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So, if there are two vessels side by side, and one is twice the radius of the other, and they absorb the same amount of total energy, then the larger vessel will experience an increase in temperature equal to one quarter that of the smaller vessel (because its mass/volume is 4 times larger).
[Now, this is a simplified explanation. In reality the larger vessel will absorb more of the incoming laser light and the temperatures will be determined by the absorption distribution in the vessels. But, as a starting point, we can assume that the smaller vessels will be hotter than the larger vessels.]
At this point the TRT kicks in - but ONLY in terms of subsequent cooling....
As with the temperature rise calculation, the TRT also depends on the (inverse of the) square of the radius. Hence, smaller objects lose their heat energy faster than larger objects.
So, the smaller, hotter vessel/follicle will drop in temperature faster than the larger, cooler vessel/follicle.
Now it gets a bit complicated...... (too complicated for this post!!)
Why TRT?
The original Anderson and Parrish assumption was that by restricting the laser energy pulsewidth to one TRT the adjacent tissues would not be thermally damaged to any significant degree. This is basically true. By constraining the pulsewidth the total amount of energy delivered is also constrained. Hence, there shouldn't be too much energy in the dermis causing unwanted damage.
However, as heat spreads out from the hot, absorbing targets, the temperature rise around them depends, again, on a radius squared distribution. This means that as you move away from the hot object, the temperature rise due to heat conduction from that object, depends on the square of the distance from that object.
So, even though the target vessel/follicle may achieve high temperatures, the surrounding tissues will not (unless the laser pulse is long). Short pulsewidths will confine the thermal damage to the absorbing target with only a little damage to adjacent tissues.
The choice of TRT appears to be a good one at first glance, but it does not consider the actual time needed to denature proteins sufficiently. Consequently, we need to stop thinking about treating tissues based on their cooling times, and start thinking about their required heating times. There is no direct link between and object's TRT and the time it needs to irreversibly denature - NONE!!
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