Correction of Error in Fiber Length Due to Lever Arm Rotation During Mechanical Tests of Single Muscle Fibers

Abstract

The single muscle fiber preparation is a popular technique to assess mechanical properties at the cellular level and how these properties change with aging, disease, exercise, etc. Fibers are usually attached to wires extending perpendicularly from the lever arm of a high speed motor and force transducer that are then mounted to the stage of a microscope. Because of lever arm rotation, the fiber does not move along the optical plane, introducing a length measurement error if length is measured along the optical plane. The purpose of this study was to 1) calculate the error of lever arm movement and 2) provide a correction equation. The error was calculated assuming 2 mm fiber length at up to 50% displacement, because this is a commonly used stretch or slack magnitude (∼15% slacking with unloaded shortening velocity, ∼30% lengthening response to eccentric contraction, ∼50% stretch with passive tension). The range of error was hyperbolically enlarged as either lever arm length or optical plane stretch magnitude increased, and this error was exacerbated with the increase of both factors. For example, with a 5 mm connector attached to the lever arm, the relative error [100×(actual displacement-target displacement)/target displacement] was 0.59%, 1.36%, and 1.78% with 10, 30, and 50% of stretch or slacking, respectively. However, with a 10 mm connector, the relative error was 2.38%, 5.66%, and 7.64%, and in the case of a 15 mm connector, the relative error increased dramatically up to 5.36%, 12.69%, and 17.10%. We suggest the following correction equation to eliminate potential errors; q=b+f−r|mT+1|/(m2T2+m2+T2+1)1/2, where q = observed fiber length, b=connector length, f=fiber length, h=lever arm length, r=(b2+h2)1/2, m=-h/(b+f), T=[p2-(d-r)1/2/(d2+r2-p2)]1/2, p=target fiber length, and d=[(b+f)2+h2]1/2.