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Abstract
LED-based photobiomodulation (LED-PBM) for the treatment of knee osteoarthritis (KOA) is a promising technology. However, the light dose at the targeted tissue, which dominates the phototherapy effectiveness, is difficult to measure. This paper studied the dosimetric issues in the phototherapy of KOA by developing an optical model of the knee and performing Monte Carlo (MC) simulation. The model was validated by the tissue phantom and knee experiments. In the study, we investigated the effect of luminous characteristics of the light source, such as divergence angle, wavelength and irradiation position, on the treatment doses for PBM. The result showed that the divergence angle and the wavelength of the light source have a significant impact on the treatment doses. The optimal irradiation location was on both sides of the patella, where the largest dose could reach the articular cartilage. This optical model can be used to determine the key parameters in phototherapy and help the phototherapy of KOA patients.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Knee osteoarthritis (KOA) has become one of the most common diseases in people over 60 [1]. It is a painful and disabling disease that affects millions of patients [2]. As the population ages and the proportion of people over 65 years of age increases, the prevalence of symptomatic KOA may increase to 33% by 2030 worldwide [3]. Therefore, it is necessary to provide effective KOA treatments [4]. Clinical results show that performing exercise programs can significantly improve KOA symptoms [5]. However, many patients with joint pain refuse to engage in physical activity, demonstrating a lower compliance with exercise therapy [6,7]. As another non-pharmacological treatment option of KOA, photobiomodulation (PBM) has shown comparative effectiveness and is more acceptable for patients [8,9]. Lasers are the dominant light source for PBM therapy, but in recent years, numerous studies have also shown the efficacy of LED-based photobiomodulation (LED-PBM) [10]. Compared to laser-based PBM, LED-PBM is less expensive and more secure [11].
The key issues in LED-PBM therapy are how the energy from LEDs works at the cellular and organismal levels, as well as what the optimal light dose is for different applications [12]. For the mechanisms of PBM for KOA, research showed that it acts as a homeostasis regulator to maintain the balance between anti- and pro-inflammatory responses [13,14]. For the dosimetry of PBM, the first law of photochemistry states that light must be absorbed by a compound for a photochemical reaction to take place. It has been found that a dose of too high or too low will result in a diminished therapeutic outcome [15,16]. Since the therapeutic effect of PBM is closely related to the light dose, it is important to study dosimetry at KOA treatment.
There are still some conflicting findings in the studies related to LED-PBM for KOA [17]. For example, Alves’s group reported that 50 mW of optical power was more effective than 100 mW in PBM for arthritis [18]. In contrast, Morais’ group reported that LED-PBM has no therapeutic effects on KOA [19]. This problem may be caused by not using the appropriate light dose in the clinical treatment [20]. But, detecting light dose within the knee is still difficult in clinical practice. Detecting the spatial distribution of light within the knee joint is challenging for commonly used photodetection devices without invasive procedures [21]. Even if the World Association for Laser Therapy (WALT) has given some dosage guidance for PBM, the light dose could only be adjusted at the skin surface [22]. Although Alves and Morais set the initial conditions for their study, the light dose within the tissue still remains unclear. Due to many factors, such as the luminous characteristics of LEDs light source and irradiation location may change the light dose at the targeted tissue, some studies showed conflicting results [23]. Accordingly, there is a requirement to provide a tool to analyze the LEDs light dose within the knee, and Monte Carlo (MC) simulation may be one option.
MC method has been applied to calculate the light dose in tissue optics [24]. Compared with diffusion theory, MC method is more flexible and accurate. It can also be easily applied to tissues with different structures [25,26]. Since the development of MC model for multilayered structures by Wang’s team, it has gradually become the gold standard in this field [27]. For example, Cassano’s group used MC method to perform a dosimetry study of PBM in emotion regulation. They scanned the patient’s head with MRI to create a head optical model and determined the optimal illumination position [28]. Li’s group studied the therapeutic dose of phototherapy for hemorrhagic stroke using the visible Chinese human dataset to provide a reference for phototherapy [29]. Matija’s team simplified the finger joints into a columnar structure and studied the feasibility of using hyperspectral imaging technology to diagnose finger arthritis [30]. However, in the knee joint, using only a simple model is difficult to analyze the light dose comprehensively. There is still a lack of sufficiently accurate knee models for light dosimetry studies.
Due to these problems, this paper built a LED-PBM optical model for KOA, which adopted MC method to analyze the photon propagation properties within the knee. A numerical calculation method was used to analyze the light dose at the targeted tissue. This paper also conducted tissue phantom experiments to verify the model. As a standardized test method, the tissue phantom has been utilized in many mature technologies for dose analysis, such as ultrasound testing, CT, and MRI [31–33]. The complete simulation included the skin model and knee model analysis. The entire process of the study is shown in Fig. 1: Firstly, we built a skin model to analyze the effect of skin on photon transport and performed phantom experiments to verify the model; secondly, a knee model was built and corrected by the transmittance experiment of the knee in vivo; finally, based on the optical model, using MC method, the effects of luminous characteristics (divergence angle, wavelength) and irradiation position on the light dose at the targeted tissue has been analyzed. The model helps to determine the light dose during clinical treatment and provides an essential reference for the phototherapy of KOA.
2. Theory and modeling
This chapter presented the process of using MC method to simulate photon propagation. Section 2.1 described the theoretical basis of MC simulation. Section 2.2 presented the modeling method of the skin model, based on which the skin’s role in PBM is verified. Section 2.3 presented the knee modeling approach applied to analyze photon transport during KOA treatment.
2.1 Monte Carlo simulation theory
Based on tissue optics, light propagation in tissue was described by the radiative transfer equation (RTE) [34,35]. In 1983, Wilson’s group first introduced MC method to study light-tissue interactions by solving the RTE [36]. In this method, the light was simulated as packets of photons that are gradually absorbed as they travel through the medium. And photons were scattered randomly at a rate that depended on the local optical properties of the medium. Over the years, many advanced MC methods have been applied to simulate. This paper used the GPU-accelerated Mcxlab (http://mcx.space/) program [37]. Mcxlab is the native MEX version of MCX for MATLAB and GNU Octave. It launched millions of photon packets and tracked their propagations through the tissue. The primary input optical parameters have tissue’s refractive index n, absorption coefficient ${\mu _a}$, scattering coefficient ${\mu _s}$, and anisotropy factor g. The hardware platform information on which we run the MC simulation is as follows: (CPU: (Xeon E5-2680 v4, Intel, USA), GPU: (GeForce RTX 3090, NVIDIA, USA)).
2.2 Skin model
In the skin model of knee joint, three layers of tissue were established: the epidermis, dermis, and subcutaneous fat. Their thicknesses are D1, D2, and D3 (see Fig. 2). A thin layer of air was added outside the epidermis. Upper and deep dermis blood vessels were embedded in the dermis. To simplify the calculation, the skin model was appropriately simplified based on previous research [38]. The number of cubicle voxels in the skin tissue model was 500 × 500 × 400. The size of each voxel ${v_{skin}}$ was 0.01 × 0.01 × 0.01 mm3 [39]. Table 1 contained the skin model’s relevant structural and light source parameters. According to our previous studies, the luminous characteristics of the light source impacted the photon penetration ability [38]. Therefore, this paper used sources with different divergence angles $\alpha $ to verify the accuracy of the simulation. The $\alpha $ was defined in the Mcxlab program as the uniform emission of photons in all directions within the divergence angle. The spot size of the incident surface was kept constant by changing the position of the light source (see Fig. 2). To achieve a stable distribution of photons in skin tissue, the number of photons is 108.
Table 1. Skin model structure parameters and light source parameters.
Based on the data in Fig. 3(a)-(d), the average tissue optical parameters of the epidermis, dermis, subcutaneous fat, and blood in the range of 400-1000 nm have been obtained [39–41]. The blue area represented ${\mu _a}$, and the red area represented ${\mu ^{\prime}_s}$. The tissue optical parameters in Fig. 3 may have a large standard deviation due to the samples’ individual differences. According to Fig. 3, suitable optical parameters can be found from the fluctuation range. This paper used the wavelength $\lambda $ of 650 nm in simulations and experiments. The 650 nm red light was commonly used in the LED-PBM treatment of KOA [42]. Except for ${\mu _a}$ and ${\mu ^{\prime}_s}$, the refractive index n set to 1.37 for the three skin tissues and 1.33 for the blood. The anisotropy factor g of the tissues was assumed to follow the wavelength dependency, and it can be determined by Eq. (1) [43].
Fig. 3. (a)-(d) absorption coefficient ${\mu _a}$ (blue area to the left axis) and reduced scattering coefficient ${\mu ^{\prime}_s}$ (red area to the right axis) of the epidermis, dermis, subcutaneous fat, and blood.
2.3 Knee model
A knee model was built to analyze the photon transport during KOA treatment. This section presented a knee model based on the Harris team’s MRI data (see Fig. 4(a)) [44]. It contained the femur, tibia, fibula, patella, patellar cartilage, femoral cartilage, and meniscus. Then, the patellar tendon, cruciate ligament, and joint capsule were added to the model based on MRI images. The skin tissue was simplified into the epidermis, dermis, and subcutaneous fat layer. To reduce the computational cost, some tissues was simplified in the knee model. After the geometric model was established, this paper used the Mesh voxelisation function in the commercial software Matlab to voxelize the model [45]. The voxelized model was compatible with MC programs. The number of cubicle voxels in the knee model was 359 × 392 × 366. The size of each voxel ${v_{knee}}$ was 0.3 × 0.3 × 0.3 mm3.
Fig. 4. (a) MRI image of knee joint; (b) Overall model image of knee joint; (c) Sagittal plane of the model; (d) Coronal plane of the model; In (b)-(d), to better distinguish the difference between the optical properties of the tissue, different colors are utilized to indicate tissues.
The completed model was shown in Fig. 4(b)-(d): the knee model’s overall view, sagittal section, and coronal section. In addition to the black air background, seven other tissues in the knee joint model are classified according to optical properties: the epidermis, dermis, subcutaneous fat, bone, cartilage, tendon, and synovia. Cartilage tissue included patellar cartilage, femoral cartilage, and meniscus. The optical properties of the cruciate ligament were approximated in the model as cartilage tissue. The optical parameters of the epidermis, dermis and subcutaneous tissue according to the data were obtained in Fig. 3. The others were obtained in Table 2. So far, the total knee joint optical model has been established.
3. Model validation and correction
In this chapter, we performed skin phantom experiments and knee experiments in vivo. The skin phantom was built to validate the accuracy of skin models in Section 3.1. Then, the optical parameters of the skin in the knee model were corrected by knee experiments in Section 3.2. It could make the simulation model more accurate.
3.1 Phantom experiment for skin model validation
The skin phantom contained the epidermis and two dermal layers (upper and deep dermis). It used scatterers and absorbers to simulate the transmission of photons in real human skin [48]. The phantom was made with agar (V900510, Sigma, USA) as matrix, India Ink (4001, Pelikan, GER), porcine whole blood (B1612, Bersee, CHN) as absorbent, and Intralipid (20%, SSPC, CHN) as scattering agent. The volume fractions of each reagent were listed in Table 3. The experiment of skin phantoms was based on the methods of previous studies [49]. The phantoms were superimposed, and saline buffer was added to the contact surface to form a three-layer phantom. Figures 5(a)-(c) showed the produced epidermal, upper dermal, and deep dermal phantoms. Figure 5(d) showed the top view of the three-layer phantom in the fixture. Figure 5(e) showed the side view of the three-layer phantom on the slide.
Fig. 5. (a)-(c) the phantoms of the epidermis, upper dermis, and deep dermis; (d) the top view of the three-layer phantom; (e) a side view of the three-layer phantom.
Table 3. The specific formula of the phantom (V means volume fractions and nan means not added).
The phantom with different formulations shows different trends in transmittance at different divergence angles of incidence. By correlating the trends in transmittance between the phantom and the MC simulation results, the accuracy of the skin model in Section 2.2 can be verified. The transmission of LED light sources with different divergent angles $\alpha $ in the skin phantom was tested. The device mainly consists of a light source (LumiEngin, Keyi-Sky, CHN), a condenser lens (ACL5040U, Thorlabs, USA), a diaphragm (ID36, Thorlabs, USA), an integrating sphere (AIS-2-0.5 m, EverFine, CHN), and a spectrometer (HAAS-1200, EverFine, CHN) (see Fig. 6).
Fig. 6. (a) the experimental device of the phantom transmittance; (c)-(d) the light sources with three $\alpha $(0°, 60°, and 120°); (e) the device when measuring local optical power; (f) the area division diagram when measuring the local transmittance of the phantom.
Fix the skin phantom to the light entrance of the integrating sphere (see Fig. 6(a)). Then, select a LED light source with a center wavelength $\lambda $ of 650 nm, use a condenser lens to adjust the $\alpha $, and keep the diameter of the incident surface consistent by changing the distance between the light source and the sample. Figure 6(b)-(d) showed the schematic diagrams of light sources with three $\alpha $(0°, 60°, 120°). Optical power data was collected using an integrating sphere and a spectrometer. The average light transmittance obtained from the phantom experiment ${T_e}$ can be calculated according to Eq. (2):
${P_{\textrm{ }1}}$ represented the light power of the LED light source after passing through the empty fixture, and ${P_{\textrm{ }2}}$ represented the power after passing through the skin phantom. In addition to measuring the average transmittance, the optical power of the nine regions in Fig. 6(f) before and after the incident skin phantom was measured using an optical power meter (PM100D, Thorlabs, USA, S120VC probe). The optical power meter probe was placed at the bottom of the fixture in Fig. 6(e). The local transmittance can also be calculated according to Eq. (2).
Corresponding to the phantom experiment, the transmittance of the region in Fig. 6 was counted in the MC model, defined as ${T_s}$ (see Eq. (3)).
${\Phi _{in}}$ and ${\Phi _{out}}$ are the fluence rate of the incident and emitted regions in MC simulation. The sampling area of the local transmittance is 1mm*1 mm. The knee skin model can be considered accurate if the ${T_s}$ corresponding to different regions correlates well enough with ${T_e}$ in the three $\alpha $ experiments.
According to Eq. (2) and Eq. (3), the ${T_s}$ and ${T_e}$ of the light source with different $\alpha $ were analyzed. Figure 7 described the absolute value differences (see Fig. 7(a)(c)(e)) and correlations (see Fig. 7(b)(d)(f)) of ${T_s}$ and ${T_e}$. The following conclusions were drawn from Fig. 7:
- 1. Although there was a certain difference in the absolute values of ${T_s}$ and ${T_e}$, it can be seen that the trend is consistent. After calculation, the ${R^2}$ are all above 0.9. Hence, ${T_s}$ and ${T_e}$ have a high correlation, and the accuracy of the skin model can be verified.
- 2. There is an absolute deviation between the simulated and experimental values, which is due to multiple factors. Firstly, the content of absorber and scatterer in the phantom is highly correlated with the transmittance of light in the experiment. Changing the composition for making the phantom and increasing the content of absorber and scatterer in the phantom will reduce the transmittance of the experiment. In addition, reports have pointed out that the size of the light spot is positively correlated with the penetration ability of light [50]. Therefore, the use of a larger light spot size in the phantom experiment may also be a reason for the higher transmittance.
- 4. When the PBM area was large, the transmittance was different in different areas. It was related to the distance from the PBM treatment center. The transmittance was higher for the portion closer to the center.
- 5. When the photons pass through the epidermis and dermis of the skin, there would be significant attrition. It can be considered that the skin was the most crucial part affecting light transmission when LED-PBM of KOA.
Fig. 7. (a)(b) the absolute value and correlation analysis of ${T_s}$ and ${T_e}$ when the $\alpha $ is 0°; (b)(c) and (d)(e) the absolute value and correlation when $\alpha $ is 60° and 120°. In (b)(d)(f), linear fitting is performed on the phantom experimental transmittance and MC simulated transmittance for each sampling area (indicated by the blue ball in the figure). The dotted line is the fitted curve, and the equation, R2 coefficient of determination, and p-value of the fitted dotted line are given; p < 0.05*, p < 0.05**, p < 0.01***.
3.2 Knee experiment in vivo for knee model correction
Due to differences in the optical properties between patients’ skin, the knee model must be calibrated to assess a specific patient accurately. Skin tissue influenced light transmission significantly. Therefore, the optical parameters of the epidermis and dermis were the subject of correction. And because of the small spot size and high energy density that lasers can produce, we chose lasers for optical corrections. Figure 8 showed the process of using the optical power meter to correct the model on the patient’s knee, as follows:
- 2. Use a laser transmitter (OBIS 647 LX, Coherent, USA) to irradiate at Source 1 and use the optical power meter probe to measure the optical power above the patella;
- 3. Set the laser light source in MC simulation, and count the output light power of the detection surface when the laser was incident at the position of Source 1;
- 4. Compare the optical power detected in the simulation and the experiment in vivo, adjust the optical parameters of the skin based on the range of the optical properties of the skin in Fig. 3, and re-simulate to match the results;
- 5. Move the laser from Source 1 to Source 2, and observe whether the results of simulation and experimental match. If there was a large deviation, continue to repeat Steps 2-4.
Fig. 8. (a) the photo of the left knee detection experiment using the optical power meter; (b) the irradiation at the position of Source 1; (c) the irradiation at the position of Source 2; (d) the irradiation position and detection position in simulation. Cover source with black tape can prevent source from spilling out in all directions and affecting the detection results.
According to the above process, experiments and simulations were carried out on the left knees of three volunteers A (male, 26 years old, Fitz. Type 3), B (male, 29 years old, Fitz. Type 1), and C (male, 33 years old, Fitz. Type 4). This article employs the Fitzpatrick scale to classify volunteers of different skin tones [52]. The incident light power in both experiment and simulation was 100 mW. The corrected results and optical parameter data of knee skin tissue were shown in Table 4. Due to the experimental errors, the deviation of the optical power obtained from the detector in the simulation and experiment below 30% was considered acceptable. In this paper, the optical model of the knee obtained by modifying the optical parameters of the knee skin has higher accuracy and robustness than others [53].
Table 4. Relevant parameters in the knee joint experiment of three volunteers
4. Simulation results and discussion
The therapeutic effect of LED-PBM for KOA was uncertain because of the difficulty of monitoring light dose at the targeted tissue. Based on the skin and knee models, this chapter investigated the effects of divergence angle, wavelength and irradiation position of the light source on the dose at the targeted tissue. Finally, we discussed some clinical issues of PBM.
4.1 Effect of the divergence angle of the light source on photon transport in the skin
Since the targeted tissues for KOA treatment were located in the subcutaneous layers, excessive photon energy deposition in the skin may result in insufficient light doses at the targeted tissues. And compared to lasers, LEDs have a divergence angle issue. So, this section investigated the effect of the divergence angle of the light source on photon transport in the skin. The normalized energy density Q along the Z-axis direction of the skin model center was chosen to simulate.
Several different divergence angles of light sources were chosen for the simulations in this section (see Fig. 9). The wavelength of the light sources was 650 nm. It showed that three apparent bulges, which were the effects of the epidermis, the upper and the deep dermis blood vessels. The Q value at a divergence angle $\alpha $ of 0° was 45% of that at a divergence angle $\alpha $ of 60°. And the larger divergence angle $\alpha $, the higher Q. One of the reasons is that according to the inverse square law of illuminance, the larger $\alpha $, the more unevenly the light is incident on the skin surface and the power density is characterized by a medium-high to low level [54]. In addition, the divergence angle $\alpha $ would increase the path of photons within the tissue and enhance backscattering [51]. When the $\alpha $ below 30°, it caused lower energy deposition in the skin. Based on the above analysis, we can conclude that controlling the light beam to a smaller angle is beneficial for improving the penetration ability of light in tissues. Due to the increased divergence angle of the light source, the photon’s path of motion in the tissue and its ability to undergo backscatter are increased, resulting in higher energy deposition in the surface and decreased energy reaching deeper layers [51]. To ensure enough light dose is delivered to deep tissues while avoiding skin damage to surface tissues, the light therapy time or power of the light source can be appropriately increased.
Fig. 9. the Q distribution at different $\alpha $ (0, 30, 60, 90, 120$^\circ $) of incidence; The two dashed lines refer to the interface of the epidermis-dermis and dermis-subcutaneous fat layer.
4.2 Effect of the wavelength of the light source on photon transport in the skin
This section analyzed several common wavelengths 650, 820, and 940 nm in the LED-PBM (see Fig. 10) [17]. The Q along the Z-axis direction of the skin model center was also chosen to simulate. The skin and blood optical parameters corresponding to these wavelengths were shown in Fig. 3. As also seen in Fig. 3, the optical properties of the tissue are highly wavelength dependent and can have a significant impact on the propagation of light through the tissue. These three wavelengths of light were incident on the skin vertically.
Fig. 10. the Q distribution at different wavelengths(650, 820, 940 nm) of incidence; The two dashed lines refer to the interface of the epidermis-dermis and dermis-subcutaneous fat layer.
Figure 10 showed that the $Q$ in epidermal layer gradually decreased as the wavelength increased, allowing more energy to reach deeper into the skin. At a divergence angle of 0°, the normalized energy density in the epidermis for a light source at 820 nm was 39.5% of that at 650 nm, and the normalized energy density at 940 nm was 52.5% of that at 820 nm. This may be due to the reduced melanin absorption and the reduced scattering coefficient at 820 and 940 nm, making the difference in Q less pronounced [55,56]. And the effect of wavelength on energy density matched the WALT guideline recently published. WALT showed that the light dose at 904 nm was half that of 780-820 nm [22]. Comparing the energy density of the upper and the deep dermis blood vessels, the Q values of the 820 nm and 940 nm wavelength light sources were very close.In contrast, the 650 nm wavelength light source produced only 37.8% of the Q values of the other two wavelengths. Higher energy absorption by the two vascular plexuses could promote blood circulation and produces a range of biochemical mechanisms, which may also play a positive role in KOA treatment [12]. Therefore, different wavelengths of light need to be considered not only for photochemical reactions but also for light dose.
4.3 Effect of irradiation position of the light source on photon transport in the knee
This section analyzed the effect of irradiation position on photon deposition in the knee. We chose the optical parameters of volunteer A in Table 4. Volunteer A’s skin color was moderate. The light source setup process (see Fig. 11(a)), which divided the light source into three layers along the Z-axis direction. And Fig. 11(b)-(d) showed the light source arrangement at the three heights (low height: Z = 86, middle height: Z = 166, top height: Z = 246 voxels). A narrow-beam LED was modeled using an angular Gaussian beam with a variance of 0.1 rad [28]. This light source was commonly used in phototherapy equipment [57]. Each light source is simulated sequentially and light transport information is recorded. This section simulated the light dose to the cartilage within the knee joint and the patellar tendon below the patella, which were commonly targeted tissues for KOA. The gross energy($GE$, see Eq. (4)) within each tissue was used to analyze the effect of irradiation location on dosimetry. In Eq. (4), $G{E_{tissue}}$ represented the gross energy deposition in each tissue after per W of optical power incident and its unit was mW per W delivered;${N_{tissue}}$ represented the number of voxels in each tissue; ${q_{tissue}}$ represented the energy density of a single voxel in each tissue; ${v_{knee}}$ represented the size of a single voxel in the knee model.
Figure 12 counted the $GE$ in the sagittal (see Fig. 12(a)) and coronal planes (see Fig. 12(b)) of the knee at three heights. They correspond to the positions of light sources NO.1 and NO.4 in Fig. 11(b)-(d). The light source could better reach the targeted tissue inside the joint when it was located at middle height. The light penetration was significantly weakened when the light source was located at a higher position. In Fig. 12(a), the $GE$ reaching the cartilage was at a lower level. This is due to the fact that the tendon was rich in blood cells with a higher absorption of photons and can produce higher energy deposition. Therefore, this location was more suitable for tendon-specific PBM. When the light source was at the top height, the $GE$ was highest in the bone, which inhibited photon penetration. In Fig. 12(b), there was a great difference in the $GE$ reaching the cartilage. The thicker subcutaneous tissue at the lower position and bone at the higher position both resulted in a lower $GE$ value at the cartilage. The light penetration energy was higher in the middle position, with an energy difference of four to five orders of magnitude compared to the other positions. The effect of PBM treatment may be lost when the light dose was too low. In these two examples, the location of the treatment light source was critical to the treatment of the knee joint, and the light dose reaching the targeted tissue varies significantly between different locations of the source.
Fig. 11. (a) the schematic diagram of the knee divided into three layers; (b)(c)(d) the arrangement of light sources at heights Z of 86, 166, and 246 voxels.
Fig. 12. (a) gross energy(GE) deposition in knee tissue (Epidermis, Dermis, Subcutaneous fat, Bones, Cartilage, Tendon, Synovia) at three heights of light source incidence in the sagittal plane; (b) gross energy(GE) deposition in knee tissue during light source incidence at three heights in the coronal plane; The right panel shows the distribution of photon energy deposition in the sagittal and coronal planes.
To further analyze the effect of location on the cartilage light dose, the gross energy $GE$ deposition of the 36 light sources (see Fig. 11) in cartilage was counted in Fig. 13. The cartilage tissue was subdivided into cruciate ligament, femoral cartilage, and meniscus. Since the patellar cartilage was not inside the knee joint, we ignored its dosage. Figure 13(a)(b)(c) corresponded to the low, middle, and top heights of the light sources. It could be seen that there is a significant decreasing trend of $GE$ in all targeted tissues at positions NO.5 and NO.9. Irradiation in these locations may seriously affect the effectiveness of light therapy within the knee joint. In addition, the middle-height light source was located at the junction of the femur and tibia, which was relatively close to the articular cavity and produced a more stable $GE$. At positions NO.2 to 4 and NO.10 to 11 (corresponding to the medial and lateral positions of the knee patella) have higher $GE$ for the targeted tissue. To increase the dose reaching the cartilage, the treatment should be performed near the NO.2 to 4 area and NO.10 to 11 area. Thus, the optimal irradiation location was on both sides of the patella, where the largest dose was deposited to the articular cartilage. The optimal height of the light source was located at the middle-height parallel to the knee joint space.
Fig. 13. (a)(b)(c)#are the statistics of gross energy(GE) deposition on the targeted tissue when illuminated by light sources at three heights, low, middle, and top(Simulation data for the other two volunteers are available in the Supplement 1).
4.4 Discussion
The dose reaching the targeted tissue mainly decided the therapeutic effect of LED-PBM. Therefore, determining the dose within the tissue was critical to ensure predictable LED-PBM outcomes. The proposed MC-based optical model with light dose analysis may benefit KOA treatment. Simulation results based on this model may explain some clinical cases.
For example, Morais’ team showed that Laser-PBM effectively reduced inflammation levels in an animal model of arthritis with similar irradiation times, average output and energy dose, while LED-PBM had no significant effect [19]. However, the authors seemed to have overlooked the divergence angle and wavelength effect. In this article, the LED light source was not collimated and the wavelengths between the LED and the laser were different. They may result in differences in the light dose within the tissue and affect the therapeutic effect of LED-PBM. In contrast, Keshri’s team controlled the divergence angle and wavelength, showing that LED and Laser have the same therapeutic effect [58].
The simulation results can also provide evaluations of some existing phototherapy devices. For example, Liu’s team proposed a knee phototherapy device consisting of 55 LEDs (630 nm, 200 mW) [9]. The treatment location of some LED chips would result in poor light penetration and may be ineffective for deep tissue treatment. In contrast, the light therapy device of Move+ (Kineon, USA) combines 8 LEDs (650 nm, 80 mW) with 10 Lasers (808 nm, 5 mW). Due to the difference in lighting characteristics between LED and laser, Move+ adjusted the optical power of the two light sources to balance the phototherapeutic dose in the tissue. And Move+ could easily change the illuminated position. This method may be a better solution for KOA light therapy.
The proposed method in this paper can investigate relevant variables during the treatment of knee osteoarthritis, which can help personalize the dosage of light therapy for KOA patients. However, there may be some issues such as the need for MRI to establish the optical model of the patient's knee joint, which will increase the treatment time and cost. We believe that the establishment of a knee joint model database by collecting MRI data from KOA patients with different features will be an important future work for our team. Clinically, patients can input parameters such as BMI, age, gender, and skin type, and then match the appropriate optical model from the database to conduct relevant light dose simulations, which can reduce the cost of light dose customization. The time required for light dose simulation will also gradually decrease due to the updating and iteration of hardware platforms.
5. Conclusion
This paper presented a reliable method to analyze the light dosimetry in the LED-PBM treatment of KOA. The proposed optical model analyzed the effects of the divergence angle, wavelength and irradiation position of the light source on the dose at the targeted tissue. According to the simulation results, the optimal irradiation location was on both sides of the patella, and the optimal height was at the middle-height parallel to the knee joint space. And the conclusions of this paper can explain the contradictions between some PBM-related reports. Our follow-up research will focus on improving the precision of the model and do some clinical experiments to verify the simulation results. This work will help in the optical diagnosis and phototherapy of KOA. And it contributes to the light dosimetry dynamic planning and monitoring for deep light therapy.
Funding
National Natural Science Foundation of China (51376191); National Key Research and Development Program of China (2021YFC2400100, 2022YFC2404400); Suzhou Key Industrial Technology Innovation Project (SYG202035).
Acknowledgments
We would like to express our gratitude to all the volunteers and reviewers who have contributed to this project. Without your time and effort, our work would not have been possible.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
References
1. A. Cui, H. Li, D. Wang, J. Zhong, Y. Chen, and H. Lu, “Global, regional prevalence, incidence and risk factors of knee osteoarthritis in population-based studies,” EClinicalMedicine 29, 100587 (2020). [CrossRef]
2. K. Sinusas, “Osteoarthritis: diagnosis and treatment,” American Family Physician 85(1), 49–56 (2012).
3. P. Croft, “The epidemiology of osteoarthritis: Manchester and beyond,” Rheumatology 44, 27–32 (2005). [CrossRef]
4. A. E. Jorge, L. O. Dantas, P. R. Serrão, F. Alburquerque-Sendín, and T. F. Salvini, “Photobiomodulation therapy associated with supervised therapeutic exercises for people with knee osteoarthritis: a randomised controlled trial protocol,” BMJ Open 10(6), e035711 (2020). [CrossRef]
5. E. Cottrell, E. Roddy, and N. E. Foster, “The attitudes, beliefs and behaviours of GPs regarding exercise for chronic knee pain: a systematic review,” BMC Fam. Pract. 11(1), 1–9 (2010). [CrossRef]
6. E. M. Roos and N. K. Arden, “Strategies for the prevention of knee osteoarthritis,” Nat. Rev. Rheumatol. 12(2), 92–101 (2016). [CrossRef]
7. J. C. Mora, R. Przkora, and Y. Cruz-Almeida, “Knee osteoarthritis: pathophysiology and current treatment modalities,” J. Pain Res. 11, 2189–2196 (2018). [CrossRef]
8. L. M. Ailioaie and G. Litscher, “Molecular and cellular mechanisms of arthritis in children and adults: New perspectives on applied photobiomodulation,” Int. J. Mol. Sci. 21(18), 6565 (2020). [CrossRef]
9. K. Liu, H. Chen, Y. Wang, M. Wang, and J. Tang, “Wearable flexible phototherapy device for knee osteoarthritis,” Electronics 10(16), 1891 (2021). [CrossRef]
10. V. Heiskanen and M. R. Hamblin, “Photobiomodulation: lasers vs. light emitting diodes?” Photochem. Photobiol. Sci. 17(8), 1003–1017 (2018). [CrossRef]
11. F. Shen, H. Deng, L. Yu, and F. Cai, “Open-source mobile multispectral imaging system and its applications in biological sample sensing,” Spectrochim. Acta, Part A 280, 121504 (2022). [CrossRef]
12. M. R. Hamblin and T. N. Demidova, “Mechanisms of low level light therapy,” Mechanisms for Low-light Therapy 6140, 614001 (2006). [CrossRef]
13. H. Araki, A. Imaoka, N. Kuboyama, and Y. Abiko, “Reduction of interleukin-6 expression in human synoviocytes and rheumatoid arthritis rat joints by linear polarized near infrared light (Superlizer) irradiation,” Laser Therapy 20(4), 293–300 (2011). [CrossRef]
14. L. Zhang, J. Zhao, N. Kuboyama, and Y. Abiko, “Low-level laser irradiation treatment reduces CCL2 expression in rat rheumatoid synovia via a chemokine signaling pathway,” Lasers Med. Sci. 26(5), 707–717 (2011). [CrossRef]
15. G. L. Flores Luna, A. L. M. de Andrade, P. Brassolatti, P. S. Bossini, F. d. F. Anibal, N. A. Parizotto, and Â. M. d. O. Leal, “Biphasic dose/response of photobiomodulation therapy on culture of human fibroblasts,” Photobiomodulation, Photomed., Laser Surg. 38(7), 413–418 (2020). [CrossRef]
16. R. A. Mussttaf, D. F. Jenkins, and A. N. Jha, “Assessing the impact of low level laser therapy (LLLT) on biological systems: a review,” Int. J. Radiat. Biol. 95(2), 120–143 (2019). [CrossRef]
17. M. R. Hamblin, T. Agrawal, and M. de Sousa, Handbook of Low-level Laser Therapy (CRC Press, 2016), pp. 303–317.
18. A. C. A. Alves and P. d. T. C. de Carvalho, “Low-level laser therapy in different stages of rheumatoid arthritis: a histological study,” Lasers Med. Sci. 28(2), 529–536 (2013). [CrossRef]
19. A. M. B. Núbia Cristina Rodrigues de Morais and Mariana Lima Vale, “Anti-inflammatory effect of low-level laser and light-emitting diode in zymosan-induced arthritis,” Photomed. Laser Surg. 28(2), 227–232 (2010). [CrossRef]
20. C. S. Enwemeka, “Intricacies of dose in laser phototherapy for tissue repair and pain relief,” Photomed. Laser Surg. 27(3), 387–393 (2009). [CrossRef]
21. S. Shen, M. Xu, F. Zhang, P. Shao, H. Liu, L. Xu, C. Zhang, P. Liu, Z. Zhang, and P. Yao, “A low-cost high-performance data augmentation for deep learning-based skin lesion classification,” BME Front. 2022, 1 (2022). [CrossRef]
22. J. M. Bjordal, Low level laser therapy (LLLT) and World Association for Laser Therapy (WALT) Dosage Recommendations, (Mary Ann Liebert, Inc., 2012), pp. 61–62.
23. R. J. Lanzafame, I. Stadler, A. F. Kurtz, R. Connelly, P. Brondon, and D. Olson, “Reciprocity of exposure time and irradiance on energy density during photoradiation on wound healing in a murine pressure ulcer model,” Lasers Surg. Med. 39(6), 534–542 (2007). [CrossRef]
24. V. Periyasamy and M. Pramanik, “Advances in Monte Carlo simulation for light propagation in tissue,” IEEE Rev. Biomed. Eng. 10, 122–135 (2017). [CrossRef]
25. J. Guo, S. Meng, H. Su, B. Zhang, and T. Li, “Non-invasive optical monitoring of human lungs: Monte Carlo modeling of photon migration in Visible Chinese Human and an experimental test on a human,” Biomed. Opt. Express 13(12), 6389–6403 (2022). [CrossRef]
26. C. Zhu and Q. Liu, “Review of Monte Carlo modeling of light transport in tissues,” J. Biomed. Opt. 18(5), 050902 (2013). [CrossRef]
27. L. V. Wang and H.-I. Wu, Biomedical Optics: Principles and Imaging (John Wiley & Sons, 2012).
28. P. Cassano, M. R. Hamblin, Y. Yuan, and Q. Fang, “Selective photobiomodulation for emotion regulation: model-based dosimetry study,” Neurophotonics 6(01), 015004 (2019). [CrossRef]
29. T. Li, P. Wang, L. Qiu, X. Fang, and Y. Shang, “Optimize illumination parameter of low-level laser therapy for hemorrhagic stroke by Monte Carlo simulation on visible human dataset,” IEEE Photonics J. 10(3), 1–9 (2018). [CrossRef]
30. M. Milanic, L. A. Paluchowski, and L. L. Randeberg, “Hyperspectral imaging for detection of arthritis: feasibility and prospects,” J. Biomed. Opt. 20(9), 096011 (2015). [CrossRef]
31. A. C. O. Radiology, “Computed Tomography Accreditation Program Phantom Testing Instructions,” USA: ACR (2004).
32. C. H. McCollough, M. R. Bruesewitz, J. A. Brink, and R. K. Zeman, “The phantom portion of the American College of Radiology (ACR) computed tomography (CT) accreditation program: practical tips, artifact examples, and pitfalls to avoid,” Med. Phys. 31(9), 2423–2442 (2004). [CrossRef]
33. Z. Dong, J. Kim, C. Huang, and M. R. Lowerison, “Three-dimensional Shear Wave Elastography Using a 2D Row Column Addressing (RCA) Array,” BME Front. 2022, 1 (2022). [CrossRef]
34. A. Capart, K. Metwally, C. Bastiancich, and A. Da Silva, “Multiphysical numerical study of photothermal therapy of glioblastoma with photoacoustic temperature monitoring in a mouse head,” Biomed. Opt. Express 13(3), 1202–1223 (2022). [CrossRef]
35. T. Durduran, R. Choe, W. B. Baker, and A. G. Yodh, “Diffuse optics for tissue monitoring and tomography,” Rep. Prog. Phys. 73(7), 076701 (2010). [CrossRef]
36. B. C. Wilson and G. Adam, “A Monte Carlo model for the absorption and flux distributions of light in tissue,” Med. Phys. 10(6), 824–830 (1983). [CrossRef]
37. Q. Fang and D. A. Boas, “Monte Carlo simulation of photon migration in 3D turbid media accelerated by graphics processing units,” Opt. Express 17(22), 20178–20190 (2009). [CrossRef]
38. Z. Feng, P. Wang, X. Yang, H. Liu, and D. Xiong, “Evaluation of light penetration of LED phototherapy apparatus in skin LED,” Optics and Precision Engineering 30(10), 1139–1150 (2022). [CrossRef]
39. Y. Shimojo, T. Nishimura, H. Hazama, T. Ozawa, and K. Awazu, “Measurement of absorption and reduced scattering coefficients in Asian human epidermis, dermis, and subcutaneous fat tissues in the 400-to 1100-nm wavelength range for optical penetration depth and energy deposition analysis,” J. Biomed. Opt. 25(04), 045002 (2020). [CrossRef]
40. S. Prahl, “Optical absorption of hemoglobin,” http://omlcogi.edu/spectra/hemoglobin. (1999).
41. T. Wang, F. Shen, H. Deng, F. Cai, and S. Chen, “Smartphone imaging spectrometer for egg/meat freshness monitoring,” Anal. Methods 14(5), 508–517 (2022). [CrossRef]
42. H. Goo, S. Mo, H. J. Park, M. Y. Lee, and J.-C. Ahn, “Treatment with LEDs at a wavelength of 642 nm enhances skin tumor proliferation in a mouse model,” Biomed. Opt. Express 12(9), 5583–5596 (2021). [CrossRef]
43. M. Van Gemert, S. L. Jacques, H. Sterenborg, and W. Star, “Skin optics,” IEEE Trans. Biomed. Eng. 36(12), 1146–1154 (1989). [CrossRef]
44. M. D. Harris, A. J. Cyr, A. A. Ali, C. K. Fitzpatrick, P. J. Rullkoetter, L. P. Maletsky, and K. B. Shelburne, “A combined experimental and computational approach to subject-specific analysis of knee joint laxity,” J. Biomech. Eng. 138(8), 1 (2016). [CrossRef]
45. A. H. Aitkenhead, Mesh voxelisation, MATLAB (2013).
46. J. Beuthan, U. Netz, O. Minet, A. D. Klose, A. Hielscher, A. Scheel, J. Henniger, and G. Müller, “Light scattering study of rheumatoid arthritis,” Quantum Electron. 32(11), 945–952 (2002). [CrossRef]
47. V. V. Tuchin, “Tissue optics,” in (SPIE, 2015).
48. R. Cubeddu, A. Pifferi, P. Taroni, A. Torricelli, and G. Valentini, “A solid tissue phantom for photon migration studies,” Phys. Med. Biol. 42, 1971 (1997). [CrossRef]
49. A. Mustari, I. Nishidate, M. A. Wares, T. Maeda, S. Kawauchi, S. Sato, M. Sato, and Y. Aizu, “Agarose-based tissue mimicking optical phantoms for diffuse reflectance spectroscopy,” J. Visualized Exp. 1, e57578 (2018). [CrossRef]
50. C. Ash, M. Dubec, K. Donne, and T. Bashford, “Effect of wavelength and beam width on penetration in light-tissue interaction using computational methods,” Lasers Med. Sci. 32(8), 1909–1918 (2017). [CrossRef]
51. L. Finlayson and I. R. Barnard, “Depth penetration of light into skin as a function of wavelength from 200 to 1000 nm,” Photochem. Photobiol. 98(4), 974–981 (2022). [CrossRef]
52. Y. Mantri and J. V. Jokerst, “Impact of skin tone on photoacoustic oximetry and tools to minimize bias,” Biomed. Opt. Express 13(2), 875–887 (2022). [CrossRef]
53. Y. Chen, Y. Chen, H. Yan, and X. Wang, “Analysis of light incident location and detector position in early diagnosis of knee osteoarthritis by Monte Carlo simulation,” in International Conference on Innovative Optical Health Science, (SPIE, 2017), 24–29.
54. J. B. Murdoch, “Inverse square law approximation of illuminance,” J. Illum. Eng. Soc. 10(2), 96–106 (1981). [CrossRef]
55. W. S. Pegau, D. Gray, and J. R. V. Zaneveld, “Absorption and attenuation of visible and near-infrared light in water: dependence on temperature and salinity,” Appl. Opt. 36(24), 6035–6046 (1997). [CrossRef]
56. P. Wang and T. Li, “Which wavelength is optimal for transcranial low-level laser stimulation?” J. Biophotonics 12(2), e201800173 (2019). [CrossRef]
57. X. Wang, T. Jin, J. Xiong, H. Zhao, X. Hu, Q. Li, J. Ren, and Y. Zhao, “Three-dimensional image-guided topical photodynamic therapy system with light dosimetry dynamic planning and monitoring,” Biomed. Opt. Express 14(1), 453–466 (2023). [CrossRef]
58. G. K. Keshri, B. Kumar, and A. Gupta, “Photobiomodulation effects of pulsed-NIR laser (810 nm) and LED (808 ± 3 nm) with identical treatment regimen on burn wound healing: A quantitative label-free global proteomic approach,” Journal of Photochemistry and Photobiology 6, 100024 (2021). [CrossRef]
