### Physical modeling

In this study to determine the effects of the imbalance in the jaw to the strength of the arms, we conducted experiments with a pool of 20 (age: 19.8 ± 0.9 years old) and healthy subjects of both genders. All participants were healthy and showed no musculoskeletal or neurological restrictions or diseases. They had a complete dentition, i.e. no premolar or molar was missing in a quadrant. There were no signs of severe malocclusions or facial malformations. All subjects were not on any medication and had no complain of any kinds of muscle pains throughout the experiments.

Before the experiments, each subject filled out a questionnaire, which was kept confidential and included patient’s identification, age and gender. The tenets of the Declaration of Helsinki were followed; local Institutional Review Board approved the study and informed consent was obtained for all subjects.

The subjects were asked to stand with their arms and legs extended in frontal plan in such a way that the ratio subject intra-feet distance/ subject height equal 0.25 (Figure 2). This ratio was chosen based on the fact that many subjects felt comfortable and stable. The experimental protocol started with asking the subject hold the handle of a load which was at rest. Next at the warning signal the load was released at once; this generated a pull-down force on the subject’s arm. The subject must hold the load for a maximum of 15 seconds without moving his body. The pull-down force consisted of a load in kilogram that can be adjusted in the increment of 100 g and then converted into Newton. In these paradigms, the subject was asked to bite on a spacer using his premolar and molar teeth.

The subject held a spacer placed on one side of the jaw using premolar and molar teeth. The heights of the spacers were 0.6, 1.3 and 2.0 mm; however, they were applied in random order. Ten males (age 20 ± 0.9 years old) and 10 females (age: 19.8 ± 9.0 years old) participated.

We found that when the spacers were put in the left side of the jaw the loss of arm strength occurred on the right side of the arms and the strength of the arm on the same side intact. Similarly, when the spacers were put in the right side of the jaw the loss occurred on the left side of the arm while the strength of the arm on the same side was intact. This suggested that the bite imbalance causes a contralateral loss of strength in the arm (Figure 3).

In the process of understanding the origin of this phenomenon is muscular; we investigated the activities of muscles by using EMG. Ten male subjects participated in this investigation. The spacers had different heights of 2 mm and 3 mm and were applied in random order. The spacers were made out of a firm material to assume a good occlusal support. While the subject was biting on a spacer pull -down force was applied on the subject’s arm as aforementioned.

Myoelectric signals of jaw (masseter), neck (trapezoid) and arms (deltoid, brachiodiolis,) muscles were measured. The masseter was selected due to its main active role during biting at the temporomandibular (TM) joint. The concentric and eccentric contractions of the masseter create the biting motions as well as control the bite’s force. The trapezoid was selected due to its essential loading contribution in supporting the arm during persistent extension position. Arm extensors such as deltoid, brachiodiolis or extensor digitorum muscles were selected according to their role of support for maintaining the arm in extension under external loading conditions.

BIOPAC Systems Channel 1 was used to measure the activities of masseter muscle, channel 2 was used for trapezoid muscle, channel 3 was used for deltoid muscle, and channel 4 was used for branchi muscle. EMG (5- 500 Hz) was chosen to record EMG signal. The sampling rate was 1000/ second.The EMG measurement repeated twice for each experiment. The relaxation times within the experiments were 5 to 10 minutes. The recording time is 15 seconds in order to obtain the muscle fatigue [12, 13]

Paradigm 1: The maximum force that the subject can resist in 15 seconds was recorded before taking EMG measurements. From the initial position (0 mm, Fmax-40 N), external loading weight was added incrementally with Fmax -20 N and Fmax. Check EMG signal quality and data storage.

Paradigm 2: Perform variation in spacer thickness from 2 mm to 3 mm and execute step 1 for Fmax and Fmax -20 N.

### Integrated EMG

To explain the fatigue of muscles by EMG signal in time domain, integrated EMG (iEMG) was calculated. Integrated EMG is the mathematical integration of rectified EMG signal. Simpson's rule was used to calculate iEMG**.** It is a method for numerical integration, the numerical approximation of definite integrals. Specifically, it is the following approximation:

Y={\int}_{a}^{b}f\left(x\right)dx\approx \frac{b-a}{6}\left[f\left(a\right)+4f\left(\frac{a+b}{2}\right)+f\left(b\right)\right]

(1)

In this formula (1), a and b are the unit spacing. f(a) and f(b) are the amplitudes of EMG signal at a and b. In fact, the iEMG was calculated as an approximation of the cumulative integral of the whole EMG signal amplitude during 15 seconds via the Simpson method with unit spacing.

The iEMG mean of ten subjects significantly increased with respect to the increasing of external loading (Figure 4). With a bigger applied force, the muscles strongly contracted in respect to iEMG.

### Higuchi fractal dimension

Moreover, to understand the behavior of muscle through EMG signal, Higuchi fractal dimension was used. Higuchi is an efficient algorithm for measuring the fractal dimension of discrete time sequences [14]. Higuchi's algorithm calculates the fractal dimension from time series. Higuchi fractal dimension has already been used to analyze the complexity of surface EMG signal of the biceps [15].

Given a one dimensional time series X = x[1], x[2], …, x[N], the algorithm to compute the HFD can be described as follows [12]:

Form k new time series {X}_{k}^{m} is defined by:

{X}_{k}^{m}=\left\{x\left[m\right],x\left[m+k\right],x\left[m+2k\right],\dots ,x\left[m+int\left(\frac{N-m}{k}\right)\times k\right]\right\}

(2)

where k and m are integers, and int(·) is the integer part of ·. k indicates the discrete time interval between points, whereas m = 1, 2, …, k represents the initial time value.

The length of each new time series can be defined as follows:

\stackrel{int\left(\left(N-m\right)/k\right)}{i=1}\left|x\left[m+ik\right]-x\left[m+\left(i-1\right)\times k\right]\right|\left)\left[\left(N-1\right)/\left(int\left(\left(N-m\right)/k\right)\times k\right)\right]\right\}

(3)

where N is length of the original time series X and (N − 1)/{int [(N − m)/k] × k} is a normalization factor.

Then, the length of the curve for the time interval k is defined as the average of the k values L(m,k), for m = 1, 2, …, k:

L\left(k\right)=\frac{1}{k}\times {\displaystyle \sum _{m=1}^{k}L\left(m,k\right)}

(4)

Finally, when L(k) is plotted against 1/k on a double logarithmic scale, with k = 1, 2, …, k_{max}, the data is expected to fall on a straight line, with a slope equals to the fractal of X. Thus, Higuchi fractal dimension is defined as the slope of the line that fits the pairs {ln[L(k)], ln(1/k)} in a least-squares sense. A value of k_{max} = 10 was chosen for our study.