Measurement of thermal expansion coefficient of melanin for photoacoustic technology

Abstract

Photoacoustic technology can non-invasively obtain the temperature and pressure of tissues, holding great promise for applications in the laser thermal ablation of pigmented skin diseases. The coefficient of thermal expansion is the primary source of temperature sensitivity in photoacoustic technology. In this paper, a non-contact full-field strain measurement system based on temperature-variable three-dimensional digital image correlation is used to measure the variation of the thermal expansion coefficient of melanin in the retinal pigment epithelium layer of porcine eyes. It is found that the thermal strain of melanin exhibits non-uniformity and nonlinear increase in radial Angle and circular domain. Before the glass-transition temperature (49°C), the average coefficients of thermal expansion for concentric circular regions and different radial directions are 4.14 × 10⁻⁴ K⁻¹ and 3.82 × 10⁻⁴ K⁻¹, respectively. Approximating the thermal expansion coefficient of melanin with that of graphite leads to a large error, with a difference of two orders of magnitude.

Keywords

Melanin non-linear thermal expansion digital image correlation technology photoacoustic technology

Introduction

Ota's nevus is a kind of pigmented skin disorder that usually occurs in Asian populations, manifesting as blue-black or brown patches on the facial and zygomatic regions. According to the principle of selective photothermolysis, pulsed lasers with specific wavelengths can target and disrupt hyperplastic melanin in the dermis, thereby achieving effective skin bleaching.¹ Given the small size of melanosome granules and their short thermal relaxation time, nanosecond- or picosecond- pulsed lasers, such as the 755 nm Alexandrite laser or the 1064 nm Nd:YAG laser, are commonly used in clinical practice. Laser ablation of Ota's nevus involves a photothermal-mechanical coupling mechanism, encompassing thermal damage caused by endothermic phase transition and thermal expansion, as well as mechanical damage such as disintegration and fragmentation.² However, the interaction mechanisms between lasers and melanin remain poorly understood, leading to low clinical cure rates and notable side effects such as significant bleeding, pain, erythema, hyperpigmentation, and hypopigmentation.³

Noninvasive and high-speed measurements of temperature and pressure variations in hyperplastic melanin are of crucial significance for uncovering the laser ablation mechanisms underlying pigmented skin disorders. Nevertheless, the existing techniques, including ultrasound thermography, infrared thermography, and magnetic resonance imaging, are ill – suited for this particular purpose. In transient nanosecond laser ablation of melanosomes, thermal stress induces a rapid expansion–tear–rebound cycle in surrounding tissues. This process generates ultrasonic waves. This phenomenon is known as the photoacoustic effect. Both the oscillations and amplitude of the photoacoustic signal exhibit a positive correlation with temperature. By extracting temperature signals from the photoacoustic pressure signals, it is possible to simultaneously measure temperature and pressure during the laser ablation of melanosome granules.

The initial acoustic pressure shows a positive correlation with the Grüneisen coefficient Γ, and this coefficient is proportional to the volume expansion coefficient (CTE) of the chromophore (in the present case, hyperplastic melanin). To characterize the thermal expansion properties of materials, the linear thermal expansion coefficient (α) is defined as the percentage increase in length per unit rise in temperature. Meanwhile, the volumetric thermal expansion coefficient (β = 3α) denotes the ratio of the volume after expansion to the initial volume.⁴ High-temperature thermo-mechanical techniques have been employed to measure CTEs of diverse substances. However, accurately measuring the CTEs of biological tissues remains a challenge owing to their temperature – dependent stiffness and intricate structures.⁵ Although existing data indicate notable disparities in the thermal expansion coefficients among bone, blood, and fat, there is still a paucity of specific data for individual tissues.⁶

Accurate CTEs of biological tissues are crucial for thermal therapies and the advancement of photoacoustic imaging technologies: 1) They enable precise regulation of the target tissue's temperature during thermal therapies, including thermal ablation, radiofrequency ablation, high-intensity focused ultrasound, and laser resurfacing.^7–10 This helps minimize thermal damage to the surrounding healthy tissues. 2) Most current studies primarily concentrate on temperature distribution and neglect the dynamic changes in thermoelastic deformation.¹¹ Gaining insights into the thermal expansion properties of biological tissues can enhance the control of mechanical damage within the tissues. 3) Photoacoustic signals generated from biological tissues carry information about their optical absorption characteristics. Through the analysis of these signals, the optical absorption distribution within tissues can be reconstructed. Photoacoustic imaging combines the high selectivity of optical methods with the deep penetration of ultrasound. This integration provides high-resolution, high-contrast images while reducing the effects of light scattering. This technique can break through the “soft limit” (approximately 1 mm) of high-resolution optical imaging and facilitate in vivo imaging of deep tissues at depths of up to 50 mm.

In summary, to develop noninvasive and high-speed temperature and pressure measurement, as well as photoacoustic imaging for subcutaneous tissue in laser ablation for pigmented skin disorders, accurately determining the thermal expansion coefficient of melanin is of crucial importance. Owing to chemical similarities, researchers often approximate CTE of melanin by leveraging that of graphite.^12–15 Nevertheless, it should be noted that melanin is an organic compound synthesized by melanocytes, while graphite is an inorganic material with a simple and orderly structure. Within the layered structure of graphite, its CTE exhibits a tendency to decrease as the temperature rises. Conversely, it increases with the density between the layers, reaching a maximum of 33 × 10⁻⁶ K⁻¹.¹⁶ Evidently, the practice of approximating the CTE of melanin using that of graphite fails to account for their fundamental differences, necessitating the precise measurement of CTE of melanin.

High-temperature thermo-mechanical measurement techniques can be categorized into contact and non-contact approaches. Conventionally, the volumetric thermal expansion coefficient β of biological tissues can be measured using a densitometer or an expansion meter equipped with a linear variable differential transducer.¹⁷ Nevertheless, these methods typically expose the sample to long-term push-rod compression loads. This exposure may lead to buckling of the sample, disrupt its free deformation process, and ultimately impose limitations on the measurement accuracy. Non-contact methods focus on the molecular and structural changes in specimens under thermal loads without altering the structure or hindering free expansion of the sample. Key techniques include moiré interferometry, electronic speckle interferometry, dual-laser displacement, and digital image correlation (DIC). Optical methods based on interference and diffraction have a simple theory and high – precision capabilities. However, they demand strict control over the measurement optical system, grating fabrication, and environmental conditions, resulting in high costs. In contrast, DIC, which hinges on digital image analysis and numerical computation, presents a straightforward measurement process while maintaining high precision.¹⁸ It empowers noninvasive, high-resolution, full-field deformation and strain measurements across tissues of varying scales. Distinguished from other non-contact methods like ellipsometry and electronic speckle interferometry, DIC obviates the need for fringe pattern analysis.⁵ Moreover, it can broaden its measurement scope by leveraging scanning electron microscopy and atomic force microscopy. Consequently, this study constructs a temperature-variable DIC based non-contact full-field strain measurement system. This system is designed to obtain full-field displacement and strain data, analyze the thermal expansion behavior of melanin, and furnish fundamental parameters for the development of noninvasive, high-speed collaborative measurement and photoacoustic imaging technologies tailored for the laser ablation of pigmented skin disorders.

Experimental principles and methods

DIC method and its principle

As a non – destructive deformation measurement technique rooted in computer vision, DIC serves as a highly effective means for quantifying full-field thermal deformation of polymer films, coatings, and other soft materials. Additionally, it is instrumental in determining the thermal expansion coefficient of biological tissues.^19,20 The basic principle of the DIC method is depicted in Figure 1, and its primary steps are as follows:

Figure 1.

Basic schematic diagram of DIC method.

Initially, a tracking pattern, commonly referred to as a speckle pattern, with high contrast (adequate light intensity variation) is meticulously configured on the surface of the object. This pattern typically manifests as dots, lines, or grids and can be introduced through multiple means, such as spray painting, dyeing, coating, physical surface modification, deposition of powder particles, or even capitalizing on the natural texture inherent in the sample.²¹ These speckle patterns serve as crucial carriers of deformation information. The deformation state can be precisely determined by tracking the movement trajectories of feature points within the pattern. Subsequently, a portion of the speckle image (termed the subregion) is selected for tracking, with dimensions of (2M + 1) × (2M + 1) pixels. The speckle images before and after deformation are acquired. The pre-deformation image is designated as the source image, while the post-deformation image is defined as the target image. The deformation state can be precisely determined by tracking the movement trajectories of feature points within the pattern. Thereafter, cross-correlation gray scale matching between the source and target images is performed to calculate the displacement and deformation, by the one-to-one correspondence of the coincidence formula before and after the point deformation:

{\begin{matrix} x^{'} = x_{0} + Δ x + u + u_{x} Δ x + u_{y} Δ y + u_{z} Δ z \\ y^{'} = y_{0} + Δ y + v + v_{x} Δ x + v_{y} Δ y + v_{z} Δ z \\ z^{'} = z_{0} + Δ z + w + w_{x} Δ x + w_{y} Δ y + w_{z} Δ z \end{matrix}

(1)

where Δx, Δy and Δz are the distance between point Q and the central point P of the subregion in source image. u, v and w are the displacement components of the subregion center of the source image in the x, y and z directions; u_x, u_y, u_z, v_x, v_y, v_z, and w_x, w_y, w_z are the displacement gradients. Zero-mean normalized sum of squared difference (ZNSSD) correlation is used to describe the change of the overall light intensity of the image²²:

C_{f . g} = \sum_{x = - M}^{M} \sum_{y = - M}^{M} {[\frac{f (x, y) - f_{m}}{\sqrt{\sum_{x = - M}^{M} \sum_{y = - M}^{M} {(f (x, y) - f_{m})}^{2}}} - \frac{g (x^{'}, y^{'}) - g_{m}}{\sqrt{\sum_{x = - M}^{M} \sum_{y = - M}^{M} {(g (x^{'}, y^{'}) - g_{m})}^{2}}}]}^{2}

(2)

where f_m and g_m are the average gray values of subregions in source and target images, respectively:

{\begin{matrix} f_{m} = \frac{1}{{(2 M + 1)}^{2}} \sum_{x = - M}^{M} \sum_{y = - M}^{M} (f (x, y))^{2} \\ g_{m} = \frac{1}{{(2 M + 1)}^{2}} \sum_{x = - M}^{M} \sum_{y = - M}^{M} (g (x^{'}, y^{'}))^{2} \end{matrix}

(3)

Sample preparation and experimental facility

The eye represents a distinctive organ in the research of pigment cells, since its Retinal Pigment Epithelium (RPE) is a single-celled layer of pigmentation. This is because its Retinal Pigment Epithelium (RPE) constitutes a single-celled layer of pigmentation. The RPE exhibits an extremely dense distribution of melanin, with its content being 4–10 times that of skin tissue. Specifically, the volume fraction of melanin in yellow skin is 11–16%.²³ By inference, the volume fraction of melanin in the RPE is 44% or higher. A substantial number of melanin-related studies have utilized the RPE layer derived from freshly obtained porcine and bovine eyes.^18,24,25 The RPE is selected for several reasons. Firstly, it is abundantly rich in melanin. Secondly, its extraction process is relatively straightforward. Moreover, it is sufficiently thin (approximately 22.1 μm), and during the experiment, it does not necessitate additional slicing, which enables a faster and more uniform thermal balance to be achieved.²⁶

In this study, the RPEs of porcine eyes sourced from a slaughterhouse are surgically extracted. These RPEs are stored at 2°C for 6–24 h and then the experiments are conducted at room temperature. Given The test sample is black, the speckle pattern is generated by spraying ordinary white matte paint, as presented in Figure 2(a). The treated sample is carefully positioned on a temperature-controlled double-layer water bath heater, as shown in Figure 2(b) and (c). The bottom of the water bath is electrically heated, after which the upper normal saline is reheated to ensure uniform heating while maintaining the moisture balance of the tissue. The temperature change during the experiment is recorded by an infrared temperature gun (304D, Shengli Instrument, Shenzhen, China), with a temperature measurement accuracy of ±0.1°C.

Figure 2.

Schematic diagram of the experiment. (a) speckle pattern, (b) side view of the heater, (c) top view of the heater.

Before the thermal expansion measurements, the initial temperature is maintained at room temperature, specifically 25°C. Initially, a controlled experiment is performed on each sample. During this control experiment, image sequences are captured at room temperature for a total duration of 7 min, which is consistent with the testing time required for the experimental group. Once the control experiment is completed, the experimental group is gradually heated from room temperature. The temperature rise process is approximately linear, as illustrated in Figure 3. The image sequence of the experimental group is captured at the same time resolution and sample position. When the temperature exceeds 65°C, the speckle pattern starts to adhere, and the bubble disturbance in the water bath environment intensifies. Therefore, the maximum test temperature is restricted to 65°C. Albano et al. conducted thermogravimetric analysis on natural squid melanin, and the results showed that below 124 ± 5°C, there will be no loss of strongly-bound water, decarboxylation of DHICA, nor the breaking of non-covalent bonds between supramolecular structure, sub-structure, and oligomer planes.²⁷ This indicates that within the temperature scope of this study, the natural structure of melanin has remained undamaged.

Figure 3.

Temperature rise of the experimental group.

DIC analysis

For the images of the experimental group, each sequence is first calibrated using the scale embedded in the source image (undeformed) to ensure a consistent resolution (approximately 27 μm/pixel). In all experiments, concentric circles at the image center are defined as the Area of Interest (AOI). The radii of these concentric circles increase successively from the inside to the outside, and they are named O1-O5 respectively, as shown in Figure 4. To ensure the consistency of analysis, a subset size of 29 × 29 pixels and a step size of 7 pixels are selected for all experiments. The selection of these parameters provides a relative small average uncertainty interval while ensuring computational efficiency. A Gaussian weight function, an optimized 8-point spline interpolation method, a zero-mean normalized distance square sum correlation criterion and a low-pass filter are chosen to generate results with high-precision and low-background noise. In post-processing, the strain is extracted from each concentric circle for filtering and smoothing.

Figure 4.

Schematic diagram of concentric circle area.

Although the sample thickness is relative thin, the RPE inevitably has a curvature due to the eyeball structure. In this regard, 3D analysis is implemented to measure the displacement within the imaging space from the image sequence. Since the sample is placed in an unconstrained space and there is a small amount of water at the bottom for heating and moisturizing, potential evaporation or bubble disturbance in the micro-chamber may create a certain pressure gradient or fluid flow. As a result, the sample may experience some inevitable small-scale translations and rotations within the computational region, which can be eliminated using the method described in Ref.²⁸

Results and discussion

Relation between strain and radial distance

Figures 5(a) and (b) show the changes of strain e (the relative change in length) with time in the image sequences of the control group and the experimental group, respectively. It can be clearly seen from the controlled experiment that almost no strain is generated when there is no heating. The small downward shift in the curve is due to the temperature correction of the system while ensuring the same initial room temperature conditions. The residual temperature drop causes the sample to shrink, but it reaches a stable value soon. In the heating experimental group, owing to the temperature increase and thermal inertia, the strain is almost zero in the initial stage (the first 2.5 min). As the sample is heated, the strain first increases slowly and then rises sharply, showing a non-linear variation pattern (even though the temperature rises linearly with time at this moment).

Figure 5.

Comparison of strain history between the control group and the experimental group at different radial distances.

Maskarinec et al. indicated that the leading edge of migrating cells has higher cell traction forces, corresponding to the maximum displacement at a given instant.²⁹ In the present study, however, there is no correlation between the radial position away from the center of the image and the magnitude of strain (see the enlarged view in Figure 5(b)). In the study of the thermal expansion of fresh brain tissue, Dagro et al. demonstrated that although there seems to be an overall tendency for slightly larger strain at larger radial positions, there is also no significant relationship between the radial strain and the radial distance.³⁰

The relationship between strain and radial angle

The strain contour in various regions in Figure 4 exhibit differences, and there even appear unique regions of contraction strain. It should be noted that these negative radial strains may not represent tissue contraction but rather the result of heterogeneity at this length scale. Therefore, the relationship between strain and each radial angle is investigated. Starting from the positive direction of the horizontal coordinate, a diameter is taken every 30° as the calculation length, and the relevant strain data are plotted in Figure 6. As can be seen from the figure, the variation trend of radial strain is consistent with the strain pattern of the circle of interest. However, the differences in different radial directions are more pronounced. As shown in Figure 7, the numbers represent the magnitude of strain, with 1 to 6 indicating the strain decreasing from large to small; 30°–180° is the angle in the polar coordinate system starting from the positive direction of the x-axis. After arranging the strains from largest to smallest and labeling them in Figure 7, it can be seen that the thermal expansion of the tissue is anisotropic: the closer to the horizontal direction, the greater the strain, indicating that there is a preferred direction for the strain of the sample. This may be attributed to the fact that the horizontal direction is closer to the edge of the sample, heats up faster, and thus exhibits more obvious thermal expansion.

Figure 6.

Strain variations at different radial angles.

Figure 7.

Schematic diagram of strain orientation (labeled as the sequence of strain from large to small according to the experimental group data).

The non-linearity of the thermal expansion coefficient

The coefficient of thermal expansion is usually calculated as the slope of the strain and temperature curve.³¹ However, direct numerical differentiation will significantly amplify the noise in the measurement data (including measurement error, truncation error, rounding error, floating point calculation error, etc.). As a result, the obtained coefficient of thermal expansion will become extremely inaccurate. To address the problem of error amplification, the average coefficient of thermal expansion is first obtained by discretizing Equation (4), and then the optimal coefficient of thermal expansion is determined by curve fitting.

β = 3 α = 3 \times \frac{L - L_{0}}{L_{0}} \times \frac{1}{T - T_{0}}

(4)

where L₀ and L are the lengths under the initial temperature T₀ and temperature T. L represents the length after deformation, with the unit being meters (m). L₀ stands for original length, with the unit being meters (m). Both of these variables are used to calculate Strain.

The coefficients of thermal expansion calculated according to concentric circular regions and radial angles are shown in Figure 8. For all concentric circular regions and radial angles, the coefficient of thermal expansion varies non-linearly with temperature. The CTE in concentric circular regions is more stable than the calculation results in different radial directions. In all specimens, the discrete and sharp increase in the CTE occurs approximately after 49°C, showing a relatively high CTE. While at temperatures below 49°C, the CTE is much lower and nearly constant.

Figure 8.

Thermal expansion coefficient of melanin.

Similar non-linear behavior is often observed in some polymer materials. The glass transition temperature (T_g) is the inflection point in the thermal expansion-temperature curve. The CTE above T_g is larger than that below T_g. Beyond this inflection point, the CTE increases by about 3–5 times.³² The sudden change in the CTE of polymers is usually attributed to transitions between small vibrations of molecules and larger molecular rearrangements, as well as increases in free volume between molecules. When the temperature is below T_g, the polymer chains are tightly packed by strong intermolecular forces, resulting a much lower CTE.³³ In polymer testing, two CTE parameters are usually specified, one before the glass transition and one after. The piece-wise linearization of the curve also indicates that the CTE is nearly constant in some cases. In this work, the average coefficient of thermal expansion before T_g = 49°C is calculated. The total sample size n was 11, and the results are listed in Tables 1 and 2. The calculated average CTE value is 3.985 × 10⁻⁴ K⁻¹, and the standard deviation is 0.03, as shown in Table 3. The mean values for concentric circle regions and different radial directions are 4.17 × 10⁻⁴ K⁻¹ and 3.83 × 10⁻⁴ K⁻¹, respectively. Table 4 lists the comparison of CTE values of various soft tissue in this work with those in the literature. It is worth noting that Méndez et al. also measured a similar non-linear relationship of CTE in their research.36 Fidanza also noted that the CTE of most soft tissues increases with rising temperature.³⁷ Since all reported CTE values of biomaterials in the literature are at room temperature or below 40°C, the variation of CTE at higher temperatures requires further study.

Table 1.

The CTE values in different concentric circular domains.

O1	O2	O3	O4	O5	Mean1
3.57 × 10⁻⁴	4.33 × 10⁻⁴	4.41 × 10⁻⁴	4.12 × 10⁻⁴	4.42 × 10⁻⁴	4.17 × 10⁻⁴

Table 2.

The CTE values under different radial directions.

30°	60°	90°	120°	150°	180°	Mean2
3.96 × 10⁻⁴	3.66 × 10⁻⁴	3.86 × 10⁻⁴	3.78 × 10⁻⁴	3.81 × 10⁻⁴	3.91 × 10⁻⁴	3.83 × 10⁻⁴

Table 3.

The mean and standard deviation of CTEs.

Mean	Standard deviation
3.985 × 10⁻⁴	0.03

Table 4.

Comparison of the CTEs between this work and previous literature.

Researchers	Tissue	Temperature/°C	β × 10⁴/ K⁻¹
The present work	RPE of porcine eyes	25–56	3.82
Dagro et al.³²	mouse brain	30–40	16.5
Méndez et al³⁴	rabbit Fat	25–37	11.4
Fidanza et al³⁵	human fat	15–37	9.3

Table 5.

The differences between porcine RPE melanin and human skin melanin.

Comparison dimension	Porcine RPE melanin	Human skin melanin
Embryo source	Neuroepithelial/optic cup	Neural crest
Melanin concentration (per unit volume)	17 mg/mL ³⁴	0–1.25 mg/mL ³⁵
Types of melanin	Mainly contains true melanin	The ratio of eumelanin to pheomelanin varies from person to person⁴⁰

In view of the non-linearity observed in the experiment, the CTE of melanin may depend not only on temperature but also on the rate of temperature rise. The heating rate in this study is about 0.1°C·s⁻¹. For biomedical laser applications involving the conversion of electromagnetic energy into sound waves, the heating rate could be much faster. Previous studies on materials with non-linear CTE generally indicate that T_g increases at faster rates of temperature rise.³⁸

Comparison of thermal expansion coefficient with graphite

Cermak et al. measured the CTE of natural graphite sheets in the temperature range of 30–100°C used a thermomechanical analyzer.¹⁷ They found that the in-layer CTE is low and negative (shrinking with increasing temperature), while the inter-layer CTE is high and increased with increasing density, reaching 33 × 10⁻⁶ K⁻¹. Fan summarized the CTE of graphite crystals in the range of 0–360 K: except 0 K, the CTE is zero at around 15 K and 42 K.³⁹ In the temperature range of 15–42 K, it is negative, and in the higher temperature range, it is approximately constant. In the temperature range corresponding to this paper, the value is approximately 6.2 × 10⁻⁶ K⁻¹. The differs from the results in this paper by two orders of magnitude. Apparently, there is a large error in characterization of the thermal expansion law of melanin with graphite.

Biological applicability between porcine RPE melanin and human skin melanin

Table 5 compares porcine RPE melanin and human skin melanin from three dimensions.

There are indeed differences in tissue origin and microenvironment between RPE and human skin melanin, which impose limitations on direct clinical translation. However, this issue can be addressed by combining multi-level models:

At the mechanism research level: Although the tissue origin of pig RPE and skin melanocytes is different, both share the same melanin synthesis pathway and melanosome biogenesis mechanism, including key enzymes such as tyrosinase and the process of melanin formation. Therefore, melanin and melanosomes in RPE have a high degree of similarity in structure, chemical composition, and optical function to those in the skin. Existing studies have shown that there is good similarity between pig and human tissues (including skin and ocular tissues), and pig RPE has been widely used for melanosome isolation and the study of melanin properties^41,42 These evidences support the feasibility of using pig RPE as a feasible alternative model for studying human skin melanin. It should be noted that although the melanin concentration in RPE is usually higher than that in the skin, this point provides a more stable, easily accessible, and reproducible source of melanin for in vitro research, thus offering unique advantages in mechanism research.

At the validation level: Mechanism findings obtained from RPE experiments can be verified through human melanocyte cell lines, primary keratinocyte co-culture systems, or organoid models, thereby bridging the differences between ocular and skin environments.

At the translational level: Animal models and humanized skin models can further validate the applicability of the results, forming a three-level validation path of “RPE→human cells/organoids→skin tissue”.

Conclusion

Thermal expansion coefficient of melanin is an important parameter in the laser thermal ablation of pigmented skin diseases. At higher temperatures, the increase in thermal expansion may have a significant impact on the potential damage and deformation behavior of diseased tissues exposed to electromagnetic fields, and also affect their pressure values observed in photoacoustic imaging technique. In this paper, a temperature-variable 3D DIC strain measurement system was used to conduct experimental research on the melanin-rich RPE layer of porcine eyes. The main conclusions are as follows:

The thermal strain of melanin exhibits non-uniformity and nonlinear increase in radial Angle and circular domain. The thermal expansion of melanin is heterogeneous, and the closer the strain direction is to the horizontal direction, the greater the strain will be, so the sample strain has a preferred direction.

There is a glass-transition temperature for the coefficient of thermal expansion of melanin, which is approximately 49°C. Before this temperature, the average coefficients of thermal expansion for concentric circular regions and different radial directions are 4.14 × 10⁻⁴ K⁻¹ and 3.82 × 10⁻⁴ K⁻¹, respectively, and then it increases sharply.

Approximating the thermal expansion coefficient of melanin with that of graphite leads to a large error, with a difference of two orders of magnitude. This error is likely to be even greater at higher temperatures.

Footnotes

Acknowledgements

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This study was supported by Major Scientific and Technological Projects in Henan Province (Grant No. 251100310100) and the Henan Provincial Science and Technology Research Project (Grant No. 252102310440).

ORCID iD

Bin Chen

Ethical considerations

This article does not contain any studies with human or animal participants, the only animal material used is pig eyes purchased from slaughterhouses. Fresh porcine eyes were obtained as by-products from a licensed local slaughterhouse, with no animals sacrificed specifically for research purposes. Upon arrival at the laboratory, the eyes were kept at 2°C and processed within 6–24 h. The retinal pigment epithelium (RPE) layers were surgically extracted under sterile conditions for subsequent experiments. Because the tissues were commercially sourced by-products, institutional ethical approval was not required, in accordance with local regulations. After the experiments, all residual porcine ocular tissues and related biological materials were disposed of as biohazardous waste, in strict accordance with institutional biosafety protocols and local regulations. Specifically, the tissues were collected in designated biohazard containers and subsequently autoclaved before being transferred to a licensed facility for safe disposal.

Author contributions

Yang Liu conceived of the study, designed the experiments, carried out the temperature monitoring procedures, and drafted the manuscript. Zeyang Li conducted the sample preparation and laser irradiation experiments. Bin Chen supervised the overall study, guided the experimental design, and revised the final manuscript. Liushuan Niu and Qiang Li participated in the modeling and data analysis. Dong Li contributed to the manuscript editing. All authors read and approved the final manuscript. All contributors who do not meet the criteria for authorship should be listed in the acknowledgements section.

Funding

The authors received no financial support for the research, authorship, and/or publication of this article.

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Data availability statement

The data are not available due to commercial restrictions.

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