Upper and Lower Limb Muscle Architecture of a 104 Year-Old Cadaver

Muscle architecture is an important component to typical musculoskeletal models. Previous studies of human muscle architecture have focused on a single joint, two adjacent joints, or an entire limb. To date, no study has presented muscle architecture for the upper and lower limbs of a single cadaver. Additionally, muscle architectural parameters from elderly cadavers are lacking, making it difficult to accurately model elderly populations. Therefore, the purpose of this study was to present muscle architecture of the upper and lower limbs of a 104 year old female cadaver. The major muscles of the upper and lower limbs were removed and the musculotendon mass, tendon mass, musculotendon length, tendon length, pennation angle, optimal fascicle length, physiological cross-sectional area, and tendon cross-sectional area were determined for each muscle. Data from this complete cadaver are presented in table format. The data from this study can be used to construct a musculoskeletal model of a specific individual who was ambulatory, something which has not been possible to date. This should increase the accuracy of the model output as the model will be representing a specific individual, not a synthesis of measurements from multiple individuals. Additionally, an elderly individual can be modeled which will provide insight into muscle function as we age.


Introduction
One of the first models of muscles that accounted for muscle architecture was developed by Niels Stensen in 1667 [1]. More recently, Gans and Bock [2] described how muscle architecture can be used to gain insight into a muscle's function. Numerous authors have used this form and function relationship to describe the function of muscles [3][4][5]. Using this form/ function relationship, many musculoskeletal models seek to estimate a muscle's function based on its architecture [6]. Based on the estimated muscle function, these musculoskeletal models have been proposed to guide tendon transfer and other musculoskeletal surgeries [7]. Given the connection between a muscle's form and its function the importance of obtaining muscle architectural measures is central in the understanding of muscle function and in the construction of musculoskeletal models for use in clinical areas such as rehabilitation and surgery. a1111111111 a1111111111 a1111111111 a1111111111 a1111111111 length (L mt ) and tendon length (L t ) were measured to the nearest 0.1 cm. Once the muscles were removed, palpable bony landmarks were measured to provide additional anthropmetric information about the cadaver and are presented in Table 1.
Given the force-length properties of muscle [24] the length at which a muscle fascicle can produce maximal force was determined. Since muscle mass varies greatly across the human body [25] the number of fascicles sampled from each muscle was based upon its mass. Looking at previous research to determine the span of muscle masses it was determined that three fascicles would be removed for every 50 g of muscle mass. Muscles under 50 g would have three fascicles removed. These samples were taken from all parts of each muscle to ensure that the whole muscle was sampled equally. Once a fascicle was removed, its length (L f ) was determined using a standard rule and recorded. Using a stereo dissection microscope and fine forceps, individual muscle fibers were removed from the fascicles. The muscle fiber was then mounted on a microscope slide and digital images of the muscle fiber at 400x magnification were taken. Custom written MATLAB code [26] (The Mathworks, Natick, MA) was used to measure average sarcomere length (L s ). A minimum of 60 sarcomeres (averaged across all fascicle samples per muscle) was required to ensure adequate sarcomere sample size [15]. Optimal fascicle length was calculated using, Where L sopt was 2.7 μm for human muscle fibers [27]. Pennation angle was measured using a clear plastic goniometer and recorded to the nearest degree when the muscle was first removed. However, since pennation angle varies with muscle fascicle length [28] pennation angle was reported at optimal fascicle length. To adjust the measured pennation angle to the pennation angle at optimal fascicle length a planimetric model of muscle was used and muscle thickness was assumed to remain constant for all fascicle lengths [5]. Based on this model, muscle thickness (t) was calculated using, Where θ is the pennation angle measured directly after removal from the cadaver. Assuming that muscle thickness remains constant the pennation angle at optimum fascicle length (θ opt ) was calculated using, Muscle force is directly proportional to PCSA which was calculated from Wickiewicz et al. [13], Where M m is the mass of the muscle, and ρ m is the density of embalmed muscle [29] (1.112 g/ cm 3 ). Tendons were approximated as having circular cross-sections which allowed for TCSA to be calculated using, Where ρ t is the density of tendon [30] (1.12 g/cm 3 ). The ratio of PCSA to TCSA was calculated to demonstrate how muscle force (approximated by PCSA) is related to the ability to resist/transmit the force to bone [31]. Additionally, the ratio of L t to L fopt was calculated to provide insight into the energy storage capacity of the muscles [32].

Statistics
Descriptive statistics were used for the measured variables. Additionally, the ratio of PCSA/ TCSA was calculated for each muscle. Common tendons (Achilles and Patellar) were included for each individual muscle since each muscle would produce a force on the common tendon. The coefficient of variation was calculated for the lower and upper limbs. To compare this variability against functionally similar groups of muscles the ratio of PCSA/TCSA was calculated for the quadriceps, hamstrings, plantarflexors, dorsiflexors, elbow flexors and extensors, and the finger flexors and extensors. Table 2 presents the data from the upper limb while Table 3 presents the data from the lower limb. Unilateral absence of Palmaris longus was noted on the right side of the cadaver and therefore this muscle is not included in the analysis.

Results
The total PCSA of major muscle groups were compared. For the lower limb, the total PCSA of the quadriceps was larger than that of the hamstrings (55.9 cm 3 vs. 34.7 cm 3 ) while the PCSA of the plantarflexors was greater than that of the dorsiflexors (45.0 cm 3 vs. 12.0 cm 3 ). In the upper limb, the PCSA of the elbow extensors was larger than that of the flexors (20.1 cm 3 vs. 9.8 cm 3 ) while the PCSA of the finger flexors was larger than that of the extensors (9.5 cm 3 vs. 3.0 cm 3 ).
Elliott and Crawford [31] reported that the PCSA and TCSA of muscles are not always strictly correlated. Muscles were grouped according to their gross function (knee flexion, hip extension, etc.) to determine if as a group the coefficient of variation was relatively low and therefore for functional groups of muscles the PCSA and TCSA values would be strictly correlated. Table 4 presents the coefficient of variation data.     The ratio of L t /Lf opt was calculated for each muscle and again common tendons were included for each individual muscle. The average ratio was calculated for the lower and upper limb as well as for the quadriceps, hamstrings, plantarflexors, dorsiflexors, elbow flexors and extensors, and the finger flexors and extensors. Table 5 presents the mean and standard deviation of the L t /Lf opt ratio data.

Discussion
The musculoskeletal architecture of major muscles for the upper and lower right limb of a 104 year old female cadaver was presented. This is the first data set that combines an upper and lower limb from one single cadaver. In many cases, data (whole or partial) on muscles presented in the current study have been presented for other cadavers elsewhere. S1, S2, and S3 tables in the Supplemental Material present all the data from the major cadaver studies undertaken since 1975. S4 provides notes pertaining to the other three Supplemental files. Where possible, normalized data is presented for further comparisons to be drawn. Unfortunately, in many cases no data is presented in previous studies which would allow for normalization. This greatly reduces the ability to generalize the data to other populations.
Comparing PCSA values from this study to previous studies (Supplemental Tables 1 and 2) it was noted that in some cases the PCSA from this study was the largest, sometimes the smallest, and other times in the middle. Considering the cadaver in the current study is the oldest out of the studies represented in the supplemental tables this suggests that one cannot assume that all PCSA values can simply be scaled up or down to reflect changes in muscle function with age. Looking at normalized parameters across previous studies (supplemental Table 3) when muscle mass is normalized by body mass and muscle length, tendon length and optimal fascicle length are normalized by body height no discernable pattern can be found either. In some muscles the tallest cadaver has the largest normalized length values while in other muscles the tallest cadaver will have the smallest normalized values. This further underscores the error in using simple scaling parameters for all muscles when scaling a model to a subject's height or mass. The ratio of PCSA/TCSA was shown to have a large amount of variability across different muscles in the current study which is consistent with the finding of Elliott and Crawford [31]. While this may be explained by different muscles having different functional roles in movement, a similar finding has been reported previously in a study focused on a single muscle [33]. Cutts et al. [21] and Langenderfer et al. [15] both presented PCSA and TCSA values for muscles in the arm which allows for comparisons among the two previous studies and the current one. Cutts et al. [21] reported PCSA and TCSA for muscles of the wrist and fingers. There was a significant difference (p < 0.05) between the PCSA/TCSA ratios between the study by Cutts et al. and  The cause of death is an important factor in muscle architecture studies. In many cases, a disease that causes death will also have a negative effect on muscle mass and tendon properties due to decreased use of muscles. This change can skew the architectural data presented and if the primary cause of death is not reported it can be difficult to know how the data would compare to a living individual. In this study the reported cause of death was old age which, if nothing else, seems to indicate that the individual was relatively healthy (not under the care of a physician for a serious illness). Obviously this is purely conjecture and more detailed medical records would be extremely useful but it gives some insight into the relative quality of the muscle and tendons of the cadaver.
This study is the first of its kind in that it reported muscle architectural measures for the major muscles of the upper and lower limbs. Additionally, the cadaver in this study is the oldest reported individual female cadaver by 13 years for the upper limb [15] and 41 years for the lower limb [10]. This type of data should aid in producing whole body musculoskeletal models that are more representative of subjects. Variability in muscle architecture parameters has been demonstrated in other studies [12,33]. Unfortunately, since only one cadaver was used in the current study the variability of upper and lower limb muscle architectural parameters could not be assessed.
Some limitations existed in this study. One limitation was the assumption of sarcomere length homogeneity. Infantolino et al. [26] showed that sarcomere length inhomogeneity existed for the First Dorsal Interosseous muscle and that large sample sizes of sarcomeres are necessary to accurately estimate optimal fascicle length. This is in contrast to Langenderfer et al. [15] who estimated that 40-60 sarcomeres are necessary to accurately estimate optimal fascicle length using a bootstrap simulation. Given the number of muscles in this study the recommendation of Langenderfer et al. was followed realizing that this would introduce some error into our optimal fascicle length calculations. Shrinkage of muscle tissue was not an issue since the muscles was fixed while still attached to the bone [34] and any shrinkage would have been corrected for when optimal fascicle length was calculated. A second limitation was the use of only one cadaver in this study. While this is indeed a limitation and is not representative of the whole population; as discussed above, much of the previous cadaveric work is lacking critical information and therefore it has not been possible to construct a musculoskeletal model of both limbs that was based on a single individual who lived.
The results of this study present the first dataset to include both the upper and lower limb musculature of a cadaver. This data provides the necessary muscle architectural information needed to construct a whole body musculoskeletal model of a single individual who was ambulatory. Additionally, this data increases the body of knowledge of muscle architectural parameters in an elderly population. This will allow for the creation of more realistic models to investigate the effects of aging on human movement.
Supporting Information S1