1. Introduction

During highly intense workout, the body energy production pathway shifts from an aerobic pathway to anaerobic pathway during times of low oxygen levels. In the latter lactic acid is produced. A case of lactic acid accumulation in the muscle may cause local muscle burn and in an extreme scenario immediate ceasing of the muscle activity. Today, lactate tests are performed regularly on athletes in order to acquire the anaerobic threshold and develop individual training programs. The anaerobic threshold (or maximal lactate steady state) is known as the maximal lactate blood level that allows the athlete to continue the highest intensity level of activity for the longest time. The current standard method to measure lactate level in the blood is by drawing blood samples from the subjects. There are numerous devices used to take this measurement in the market [1–3]. In this manuscript, we propose an optical, non-invasive method to estimate the lactate levels by examining the connection between physiological tremor, which occurs when the muscle contracts, and the lactate blood levels. In previous work [4] it was shown that the physiological tremor induced by static load can be measured by using speckle self-interfering patterns reflected from the skin and imaged by a defocused optical system. By the shown optical system it was possible to measure the microscopic skin movement which changes depending on the muscle tremor during static load on the muscle. This concept was already proven to be suitable to estimate heart beating, breathing [5], blood pulse pressure [6], intra ocular pressure [7] as well as concentration of various chemicals in the blood stream such as glucose [8] and alcohol [9] in a non-contact way. Both frequency and amplitude of the skin displacement are measured. In our research, we focus on tremor induced by dynamic activity (running), and we examine the relation to the lactate level in the blood. In section 2, we first display the theoretical explanation, both from the physiological point of view as well as from the optical one. Section 3 displays the experimental settings for the tests (methods and materials). The results of several experiments conducted to establish the theory are displayed in section 4. In section 5 we analyze the results and in section 6 we conclude the paper.

2. Theoretical explanation

2.1. Physiological tremor

The physiological tremor occurs in every normal individual in all voluntary muscle groups. This phenomenon was defined by Schafer (1886) (quoted [10],) as “the rhythmicity found during muscular contraction that was thought to be produced by the periodically nervous system excitation”. In later work [10] it was shown that a large change of the motion's rate altered the amplitude but not the frequency of the muscle's measured oscillations. This observation was very important to establish our hypothesis. The findings of many researches performed in the matter were concluded [11], and most pointed out that the muscle oscillates in a frequency range of 7-20 Hz. Several researches, however, analyzed a lower frequency range of oscillation, depending on the muscle type. In our work, we measured the physiological tremor induced upon running. During running the active primary muscles include the quadriceps femoris, hamstrings and the calf muscles [12]. In our research we chose to perform the measurement on the calf muscles, due to its location being close to the skin surface. In addition, we have performed one measurement on the quadriceps femoris muscle to establish a basis for future work.

2.2. Lactic acid and lactate

The body's normal pathway of producing energy is aerobic, meaning in the presence of oxygen. In this energy production pathway there are three phases. Firstly, the glycolysis phase occurs, where the body produces overall two ATP molecules. The next phase is the Krebs cycle where two extra ATP molecules are produced. The final phase is the Electron Transport Phosphorylation that requires oxygen molecules and produces thirty two ATP molecules. When the body performs strenuous activity, the respiratory rate rises, in order to transfer enough oxygen to the working muscles for the aerobic production of ATP molecules. In some circumstances, the oxygen delivery to the muscles is not performed fast enough to produce the adequate amount of energy the muscle requires. In these cases the body’s energy production method shifts to the anaerobic pathway. In this pathway, the second and third phases are replaced by lactic acid fermentation [13]. This phase produces no extra energy, but is required to produce substance to be used in the glycolysis phase. As soon as it is produced, the lactic acid disassociates into lactate and hydrogen. Then the lactate is transferred to the blood. The normal lactate level in the blood is 0.5-2.2 [mmol/l]. It may vary between different individuals and in the same individual when measuring at different time of the day, in different physiological states and more. The lactate level rises as the physical activity level rises and, as stated in section 2.1, the wave amplitude rises as the rate of the movement performed increases. Therefore, we assume that there is a connection between the lactate level and the physiological tremor oscillation amplitude.

2.3. Optical aspect - secondary speckles pattern

The use of secondary speckles pattern as a way to measure microscopic vibrations has been described in previous work mentioned in section 1. Here we will give a short review of the method and how it is used to evaluate the physiological tremor. Speckles are random light patterns that are generated when a rough surface is illuminated by a laser beam. The human skin is an example of such rough surface. The speckles’ appearance is caused by the light rays' self-interference. In order to estimate the vibrations of the physiological tremor, we observed the Fourier transform of the speckles patterns and analyzed their shift in time. We defocused the camera, so that the imaged object, in our case the human skin, is in the far field (Fraunhofer) approximation, so that the image acquired by the camera is the Fourier transform of the speckle distribution that could have been generated close to the skin surface. When the skin tilts, there is an added phase to the electromagnetic wave in the space domain which translates to a shift in the spatial frequency domain. This allows us to calculate the temporal change in skin tilting by calculating the shift in the speckle patterns between two consecutive frames. The added phase is described by Eq. (1) [5]:

Where$\lambda$is the wavelength, $\alpha$ is the tilting angle (hold components in x and y directions), and an added factor 2 is due to the back and forward axial change. Therefore, the displacement of the generated speckle pattern on the camera d equals to the added spatial phase and under paraxial approximation, we obtain the connection in Eq. (2)

3. Experimental settings

3.1. Materials

In our experiment we used a 15 mW, 532 nm laser pointing towards the calf muscle (see setup illustration in Fig. 1). It is important to state here, that thanks to the high tolerance of the optical measurement method, the required location for the measuring point is up to 20 cm from the exact location of the muscle. Therefore, the laser pointed towards the lower leg calf area, was with good enough accuracy for the method to work, without having to locate a certain point of the muscle. In addition, the laser spot location was marked in order to refer to the exact same location in different measurements. Another significant aspect of the setup was the subjects' positioning. We did not use any fixation to the leg; however we did instruct the subjects to support their posture by an optical table. This posture was steady enough to obtain a good signal and we have still managed to filter out noises derived by momentarily leg movement. Still, we may assume the by use of fixation to avoid any leg twitches and movements, the results would be even more significant.

 

Fig. 1 Illustration of the experimental setup.

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The imaging system we used was a PixelLink camera. We selected a frame size of 96 x 96 pixels. This frame size was determined as the optimum size to capture as many speckles as possible in the image for a more robust statistics, while small enough to neglect changes in surface of the skin.

The video camera's frame rate was set to 120 frames per second (fps) to agree with Nyquist sampling frequency. The cutoff frequency of the tremor according to the literature is 20 Hz, therefore a frame rate of 40 fps would be sufficient to reconstruct the signal. However, we used higher frame rate to acquire a better sampled signal (higher SNR). The camera was connected via USB port to a PC installed with PixelLink SW that recorded the videos. Each video consisted of 2400 frames, meaning 20 seconds of data. The laser and the camera were attached to an optical breadboard placed on the floor. We also performed one test on the quadriceps femoris muscle, in order to examine future prospects in measuring different muscles activity. In order to measure the lactate levels we used the Nova Biomedical lactate plus meter [1,14].

3.2. Test protocol and methods

The lactate test is normally performed in the graded exercise test protocol [15,16]. The athlete performs 3-5 intervals of activity suited to his training program for five minutes each. The intensity of exercise increases in each interval. This is until the lactate level elevates above a certain value suited to the athlete. At the end of each interval, a blood sample is collected in order to measure the lactate level. We used the same protocol, where the physical activity was running. Eight healthy subjects participated in the research: 3 women and 5 men, in different physical and shape levels. Prior to the run, a reference measurement was performed, both of the lactate blood levels and the muscle tremor. Then, in the first interval, the subject began to run in a slow pace, adjusted to his physical shape. Later, the subject increased his pace in each interval as described in Table 1.

Table 1. Lactate test protocol

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Following each interval the optical measurement and the blood measurement were performed immediately, taking at most one minute before the next running interval. The recorded video was processed as described in section 2.3 to acquire a temporal signal which later was multiplied by Blackman window in order to avoid artifacts derived by the rectangular window. Faulty measurements (high percentage of loss of correlation between two consequent frames in the temporal signal) were discarded and were not taken into account in the analysis. We analyzed the signal's energetic spectral density (ESD), or the squared absolute value of the signal's Fourier transform, in the tremor frequency range. Then, we extracted the peak ESD in the relevant range for each subject, per each running interval. Here we analyze the energetic spectral density associated to the lactate blood level measured at the end of each interval, as well as the normalized lactate level and peak ESD amplitude as function of the running interval. Prior to the beginning of the experiment, in order to ensure that the signal measured is the human signal and not periodical noises from the environment (such as ventilator, air-conditioning, building vibration, cables vibration etc.), we took several measurements without the subject. The output can be seen in Fig. 2.

 

Fig. 2 The ESD measurement of the signal acquired by our system, without a subject.

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It can be seen that the signal ESD had peaks around 15 Hz and 35 Hz that are not in our range. In addition the amplitude is extremely low and not in the order of magnitude of amplitude values received upon measurement, as shown below.

4. Results

Figure 3 displays the ESD of the signal acquired from the calf muscle of a twenty seven year old female for all running intervals. It can be seen that the peak ESD value in all intervals is in the range of 7-12 Hz as described in section 2.

 

Fig. 3 ESD of the signal measured from the leg in 4 running intervals. The reference lactate level measured here was 9 [mmol/l] and displayed in the red continuous line.

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Lactate level at rest was measured and found to be 9.0 [mmol/l], and it increased as the running pace increased. It is distinctly seen that the main peak in the 9-11 Hz range is elevated as the exercise intensity increases, besides the final interval – this will be discussed in section 5. Figure 4 displays the normalized value of the lactate vs. the normalized maximal energetic spectral density of each subject. The maximal amplitudes were selected in the relevant range of frequencies, taking into account that different people have different tremor frequencies. Normalized lactate level was calculated using Eq. (3).

 

Fig. 4 Normalized value of lactate level (black line) and normalized value of maximal energetic spectral density (red line) in the relevant frequency range vs. the running interval number.

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In addition, as mentioned in section 2.1, we have also performed one test on the “quadriceps femoris” muscle upon a 26 year old female using the same test protocol and the results are presented here in Figs. 5 and 6.

 

Fig. 5 A test performed on the “quadriceps femoris” muscle in a 26 year old athletic female using the same protocol as mentioned above. The dotted line is the reference measurement where the lactate level was 1.2 [mmol/l]. (a) The signal spectrum measured after the first running interval. (b) The signal spectrum measured after the second running interval. (c) The signal spectrum measured after the third running interval. (d) The signal spectrum measured after the fourth running. (e) The signal spectrum measured after the fifth running interval.

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Fig. 6 The normalized lactate level and maximal energetic spectral density of the 27 year old thigh muscle as function of the running interval.

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5. Results analysis

As can be seen in Fig. 3 the peak of the tremor signal decreases after the final interval whereas the lactate level elevates throughout the whole measurement. This decrease in tremor signal amplitude raises the assumption that the subject has reached the point of muscle metabolic fatigue. In this point, insufficient energy production for muscle activity, together with lactic acid accumulation in the muscle, interfere with muscle contraction. The lactate level continues to rise whereas the muscle contraction force decreases due to fatigue. This explains the decrease in tremor amplitude in the final interval.

In Fig. 4, subjects 3-8 (80% of the subjects) present an approximate linear connection between the lactate level and the measured tremor activity. The lactate level was elevated in accordance to the interval level up to a certain point – as expected. Similarly, the peak of the tremor energetic spectral density signal was also elevated. It is also apparent that different subjects show a different behavior. This is as expected, since the tests were performed on different groups of people and we did not divide the test to categorized groups (divided by gender, age, athletic shape, weight, height etc.). Also when looking at the results of subject 1 obtained in different times of the day, it is seen that the graph outlines are quite similar during day as opposed to night time. It is important to state here that the peak frequency of subjects 7-8, who work out on a regular basis and are healthy and fit, was in a lower range than 7-20 Hz. Furthermore, when examining the results of the “quadrocipes femoris” test, in Figs. 5 and 6, it can be seen that the lactate level elevates logarithmically where the spectral energy graph behaves exponentially until a certain point where the tremor amplitude drops. This fits the assumption that the subject has reached the muscle fatigue stage. This behavior also supports our assumption that there is a connection between the two physiological parameters.

In order to test the performance of the system, the same subject repeated the experiment three times which overall summed up to 14 measurements (each running test included several intervals). Both lactate and the energetic spectral density were normalized with the minimum and maximum values of the same test. Even though the measurements were taken on the same subject, we could not treat all as equivalent as each test was taken in a different day in different times of the day. See results in Table 2.

Table 2. Three test protocols results performed on the same subject.

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We then calculated the correlation factor between the normalized max ESD values and the normalized lactate levels. The result was that R (correlation value) was equal to the value of 0.7, where the P value was equal to 0.005 < 0.05, meaning there was a significant positive relationship between the two variables.

6. Conclusions

The obtained results match our expectations as we would expect to see an elevated maximal amplitude of the muscle signal as the lactate level is elevated in each time interval until the muscle fatigue. This connection was displayed clearly in the graphs. Moreover, as described in section 5, there was an evident correlation between the lactate value and the physiological tremor, when examining the signal of one subject in different times of day for different days.

Further tests ought to be performed in order to quantify this physiological relation. However, the results presented in this paper could be used as proof of concept that this connection indeed stands. It is evident that different subjects with close enough lactate levels, yielded different measured amplitude levels. This means that each individual should have his personal scale, calibrated according to his/her physics. In addition, it is important to state that in this research we did not perform a comparison between different weights, genders, heights and other anatomical properties that should be taken into account when establishing this method. Having that said, these results are encouraging and lead the way to estimating the lactate levels in general and the lactate threshold in particularly, in a non-invasive, non-contact manner that can be used for both professional use in the athletic world, as well as for home care use, for people who wish to better their physical shape.