Ablation

Introduction:

    The word ablation comes from the latin 'ablatus' which is the past participle of the verb 'auferre' and means 'to remove. There are two types of meaning of the word ablation. In a physics/engineering sense it refers to the physical removal of material (tissue), while in the medical/biological sense it refers to the physiological removal of tissue (i.e. causing the tissue to stop performing the processes needed for survival of the tissue, that is killing the cells but not necessarily physically removing them)

    The disciplines in medicine where laser ablation has received the much attention are:

        a) cardiology - angioplasty, arrhythmia treatment, TMR
        b) ophthalmology - corneal reshaping, cateract surgery
        c) orthopedic surgery - cartilage, bone ablation (knees, joints, herniated discs)
        d) dentistry - drilling cavities, soft tissue (gums)
        e) dermatology - burn eschar debridement, skin resurfacing, hair removal



Summary:

    In summary, long pulses cause collateral thermal damage to tissue adjacent to the ablation crater while short pulses cause collateral mechanical damage. Thermal damage can be the result of thermal diffusion or direct irradiation of tissue at subthreshold levels. Mechanical damage can be result of explosive vaporization or laser-induced pressure transients. The latter can originate by thermoelastic expansion, ablative recoil or as a side effect of rapid explosive vaporization. The pulse duration and depth of penetration determine whether the interaction of the laser pulse with tissue is thermally confined and/or mechanically confined.

    Check out the LASIK video at http://www.lasersite.com/lasik/index.htm

Continuous Wave Ablation (cw ablation)

Continuous wave ablation typically constitutest the vaporization of tissue water followed by ablation of the remaining dry mass of the tissue. As light is absorbed, the tissue temperature rises and the ablation process starts. The chronicle of ablation with a continuous wave lasers follows the following sequence:

    1. light interaction with tissue (governed by tissue optical properties)
    2. the light energy is converted to thermal energy (heat generation)
    3. tissue temperature rises (heat source and conduction)
    4. denaturation and dehydration of the tissue occurs (this may affect the thermal and optical properties of the tissue)
    5. the subsurface pressure increases
    6. explosion ("popcorn effect") resulting in the expulsion of heated tissue fragments - this removes energy
    7. cooler subsurface layers exposed to light energy and the process repeats itself
    8. at some point all the tissue water has been evaporated and carbonization/pyrolyses ('burning' of tissue will occur).


During tissue vaporization, the position of the tissue surface, where tissue and air meet, moves deeper into the tissue. In other words, one is drilling a hole into the tissue. The velocity at which the ablation front moves into the tissue is called the "ablation velocity".

By using a moderate irradiance and measuring surface temperatures with an IR thermal camera, it is possible to document the initial surface heating and explosive ejection of tissue. The onset of ablation occurs above 100°C due to subsurface superheating. As hot tissue is removed, a cooler layer is exposed to the laser irradiation. The temperature of the exposed layer remains at approximately 100°C while continued irradiation dehydrates the tissue. The removal of water decreases the local thermal conductivity reducing heat conduction to the surrounding area. Continued radiation rapidly increases the tissue temperature until it reaches about 350 to 450°C; the tissue burns and carbonizes.

All tissue exposed to air will lose water vapor to the atmosphere because of the differences between the partial pressures of water vapor across the tissue/air boundary. As tissues are heated water vapor will first be generated superficially, then deep within the tissues. The vapor will diffuse toward the surface to escape.

At, or just above 100°C water vapor is generated volumetrically, the equilibrium is pushed toward the vapor phase, and, for sufficiently high laser fluence rates (irradiances), more vapor is produced than can escape by simple diffusion. The excess vapor is trapped in the tissue layers forming vacuoles. The superheated vapor contained in the vacuoles will expand quickly, compressing the surrounding, rapidly drying tissues that form the vacuolar walls. As the vacuoles expand, the wall separating the vapor pockets from each other or the tissue surface become thin. The walls rupture as the force of the increasing pressures of expanding vapor overcomes the mechanical strength of the tissue. This is known as the "popcorn effect". (Pearce and Thomsen)

The ablation process can be described by two different models: the Steady State Ablation model and the Blow-Off model. For continuous wave ablation the Steady State model gives the most accurate description of the events that go on.

Steady State Ablation Model

The basis of the steady state model is that some time after the laser was switched on, the tissue removal process starts, and that once it starts, the ablation front moves into the tissue with a constant velocity.

If one makes the following the assumptions: 1) boiling/vaporization constitutes the ablation process; 2) for vaporization a heat of ablation, Wabl is defined; and 3) the ablated material is instantly removed, the following model can be written:

The ablation velocity, vss, is:

The energy needed for ablation of a layer with thickness dz is the energy needed to heat the layer from its starting temperature to the boiling temperature plus the latent heat of vaporization:


The energy available for ablation is:



    Thus the ablation velocity can be written as:



        where E0 is the irradiance (W/m2) and Wabl is the heat of ablation (J/m3).

The implications of this model is that it takes a certain amount of time before ablation starts, i.e. to reach ablation, which we call t0. Once ablation starts, the ablation velocity is immediately constant ('steady state velocity'). It can be shown (which I won't derive here) that the total depth of ablation is given by:

    To see this derived:

        - divide the laser pulse into short segments
        - assume a top-hat (both spatial and temporal)
        - apply Beer's law
        - assume no thermal losses
        - radiant exposure is H (= irradiance * time)
        - number of pulse segments is n
        - radiant exposure per time segment Hs = H/n

1) use m subpulses to supply Wabl à energy distribution after m subpulses, according to Beer's law is:


2) ablation starts after subpulse m+1 à depth to which tissue is removed is:

3) now after m+1 subpulses are delivered, the energy distribution is the same before with z now at the bottom of the crater. The next Dz removed is also the same, etc. until all n subpulses are delivered.

    The total depth of the crater is:
    d = (n-m)dz

        knowing that:

            if follows that:

            Then by letting the number of subpulses increase (n à infinity):


                and thus:

4) Threshold:

At threshold, per definition d=0 and H=Hth, thus:

        Hence:

 

            This holds also for non-uniform profiles as long as heat diffusion is ignored.

            Knowing the depth of the crater and the area, the total ablated volume is:



5) Mass loss:
Since the depth of a crater is oftentimes difficult to measure, it is much easier to measure the mass lost due to ablation from the tissue.

Mass loss as function of irradiance (fluence) looks like the graph below. The intersect with the x-axis represents the threshold and the slope of the curve the ablation efficiency (g/W/m2)


6) Summary:
The steady state model is valid for longer exposures where 'steady state' situation of a moving ablation front occurs. So, in summary for the steady state model we have seen (and derived):

    at threshold, d=0:

Also we have found expression for the ablation velocity, ablation volume and mass loss:



Think about the following question: what is the effect of the absorption coefficient on the ablation velocity and what is the effect of the irradiance on the ablation velocity??

Blow-off Model

A different model that is more applicable to short laser pulse exposures is based on the assumption that all energy from the laser pulse is deposited in the tissue before any ablation occurs (i.e. no material removal during the laser pulse). This model is thus more applicable to laser ablation with short laser pulses (note: this can still be considered continuous wave ablation).

In this case one can apply Beer's law:


    if Ho>Hth material will be removed up to a depth of z = d. At d the (attenuated) radiant exposure is per definition Hth


        Then the depth of the crater, d, is:

            In this model ablation is the same as vaporization, therefore:

                with that we can write expressions for the depth of ablation and the ablated volume:


Example:

The ablation of myocardium with the CO2 laser as it is done in TMR is usually done with an 800 W CO2 laser, a spotsize of 1 mm in diameter and a pulse duration of 50 ms.

    a) Show that these parameters can indeed be used to ablate a 1 mm diameter channel in the 20 mm thick myocardium.
    b) Calculate the time it takes before the ablation onset actually starts
    c) Calculate the ablation velocity for this case

Solution:

a) A laser power of 800 W and exposure time of 50 ms results in total energy deposited of 40 J. Now let's calculate the energy needed to vaporize a cylinder of tissue 20 mm high and with a diameter of 1 mm.
Volume = Area * height = 0.785 mm2 * 20 = 15.6 mm3

    The heat of ablation for this tissue, assuming thermal properties of water, is:

        = 4.18 * 63 + 2260 = 2523 mJ/mm3

        Energy needed to vaporize the volume: V * Wabl = 39.4 J

    This means that 39.4 J is needed to vaporize the volume of the cylinder while 40 J is available.

b) This is a classical example of a situation in which the steady state model would be valid. The laser pulse duration is relatively long (50 ms) and the optical penetration depth shallow.

    For ablation to start, the temperature at the tissue surface (z=0) needs to be 100 oC. Assuming a starting temperature of 37 oC and thermal properties of water:

    DT = 63 oC à the heat source, W = r c DT = 4.18 * 63 = 0.263 J/mm3
    This is the energy density needed at z=0 just before ablation starts.

    Laser power = 800 W and spotsize = 0.785 mm2 thus the irradiance = 1018.59 W/mm2.

        Absorption coefficient for this wavelength = 80 mm-1. So we can calculate the rate of heat generation at z=0: S = ma E(z=0) = 81,487 W/mm3

    Thus the time the laser needs to be on to get to threshold (= the time needed to get to the calculated energy density) = 0.263 / 81,487 = 3.22 10-6 s (or 3.22 ms).

c) From the previous part we know that the ablation starts almost instantaneously, certainly relative to the pulse duration. If we apply the steady state model:

Tissue Damage

In most applications of lasers as ablative devices, the goal is to remove the target tissue while minimizing collateral damage to adjacent tissue layers. Based on the very nature of the interaction of laser radiation with tissue as we have seen, the damage mechanisms may be thermal or mechanical. A nice review of this is given in the paper by Thomsen. In brief, mechanical damage is caused by subsurface explosion of heated tissue material (in particular in cases where the absorption coefficient is relatively small), while thermal damage is caused by two sources:

    1) thermal diffusion (from heated tissue to surrounding cooler tissue), and

    2) direct deposition of heat in layers beyond the point where the energy density was sufficient for ablation, i.e. below threshold.

The irony is that reducing the pulse duration will minimize the amount of heat diffusion that can take place before heated material is ejected. However, this same reduction of the duration of the pulse will cause the ablation process to be even more explosive and violent thus increasing the collateral mechanical damage to the tissue.

It should be obvious that by choosing wavelengths that are highly absorbed (i.e. large absorption coefficient) in tissue, the energy is confined to a smaller volume and thus the irradiance or radiant exposure necessary to achieve ablation will be less. In addition, the extent of the zone of tissue that is heated to subablative energy densities will be greatly reduced in this case.

Pulsed Laser Ablation

The question we now need to ask ourselves is 'when is a laser a pulsed laser?'. While there are certainly good answers and clear definitions from a laser physics point of view (i.e. how the machine works), we will look at it with a 'laser-tissue interaction' mindset.

First, from a modeling point of view, pulsed laser ablation fits the assumptions of the blow-off model which we discussed before under continuous wave ablation quite well. As we have just seen, laser ablation appears to be a trade-off between causing thermal damage with long pulses and mechanical damage with short pulses.

    First let's look at thermal diffussion. When laser penetration depth is less than the laser spot radius, the thermal diffusion time, tth, can be defined as:


        where d is the penetration depth of laser light in tissue with thermal diffusivity, a = 0.15 m2/s for water at 37 °C. For laser pulses shorter than the thermal diffusion time, the distribution of thermal energy is determined by the laser light distribution. This situation is known as thermal confinement. If the laser pulse is larger than the thermal diffusion time, the thermal energy propagates into the tissue during the laser pulse. The criterion for thermal confinement is:

Now let's consider the mechanical effects. A major photomechanical interaction during most tissue ablation events, is tissue water vaporization, resulting in explosive removal of tissue structures, which has been described as 'pop-corn' effect for CW lasers. Note that in this scheme, the explosiveness of the process may be severe enough to eject liquid or solid tissue fragments. As such the energy needed to accomplish a certain crater size may be significantly less than expected based on calculations that assume true vaporization of the tissue. This ejection process is driven by the fact that water when converted to steam has a volumetric expansion of approximately 1620 at 1 atm.

Laser-Induced Acoustics

In addition to the explosion and material ejection, a second mechanical effect is the formation of pressure and shock waves. These pressure waves can be caused for example, by the thermoelastic expansion of tissue, or due to heating of the target tissue by a laser pulse and recoil caused by the ejection of ablation material. Thermoelastic expansion describes the event that due heating of a material, the material expands (due to an on average larger molecular spacing). If the heating is rapid enough, significant expansion of the material may take place leading to pressure waves that are formed in the heated volume and which will propagate in the tissue outside the heated volume.

The instantaneous pressure rise is proportional to the temperature rise and can be calculated from:

        gamma = coefficient of isothermal compressibility [Pa-1]
        beta = volumetric expansion coefficient [K-1]
        cv = specific heat at constant volume [J/kg K]
        cp = specific heat at constant pressure [J/kg K]

        Thus we can write DP as:

            where  is known as the Gruneisen Coefficient, G [dimensionless]. This simplifies the expression for the pressure rise to:


                The Gruneisen coefficient is a temperature dependent parameter, approximately 0.11 for water at 20 °C. It can be seen from the above equation that the pressure as function of depth of the acoustic wave will be proportional to (and thus exactly follow) the temperature distribution as function of depth. This in turn means it will exactly mimic the light distribution in tissue. Hence for an absorption dominated case where the light distribution follows a Beer's law, exponential distribution, the shape of the pressure wave will also be an exponential decay with depth.


These photomechanical interactions (thermoelastic expansion, ablative recoil and explosive vaporization) cause stress waves, which propagate with the speed of sound, s = 1,500 m/s, or even faster as in the case of shockwaves. Analogous to heat diffusion, we can define a 'stress diffusion time':

    where tstr is the stress confinement time, d is the penetration depth of the light in the tissue and s is the speed of sound in the medium.
    If the laser pulse length, tpulse is shorter than the time it takes the stress wave to propagate out of the irradiated volume, large peak stresses can be reached. These stresses may contribute to the ablation mechanism and may inflict damage to adjacent tissues, even far away from the irradiated zone. The criterion for so-called stress confinement is given by:

Confinement (and with it the determination if the effect of the laser is considered pulsed or not) depends on the laser pulse length and the optical penetration depth (i.e. absorption coefficient). In the figure below the pulse length versus penetration depth is shown and marked in it are various common lasers with their characteristic pulse durations and optical penetration depths (remember: these depend on the wavelength). For example, from this figure it follows that the interaction of both the XeCl excimer and the Holmium:YAG laser are thermally confined but not stress confined.