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Journal of Biomechanics 67 (2018) 91–97 Contents lists available at ScienceDirect Journal of Biomechanics journal homepage: www.elsevier.com/locate/jbiomech www.JBiomech.com Intraoperative and biomechanical studies of human vastus lateralis and vastus medialis sarcomere length operating range ⇑ Jongsang Son a, Andy Indresano b, Kristin Sheppard b, Samuel R. Ward b,c, Richard L. Lieber a,b,d, a Shirley Ryan AbilityLab (formerly Rehabilitation Institute of Chicago), IL, United States b Department of Orthopaedic Surgery, University of California San Diego, La Jolla, CA, United States c Department of Radiology, University of California San Diego, La Jolla, CA, United States d Research Service, Hines V.A. Hospital, Maywood, IL, United States article info abstract Article history: The vast majority of musculoskeletal models are not validated against primary experimental data. Accepted 26 November 2017 Conversely, most human experimental measurements are not explained theoretically using models to provide a mechanistic understanding of experimental results. Here we present a study with both primary human data and primary modeling data. Intraoperative sarcomere length was measured on the human Keywords: vastus lateralis (VL) and vastus medialis (VM) muscles (n = 8) by laser diffraction. These data were com- Muscle physiology pared to a biomechanical model based on muscle architecture and moment arms obtained independently Sarcomere length from cadaveric specimens (n = 9). Measured VL sarcomere length ranged from about 3.2 mm with the Biomechanical modeling knee flexed to 45° to 3.8 mm with the knee flexed to 90°. These values were remarkably close to theoret- Patellar pain ical predictions. Measured VM sarcomere length ranged from 3.6 mm with the knee flexed to 45° to 4.1 mm with the knee flexed to 90°. These values were dramatically longer than theoretical predictions. Our measured sarcomere length values suggest that human vasti may have differing functions with regard to knee extension and patellar stabilization. This report underscores the importance of validating experi- mental data to theoretical models and vice versa. Published by Elsevier Ltd. 1. Introduction what is known about human muscle fiber types and plasticity is primarily known about the vastus lateralis muscle. Elucidating the design and function of human skeletal muscles A detailed understanding of the design and function of human is required to understand normal function, pathological conditions muscles in hampered by the lack of tools available to provide the and suggest surgical interventions to recover function after injury types of detailed studies in humans that have often been per- (Fridén and Lieber, 2002; Gans, 1982; Lieber and Friden, 2000; formed in animal models. One of the most important parameters Lieber and Ward, 2011). Across the human body, it could be argued needed to understand the design and function of muscle is sarcom- that quadriceps muscles are the most important functional muscle ere length (Lieber and Friden, 2000; Lieber and Ward, 2011). The group. Their function is obviously critical for locomotion and muscle sarcomere is the functional unit of force generation in opposing gravity (Perry, 1992). However, their strength is also skeletal muscle and its length is an excellent predictor of active related to clinical problems such as patellar pain and tracking muscle force (Edman, 1966; Gordon et al., 1966; Winters et al., and locomotion efficiency and there is even evidence that quadri- 2011). Our laboratory has published sarcomere length values in ceps strength loss can predict the onset of osteoarthritis (Mahir humans for over twenty years (Lieber et al., 1994) and sarcomere et al., 2016). At the tissue level, human vastus lateralis muscle lengths in animal models for over thirty years (Lieber and Baskin, biopsies represent the gold standard for study of human muscle 1983; Lieber et al., 1983), primarily using laser diffraction (Bergstrom, 1975; Lexell et al., 1986; Sjöström et al., 1982; approaches (Lieber et al., 1984). Laser diffraction provides a robust Willan et al., 2002) so it is not an understatement to state that sarcomere length value because it spatially averages across hun- dreds of thousands of sarcomeres (see Table 1 of reference Young et al., 2014) to yield a single value with a resolution of 5–10 nm. In cadaveric samples, sarcomere length measurements across the ⇑ Corresponding author at: Shirley Ryan AbilityLab, 355 E. Erie Street, Chicago, IL 60611, United States. muscle can provide sarcomere length estimates for the entire mus- E-mail address: [email protected] (R.L. Lieber). cle (Takahashi et al., 2007) while, in patients, sarcomere length is https://doi.org/10.1016/j.jbiomech.2017.11.038 0021-9290/Published by Elsevier Ltd. 92 J. Son et al. / Journal of Biomechanics 67 (2018) 91–97 typically measured only in single muscle region exposed based on of moment arm and quadriceps muscle architecture (n = 9). In surgical indications (Lieber et al., 1994; Ward et al., 2009). addition to the VL and VM, rectus femoris (RF) and vastus inter- In light of the fact that laser diffraction studies are limited to medius (VI) were dissected from extremities with care taken to surgical patients, it is encouraging that microendoscopy has been maintain the integrity of the skin and associated tissues of the recently emerged for intravital use in human volunteers not under- knee. Muscles were removed and their architectural properties going surgery (Llewellyn et al., 2008). Because microendoscopy is determined using methods previously described (see below). much less invasive than laser diffraction, sarcomere lengths can The dissected knee was mounted onto a mechanical jig securing now be recorded from muscles not previously available. This rep- the distal femur by Steinman pins to vertical braces while an addi- resents a significant technical advance in the field, perhaps even tional pin engaged the middle third of the tibia allowing knee flex- enabling dynamic sarcomere length measurements. ion and extension (Fig. 1). Thirty-gauge stainless steel sutures were Another approach used to understand musculoskeletal func- secured to the distal stumps of quadriceps tendon and routed to tion, is to create biomechanical models based on previously mea- electrogoniometers recreating the line of force for each muscle. sured muscle, joint and tendon properties. The vast majority of These stainless steel sutures were secured to toothed nylon cables these theoretical models are not validated against primary experi- and connected to nonbacklash gears mounted to potentiometers as mental data (Hicks et al., 2015). It is also fair to critique most described by An et al. (1983) and placed under 500 g tension. Neu- human experimental measurements as not being explained theo- tral (0°) was defined as alignment of the tibia and the distal femur retically using models to provide a mechanistic understanding of in the sagittal plane. The knee was passed manually from 0 to 100° experimental results. Our goal was to measure human quadriceps of flexion. Individual excursions of quadriceps tendons and joint sarcomere length during knee flexion in joint replacement patients angular displacements were digitized simultaneously. Each excur- and then to validate these measurements against a model gener- sion trial was repeated three times. ated from independent measurements obtained from cadaveric Tendon excursion was differentiated with respect to joint angle specimens. Because sarcomere lengths from one of these same yielding moment arm as a function of joint angle. Before differen- muscles was recently reported (Chen et al., 2016), it is also possible tiating, excursion data were resampled every 10° to avoid superflu- to compare laser diffraction and microendoscopy methods for the ous noise. Moment arm-knee angle relationships were then fit by vastus lateralis muscle. stepwise polynomial regression using an algorithm developed to With regard to the modeling approach, biomechanical and minimize the influence of the fitting method on the resulting equa- anatomical data are often combined to make predictions. Because tion (Burkholder and Lieber, 1996; Loren et al., 1996). This was a high degree of inter-individual variation occurs, it is not clear done by including only the polynomial terms that significantly whether it is justified to combine disparate datasets collected on improved the curve fit (p-to-enter = 0.05) and not requiring all different individuals and combining them to create models. lower order terms to be included beneath the highest order term. Addressing this question is relevant to the current trend toward The explanation power of the stepwise polynomial regression developing patient-specific models. Thus, the purpose of this study was confirmed according to the different maximum polynomial was to compare the sarcomere length range of the human vasti order ranging 0–10. As a result, 3rd-order stepwise regression between directly measured values and those obtained via biome- was used for further analysis because 3rd-order stepwise fitting chanical modeling. explained 90% of the variability in the raw data (Fig. 3A). 2. Methods 2.3. Muscle architecture 2.1. Intraoperative sarcomere length For architectural measurements, fascicles were dissected from specimens that were Formalin-fixed with the body fully supine. Sarcomere length was measured from human patients (n = 7) Thus, the hip and knee were at approximately 0° and the ankles using a protocol approved by the Committee