A Simulation Study of Carbon Dot-Assisted Photothermal Heating in Tumor Tissue

Abstract

Purpose:

The purpose of the study was to investigate photothermal heating and thermal damage in breast tumor tissue under laser irradiation in the presence of carbon dots acting as enhanced optical absorbers.

Methods:

A two-dimensional numerical model based on the transient bioheat transfer equation was developed by coupling radiative heat transfer and solved using the finite element method in COMSOL Multiphysics. The tumor region was modeled as a circular domain embedded within normal breast tissue. Thermal damage was quantified using the cumulative equivalent minutes at 43°C (CEM43) model. Parametric analysis was carried out to evaluate the effects of tumor absorption coefficient, carbon dot absorption coefficient, photothermal conversion efficiency, blood perfusion rate, and tumor depth on temperature evolution.

Results:

Localized heating was observed within the tumor region, with peak temperatures reaching approximately 60°C after 600s of irradiation. Temperature elevation increased with increasing optical absorption and irradiation duration, whereas blood perfusion reduced thermal accumulation. Thermal damage analysis indicated that the irreversible damage threshold (CEM43 >60 min) was achieved throughout the tumor region after 600s of irradiation, suggesting effective thermal destruction of tumor tissue, while damage to surrounding healthy tissue remained limited.

Conclusions:

The model demonstrates that carbon dots can effectively enhance photothermal heating in tumor tissue and achieve thermal damage. The findings provide a computational framework for optimizing laser-based tumor therapy while maintaining thermal safety.

INTRODUCTION

Photothermal therapy (PTT) is a minimally invasive tumor treatment technique, in which photothermal agents absorb incident laser radiation and convert it into heat, resulting in localized hyperthermia and tumor cell ablation.[1] Compared to conventional tumor treatments, PTT offers advantages such as spatial selectivity, reduced side effects, and controlled thermal dosage.[2] Understanding heat transport and temperature regulation in biological tissues during laser irradiation is essential for ensuring effective tumor ablation while minimizing damage to surrounding healthy tissue.[3]

CDs are carbon-based nanomaterials, typically with sizes below 10 nm, with excellent water solubility, chemical stability, and high biocompatibility, making them suitable for biomedical applications.[4,5] Several studies have demonstrated that CDs can efficiently convert absorbed light energy into thermal energy under laser irradiation, enabling localized heat generation for the destruction of tumor cells during PTT.[6] Carbon dots are emerging as promising photothermal agents due to their low toxicity compared with conventional photothermal agents, such as metal nanoparticles and semiconductor nanomaterials.[7,8]

In recent years, the use of numerical models in biomedical applications has been increased significantly.[9,10,11] Acharya et al. investigated thermal damage in biological tissues under external heating using a non-Fourier formulation of the bioheat transfer equation and a finite difference approach, demonstrating how heat transport dynamics influence the extent of temperature rise and tissue damage during thermal therapy.[12] Gómez-Araque et al. implemented Delta-P1 Model for Simulation of Photothermal Cancer Therapy in Heterogeneous Tissues.[13] In 2025, Horvat and team have employed non-Fourier dual-phase-lag bioheat models to simulate heat transfer in multilayer biological tissues for improved thermal detection of skin tumors.[14] Junaid et al. conducted a finite element study based on the Pennes’ bioheat transfer equation to analyze bioheat transfer in healthy and malignant breast tissues, demonstrating how physiological conditions such as blood perfusion and metabolic activity influence temperature distribution in breast tumors.[15]

Among them, computational tools such as COMSOL Multiphysics have been extensively employed to model laser–tissue interaction and nanoparticle-assisted PTT.[16] Sadeghi et al. developed a two-dimensional numerical model based on the Pennes’ bioheat transfer equation to investigate combined photothermal and magnetic hyperthermia therapies, demonstrating that optimized laser and magnetic field parameters can maximize tumor cell destruction while minimizing damage to surrounding healthy tissue.[17] Manrique-Bedoya et al. developed a numerical model to study nanoparticle heating for the treatment of plasmonic PTT in Pancreatic cancer in 2019.[18] Accurate prediction of temperature distribution through computational modeling is essential for optimizing treatment parameters and improving the safety and effectiveness of PTT.[3] Numerical modeling provides an efficient approach to investigate heat transfer in living tissues under laser irradiation. Among the available models, the Pennes’ bioheat transfer equation is widely used due to its simplicity and ability to incorporate blood perfusion effects.[19,20]

However, simplified computational models specifically addressing carbon dot-assisted photothermal heating with systematic parametric evaluation of clinically relevant thermal parameters remain limited. Therefore, the present study aims to develop a two-dimensional bioheat model to analyze temperature evolution under physiologically relevant conditions using COMSOL Multiphysics 6.0. To account for optical absorption and scattering within tissue, laser transport is modeled using the P1 approximation. The effects of the optical properties of carbon dots and tumor, photothermal conversion efficiency of carbon dot-loaded tumor tissue, blood perfusion rate, and tumor depth are systematically investigated. In addition, thermal damage is evaluated using the cumulative equivalent minutes at 43°C (CEM43) metric.

METHODS

Model geometry

A two-dimensional square domain of size 40 mm × 40 mm represents the cross-section of normal breast tissue parallel to the direction of the laser beam. A circular tumor region of radius 5 mm is embedded at the center of the tissue domain, representing the carbon dot-loaded tumor as shown in Figure 1a.

Figure 1.

Computational model: (a) Tissue–tumor geometry and (b) radiation intensity distribution

The following assumptions were made:

1. The computational domain consists of normal breast tissue and a tumor region. Each region is assumed to be homogeneous and isotropic with constant thermophysical properties within that respective region

2. Carbon dots, which are known to impart enhanced optical absorption, are uniformly distributed within the tumor region

3. Metabolic heat generation was neglected in the present study because its magnitude is substantially smaller than the laser-induced heat source during PTT.[3]

These simplifications enable a systematic parametric analysis while preserving the essential thermal behavior of breast tissue.

Material properties

The thermophysical properties of normal breast tissue and tumor breast tissue, such as density, thermal conductivity, specific heat capacity, and blood perfusion rates, were obtained from the literature and listed in Table 1.[21] Although carbon dots are incorporated in the tumor region, their concentration is typically very low in PTT applications. Therefore, the resulting change in density is considered negligible, and the tissue density is assumed to remain unchanged. The blood perfusion rate ranges from 0.0004 to 0.0009 s⁻¹ for normal breasts and from 0.001 to 0.005 for tumors.[15,21] In this study, the blood perfusion rate of normal breast is fixed at 0.0007 s⁻¹ and that of tumor breast tissue is varied from 0.001 to 0.005 using parametric sweep.

Table 1.

Thermophysical properties of normal breast tissue and breast tumor tissue

Parameter	Normal breast tissue	Tumor breast tissue	Unit
Density, ρ	1066	1066	kg/m3
Specific heat, Cp	3398	3610	J/kg/K
Thermal conductivity, k	0.5	0.594	W/m/K
Blood perfusion rate	0.0007	0.001–0.005	s−1
Absorption coefficient, µa	5	10-30	m−1
Scattering coefficient, µs	600	700	m−1
Initial temperature, T	310.15	310.15	K

In the near-infrared (NIR) region, normal breast tissue exhibits relatively low optical absorption, with reported absorption coefficients in the range 1-10 m⁻¹ depending on the specific wavelength and tissue composition.[22] For tumor breast tissue, the absorption coefficient is higher, ranging from 10 to 30 m⁻¹ in the NIR range, as tumor tissues tend to have higher water and blood content compared to normal breast tissue.[23] Accordingly, the tumor absorption coefficient is varied parametrically within this range to examine its influence on photothermal heating, whereas the absorption coefficient of normal breast tissue is set as 3 m⁻¹. The optical scattering coefficients of normal breast tissue and tumor tissue for a wavelength of 808 nm were taken as 600 m⁻¹ and 700 m⁻¹, respectively, based on reported optical properties of breast tissues in the NIR region.[24,25]

The absorption coefficient of carbon dots is obtained using the Beer–Lambert relation where (A) is the optical absorbance and (L) is the optical path length. Assuming a standard ultraviolet–Visible cuvette path length of 1 cm and a representative absorbance of approximately 0.2 at 808 nm, the calculated absorption coefficient is approximately 46 m⁻¹. Therefore, a value of 50 m⁻¹ was adopted in the present simulations to represent the enhanced optical absorption introduced by carbon dots in the NIR region. Furthermore, a parametric sensitivity analysis was performed by varying the absorption coefficient between 25 and 100 m⁻¹ to evaluate the influence of this parameter on the predicted thermal response.

The photothermal conversion efficiency η represents the fraction of absorbed optical energy converted into heat within the tumor tissue. Previous studies on carbon dots for PTT have reported photothermal conversion efficiencies spanning a broad range, with values commonly ranging from 20% to 60% depending on composition, doping, and excitation wavelength.[6,7,26] For simplicity, a baseline value of 0.59 was adopted based on the photothermal performance reported by Bao et al. for carbon-dot-based photothermal agents.[27] To evaluate the influence of photothermal conversion efficiency on temperature evolution, a parametric study was performed by varying its value from 0.2 to 0.6 while keeping all other parameters constant.

The optical parameters used in the simulations are summarized in Table 2.

Table 2.

Optical parameters used in the COMSOL model

Parameter	Value	Unit
Laser intensity, I	10,000	W/m²
Absorption coefficient (CDs), µaCD	25–100	m−1
Photothermal efficiency, η	0.2–0.6	—

Theory

The transient heat transfer in breast tissue is governed by the Pennes’ bioheat equation which accounts for thermal conduction, blood perfusion, metabolic heat generation, and laser-induced heating.[10,12,19,20]

The classical Pennes’ equation is

Transient heat storage term represents the rate of change of thermal energy stored in tissue and governs time-dependent temperature evolution, where ρ and c are the density and specific heat capacity of the tissue, respectively. T is the local tissue temperature, and t is time.

Heat conduction term ∇.(k∇T) describes heat diffusion within tissue due to temperature gradients and accounts for spatial heat spreading, where k is the thermal conductivity of tissue and ∇T is the temperature gradient.

The heat source term Q_ext in the COMSOL implementation of the Pennes’ bioheat equation generally represents externally applied heat sources. In PTT, this term accounts for laser-induced heating, which can also include nanoparticle-mediated absorption (e.g., carbon dots). In the present model, laser irradiation mediated by carbon dots was considered as the sole heat source.

Metabolic heat generation Q_met represents heat generated by biochemical reactions in living tissue. Reported metabolic heat generation rates for breast tumors typically lie in the range of 3 × 10³ – 1 × 10⁴ Wm⁻³.[15] The absorbed optical power density predicted by the P1 radiation model was of the order of 7.28 × 10⁵ Wm⁻³ under the baseline irradiation conditions. Using a photothermal conversion efficiency of 0.5, the corresponding effective heat generation term was approximately 3.64 × 10⁵ Wm⁻³. This value is about 36 times larger than the highest reported metabolic heat generation rate (10⁴ Wm⁻). Therefore, the contribution of metabolic heat to the overall temperature rise was considered negligible and was omitted from the simulations.[3]

The blood perfusion heat exchange term −ρ_bC_bω_b (T − T_b) represents heat loss or gain due to blood flow, where ρ_b, C_b, and ω_b are the density, specific heat, and perfusion rate of the blood, respectively. T_b is the arterial blood temperature.

The governing bioheat equation is solved numerically using the finite element method (FEM) implemented in COMSOL Multiphysics, which discretizes the computational domain into finite elements and computes the temperature distribution over space and time.

Simulation methodology

Laser-induced heat source

NIR lasers are generally employed in PTT due to their deeper tissue penetration and reduced damage to surrounding healthy tissue. Laser-induced heating was represented through the laser intensity I (Wm⁻²) which is defined as the incident power per unit area, and selected values based on the literature.[18,28] In the present study, a laser intensity of 10,000 Wm⁻² was applied at the tissue surface based on values reported in the literature.[27]

To account for both optical absorption and scattering within biological tissue, laser transport was modeled using the P1 approximation implemented through the Radiation in Absorbing–Scattering Media interface in COMSOL Multiphysics. The resulting radiation intensity distribution is shown in Figure 1b, where the incident radiation enters through the tissue surface and progressively attenuates with depth due to absorption and scattering effects. The optical properties of healthy tissue and tumor tissue were defined using their respective absorption and scattering coefficients. Carbon dots were incorporated through an enhanced effective absorption coefficient within the tumor region.

The spatial distribution of absorbed optical energy obtained from the P1 radiation model was coupled to the bioheat transfer equation as a volumetric heat source. The resulting absorbed optical energy was converted into heat according to the photothermal conversion efficiency of the carbon dot-loaded tumor tissue. The external heat source was defined as Q_ext = η Q_r where Q_r is the absorbed radiative power density obtained from the Radiation in Absorbing–Scattering Media interface in COMSOL (represented by the variable rasm. Q_r), and η is the photothermal conversion efficiency of the carbon dot-loaded tumor tissue.

Initial and boundary conditions

The initial temperature of the tissue is set to 310.15 K. The outer boundaries of the tissue domain were assumed to be thermally insulated, corresponding to zero heat flux across the boundaries. Time-dependent simulations are performed for a duration of 600 s.

Thermal damage assessment

Although temperature provides valuable information regarding photothermal heating, the biological response of tissue depends on both the achieved temperature and the duration of exposure. Therefore, thermal dose analysis is required to evaluate the extent of tissue damage during PTT. In this study, thermal damage was evaluated using the CEM43, a widely used thermal dose metric proposed by Sapareto and Dewey that combines temperature and exposure time into a single parameter.[29]

The thermal dose is calculated as

where T(t) is the local tissue temperature, and R is a temperature-dependent factor. A value of R = 0.25 was used for temperatures below 43°C, whereas R = 0.5 was used for temperatures ≥43°C. Higher CEM43 values correspond to greater accumulated thermal damage, and values exceeding 60 min are commonly associated with irreversible tissue injury.

In the present study, a threshold value of 60 min was adopted as an indicator of irreversible tissue damage.[30] Regions with CEM43 values exceeding this threshold were considered to have received a therapeutically effective thermal dose capable of producing substantial tumor cell destruction.

Mesh and numerical accuracy

A physics-controlled triangular mesh was employed, with local refinement in the tumor region to accurately resolve steep temperature gradients near the photothermal heat source. Mesh independence was assessed by comparing the final temperature at the tumor center for progressively refined meshes. Figure 2 presents the temperature distributions obtained using coarser, normal, finer, and extremely fine meshes, whereas Table 3 summarizes the corresponding number of elements and tumor-center temperatures. No measurable variation in the tumor-center temperature was observed with mesh refinement, confirming mesh independence of the numerical solution. Consequently, the finer mesh was adopted for all subsequent simulations to ensure computational efficiency while maintaining numerical accuracy.

Figure 2.

Mesh independence study showing temperature distributions obtained using coarser, normal, finer, and extremely fine meshes

Table 3.

Mesh independence analysis

Mesh type	Number of elements	Maximum temperature (K) at tumor center
Coarser	149	330.25
Normal	459	330.25
Finer	2154	330.25
Extremely fine	27206	330.25

RESULTS

Temperature distribution and heating characteristics

The two-dimensional temperature distribution at the end of the 600s irradiation period is shown in Figure 3a. Localized heating was observed within the tumor region following laser irradiation, with a maximum temperature of approximately 333.5 K (60.4°C) occurring at y = 32.97 mm. The corresponding isothermal contours shown in Figure 3b indicate that thermal energy is concentrated primarily within the tumor region and decreases progressively in the surrounding tissue.

Figure 3.

Temperature distribution and heating characteristics: (a) Spatial temperature distribution, (b) isothermal contours, (c) temperature variation along the central line passing through the tumor center, and (d) temperature evolution at the tumor center with and without carbon dots

The temperature variation along the vertical centerline passing through the tumor center is presented in Figure 3c. Temperatures of 331.0 K (57.8°C), 330.7 K (57.5°C), and 322.0 K (48.9°C) were obtained at the tumor top, center, and bottom, respectively. Outside the tumor region, the temperature decreased gradually from approximately 322 K to near physiological values, reflecting attenuation of incident radiation due to absorption and scattering within the tissue. The rapid decline in temperature away from the tumor indicates confinement of the majority of the deposited thermal energy within the target region.

Figure 3d compares the temporal temperature evolution at the tumor center with and without carbon dots. The carbon dot-loaded tumor exhibited a substantially higher temperature rise throughout the irradiation period, confirming the enhanced photothermal heating achieved through increased optical absorption.

The elevated temperatures observed within the tumor suggest that a therapeutically significant thermal dose may be achieved, which is further evaluated using CEM43 thermal damage analysis.

Temporal evolution of thermal damage

The temporal evolution of thermal damage predicted using the CEM43 model is shown in Figure 4. The CEM43 = 60 min contour indicates the boundary of irreversible thermal damage,[30] whereas the CEM43 = 240 min contour identifies regions subjected to substantially higher thermal doses associated with severe thermal injury and tissue necrosis.[11] As the irradiation time increases, the accumulated thermal dose progressively increases within and around the tumor region. During the initial stages of treatment, thermal damage is confined to a relatively small region near the tumor surface where the absorbed optical energy is highest. With continued laser irradiation, the thermal dose accumulates, and the damaged region expands gradually throughout the tumor volume.

Figure 4.

Temporal evolution of thermal damage predicted using the cumulative equivalent minutes at 43°C criterion during photothermal therapy

At 300 s, only a portion of the tumor exceeded the irreversible damage threshold. As the treatment duration increased to 500 s, the extent of thermal damage increased substantially, covering a larger fraction of the tumor. After 600 s of irradiation, the entire tumor region exceeded the CEM43 = 60 min threshold, indicating complete irreversible thermal damage throughout the target volume. In addition, a significant portion of the tumor exceeded the CEM43 = 240 min contour, suggesting exposure to considerably higher thermal doses.

The surrounding healthy tissue experienced comparatively lower thermal doses, indicating that thermal damage remained largely confined to the tumor region despite progressive heat accumulation. These results demonstrate the strong dependence of thermal damage on irradiation time and highlight the importance of thermal dose assessment in evaluating treatment efficacy during PTT.

Effect of carbon dot absorption coefficient

Figure 5a illustrates the influence of the carbon dot absorption coefficient on the temperature evolution at the tumor center during PTT. For all investigated absorption coefficients, the temperature increased rapidly during the initial stages of irradiation and continued to rise gradually throughout the treatment period. At the end of the 600 s irradiation period, the tumor temperature reached approximately 53.5°C, 57.4°C, 59.2°C, and 60.5°C for carbon dot absorption coefficients of 25, 50, 75, and 100 m⁻¹, respectively. Increasing the carbon dot absorption coefficient from 25 m⁻¹ to 100 m⁻¹ therefore produced an increase of approximately 7°C in the final tumor temperature.

Figure 5.

Effect of absorption coefficients of (a) carbon dots and (b) tumor on temperature evolution at the tumor center

As the absorption coefficient increases, a larger fraction of the incident optical energy is absorbed by the carbon dots and converted into heat, resulting in enhanced temperature elevation within the tumor region. The separation between the temperature curves becomes progressively larger with irradiation time, demonstrating the strong influence of carbon dot optical absorption on photothermal heating performance. These results indicate that the absorption characteristics of carbon dots play a critical role in determining treatment efficacy and should be carefully considered when designing photothermal agents.

Effect of tumor absorption coefficient

The effect of tumor absorption coefficient on the temporal evolution of temperature at the tumor center is shown in Figure 5b. For all investigated absorption coefficients, the temperature increased continuously with irradiation time, exhibiting a rapid initial rise followed by a more gradual increase at longer irradiation times. At the end of the 600 s irradiation period, the tumor temperature reached approximately 57.5°C, 58.5°C, and 59.4°C for tumor absorption coefficients of 10, 20, and 30 m⁻¹, respectively.

Increasing the tumor absorption coefficient enhanced optical energy absorption within the tumor and consequently increased the local temperature. However, the effect was relatively modest, with <2°C difference between the lowest and highest absorption coefficients investigated. This comparatively small variation indicates that although intrinsic tumor absorption contributes to photothermal heating, the overall thermal response is influenced more strongly by the absorption characteristics of the carbon dots.

Effect of photothermal conversion efficiency

Figure 6a presents the influence of photothermal conversion efficiency on the temperature evolution at the tumor center during laser irradiation. The results show that increasing the photothermal conversion efficiency substantially enhances tumor heating. For all investigated values, the temperature increased continuously with irradiation time, with higher efficiencies producing consistently greater temperature rises throughout the treatment period.

Figure 6.

Effect of (a) photothermal conversion efficiency and (b) blood perfusion rate on temperature evolution at the tumor center

At the end of the 600 s irradiation period, the tumor temperature reached approximately 43.9°C, 47.4°C, 50.8°C, 54.3°C, and 57.7°C for photothermal conversion efficiencies of 0.2, 0.3, 0.4, 0.5, and 0.6, respectively. Increasing the efficiency from 0.2 to 0.6 therefore produced an increase of approximately 14°C in the final tumor temperature.

This behavior occurs because a higher photothermal conversion efficiency enables a larger fraction of the absorbed optical energy to be converted into heat. Consequently, increasing the photothermal conversion efficiency results in enhanced temperature elevation within the tumor and promotes greater thermal dose accumulation during treatment. Among the investigated parameters, photothermal conversion efficiency was found to exert one of the strongest influences on the photothermal response.

Effect of blood perfusion

Figure 6b illustrates the influence of blood perfusion rate on the temporal evolution of temperature at the tumor center during PTT. For all investigated perfusion rates, the temperature increased rapidly during the initial stages of irradiation and subsequently rose at a slower rate with increasing treatment time. However, increasing blood perfusion significantly reduced the temperature achieved within the tumor.

At the end of the 600s irradiation period, the tumor temperature decreased from approximately 57.4°C for a blood perfusion rate of 0.001 s⁻¹ to 51.5°C for 0.005 s⁻¹. Intermediate perfusion rates of 0.002, 0.003, and 0.004 s⁻¹ produced final temperatures of approximately 55.6°C, 54.0°C, and 52.7°C, respectively. Thus, increasing the blood perfusion rate from 0.001 s⁻¹ to 0.005 s⁻¹ resulted in a reduction of nearly 6°C in the final tumor temperature.

This behavior arises because blood perfusion acts as a physiological heat sink, removing thermal energy from the heated tissue and transporting it away through circulating blood. Consequently, higher perfusion rates suppress temperature elevation and reduce thermal dose accumulation within the tumor. These results demonstrate that blood perfusion is an important physiological parameter influencing photothermal treatment response and should be considered when predicting treatment outcomes.

Effect of tumor depth on temperature distribution and thermal damage

Figure 7 illustrates the influence of tumor depth on the spatial temperature distribution and thermal damage pattern obtained using the CEM43 criterion during PTT. Four tumor depths were considered to evaluate the effect of optical attenuation on heat deposition within the target region. The tumors located closer to the tissue surface experience greater heating owing to reduced attenuation of incident laser radiation. For shallow tumor locations, a large fraction of the tumor volume exceeded the irreversible damage threshold, indicating extensive thermal injury throughout the target region. Increasing tumor depth progressively reduces the maximum temperature, and the extent of thermally damaged tissue decreases. This behavior is attributed to absorption and scattering of radiation in the overlying tissue, which decreases the amount of optical energy reaching deeper tumor locations. These results highlight the importance of tumor depth as a critical treatment parameter in PTT. Tumors situated closer to the irradiation surface receive higher thermal doses and exhibit greater damage coverage, whereas deeper tumors may require higher laser intensities, longer irradiation times, or enhanced optical absorption to achieve comparable therapeutic outcomes. At the greatest investigated depth, the damaged region becomes confined primarily to the central tumor zone, demonstrating the strong dependence of treatment efficacy on tumor location.

Figure 7.

Effect of tumor depth on (a) temperature distribution and (b) thermal damage predicted using the cumulative equivalent minutes at 43°C criterion

DISCUSSION

The incorporation of the P1 radiation transport model enabled representation of both absorption and scattering effects during laser–tissue interaction, resulting in realistic prediction of optical energy deposition and temperature distribution within the tissue. The simulated temperature fields demonstrated localized heating within the tumor region while maintaining substantially lower temperatures in the surrounding tissue. Furthermore, the incorporation of carbon dots substantially enhances thermal response, thereby improving the therapeutic potential of photothermal treatment. The predicted tumor temperatures fall within the supraphysiological heating range. Thermal damage analysis revealed progressive accumulation of thermal dose with irradiation time, ultimately resulting in complete coverage of the tumor by the irreversible damage threshold. These findings demonstrate the importance of thermal dose assessment for evaluating treatment effectiveness beyond temperature measurements alone.

The resulting temperature contours showed directional heat propagation from the tissue surface toward the tumor, reflecting the attenuation of optical energy as it penetrates deeper into tissue. As tumor depth increased, a smaller fraction of the incident optical energy reached the target because of absorption and scattering within the overlying tissue. Consequently, both temperature elevation and thermal dose decreased with increasing depth. These findings emphasize the importance of tumor location when selecting irradiation parameters for PTT.

Higher absorption coefficients of tumor and carbon dots lead to increased volumetric heat generation [Figure 5]. This is because the absorbed optical power is directly proportional to the absorption coefficient, resulting in enhanced volumetric heat generation within the tumor region. Increasing blood perfusion reduced tumor temperature because circulating blood removed thermal energy from the heated tissue. This behavior agrees with established bioheat transfer theory, where perfusion acts as an effective cooling mechanism that opposes temperature elevation during thermal therapies. Among the investigated parameters, photothermal conversion efficiency and carbon dot absorption coefficient produced the largest changes in tumor temperature, whereas tumor absorption coefficient exhibited a comparatively modest influence. This indicates that photothermal performance is governed primarily by the optical and photothermal characteristics of the carbon dots rather than the intrinsic optical properties of the tumor tissue.

The results of this simulation highlight the importance of nanoparticle-mediated light-matter interactions in determining photothermal performance and emphasize the role of material design in optimizing heat transfer characteristics. The present model assumes homogeneous optical and thermal properties within each tissue region and uniform carbon dot distribution throughout the tumor. In addition, tissue optical properties were considered constant during heating. Future studies may incorporate heterogeneous tissue structures, temperature-dependent properties, and experimentally measured optical parameters to further improve predictive accuracy.

MODEL VALIDATION

Model validation was performed by comparing the predicted thermal response with values reported in published PTT studies. The maximum tumor temperature obtained in the present simulation was approximately 60°C after 600 s of laser irradiation. This temperature range is consistent with experimental observations reported for carbon dot-based photothermal systems. For example, Bao et al.[27] demonstrated efficient photothermal heating under NIR irradiation, whereas Wei et al. reported temperatures approaching 55°C-60°C after 600 s of laser irradiation using a carbon-dot-based nano platform for photothermal cancer therapy.[31] The close agreement between the predicted and experimentally reported temperature ranges provides qualitative support for the validity of the developed model.

Furthermore, the predicted thermal dose (CEM43 >60 min) exceeded the commonly accepted threshold for irreversible thermal damage, indicating that the simulated treatment conditions are sufficient to induce significant thermal injury within the tumor region. The agreement between the predicted temperature range and established thermal damage criteria suggests that the model provides a physically realistic representation of photothermal heating and thermal dose accumulation.

Although the simulated temperature trends showed good agreement with reported experimental observations, exact quantitative comparison was not possible because of differences in tumor geometry, laser wavelength, irradiation conditions, carbon dot formulation, nanoparticle concentration, and optical properties between the experimental studies and the present model. In addition, the model assumes homogeneous tissue properties and uniform distribution of carbon dots within the tumor region. Therefore, the present validation focuses on reproducing the overall thermal response and heating characteristics rather than achieving exact numerical agreement with a specific experimental system.

CONCLUSIONS

A two-dimensional finite element model was developed in COMSOL Multiphysics to investigate carbon dot-assisted PTT of breast tumors. The model combined the Pennes’ bioheat equation with the P1 radiation transport approximation to account for optical absorption, scattering, and heat transfer within biological tissue during laser irradiation.

The simulation results demonstrated that laser irradiation produced localized heating within the tumor region, with a maximum temperature of approximately 59°C after 600 s of treatment, while temperatures decreased rapidly outside the tumor region, indicating confinement of the majority of the deposited thermal energy within the target tissue. The P1 approximation successfully captured the directional propagation of optical energy and the resulting nonuniform temperature distribution within the tissue.

Parametric analysis showed that the photothermal response was strongly influenced by the optical and thermal properties of the system. Increasing the carbon dot absorption coefficient from 25 to 100 m⁻¹ and tumor absorption coefficient from 10 to 30 m⁻¹ resulted in higher final tumor temperatures. Photothermal conversion efficiency was found to be one of the most influential parameters, with the final tumor temperature increasing from approximately 44°C to 60°C as the efficiency increased from 0.2 to 0.6. In contrast, increasing blood perfusion reduced tumor temperature because of enhanced heat removal by circulating blood.

Thermal damage assessment using the CEM43 model demonstrated progressive accumulation of thermal dose with irradiation time. Complete tumor coverage was achieved after 600 s of laser irradiation, with the entire tumor region exceeding the irreversible damage threshold (CEM43 >60 min), indicating that a therapeutically effective thermal dose was delivered throughout the tumor under the investigated treatment conditions.

Overall, the results confirm the potential of carbon dots as efficient photothermal agents for tumor heating and demonstrate the usefulness of computational modeling for optimizing treatment parameters in PTT. Although the model predictions showed qualitative agreement with published experimental PTT studies, direct experimental validation using the specific carbon dot system considered in this work remains an important direction for future investigation.

Conflicts of interest

There are no conflicts of interest.

Funding Statement

Nil.