1. Introduction

The interaction of light with biological tissues is increasingly studied with the aim to develop non-destructive measurement and optical treatment techniques. Several optical techniques have been proposed for non-destructive measurement of the quality attributes of fruit and vegetables [1], meat [2,3] and dairy products [4,5]. Next to vis/NIR spectroscopy [3], which is generally accepted as a standard optical measurement technique, alternatives such as hyperspectral imaging [2,6], fluorescence measurements [7,8], spatially resolved spectroscopy [9] and time resolved spectroscopy [10,11] have demonstrated their potential for quality monitoring of food products. In this way, moderate to good correlations were found between measured optical signals and quality attributes such as firmness, soluble solids content, fat content, moisture content, pH, etc [1,12]. As such, these optical measurement techniques have also been elaborated to non-destructively study the quality of meat products [12]. For example, the potential of near infrared (NIR) spectroscopy to predict intramuscular fat, moisture content and tenderness has already been evaluated [13,14]. However, the prediction of physical attributes related to the meat structure, such as tenderness, was not robust and highly inconsistent across studies [2,3,15]. The fibrous nature of muscle tissue results in anisotropic light propagation influenced by the fiber direction [16]. Several researchers have investigated the effects of fiber direction and type on the light propagation in muscle samples.

The first to report the effect of fiber orientation on optical measurements was Elliott (1967), who found a clear effect of fiber orientation on pork muscle reflectance spectra [17]. Similar results were obtained by Swatland (2012) using a gonio-spectrophotometer [18]. Besides using spectroscopic techniques, contactless spatially resolved spectroscopy (SRS), which generally combines a point illumination with a camera system to detect the spatially resolved diffuse reflectance, can be useful to quantify the anisotropy of light propagation. In homogeneous materials, with randomly oriented scattering bodies, isotropic light propagation is expected, resulting in a circular diffuse reflectance glow spot. However, for heterogeneous samples, where the scattering particles are structured to some extent, a deviation from this circular pattern is typically observed [19]. Ranasinghesagara et al. (2006) used a contactless SRS technique to identify the amount of fiber formation in extruded soy proteins, which served as a meat analog [20]. When aligned fibers were present in the material, an elliptical shape of the reflectance glow spot was observed. They proposed a bias parameter, describing this elliptical shape, which correlated well with the amount of fibers present [20]. In a subsequent study, they found that, for actual muscle samples with their fibers running parallel to the measurement surface, the shape of the diffuse reflectance glow spot could be well represented by a rhombus [16]. It was suggested that this phenomenon might be related to the muscle sarcomere structure. Furthermore, the rhombus parameters, observed in muscle samples, also depend on animal breed, type of muscle, carcass suspension and aging time [21]. Nickell et al. (2000) noticed elliptical shaped glow spots in human skin, while Kienle et al. (2004) found similar results in porcine arteries [19,22]. Binzoni et al. (2006) used time resolved spectroscopy to study anisotropic effects in human skeletal muscle [23]. They found a higher probability of photons travelling along the muscle fiber. These studies confirm the anisotropic behavior of light in muscle tissue. Moreover, SRS has been shown to be a valuable technique to study the effect of fiber orientation on the light propagation in different fibrous materials, including muscle tissue. However, only wavelengths between 640 nm and 860 nm were considered [21], while important absorption features of both myoglobin derivatives (oxymyoglobin at 544 nm and 582 nm) and water (970 nm, 1200 nm, 1450 nm and 1940 nm) can influence the diffuse reflectance. In addition, the anisotropic effect of photon migration was mainly studied on samples with fibers running parallel to the measurement surface.

Accordingly, the objectives of this study were to:

2. Materials and methods

2.1 Muscle samples

Three muscles, biceps brachii (BB), brachialis (BR) and soleus (SOL) originating from a Jersey bull, were collected at a local commercial hot boning abattoir (New Zealand) and transferred to the research lab. Each muscle was cooled at 10°C overnight to avoid cold shortening and to reach rigor mortis. The next day, three subsamples were taken from every muscle, each according to a different slicing direction: perpendicular, transversal or parallel to the fiber orientation [Fig. 1]. This resulted in a total of 9 samples. Each sample slab had a thickness of 2 to 3 cm and a diameter of around 10 cm.

 

Fig. 1 Cross-sectional view of the different muscle slicing directions: (a) transversal, (b) perpendicular and (c) parallel to the fiber orientation.

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2.2 vis/NIR reflectance spectroscopy

As a first optical measurement, the vis/NIR reflectance spectra of all 9 subsamples were acquired. Two replicate spectra were measured using a vis/NIR spectrophotometer (LabSpec 5000, ASD Inc., Boulder, CO, USA) with a customized reflectance probe and a wavelength range from 350 to 2500 nm [24]. To obtain absolute reflectance values using this probe, a white reflectance standard was measured as a white reference measurement. The used setup is described in more detail by Reis & Rosenvold (2014) [24].

2.3 Contactless spatially resolved spectroscopy

To investigate the effect of fiber orientation on the light propagation in muscle tissue samples, a contactless spatially resolved spectroscopy (SRS) setup was used. A schematic representation of the setup is shown in Fig. 2. A tungsten-halogen light source (AvaLight-HAL-S, Avantes, Eerbeek, The Netherlands) was coupled into an optical fiber (1000 µm core diameter). The light was focused with a collimating lens (COL-UV/VIS, Avantes BV, Apeldoorn, The Netherlands) onto the sample at an angle of 20° relative to the Z-axis of the sample [Fig. 2]. This was done to limit the interference of specular reflectance in the measurement of the diffuse reflectance [9]. The diffuse reflectance glow spot was detected with a hyperspectral camera system installed in line with the Z-axis in Fig. 2 (Hyperspec® Extended VNIR, 14.42 frames/s, Headwall Photonics, Fitchburg, MA, USA). The camera system used a line-scan mode to capture one line of the spot (0.12 mm spatial resolution) for all wavelengths ranging from 470 nm to 1620 nm (4.93 nm spectral resolution). By using a linear translation stage, moving at a speed of 1 mm/s, multiple lines could be measured resulting in a complete image of the diffuse reflectance glow spot (0.07 mm spatial resolution). In this way, both the sample and the illumination spot were moved underneath the camera system. The measurement of one sample resulted in a hypercube with two spatial dimensions and one spectral dimension. Each muscle tissue sample was measured at five different yaw angles: rotated 0°, 45°, 90°, 135° and 180° around the Z-axis in Fig. 2. At every yaw angle, the sample was measured at the exact same position.

 

Fig. 2 Schematic representation of the used setup. A sample with the fibers running parallel to the measurement surface (along the y-axis) is shown. The yaw angle is the rotation angle in the xy-plane with respect to the x-axis.

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2.4 Data processing

First, the obtained images were dark corrected using a dark image, after which the spots were converted into a relative reflectance signal by scaling them with a white reference measurement. The latter was performed by directing the illumination beam into an integrating sphere with a diameter of 25.4 mm (SPH-1-2 Integrating Sphere, Laser 2000 BENELUX C.V., Vinkeveen, The Netherlands) and measuring the diffuse reflectance coming out of the sphere port (1 cm Ø) [9].

Looking at the relative reflectance images in a 3-dimensional space, with relative reflectance on the vertical Z-axis, a cone-like structure can be noticed. Defining an upper and lower reflection threshold results in the selection of a segment of the cone with equal reflectance intensity. In this way, different equi-intensity segments were defined. For a lower equi-intensity level, the resulting cone segment was larger, with the included pixels further away from the point of illumination (center). The relative reflectance closest to the illumination spot was used as the maximal equi-intensity level (100%). By decreasing the intensity in steps of 5%, a total of 20 equi-intensity levels was evaluated, with a minimal equi-intensity level at 5% of the maximum value. The upper threshold was chosen as the reflectance at the corresponding equi-intensity level, while the lower threshold equaled 75% of the upper threshold’s relative reflection value. In this way, sufficient points were always included to ensure a reliable fitting procedure.

For isotropic materials, the shape of the obtained equi-intensity contour is expected to be almost circular [19]. However, Ranasinghesagara & Yao (2007) found a rhombus shape when looking at fresh pre-rigor skeletal muscles with the fibers parallel to the measurement surface [16]. Moreover, they suggested a nonlinear fitting model, designed to describe the shape of equi-intensity contours. A point (x,y) on an equi-intensity contour can be described using the following equation:

In Eq. (2), parameter q describes the shape of the fitted function. When q = 1, Eq. (1) describes a rhombus, while when q = 2 an ellipse is fitted. In the special case when q = 2 and a = b, Eq. (1) becomes the equation of a circle [16].

Equation (1) was fitted to each of the defined equi-intensity levels, for all measured wavelengths. After fitting the nonlinear model, the rotation angle of the major axis was determined relative to the X-axis. If the fitted function resembles a circle, no reliable results for this rotation angle can be obtained. For this reason, the bias parameter B was introduced based on the findings of Ranasinghesagara & Yao (2007) [16]:

For a circular shape, this bias parameter equals 1, while higher values indicate either a rhombus or an elliptical shape, depending on the value of q in Eq. (2).

To quantify the effect of the applied yaw angle on the estimated rotation angle of the major axis, the correlation between these angles was studied within each subsample. Moreover, a linear regression model was applied for which the coefficient of determination (R²) and the root mean square error of prediction (RMSEP) were calculated. To perform these linear fits, a single equi-intensity level was considered (50% of maximum intensity) for all wavelengths. As the prediction of the major axis orientation is unstable for a rhombus or ellipse with a bias parameter close to 1, orientation angles of rhombuses with a bias parameter lower than B = 1.15 were not included in the linear regression model.

All data processing was performed using Matlab R2014a (The Mathworks Inc., Massachusetts, USA).

3. Results and discussion

3.1 Spectroscopic measurements

In Fig. 3, the reflectance spectra measured with a vis/NIR reflectance spectrophotometer, two replicas per sample, are illustrated for the three muscles [Figs. 3(a)-3(c)]. Each color in the subfigures represents the two measurements on a sample with a different slicing direction, for the respective muscle type.

 

Fig. 3 Spectroscopic profiles from the three different muscles (a-c) and the different slicing directions. The inset figure shows a close-up of the reflectance spectra for the BR muscle. The vertical dotted lines indicate the absorption wavelengths of water at 970 nm, 1200 nm, 1450 nm and 1940 nm.

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The three muscles show a difference in the obtained vis/NIR reflectance spectra. A higher overall reflection was obtained for the BB muscle, while the BR muscle showed the lowest overall reflection. These overall differences in reflection values between the different muscle types are most likely related to differences in light scattering [25]. Differences in sarcomere length and collagen concentration have been shown to influence light scattering and might explain the observed differences, as the collagen concentration and sarcomere length have been reported to differ highly among muscle types [12,26–29]. Von Seggern et al. (2005) found a collagen content of 22.34 ± 12.20 mg/g in the BB, while in the BR muscle only 7.91 ± 1.55 mg/g was found [29]. No values were found for the SOL muscle. Some variation was observed between the spectroscopic profiles of the different slicing directions, but there was no clear trend in this variation. Most likely, this variation between slicing directions can be attributed to intramuscular variation, as different slicing direction cuts originated from a slightly different part of the same muscle [30].

Some typical absorption characteristics for muscle tissue could be noticed, recognizable as areas with lower reflectance values. As water represents up to 75% of the total muscle fresh matter, specific water absorbance (O-H bonds) at 970 nm, 1200 nm, 1450 nm and 1940 nm can be observed, shown as dotted vertical lines in Fig. 3 [3]. A dual absorption peak at 544 nm and 582 nm is also present, clearly visible on the insert in Fig. 3(b), which can be attributed to the presence of oxymyoglobin. This is typical for fresh oxygenated muscle tissue and causes the muscle tissue to have a bright red color [31,32]. Besides the dual absorption peak, oxymyoglobin also causes a Soret band at 418 nm [31–33]. Furthermore, another absorption feature was present at 762 nm, which can be related to both the O-H bond 3rd overtone as well as the absorption caused by deoxymyoglobin [31,34]. Besides the absorption features discussed, protein and intramuscular fat also influence the NIR spectrum due to the absorption by N-H bonds (1460-1570 nm and 2000-2180 nm) and C-H bonds (1100-1400 nm, 1700 nm and 2200-2400 nm), respectively [3]. However, these broad absorption bands are less obvious.

3.2 Contactless spatially resolved reflectance spectroscopy

In Fig. 4, two examples of obtained SRS images at one wavelength (849 nm) are illustrated. This wavelength, with low absorption [Fig. 1], was chosen for illustration purposes. On the left side, raw images of the same piece of muscle tissue, with a different initial yaw angle, are shown. Both images were taken on the BB sample cut with the fibers running parallel to the measurement surface. In Fig. 4(a), the fibers are running from top to bottom, while in Fig. 4(c) the fibers are running diagonally, from the upper left corner to the bottom right corner.

 

Fig. 4 Examples of raw images at 849 nm from the biceps brachii muscle cut with the fibers running parallel to the measurement surface: fibers from a) top to bottom and c) diagonally from upper left corner to lower right corner. b) + d) The red dots indicate the actual data points of the 50% equi-intensity level, while the solid black lines represent the fitted rhombuses with major axis. b) q = 1.42, B = 1.15; d) q = 1.48, B = 1.15.

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The images on the right in Fig. 4 show a graphical representation of the raw images on the left, on which the entire diffuse reflectance spot is visible. Equation (1) was used to fit reflectance data points falling in-between two threshold values. In the images on the right, the red dots indicate the actual data points of the 50% equi-intensity level. The shape fitted to these data points is shown as the solid black line. The observed q-values of 1.42 and 1.48, which were well below 2, clearly indicate the presence of a rhombus shape, rather than an ellipse or a circle. This is in line with the findings of Ranasinghesagara & Yao (2007), who attributed this rhombus shape to the effect of sarcomere diffraction [16].

In Fig. 4, the major axis of the fitted rhombus is shown as a black straight line. In this example, with the fibers running parallel to the measurement surface and at one wavelength and one equi-intensity level, the rhombus’ major axis orientation was perpendicular to the fiber direction.

3.3 Effect of wavelength and distance on the spatially resolved reflectance

The result of fitting Eq. (1) to different equi-intensity levels for a single subsample, wavelength and yaw angle is shown in Fig. 5(a). Six of the fitted rhombuses are shown for the BB muscle with the fibers running parallel to the measurement surface, from top to bottom in Fig. 5(a), and at wavelength 849 nm like in section 3.2. A clear effect of the equi-intensity level on the rhombus fit, and more specifically on the orientation of the major axis, can be observed [Fig. 5(a)]. Moreover, the smallest rhombuses (closer to the point of illumination), shown in white in Fig. 5(a), have a major axis orientation perpendicular to the fiber orientation. Rhombuses at larger distances, on the other hand, are shown in red and have a major axis orientation parallel to the fiber orientation. In the BB muscle, shown in Fig. 5(a), this shift in major axis orientation occurred at an axis length of 11.87 ± 0.90 mm. In the SOL muscle, also with the fibers running parallel to the surface, this shift occurred at an axis length of 17.24 ± 2.94 mm. In the BR muscle with fibers running parallel to the surface, no shift in rhombus orientation was noticed, as all rhombus orientations were perpendicular to the fiber orientation.

 

Fig. 5 a) Rhombus fitted at six different equi-intensity levels (75%, 40%, 25%, 15%, 8% and 5%) for the BB muscle with the fibers running parallel to the measurement surface (along the Y spatial dimension). White lines indicate the rhombuses with their major axis perpendicular to the fiber direction, while the red lines indicate rhombuses with their major axis parallel with the fiber direction. b) Major axis orientation of fitted rhombuses (equi-intensity level 65% of maximum intensity) relative to the X spatial direction of the SOL muscle sample with the fibers running parallel to the measurement surface, at different initial yaw angles (in legend) and at different wavelengths.

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A similar shift in the major axis orientation was also reported by Kienle et al. (2004) from their study on the effect of aligned cylindrical microstructures in biological tissues on the propagation of light [19]. When looking at the interaction of photons with a cylindrical structure, their calculations illustrated that photons scatter in very specific directions. Moreover, the light is scattered along the lateral surface of a cone of which the axis overlaps with the axis of the scattering cylinder, in this case the muscle fibers. The cone’s half-angle is equal to the incident angle of the light relative to the cylinder axis [19]. This phenomenon is illustrated in more detail by Kienle et al. (2007) [35]. This finding explains the perpendicular direction of the rhombus major axis close to the point of illumination, as with an incident angle of 90°, the scattering cone’s half angle becomes 90° as well, transforming the scattering cone into a scattering plane perpendicular to the cylinder axis direction. However, after multiple scattering events, at further distances from the point of illumination, photons can propagate in arbitrary directions due to the slightly different orientation of different fibers and the presence of isotropic scattering particles (cfr. cell organelles, pores, etc.). As the overall scattering parallel to the cylinders is much smaller compared to the perpendicular direction, photons will propagate further along the cylinder axis [16,19,36]. Accordingly, this effect depends on the muscle’s scattering coefficient, which could explain the observed differences between the measured muscles, as different muscle types exhibit different optical properties [37].

Based on the vis/NIR reflection signals in Fig. 3, it can be assumed that the BB muscle is more scattering than the SOL muscle, which in its turn is more scattering than the BR muscle. This means that photons in the BB muscle will be scattered more and, therefore, based on the findings of Kienle et al. (2004), the change in rhombus orientation will occur closer to the point of illumination [19]. This shift occurred at further distances for the SOL muscle, while it was not observed for the BR muscle, possibly because this shift occurred at even larger distances from the point of illumination where the signal to noise ratio was too low to be detected by the camera. Additionally, variability in the type, composition and diameter of the muscle fibers between the different muscles probably also affects the observed reflectance signals [38]. In contrast to the parallel slicing direction, the relation between the rhombus diameter and the fitted rhombus orientations was less clear for the perpendicular or transversal slicing directions [Fig. 1]. This can be explained by the fact that for these slicing directions the measurement surface approximates an isotropic distribution. The fitted rhombuses resemble a more circular shape, making the prediction of the major axis orientations less relevant.

In Fig. 5(b), the major axis orientations of the fitted rhombuses (equi-intensity level 65% of maximum intensity) are shown relative to the X spatial dimension of the SOL muscle sample with its fibers running parallel to the measurement surface, at different initial yaw angles and at different wavelengths. Wavelengths below 600 nm and above 1400 nm were not included in these analyses as the signal to noise ratio for the reflectance signals at those wavelengths was too low to perform reliable rhombus orientation estimations. This is most likely caused by the high absorption by the samples in combination with a lower sensitivity of the camera at those wavelengths, as can be seen from Fig. 3.

It was found that the major axis orientation varied only little between different wavelengths [Fig. 5(b)]. For yaw angles of 45° and 135°, a small wavelength effect was noticed. Moreover, at wavelengths where high absorption occurred [Fig. 3], the rhombus’ orientation angle relative to the X spatial dimension decreased. This decrease can be seen for wavelengths below 650 nm, where myoglobin is the main absorbing component, and at the water absorption bands around 970 nm, 1200 nm and towards 1450 nm. This effect is probably related to the illumination angle. As mentioned, an incident angle of 20° with respect to the vertical axis was used to avoid measuring the specular reflectance. In this experiment, the light entered from the right side of the images. In samples with the muscle fibers running in a 45° or −45° (similar as 135°) angle with respect to the illumination direction, a small shift of the diffuse reflectance spot towards the illumination direction was observed for wavelengths at which absorption is high. For other yaw angles, this effect was probably also present. However, as this only resulted in a change of the rhombus axis oriented along the illumination direction, the overall effect in the rhombus’ major axis orientation was limited for these yaw angles.

3.4 The yaw angle affects the orientation of light propagation

Each sample was measured along five different yaw angles. In Fig. 6, all the fitted rhombuses for these different yaw angles are shown for three wavelengths (612 nm, 760 nm and 1006 nm), one equi-intensity level (35%) and for the SOL sample with the fibers running parallel to the measurement surface.

 

Fig. 6 Illustration of rhombuses fitted on the images acquired under different yaw angles for the SOL muscle cut with the fibers running parallel to the measurement surface. Three different wavelengths are shown: (a) 612 nm; (b) 760 nm; (c) 1006 nm. Every colored line indicates a fitted rhombus with major axis, with a different initial yaw angle. At yaw angle 0°, the muscle fibers are running parallel to the X spatial dimension.

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In Fig. 6, at the initial yaw angle 0°, the muscle fibers were positioned along the X spatial dimension. In general, as could be seen in Fig. 5(b), applying different yaw angles results in a change of the rhombus’ major axis orientation. This can be seen in Figs. 6(b) and 6(c) as well. In these cases, at the initial yaw angle, the rhombus’ major axis orientation was perpendicular to the fiber orientation, as was also seen before [Figs. 4 and 5]. Every following yaw angle, the sample was rotated 45° counterclockwise, which was reflected in the observed major axis rotations in Figs. 6(b) and 6(c). At a yaw angle of 180°, the fibers were oriented along the X spatial dimension again. As expected, this major axis orientation was the same as for the initial yaw angle.

Nevertheless, this effect was not seen at 612 nm, as shown in Fig. 6(a). This is most likely related to absorption effects inside the sample in combination with the illumination direction. The absorption increases at 612 nm due to the presence of myoglobin [Fig. 3]. The photon path length will be reduced as the chance of absorption increases, causing less interaction with present muscle fibers.

In Table 1, the coefficients of determination and RMSEPs are summarized for the linear relation between the applied yaw angle and the estimated rhombus major axis orientations. All muscle samples with a parallel slicing direction showed a good relation between the yaw angle and the rhombus orientation, with R² values above 0.993 and an RMSEP below 3.95°. For the other slicing directions, transversal and perpendicular, the effect of the applied yaw angle was less clear, as indicated by the lower R² and higher RMSEP values. However, the transversal BB and BR, and the perpendicular SOL sample still gave a high R² (> 0.94), although the RMSEP values were already around 4 times higher. A possible source of variation in the obtained data is the slicing direction as shown in Fig. 1. As these slicing directions were established by using a visual inspection of the main muscle fiber orientation before cutting, there may also have been some uncertainty on the reference values for the applied yaw angle.

Table 1. Linear regression results for the relation between applied yaw angle and the predicted rhombus orientation angle. R² = coefficient of determination; RMSEP = root mean square error of prediction [°].

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3.5 Effect of muscle slicing direction

To visualize the overall effect of slicing direction on the obtained diffuse reflectance signals, the obtained bias parameter values as defined in Eq. (3) are visualized in Fig. 7 as a function of the distance from the point of illumination and the wavelength. The bias parameter is 1 for a circle, while higher values indicate a deviation from a circular shape. In Fig. 7, the estimated bias parameter is illustrated for all distances from the point of illumination and wavelengths, for all measured samples. Each row indicates a different muscle, while each column corresponds to a different slicing direction. Each figure shows the obtained bias parameter for the measurement at a yaw angle of 90°. The color bars were scaled for each muscle type (or row).

 

Fig. 7 Estimated bias parameter values at a yaw angle of 90° for the different muscle types and slicing directions as a function of the wavelength and the distance from the point of illumination.

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In Fig. 7, the bias parameters are shown for the measurements obtained at a yaw angle of 90°. At other yaw angles similar trends were observed, although the overall values were lower. For all muscles measured, the bias parameter is generally highest if the fibers are parallel to the measurement surface. The transversal and perpendicular slicing direction have an overall lower bias parameter. In these cases, the measurement becomes more isotropic, resulting in a more circular glow spot and a bias parameter closer to 1. The lowest bias parameter values in all measurements were observed for the perpendicular muscle slicing direction, with the fibers running perpendicular to the measurement surface.

Different equi-intensity levels are located at different distances from the point of illumination. This distance also affects the bias parameter [Fig. 7]. Especially with the parallel slicing direction, first an increase in the bias parameter occurs with increasing distance, after which a decrease is noticed. This decrease in the bias parameter at long distances from the point of illumination was also observed by Ranasinghesagara & Yao (2007) [16]. They attributed this effect to scattering, as at larger distances, photons experience more scattering events which are not related to anisotropic structures present in the tissue. Additionally, Ranasinghesagara et al. (2006) reported that the bias parameter estimates were unstable close to the point of illumination, as these photons mainly carried information from the surface layers and are subject to the effects on initial incident conditions [20].

From Fig. 7, a clear effect of wavelength was noticed as well. In general, a larger bias parameter was found at higher wavelengths. Ranasinghesagara et al. (2010) reported that the bias parameter had a weak dependence on wavelength at large distances from the incident point [21]. However, they only considered wavelengths from 640 nm to 840 nm. The results in Fig. 7 suggest a larger wavelength dependency at higher wavelengths. Moreover, at wavelengths with a higher absorption, the bias parameter showed a different course with increasing distance. These effects were most clear in the samples with fibers parallel to the measurement surface at the absorption peaks of water around 970 nm and 1200 nm.

Next, the bias parameters clearly varied between the different muscles [Fig. 7]. High values for the bias parameter were noticed in the parallel slicing direction of the BR muscle. A difference in these values can possibly be attributed to the cause of the anisotropy, related to the muscle fiber type and composition. Different muscles exhibit a different fiber composition, with different fiber types having a different fiber diameter [38]. Although all the measured muscles are classified as red muscles, mainly consisting of slow-twitch Type I fibers, also fast-twitch Type IIa and Type IIx fibers are generally present. For example, according to Kirchofer et al. (2002) the BR muscle has 9.1 ± 1.5% of Type IIx, while the BB muscle has 18.6 ± 3.0% of this fiber type [38]. The SOL muscle was not analyzed by Kirchofer et al. (2002) [38]. These differences in fiber type might influence the observed rhombus shapes. Moreover, muscle differences in collagen content and the sarcomere length, both known to influence the amount of scattering, might also be responsible for the observed differences between the muscles [27,37].

Finally, it should be possible to model the light propagation in anisotropic tissues in order to verify the observed results. Previous research showed modelling results using Monte Carlo simulations. Kienle et al. (2004) described the theoretical basis for the observed anisotropic effects [19]. Using Monte Carlo simulations, they succeeded in simulating the anisotropic effects observed in porcine arteries. They used a semi-infinite turbid medium containing isotropic scatterers and aligned cylinders. Moreover, Kienle (2007) found that modelling this anisotropic behavior was not possible using the diffusion equation for anisotropic media, especially when the anisotropy factor was high [39]. For retrieving optical properties from diffuse reflectance measurements, nonlinear regressions using the solutions of both the isotropic and the anisotropic diffusion equations delivered useful results [40].The modelling of different initial fiber orientations using Monte Carlo simulations with aligned cylindrical structures could confirm the observed results. This could further emphasize the importance of the fiber orientation when using optical measurement techniques on fibrous structures.

4. Conclusions

A contactless spatially resolved spectroscopy setup was used to measure diffuse reflectance glow spots over the 470 nm to 1620 nm range for different muscle tissue samples. Three different muscles, biceps brachii, brachialis and soleus, were sampled from a Jersey bull and cut in three different ways: parallel, transversal and perpendicular to the fiber orientation. The muscle samples were measured with the setup at five different yaw angles, from 0° to 180° in 45° steps, by rotating the sample around its vertical axis. A rhombus was fitted to equi-intensity reflectance levels, corresponding to different distances from the point of illumination. From the fitted rhombus, the major axis orientation and a bias parameter, representing the deviation from a circular shape, were determined.

For samples with their muscle fibers running parallel to the measurement surface, the major axis orientation was related to the distance from the point of illumination. Moreover, for small rhombuses, the major axis orientation was found to be perpendicular to the fiber orientation. This was attributed to the present muscle fibers which scatter the light in a plane perpendicular to the cylinder axis direction. At longer distances from the point of illumination, as the photons have had undergone more scattering events, the effect of this scattering by the fibers diminished. This caused the major axis orientation to shift 90°, aligning with the muscle fibers. Moreover, for the different muscle types, this shift in major axis orientation occurred at different distances from the point of illumination. These effects were attributed to differences in the wavelength dependent bulk optical properties.

The major axis orientation of the fitted rhombuses correlated well with the applied yaw angles, especially for the parallel slicing direction (R² > 0.993 and RMSEP < 3.95°). Moreover, the parallel slicing direction resulted in a clear rhombus shape (high bias parameter) of the diffuse reflectance spot. For the transversal and perpendicular slicing directions, weaker correlations were observed, which could be attributed to the more circular shape (bias parameter close to one) of the diffuse reflectance spot, resulting in a less reliable estimation of the major axis orientation. The bias parameter was also influenced by the distance from the point of illumination. It was hypothesized that at longer distances more scattering events have occurred which are not related to anisotropic structures. Moreover, the bias parameter showed a clear wavelength dependency, with higher values for longer wavelengths.

Overall, the obtained results indicate that the 3D fiber orientation has a large influence on the diffuse reflection measurements acquired from muscle samples. The insights obtained in this study are highly valuable when designing optical sensors for muscle inspection and to account for potential bias on optical measurements caused by these anisotropic effects. In addition, the prediction of muscle fiber orientation can be of great value to the meat industry, for example to align meat products for mechanical slicing operations.