More on Thermal Relaxation Times



I’ve had a number of enquiries about my article on the relevance of thermal relaxation times in photothermal treatments. They were asking for clarification. So here goes….

Thermal relaxation time (TRT) describes how quickly an object loses heat energy. Typically, it is the time taken for the temperature of an object to drop to either 50% or 36.78% (the 1/e value) of its maximum value, depending on which definition you use.

Image result for cooling It is, essentially, a cooling time. The TRT describes how quickly or slowly an object cools!

The TRT was introduced into laser treatments by Anderson and Parrish back in 1981 when they wanted to put a constraint on the laser energy pulse duration to minimise thermal damage to adjacent tissues. Hence, most of the thermal damage would be confined to the absorbing target. So they, arbitrarily, chose the time equal to one TRT as the maximum for any pulsewidth when treating tissues.

That’s fine and is a rational choice. However, it was a purely arbitrary choice!


TRT is a COOLING time……..

……. NOT a HEATING time!!



Denaturing tissue

The main aim of photothermal treatments is to use heat energy to destroy ONLY the unwanted tissue(s), without significantly damaging surrounding tissue (the basis of Selective Photothermolysis).

Anderson & Parrish figured that this could be achieved if sufficient energy was deposited in the target tissue but with the TRT constraint to prevent collateral damage. However, their assumption is flawed!!

They made their choice of a pulsewidth of one TRT based on minimising the heat transfer to adjacent tissues. They DID NOT consider the heat energy required to actually denature the target tissue. Their original calculations were based on achieving some desired temperature in the target tissue, sufficient to irreversibly denature that tissue’s proteins.

However, the flaw in their argument was that they did not consider the time necessary to achieve irreversible denaturation. We all know that if we try to boil an egg then it must go into a pot of boiling water for around three minutes or so. If the egg is removed at two minutes then it will be too runny!

The first egg (above) was removed too early – hence its runny, undercooked consistency. The second egg was removed after 3.5 minutes – my personal favourite. The last egg shows the best way to enjoy boiled eggs – with soldiers….


A longer cooking time (pulsewidth) will denature more of the egg’s proteins, for the same temperature.

Exactly the same happens with laser treatments of vessels and hair follicles. Applying the heat energy for too short a time will result in partial denaturation of the target’s proteins – this may lead to insufficient damage and, hence, regrowth of that tissue. This explains why some treatments end up with poor results – usually due to a low energy input or short pulsewidths.


Heat Conduction from a Vessel or Follicle

Imagine a ‘hot’ blood vessel or hair follicle in the dermis, following the absorption of some laser energy. Within that absorbing volume the absorbed energy will generate a rise in local temperature. That temperature rise is dependent on the absorption coefficient and the mass of the absorbing volume, which, in turn, is dependent on the physical size of the absorbing volume.

Hence, the temperature rise is dependent on the square of the radius of the vessel/follicle (since the volume depends likewise).

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.

Image result for laser hair removal

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!!



The original idea behind Anderson and Parrish’s choice was to only damage the target without damaging the surrounding tissues – the basis of Selective Photothermolysis. While this works well in some cases it does not work very well in other targets, particularly larger targets.

In many cases the TRT is too short a time to allow sufficient denaturation to occur. This explains why IPL systems can be so useful when treating hair and blood vessels. They employ longer pulsewidths than most lasers, up to 100 ms in some systems. This is much longer than the TRTs of many target vessels/follicles.

It is curious that, in this age of widespread IPL usage, people still cling to the notion that the light energy must be delivered within one TRT. Cleary this is not true!


Additional note: Some people have spoken to me about ‘long pulsed lasers’ and asked if they are useful in such treatments. The problem with many of these so-called ‘long pulsed’ systems is that they utilise a train of short pulses within a long temporal envelope. Hence, the actual energy delivery occurs in short bursts with gaps between them. The critical timing here is the duration of those gaps. If they are too long then the overall temperature rise induced will be determined by how much time the laser energy is OFF, rather than ON!

I know, from measurements, that some lasers in use today have significant gaps between these short, individual pulses….






3 thoughts on “More on Thermal Relaxation Times

  1. Excellent analysis, Mr Murphy ! I suspected vaguely the same idea as yours (that the pulse duration, or pulse width, must depend on some thing else than the TRT), but I was not sure. Now, thank to you, I m sure !
    Thanks again !
    Quoc Tuan Vuong

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