity can significantly change the value reported.
https://www.ncbi.nlm.nih.gov/pubmed/20962893
An average abductor pollicis brevis has ~120 motor units
https://www.e-arm.org/upload/pdf/Jae25-05-11.pdf
The Abductor Pollicis Brevis can produce a maximum isometric force of ~ 60N of force in an adult human
https://www.jospt.org/doi/pdf/10.2519/jospt.1995.21.3.139
Estimates of the number of motor units in the biceps brachialis have a large range (211-1816)
https://deepblue.lib.umich.edu/bitstream/handle/2027.42/50158/880160506_ftp.pdf
"[T]he number of muscle fibers per motor unit is two to four times larger in humans than in the commonly used laboratory animals."
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.917.2822&rep=rep1&type=pdf
Sources / Summaries
Thelen 2003 - Complete OpenSim Implementation Description
https://simtk-confluence.stanford.edu/download/attachments/2624181/CompleteDescriptionOfTheThelen2003MuscleModel.pdf?version=1&modificationDate=1319838594036&api=v2
Seow
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3840917/
"data also provide justification for the use of a hyperbolic equation not as a mere empirical description but as a meaningful explanation for force–velocity behavior based on cross-bridge kinetics"
"During an isotonic quick release, the muscle is suddenly released from its isometric force to a lower and constant force (i.e., isotonic load). In response to the sudden change in load, the muscle shortens in a characteristic fashion"
The standard model of force velocity relationships is not perfect
"Careful measurements of force–velocity properties of single skeletal muscle fibers have revealed that at low loads (less than ∼5% Fmax), the measured velocities exceed those predicted by the Hill hyperbola. At the extrapolated zero load, Hill’s equation underestimates the value of Vmax by ∼6–7% (Edman et al., 1976; Julian et al., 1986). For whole muscle preparations with mixed fiber types, the underestimation of Vmax by the Hill hyperbola is found to be much greater (Claflin and Faulkner, 1989)"
Summary
The article generally supports the use of the standard Hill equation for the force velocity relationship. It goes on to discuss how this relationship might arise from the properties of cross-bridge creation, detachment, and force production under varying shortening velocities. Empirical data from Piazzesi et al. (2007) are used to back up this model.
Fatigue - The curvature of the force-velocity relationship increases with fatigue. "there must be a substantial decrease in the rate constant for attachment in the Huxley (1957) model to account for the observed decrease in power and increase in force–velocity curvature in fatigued muscle."
Clay Anderson (and others) BME 599
http://rrg.utk.edu/resources/BME599/assignments/BME599_lab_1_dynamic_simulation_jumping.pdf
MuscleModelEquations.pdf
Jovanović et al
Desmos comparison of Jovanović and Anderson
http://www.doiserbia.nb.rs/img/doi/1451-4869/2015/1451-48691501053J.pdf
Rosario et al.
Rosario et al. - 2016 - Muscle-spring dynamics in time-limited, elastic movements.pdf
"muscle contractile force is transmitted to skeletal structures through elastic structures, inextricably coupling muscle and spring dynamics." - GOOD QUOTE
"muscle force declines with contraction velocity" - References Hill 1938
"in situations where rapid spring-loading is beneficial (e.g. escape jumps and predatory ambushes), organisms may not have enough time to fully load their springs before the onset of movement. Although these organisms are not generating maximal muscle force, it is possible that their muscle – spring prop- erties maximize elastic energy storage for submaximal force production."
"We simulated dynamics within muscle–spring systems by con- necting, in series, a model of a muscle to a model of a spring ... Specifically, we connected a Hill-type muscle to a Hookean spring [1,5,16]."
Doesn't a hill-type model already have an in-series spring to account for tendon forces?
Equations used and a discussion of the parameters
Desmos graph including the supplied parameter values
The graph at lengths greater than 1 muscle-length never falls back to zero. Why?
Contrast with this graph or this graph which show force of the contractile portion going to zero as it nears 2 muscle-lengths
Summary
The regime we're targeting is much closer to the fast acting frog regime than slow-force-building grasshopper regime. Once satisfactory equations and paramaters for the force length and force velocity relationships have been established, the standard charts that take into account passive component force generation at muscle lengths >1 should be sufficient for our purposes.
Jones 2010
"There are three factors contributing to the loss of power in mammalian muscle at physiological temperatures, a decrease in isometric force, which mainly indicates a reduction in the number of active cross bridges, a slowing of the maximum velocity of unloaded shortening and an increased curvature of the force–velocity relationship."
The recovery of force in muscle takes minutes and follows an asymptotic return to normal
"is that it is the rate constant for attachment, f, rather than g1, which decreases with fatigue, giving rise to the change in curvature and being a major factor in the loss of power."
READ: Changes in the force–velocity relationship of fatigued muscle: implications for power production and possible causes
Summary
The paper discusses the metabolic and actin-myosin level changes that may occur during muscle fatigue. While interesting these factors are likely too specific and low level to be incorporated into a PyMuscle model.
In vitro force measurements for single fibers
https://www.jove.com/video/52695/measurement-maximum-isometric-force-generated-permeabilized-skeletal
Physics of the Body (older textbook)
https://www.medicalphysics.org/documents/WebPOTB.pdf
Muscles contract 15-20% of their length.
Curling a 44lb weight requires ~330 lb of force.
"A trained individual could probably curl about 200 N (~44 lb) requiring the biceps to provide 1500 N (~330 lb) force."
Why Animals Have Different Muscle Fiber Types - Rome 1988
Kami Link