Work Loop
Encyclopedia
The work loop technique is used in muscle physiology to evaluate the mechanical work and power
output of skeletal or cardiac
muscle contractions via in vitro muscle testing
of whole muscles, fiber bundles or single muscle fibers. This technique is primarily used for cyclical contractions such as the rhythmic flapping of bird wings
or the beating of heart ventricular
muscle.
To simulate the rhythmic shortening and lengthening of a muscle (e.g. while moving a limb), a servo motor
oscillates the muscle at a given frequency and range of motion observed in natural behavior. Simultaneously, a burst of electrical pulses is applied to the muscle at the beginning of each shortening-lengthening cycle to stimulate the muscle to produce force. Since force and length return to their initial values at the end of each cycle, a plot of force vs. length yields a 'work loop'. Intuitively, the area enclosed by the loop represents the net mechanical work performed by the muscle during a single cycle.
from motor neurons
), force development, length change and shortening velocity. However, each of these parameters were measured while holding other ones constant, making their interactions unclear. For instance, force-velocity and force-length relationships were determined at constant velocities and loads. Yet during locomotion, neither muscle velocity nor muscle force are constant. In running, for example, muscles in each leg experience time-varying forces and time-varying shortening velocities as the leg decelerates and accelerates from heelstrike to toeoff. In such cases, classical force-length (constant velocity) or force-velocity (constant length) experiments might not be sufficient to fully explain muscle function.
In 1960, the work loop method was introduced to explore muscle contractions of both variable speed and variable force. These early work loop experiments characterized the mechanical behavior of asynchronous muscle (a type of insect flight muscle). However due to the specialized nature of asynchronous muscle, the work loop method was only applicable for insect muscle experiments. In 1985, Robert K. Josephson modernized the technique to evaluate properties of synchronous muscles powering katydid
flight by stimulating the muscle at regular time intervals during each shortening-lengthening cycle. Josephson's innovation generalized the work loop technique for wide use among both invertebrate
and vertebrate
muscle types, profoundly advancing the fields of muscle physiology and comparative biomechanics.
Work loop experiments also allowed greater appreciation for the role of activation & relaxing kinetics in muscle power and work output. For instance, if a muscle turns on and off more slowly, the shortening and lengthening curves will be shallower and closer together, resulting in decreased work output. "Negative" work loops were also discovered, showing that muscle lengthening at higher force than the shortening curve can result in net energy absorption by the muscle, as in the case of deceleration or constant-speed downhill walking.
In 1992, the work loop approach was extended further by the novel use of bone strain measurements to obtain in vivo force. Combined either with estimates of muscle length changes or with direct methods (e.g. sonomicrometry
), in vivo force technology enabled the first in vivo work loop measurements.
, a muscle generating force while shortening is said to output 'positive work' (i.e. generating work), whereas a muscle generating force while lengthening produces 'negative work' (i.e. absorbing work). Therefore, a counter-clockwise vs. clockwise work loop represents work generation vs. work absorption, respectively. For example during a jump, the leg muscles generate work to increase the body's speed away from the ground, yielding counter-clockwise work loops. When landing, however, the same muscles absorb work to decrease the body's speed, yielding clockwise work loops.
Since work is defined as force multiplied by displacement, the area of the graph shows the mechanical work output of the muscle. In a typical work-generating instance, the muscle shows a rapid curvilinear rise in force as it shortens, followed by a slower decline during or shortly before the muscle begins the lengthening phase of the cycle. The area beneath the shortening curve (upper curve) gives the total work done by the shortening muscle, while the area beneath the lengthening curve (lower curve) represents the work absorbed by the muscle and turned into heat (done by either environmental forces or antagonistic muscles). Subtracting the latter from the former gives the net mechanical work output of the muscle cycle, and dividing that by the cycle duration gives net mechanical power output .
which extends linearly as a force is applied. This final case would yield a slanted straight line 'work loop' where the line slope
is the spring stiffness
.
and crustaceans
) or small vertebrates (e.g. fish
, frogs, rodents
). The experimental technique described below applies both to in vitro
and in situ approaches.
, the muscle is isolated from the animal (or prepared in situ), attached to the muscle testing apparatus and bathed in Ringer's solution
maintained at a constant temperature. While the isolated muscle is still living, the experimenter then applies two manipulations to test muscle function: 1) Electrical stimulation to mimic the action of a motor neuron and 2) strain (muscle length change) to mimic the rhythmic motion of a limb. To elicit muscle contraction, the muscle is stimulated by a series of electrical pulses delivered by an electrode
to stimulate either the motor nerve or the muscle tissue itself. Simultaneously, a computer-controlled servo motor in the testing apparatus oscillates the muscle while measuring the force generated by the stimulated muscle. The following parameters are modulated by the experimenter to influence muscle force, work and power output:
of muscle length data.
Step 2) Obtain instantaneous muscle power by multiplying muscle force data by muscle velocity data for each time sample.
Step 3) Obtain net work (a single number) by numerical integration
of muscle power data.
Step 4) Obtain net power (a single number) by dividing net work by the time duration of the cycle.
, tracing the work loop shape and quantifying its area. Or, 2) manually by printing a hard copy of the work loop graph, cutting the inner area and weighing it on an analytical balance. Net work is then divided by the time duration of the cycle to obtain net power.
Power (physics)
In physics, power is the rate at which energy is transferred, used, or transformed. For example, the rate at which a light bulb transforms electrical energy into heat and light is measured in watts—the more wattage, the more power, or equivalently the more electrical energy is used per unit...
output of skeletal or cardiac
Cardiac muscle
Cardiac muscle is a type of involuntary striated muscle found in the walls and histologic foundation of the heart, specifically the myocardium. Cardiac muscle is one of three major types of muscle, the others being skeletal and smooth muscle...
muscle contractions via in vitro muscle testing
In vitro muscle testing
In vitro muscle testing is a method used to characterize properties of living muscle tissue after having removed the tissue from an organism. This allows more extensive and precise quantification of muscle properties than in vivo testing...
of whole muscles, fiber bundles or single muscle fibers. This technique is primarily used for cyclical contractions such as the rhythmic flapping of bird wings
Bird flight
Flight is the main mode of locomotion used by most of the world's bird species. Flight assists birds while feeding, breeding and avoiding predators....
or the beating of heart ventricular
Ventricle (heart)
In the heart, a ventricle is one of two large chambers that collect and expel blood received from an atrium towards the peripheral beds within the body and lungs. The Atria primes the Pump...
muscle.
To simulate the rhythmic shortening and lengthening of a muscle (e.g. while moving a limb), a servo motor
Servo motor
thumb|right|200px|Industrial servomotorThe grey/green cylinder is the [[Brush |brush-type]] [[DC motor]]. The black section at the bottom contains the [[Epicyclic gearing|planetary]] [[Reduction drive|reduction gear]], and the black object on top of the motor is the optical [[rotary encoder]] for...
oscillates the muscle at a given frequency and range of motion observed in natural behavior. Simultaneously, a burst of electrical pulses is applied to the muscle at the beginning of each shortening-lengthening cycle to stimulate the muscle to produce force. Since force and length return to their initial values at the end of each cycle, a plot of force vs. length yields a 'work loop'. Intuitively, the area enclosed by the loop represents the net mechanical work performed by the muscle during a single cycle.
History
Classical studies from the 1920's through the 1960's characterized the fundamental properties of muscle activation (via action potentialsAction potential
In physiology, an action potential is a short-lasting event in which the electrical membrane potential of a cell rapidly rises and falls, following a consistent trajectory. Action potentials occur in several types of animal cells, called excitable cells, which include neurons, muscle cells, and...
from motor neurons
Motor neuron
In vertebrates, the term motor neuron classically applies to neurons located in the central nervous system that project their axons outside the CNS and directly or indirectly control muscles...
), force development, length change and shortening velocity. However, each of these parameters were measured while holding other ones constant, making their interactions unclear. For instance, force-velocity and force-length relationships were determined at constant velocities and loads. Yet during locomotion, neither muscle velocity nor muscle force are constant. In running, for example, muscles in each leg experience time-varying forces and time-varying shortening velocities as the leg decelerates and accelerates from heelstrike to toeoff. In such cases, classical force-length (constant velocity) or force-velocity (constant length) experiments might not be sufficient to fully explain muscle function.
In 1960, the work loop method was introduced to explore muscle contractions of both variable speed and variable force. These early work loop experiments characterized the mechanical behavior of asynchronous muscle (a type of insect flight muscle). However due to the specialized nature of asynchronous muscle, the work loop method was only applicable for insect muscle experiments. In 1985, Robert K. Josephson modernized the technique to evaluate properties of synchronous muscles powering katydid
Tettigoniidae
The family Tettigoniidae, known in American English as katydids and in British English as bush-crickets, contains more than 6,400 species. It is part of the suborder Ensifera and the only family in the superfamily Tettigonioidea. They are also known as long-horned grasshoppers, although they are...
flight by stimulating the muscle at regular time intervals during each shortening-lengthening cycle. Josephson's innovation generalized the work loop technique for wide use among both invertebrate
Invertebrate
An invertebrate is an animal without a backbone. The group includes 97% of all animal species – all animals except those in the chordate subphylum Vertebrata .Invertebrates form a paraphyletic group...
and vertebrate
Vertebrate
Vertebrates are animals that are members of the subphylum Vertebrata . Vertebrates are the largest group of chordates, with currently about 58,000 species described. Vertebrates include the jawless fishes, bony fishes, sharks and rays, amphibians, reptiles, mammals, and birds...
muscle types, profoundly advancing the fields of muscle physiology and comparative biomechanics.
Work loop experiments also allowed greater appreciation for the role of activation & relaxing kinetics in muscle power and work output. For instance, if a muscle turns on and off more slowly, the shortening and lengthening curves will be shallower and closer together, resulting in decreased work output. "Negative" work loops were also discovered, showing that muscle lengthening at higher force than the shortening curve can result in net energy absorption by the muscle, as in the case of deceleration or constant-speed downhill walking.
In 1992, the work loop approach was extended further by the novel use of bone strain measurements to obtain in vivo force. Combined either with estimates of muscle length changes or with direct methods (e.g. sonomicrometry
Sonomicrometry
Sonomicrometry is a technique of measuring the distance between piezoelectric crystals based on the speed of acoustic signals through the medium they are embedded in. Typically, the crystals will be coated with an epoxy 'lens' and placed into the material facing each other...
), in vivo force technology enabled the first in vivo work loop measurements.
Positive, negative and net work
A work loop combines two separate plots: force vs. time and length vs. time. When force is plotted against length, a work loop plot is created: each point along the loop corresponds to a force and a length value at a unique point in time. As time progresses, the plotted points trace the shape of the work loop. The direction in which the work loop is traced through time is a critical feature of the work loop. If the muscle is shortening while generating force, the work loop is traced in a counter-clockwise direction. If the muscle is lengthened while generating force, the direction is clockwise. By convention in biomehanicsBiomechanics
Biomechanics is the application of mechanical principles to biological systems, such as humans, animals, plants, organs, and cells. Perhaps one of the best definitions was provided by Herbert Hatze in 1974: "Biomechanics is the study of the structure and function of biological systems by means of...
, a muscle generating force while shortening is said to output 'positive work' (i.e. generating work), whereas a muscle generating force while lengthening produces 'negative work' (i.e. absorbing work). Therefore, a counter-clockwise vs. clockwise work loop represents work generation vs. work absorption, respectively. For example during a jump, the leg muscles generate work to increase the body's speed away from the ground, yielding counter-clockwise work loops. When landing, however, the same muscles absorb work to decrease the body's speed, yielding clockwise work loops.
Since work is defined as force multiplied by displacement, the area of the graph shows the mechanical work output of the muscle. In a typical work-generating instance, the muscle shows a rapid curvilinear rise in force as it shortens, followed by a slower decline during or shortly before the muscle begins the lengthening phase of the cycle. The area beneath the shortening curve (upper curve) gives the total work done by the shortening muscle, while the area beneath the lengthening curve (lower curve) represents the work absorbed by the muscle and turned into heat (done by either environmental forces or antagonistic muscles). Subtracting the latter from the former gives the net mechanical work output of the muscle cycle, and dividing that by the cycle duration gives net mechanical power output .
Inferring muscle function from work loop shape
Hypothetically, a square work loop (area = max force x max displacement) would represent the maximum work output of a muscle operating within a given force and length range. Conversely, a flat line (area = 0) would represent the minimum work output. For example, a muscle that generates force without changing length (isometric contraction) will show a vertical line 'work loop'. Reciprocally, a muscle that shortens without changing force (isotonic contraction) will show a horizontal line 'work loop'. Finally, a muscle can behave like a springSpring (device)
A spring is an elastic object used to store mechanical energy. Springs are usually made out of spring steel. Small springs can be wound from pre-hardened stock, while larger ones are made from annealed steel and hardened after fabrication...
which extends linearly as a force is applied. This final case would yield a slanted straight line 'work loop' where the line slope
Slope
In mathematics, the slope or gradient of a line describes its steepness, incline, or grade. A higher slope value indicates a steeper incline....
is the spring stiffness
Stiffness
Stiffness is the resistance of an elastic body to deformation by an applied force along a given degree of freedom when a set of loading points and boundary conditions are prescribed on the elastic body.-Calculations:...
.
Work loop experimental approach
Work loop experiments are most often performed on muscle tissue isolated either from invertebrates (e.g. insectsInsect
Insects are a class of living creatures within the arthropods that have a chitinous exoskeleton, a three-part body , three pairs of jointed legs, compound eyes, and two antennae...
and crustaceans
Crustacean
Crustaceans form a very large group of arthropods, usually treated as a subphylum, which includes such familiar animals as crabs, lobsters, crayfish, shrimp, krill and barnacles. The 50,000 described species range in size from Stygotantulus stocki at , to the Japanese spider crab with a leg span...
) or small vertebrates (e.g. fish
Fish
Fish are a paraphyletic group of organisms that consist of all gill-bearing aquatic vertebrate animals that lack limbs with digits. Included in this definition are the living hagfish, lampreys, and cartilaginous and bony fish, as well as various extinct related groups...
, frogs, rodents
Rodent
Rodentia is an order of mammals also known as rodents, characterised by two continuously growing incisors in the upper and lower jaws which must be kept short by gnawing....
). The experimental technique described below applies both to in vitro
In vitro muscle testing
In vitro muscle testing is a method used to characterize properties of living muscle tissue after having removed the tissue from an organism. This allows more extensive and precise quantification of muscle properties than in vivo testing...
and in situ approaches.
Experimental setup
Following humane procedures approved by IACUCInstitutional Animal Care and Use Committee
Institutional Animal Care and Use Committees are of central importance to the application of laws to animal research in the United States. Most research involving laboratory animals is funded by the United States National Institutes of Health or other federal agencies...
, the muscle is isolated from the animal (or prepared in situ), attached to the muscle testing apparatus and bathed in Ringer's solution
Ringer's solution
Ringer's solution is the name given to a solution of several salts dissolved in water for the purpose of creating an isotonic solution relative to the bodily fluids of an animal. Ringer's solution typically contains sodium chloride, potassium chloride, calcium chloride and sodium bicarbonate,...
maintained at a constant temperature. While the isolated muscle is still living, the experimenter then applies two manipulations to test muscle function: 1) Electrical stimulation to mimic the action of a motor neuron and 2) strain (muscle length change) to mimic the rhythmic motion of a limb. To elicit muscle contraction, the muscle is stimulated by a series of electrical pulses delivered by an electrode
Electrode
An electrode is an electrical conductor used to make contact with a nonmetallic part of a circuit...
to stimulate either the motor nerve or the muscle tissue itself. Simultaneously, a computer-controlled servo motor in the testing apparatus oscillates the muscle while measuring the force generated by the stimulated muscle. The following parameters are modulated by the experimenter to influence muscle force, work and power output:
- Stimulation duration: The time period over which the muscle receives electrical stimulation
- Stimulation pulse frequency: The number of stimulation pulses per stimulation duration
- Stimulation phase: The time delay between the onset of stimulation and muscle length change
- Strain amplitude: The difference between the maximum and minimum values of the length oscillation pattern
- Strain frequency: The number of shortening-lengthening periods per time period
Calculating muscular work and power from experimental data
Calculation of either muscle work or power requires collection of muscle force and length (or velocity) data at a known sampling rate. Net work is typically calculated either from instantaneous power (muscle force x muscle velocity) or from the area enclosed by the work loop on a force vs. length plot. Both methods are mathematically equivalent and highly accurate, however the 'area inside the loop' method (despite its simplicity) can be tedious to carry out for large data sets.Method 1: Instantaneous power method
Step 1) Obtain muscle velocity by numerical differentiationNumerical differentiation
In numerical analysis, numerical differentiation describes algorithms for estimating the derivative of a mathematical function or function subroutine using values of the function and perhaps other knowledge about the function.-Finite difference formulae:...
of muscle length data.
Step 2) Obtain instantaneous muscle power by multiplying muscle force data by muscle velocity data for each time sample.
Step 3) Obtain net work (a single number) by numerical integration
Numerical integration
In numerical analysis, numerical integration constitutes a broad family of algorithms for calculating the numerical value of a definite integral, and by extension, the term is also sometimes used to describe the numerical solution of differential equations. This article focuses on calculation of...
of muscle power data.
Step 4) Obtain net power (a single number) by dividing net work by the time duration of the cycle.
Method 2: Area inside the loop method
The area inside the work loop can be quantified either 1) digitally by importing a work loop image into ImageJImageJ
ImageJ is a public domain, Java-based image processing program developed at the National Institutes of Health. ImageJ was designed with an open architecture that provides extensibility via Java plugins and recordable macros. Custom acquisition, analysis and processing plugins can be developed using...
, tracing the work loop shape and quantifying its area. Or, 2) manually by printing a hard copy of the work loop graph, cutting the inner area and weighing it on an analytical balance. Net work is then divided by the time duration of the cycle to obtain net power.