The influence of neuromuscular activation on
the estimation of optimal muscle length using
a muscle model
Yang Hua Lina,∗
and Tung-Wu Lub
aDepartment of Physical Therapy, Chang Gung University, Kweishan, Taoyuan, Taiwan bGraduate Institute of Biomedical Engineering, National Taiwan University, Taipei, Taiwan
Abstract. Objective. This investigation aims to determine whether optimal muscle length was estimated with joint toque generated
by maximal voluntary isometric muscle contraction (MVIC), which differed from that was estimated with joint torques generated through electrical stimulation superimposed on MVIC (MVICES).
Design. An experimental investigation was conducted to measure joint torques of the elbow joint in the conditions with MVIC
and with MVICES. The measured joint torques were used to examine the level of neuromuscular activation under MVIC condition as well as to estimate the optimal muscle length of elbow flexors by using in a theoretical muscle model with various conditions of muscle contraction.
Background. Usually muscle model parameters such as maximum muscle force, optimal length are estimated by the joint torques
measured during MVIC, assuming maximum level of neuromuscular activation. However, several experimental studies have shown that MVIC are in fact submaximal contraction and cannot represent as complete neuromuscular activation. As a result, the use of MVIC for the estimation of muscle model parameters may not be appropriately able to produce satisfactory results.
Methods. Eight subjects first performed MVIC of their elbow flexors. Electrical stimulation was superimposed to MVIC to
induce true maximal contraction of the muscles. The resulting joint torques were measured in each test condition and used to calculated the optimal muscle lengths by a muscle model combined with an optimization procedure. Comparisons of the results for the two conditions were made with paired T test.
Results. The joint torques produced by electrically stimulated the elbow flexors at the elbow joint were statistically higher than
those produced by maximal voluntary contraction. Optimal muscle lengths estimated through the joint torques generated by MVIC with electrical stimulation were statistically different from those estimated without electrical stimulation. The optimal lengths of the elbow flexors were calculated with adjusting the neuromuscular activation to be submaximal level and showed no statistically difference from that estimated with superimposed electric stimulation.
Conclusion. Joint torques used for estimating optimal muscle lengths are better derived from electrical stimulation superimposed
on MVIC of the relevant muscles or MVIC accompanied with adjusting the level of neuromuscular activation in the range of 0.62 to 0.93.
Keywords: Maximal voluntary isometric contraction, superimposed electric stimulation, neuromuscular activation, optimal muscle length
∗Address for correspondence: Yang Hua Lin, Ph.D, Department of Physical Therapy, Chang Gung University, 259, Wen-Hwa 1st Rd., Kweishan, Taoyuan, Taiwan, 333. Tel.: +886 3 3283016 5438; Fax: +886 3 3283031; E-mail: firstname.lastname@example.org.
Muscles exert force to produce movements. The force generation of muscles determines the movement control and loading effects on skeletal system. How-ever, in vivo determination of the forces transmitted by the muscles is difficult due to technological and ethical
consideration. Therefore, mathematical models com-bined with non-invasive experimental measurements have been used to estimate such forces. The ability of these models in successfully predicting muscle forces depends not only on the models themselves but also model parameters including length, velocity and max-imal neuromuscular activation. In 1894 Blix first  described the relationship between the lengths of frog muscles and the maximal forces exerted. The maxi-mal force of a muscle also depends on the instanta-neous rate of change in length. Force-length relations as well as force-velocity relations enable the muscles to meet the functional demands imposed during everyday activities.
Force-length and force-velocity relations are the at-tributes of active tension of a muscle. In a mathematical model of length-tension relationship reported by Kauf-man et al. , one of the parameters representing the mechanical and architectural properties is the optimal length of an active muscle (L0). The optimal length of a muscle is directly related to the estimation of the force-velocity properties of intact human skeletal mus-cles . Hence, optimal length is an important feature to determine the active tension of a muscle.
Optimal lengths of various skeletal muscles have been determined via experimental measurements in
vitro as well as mathematical calculations in vivo. For
example, photographic techniques have been proposed for in vitro measurements . The optimal lengths of wrist muscles have been measured intraoperatively by laser diffraction  or derived in vivo by examining the length-tension relationship through electrical stim-ulation [6,7]. In a recent study, Chang et al.  pro-posed an optimization approach for the estimation of optimal muscle length. A model of the length-tension relationship of the following form was used
F = (α · Fl+ Fpe) · P CSA · σ (1)
whereα represents the level of neuromuscular activa-tion; Fl is the normalized active muscle tension; Fpe is the normalized passive muscle tension; P CSA is physiologic cross-section area;σ is muscle.
Experimental determination of the force-length rela-tionship of a muscle requires maximal muscle activa-tion under isometric condiactiva-tions. Usually, maximal vol-untary isometric contraction (MVIC) is used to repre-sent maximal muscle activation, setting to unity . In consequence,α was set as one assuming maximal mus-cular activation. Maximal activation in involving intact human skeletal muscles is often assumed as maximal voluntary isometric efforts (MVIC). However,
previ-ous studies have shown that electrical stimulation su-perimposed on MVIC (MVICES) elicits greater mus-cle torques than MVIC [9–11] so MVIC represents a submaximal muscle contraction. The prediction of op-timal muscle lengths using torques produced by MVIC and assuming the level of neuromuscular activation as unity is subjected to doubt.
This investigation aimed to study (1) the range of level of neuromuscular activation during MVIC, (2) the influence of MVICES on the prediction of optimal muscle lengths of elbow flexors, and (3) the influence of neuromuscular activation on the prediction of optimal muscle length with MVIC.
2. Materials and methods
2.1. Experimental method
Eight subjects (five males and three females), with a mean age of 26.5 (20 to 34), and without previ-ous history of neuromusculoskeletal or neuromuscular disorders volunteered to participate in this investiga-tion. The anthropometric data were as follows: mean body height was 168.38 cm (161–177 cm), mean body weight 60.06 kg (41–76 kg) and mean arm girth 27.43 cm (23–33.5 cm). All of the subjects in this study had not involved in regular physical activity and did not consume any substances or food such as caffeine or alcohol before tests, which might affect the muscular performance.
An isokinetic dynamometer (Cybex Norm, Cybex, Division of Lumex, Inc., Ronkonkoma, NY, USA) was used to measure the flexion torques on the elbow joint. The test and fixation were after instructions in the op-erating manual given by the manufacture . Sub-jects were secured with belt around pelvis. The axis of rotation of the elbow joint was aligned with the dy-namometer’s axis by adjusting the adapter length and the distance of seat from the dynamometer. The fore-arm was fully supinated and the shoulder was abducted at 15◦. After being fixed with the positions as men-tioned above, subjects were instructed to perform el-bow flexion with the maximal voluntary isometric ef-fort determined by the measured torque curve reaching its plateau. Eight positions of elbow flexion, from 15◦ to 120◦ at an interval of 15◦ were investigated. The orders of the MVIC and MVICes as well as the test angles of elbow flexion were randomized assigned to avoid the effects of learning and carry-over. Follow-ing sessions of MVIC an electrical stimulator (CEFAR
Medical AB, Lund, Sweden) was then superimposed to the maximal contraction of the elbow flexors. The pulse duration was 300µsec and the amplitude was set to induce maximal muscle contraction, sustained for 7 seconds and followed by a one-minute rest.
2.2. Mathematical modeling
An anatomical elbow model created by van Zuylen et al.  was adapted to calculate the moment arm and muscle length at different joint angles. The op-timal length of elbow flexors was estimated using the optimization approach. A program in MATLAB (V 5.0, 1997) was written for these calculations. The op-timization problem formulated has the optimal length as its only design variable, ranging from the minimal length at maximal elbow flexion to the maximal length at full elbow extension. The cost function was set to minimize the sum of the differences of the joint torques between the experimentally measured and theoretically predicted joint torques as follows,
min .n i=1
(Ti− τi)2 (2)
whereTi andτi denotes the measured and predicted joint torques at theith joint position, respectively.
The model was customized to each individual subject by providing individualized physiologic cross section area (PCSA). The PCSA of individual subject (PCSAi) was obtained by using the PCSA reported by An et al.  and was normalized by the cross sectional area of the arm (A) as follows.
P CSAi= P CSAan×AmAi , (3) whereAmrepresents the mean of arm cross sectional area for all subjects;Aidenotes the arm cross sectional area for the ith subject and calculated by
whereCidenotes the circumference of the arm, which was determined by measuring the largest circumfer-ence of elbow flexors at 90 degrees of elbow flexion passively positioned.
There were three conditions considered, MVIC, MVICES, and MVIC with individualized levels of neu-romuscular activation (MVICα), to calculate the opti-mal lengths of elbow flexors. The individualized level of neuromuscular activation (α) shown in Eq. (1) was demonstrated as the ratio of joint torques generated in the condition of MVIC to those in the condition of
MVICESassuming MVICESelicited a full level of neu-romuscular activation in which α was set to be one. In the present study,α in the condition of MVIC was assumed as one to interpret as a full level of neuromus-cular activation as usual.
2.3. Statistical analysis
The statistic significance level was set at 0.05. Paired t-test was used to identify the significance of differ-ences in the joint torques and muscle length of elbow flexors predicted.
The joint torques differed significantly between con-ditions with MVIC and MVICES(p < 0.05, Table 1). The level of muscle activation derived from the ra-tio of measured joint torques was calculated, which ranged from 0.62 to 0.93 and averaged as 0.8. The optimal muscle lengths of the elbow flexors (the biceps brachii, brachialis and brachioradialis) estimated were addressed in Table 2. The prediction of the optimal lengths of elbow flexors differed significantly between condition with MVIC and that with MVICES (p < 0.05), so as that existed between the condition of MVIC and MVICα(p < 0.05). Yet, there was no statistical difference between the conditions of MVICαand that MVICES. The estimation of the optimal lengths of brachialis and brachioradialis were significantly influ-enced by the condition with MVICES(p < 0.05). The level of neuromuscular activation had the significant effect on the optimal length of brachialis in particular (p < 0.05).
The joint torques recorded under condition of MVIC in the present study was smaller than those recorded un-der condition of MVICESsimilar to those reported by existing studies [8–10]. The difference in joint torques produced by MVICESfrom those produced by MVIC in most experiments demonstrated that neuromuscular tension was not entirely activated. Theα derived from the joint torques varied individually, which indicated the individualized maximal capability of muscle con-traction. The maximal torque generated in the condi-tion of MVIC was approximately 80% of that generated
Joint torques generated (N-M) with and without electrical stimulation
Elbow flexion (degrees) MVIC (N-M) Confidence interval MVICES(N-M)∗ Confidence interval
15 2.42 1.46–3.39 2.96 1.84–4.08 30 2.48 1.61–3.34 3.19 2.17–4.21 45 2.70 1.84–3.56 3.39 2.42–4.37 60 2.84 2.13–3.55 3.55 2.49–4.61 75 3.05 2.10–4.00 3.74 2.82–4.67 90 3.12 2.39–3.84 3.95 3.01–4.89 105 3.19 2.52–3.85 3.97 2.83–5.10 120 2.72 2.29–3.15 3.46 2.57–4.36 ∗p < 0.001, p = 6.33565391E-08. Table 2
Mean and (SD) of muscle length of elbow flexors (cm) estimated under various conditions
Brachial biceps Brachialis Brachioradialis MVIC 16.27 (0.88) 10.31 (2.40)a,b 22.83 (3.16)b MVICα 16.43 (0.89) 8.00 (1.67) 21.84 (3.60) MVICES 16.64 (0.95) 8.11 (1.81) 21.45 (3.57)
aA statistical difference in the muscle length at a level of
signif-icance of 0.05 in muscle length existed between the group with MVIC and those with MVICα.
bStatistical difference at a level of significance of 0.05 between the
groups of MVICESand of MVIC.
through MVICESand might correspond as submaximal muscle activation.
Consequently, the variations in the joint torques pro-duced under different conditions might lead to statis-tical differences in the estimation of optimal muscle lengths. As a result of adjusting α individually in Eq. (1) to address the level of neuromuscular activation in the condition of MVIC, the optimal muscle lengths predicted were close to those derived from joint torques generated with MVICES. Based on the results, it was concluded that it is improper to set unity as constant for maximal muscle activation during MVIC. Instead, tak-ing 0.8 as the muscle activation level is considered in case of voluntary maximal contraction for the relevant research. Otherwise, obtaining MIVC through super-imposed electrical stimulation might be considered.
Both of the brachialis and brachioradialis were af-fected by the condition of ES that demonstrated the role of primary elbow flexors and provided synergic con-traction to assist biceps brachii and prevent undesired shoulder flexion motion [15,16]. The optimal length of brachialis was sensitive to the level of neuromuscular activation, which might imply its significance in the joint torques generation during elbow flexion without being considered by the adjacent joints such shoulder and wrist joints.
The present study was a preliminary study with rel-atively small sample size, which might limit the
gen-eration of the results of this study and the confidence to approximate true population. There might be lower power to detect the variation of volitional effort of cle activation. Furthermore, recording compound mus-cle activation potential (CMAP) caused by the changes of muscle length would be suggested to ensure maxi-mal effort in addition to maximaxi-mal torques recorded in this study.
Ideally, neuromuscular activation could be consid-ered as unity with the condition of MVICES. Or muscu-lar activation should be proportionally modulated in the range of 0.62 to 0.93 during maximal voluntary mus-cle exertion alternatively. Both the brachialis and bra-chioradialis are significant in generating joint torques during elbow flexion. The present study suggests that the level of muscle contraction affects generation of joint torques that alters the muscle lengths and joint positions as well.
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