For liver tissue irradiated by the pulsed Ho:YAG laser, determine the exposure duration which the equation for heat conduction may be ignored. Assume the absorption coefficient at the Ho:YAG laser wavelength is 30cm-1 and assume the thermal diffusivity of the tissue is the same as that of water. If the threshold temperature of ablation is 150¢J, determine the threshold fluence (J/cm^2) for ablation.
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This question is about the physics of ablation and heat transfer. It is not social studies.
I do not understand the ¢J units of the laser ablation threshold temperature.
Heat conduction can be ignored if the characteristic thermal conduction distance sqrt(a*t) is less than the characteristic radiation penetration depth, 1/30 cm. a is thermal diffusivity. Use that to determine t, to answer your fist question
To determine the exposure duration for which the equation for heat conduction may be ignored, we need to calculate the thermal relaxation time of the liver tissue.
The thermal relaxation time characterizes how fast the tissue reaches a steady-state temperature after being irradiated. When the exposure duration is significantly shorter than the thermal relaxation time, heat conduction can be ignored as the heat dissipates faster than it can propagate within the tissue. However, if the exposure duration is longer than the thermal relaxation time, heat conduction becomes relevant.
The thermal relaxation time (τ) can be calculated using the following formula:
τ = ρ * C / (4π * k)
Where:
ρ is the tissue density (assumed to be the same as that of water, approximately 1000 kg/m³)
C is the specific heat capacity of the tissue (assumed to be the same as that of water, approximately 4186 J/kg·°C)
k is the thermal conductivity of the tissue (assumed to be the same as that of water, approximately 0.6 W/m·°C)
Let's plug in the values and calculate τ:
τ = (1000 kg/m³) * (4186 J/kg·°C) / (4π * 0.6 W/m·°C)
Simplifying the equation:
τ ≈ 2761 seconds
Now, we know that the threshold temperature of ablation is 150 °C. To determine the threshold fluence for ablation (F_Threshold), we can use the equation:
F_Threshold = E_Threshold / (A * τ)
Where:
E_Threshold is the threshold energy for ablation (in Joules)
A is the absorption coefficient (30 cm⁻¹)
τ is the thermal relaxation time (in seconds)
Given that the absorption coefficient at the Ho:YAG laser wavelength is 30 cm⁻¹, we need to convert it to meters:
A = 30 cm⁻¹ * (1 m / 100 cm) = 0.3 m⁻¹
Assuming uniform absorption, the threshold energy (E_Threshold) can be calculated using the equation:
E_Threshold = ρ * V * C * ΔT
Where:
ρ is the tissue density (in kg/m³)
V is the volume of the irradiated tissue (in m³)
C is the specific heat capacity of the tissue (in J/kg·°C)
ΔT is the temperature difference required for ablation (150 °C)
To determine V, we need to know the irradiated surface area (A_Surface) and the thickness of the tissue (d):
V = A_Surface * d
Now, we can calculate the threshold fluence:
F_Threshold = (ρ * V * C * ΔT) / (A * τ)
Given the specific values are not provided in the question, you need to calculate them or provide specific numbers to get an exact answer.