IOS Press

### The influence of neuromuscular activation on

### the estimation of optimal muscle length using

### a muscle model

### Yang Hua Lin

*a,∗*

### and Tung-Wu Lu

ba* _{Department of Physical Therapy, Chang Gung University, Kweishan, Taoyuan, Taiwan}*
b

_{Graduate 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: linyh@mail.cgu.edu.tw.

**1. Introduction**

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 [1] 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. [2], one of the parameters representing the
mechanical and architectural properties is the optimal
length of an active muscle (L_{0}). The optimal length
of a muscle is directly related to the estimation of the
force-velocity properties of intact human skeletal
mus-cles [3]. 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 [4]. The optimal lengths of*
wrist muscles have been measured intraoperatively by
*laser diffraction [5] or derived in vivo by examining*
the length-tension relationship through electrical
stim-ulation [6,7]. In a recent study, Chang et al. [8]
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)

where*α represents the level of neuromuscular *
activa-tion; *F _{l}* is the normalized active muscle tension;

*F*is the normalized passive muscle tension;

_{pe}*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 [3]. 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 (MVIC_{ES}) 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 [12].
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 300*µsec 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. [13] 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)

where*T _{i}* and

*τ*denotes the measured and predicted joint torques at the

_{i}*ith joint position, respectively.*

The model was customized to each individual subject
by providing individualized physiologic cross section
area (PCSA). The PCSA of individual subject (PCSA* _{i}*)
was obtained by using the PCSA reported by An et
al. [14] and was normalized by the cross sectional area
of the arm (A) as follows.

*P CSAi= P CSAan× _{Am}Ai*

*,*(3) where

*A*represents the mean of arm cross sectional area for all subjects;

_{m}*A*denotes the arm cross sectional area for the ith subject and calculated by

_{i}*Ai*=* _{4π}Ci* (4)

where*C _{i}*denotes 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,
MVIC_{ES}, and MVIC with individualized levels of
neu-romuscular activation (MVIC* _{α}*), 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

MVIC_{ES}assuming MVIC_{ES}elicited 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.

**3. Results**

The joint torques differed significantly between
con-ditions with MVIC and MVIC_{ES}(*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 MVIC_{ES} (*p <*
0.05), so as that existed between the condition of MVIC
and MVIC* _{α}*(

*p < 0.05). Yet, there was no statistical*difference between the conditions of MVIC

*and that MVIC*

_{α}_{ES}. The estimation of the optimal lengths of brachialis and brachioradialis were significantly influ-enced by the condition with MVIC

_{ES}(

*p < 0.05). The*level of neuromuscular activation had the significant effect on the optimal length of brachialis in particular (

*p < 0.05).*

**4. Discussion**

The joint torques recorded under condition of MVIC
in the present study was smaller than those recorded
un-der condition of MVIC_{ES}similar to those reported by
existing studies [8–10]. The difference in joint torques
produced by MVIC_{ES}from those produced by MVIC
in most experiments demonstrated that neuromuscular
tension was not entirely activated. The*α 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

Table 1

Joint torques generated (N-M) with and without electrical stimulation

Elbow flexion (degrees) MVIC (N-M) Confidence interval MVIC_{ES}(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
MVIC*α* 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)

a_{A 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 MVIC*α*.

b_{Statistical difference at a level of significance of 0.05 between the}

groups of MVICESand of MVIC.

through MVIC_{ES}and 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 MVIC_{ES}. 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.

**5. Conclusion**

Ideally, neuromuscular activation could be
consid-ered as unity with the condition of MVIC_{ES}. 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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