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03.01.2019 | Original Article | Ausgabe 6/2019 Open Access

Lasers in Medical Science 6/2019

Variable heat shock response model for medical laser procedures

Zeitschrift:
Lasers in Medical Science > Ausgabe 6/2019
Autoren:
Matjaž Lukač, Andrej Lozar, Tadej Perhavec, Franci Bajd

Introduction

Medical laser procedures typically involve the exposure of tissues to elevated temperatures. For example, in selective photo-thermolysis procedures [ 1], the goal is to heat the target chromophore, such as hemoglobin in blood vessels [ 2] or melanin in hair follicles [ 3], to a higher temperature than the surrounding tissue.
In order to minimize the influence of heat diffusion from the heated target into the surrounding tissue, it was proposed to use laser pulse durations shorter than the thermal relaxation time (TRT) of the target [ 13]. The TRT was defined as the time during which the target temperature decreases by 50% as a result of heat diffusion. The relaxation time of a target is proportional to the square of the diameter of the target, and therefore, according to the TRT concept, smaller targets require shorter laser pulse durations. However, it is not only the temperature but also the time of exposure that is important [ 4]. In laser procedures, the physical process of thermodynamically heating the target is typically accompanied by the chemical process of protein denaturation as a result of the heat-induced shock, i.e., the cellular exposure to the increased temperature ( T) for the exposure time ( t exp) [ 5]. The cell damage induced by the heat shock is described by the Arrhenius damage integral [ 4, 6, 7], with the damage being exponentially dependent on T and linearly dependent on t exp. Therefore, the recommended pulse durations according to the TRT concept may be too short to achieve controlled and predictable damage to the targeted structure [ 8].
A commonly used metric for tissue damage (Ω) is the ratio of the concentration of native (undamaged) tissue before thermal exposure ( C 0) to the concentration of native tissue at the end of the exposure time ( C f). The tissue damage is then calculated using the Arrhenius damage integral calculated over the time of the thermal exposure [ 7, 9]:
$$ \varOmega =\ln \left({C}_0/{C}_{\mathrm{f}}\right)=A\int \exp \left(-E/ RT(t)\right) dt $$
(1)
Here, A is the frequency factor, i.e., the damage rate (in s −1), E is the activation energy (in J/kmol), and R is the gas constant ( R = 8.31 10 3 J/kmol K).
In the standard model originally proposed by Henriques and Moritz [ 4, 6], based on measurements for t exp > 1 s, it is assumed that a single chemical process representing the kinetics of protein denaturation is involved and, therefore, the Arrhenius coefficients E and A are fixed and independent of the exposure time [ 1015]. However, with more recent studies performed at extremely short exposure times ( t exp < 10 ms), the obtained activation energies were significantly smaller and the damage threshold temperatures were significantly higher than what would be expected from the standard single-process Arrhenius model [ 1619]. This finding is of particular significance in the context of medical laser procedures, where extremely short exposures are very common.
In this paper, we propose a VHS (variable heat shock) response model where the damage integral coefficients and, therefore, the heat shock response vary with exposure time. The model is based on an assumption that the heat shock response can be modeled with two interacting biochemical processes, with different time–temperature correlations and activation energies, defining the cell viability at very long and very short exposure times [ 16, 17]. Additionally, an original “VHS” numerical method for calculating the damage integral is introduced, which takes into account that Arrhenius coefficients are not constant during the non-square-shaped heat shock pulses that are commonly present at short laser-induced exposures.
The proposed VHS model is particularly relevant for laser procedures involving targets with short thermal relaxation times, such as thin hair follicles or blood vessels, where the VHS model predicts much higher damage threshold temperatures than the values that would be expected from the standard Arrhenius model.
Another example of a target with a short thermal relaxation time is encountered during tissue rejuvenation procedures, such as skin [ 20, 21] or mucous tissue resurfacing [ 2224]. In this type of procedure, it is the bulk tissue water which plays the role of the absorbing chromophore, and the temperature elevation is not limited to a particular tissue structure but to the superficially irradiated tissue layer with its thickness determined by the laser’s optical penetration depth ( δ) and subsequent thermal diffusion [ 20, 25, 26]. In this paper, we demonstrate the potential implications of the VHS model for understanding the mechanism of action during non-ablative resurfacing of vaginal and oral tissues with mid-IR ( λ = 2940 nm) Er:YAG lasers [ 2224].

Materials and methods

Variable heat shock model

In the standard Arrhenius model of a chemical process, the tissue damage kinetics is commonly characterized by a critical (i.e., damage threshold) temperature ( T crit) which is, assuming a square-shaped temperature pulse with a constant temperature during the thermal exposure time ( t exp), defined by [ 7, 9]:
$$ {T}_{\mathrm{crit}}=E/\Big(R\ln \left(A{t}_{\mathrm{exp}}\right) $$
(2)
and represents the temperature at which the concentration of the undamaged tissue is reduced by a factor of e (i.e., when Ω = 1).
Transient heating of tissues leading to protein denaturation and, consequently, to cellular stress or death is very common in medicine and biology, and it has been extensively studied, especially for exposure times longer than approximately 1 s [ 46, 1015]. Studies of cellular survival during shorter exposures to higher temperatures, for example, in a millisecond domain, which is very common during laser exposures, are less abundant and have been published more recently [ 1619]. The published Arrhenius coefficients vary considerably, especially when comparing the results obtained at very short and very long exposures. This can be seen in Fig.  1, which shows the dependence of T crit on t exp as calculated for a number of published Arrhenius coefficients [ 4, 5, 1018].
Although some of the variability in the published Arrhenius coefficients can be attributed to the difference in studied tissue types and/or to different criteria for accessing cell damage, Fig. 1 suggests that the large variability of the reported Arrhenius coefficients can be, at least to a certain extent, attributed to the difference in the studied exposure times. This is supported by the observation that the plotted Arrhenius curves (represented by full lines in Fig. 1) appear to approximately follow the local T crit versus t exp slope of an imaginary curve (represented by the dashed line in Fig. 1) representing the combined effect of two damage processes (represented by two dotted lines) dominating at the limiting very long and very short exposure times.
Even though the observed shift to higher T crit at shorter exposure times is not completely understood [ 16], we shall in what follows assume that the cell viability depends on a combination of two biochemical processes with different time–temperature correlations and activation energies, defining the cell viability at very long (process 1 with A 1 and E 1) and very short (process 2 with A 2 and E 2) exposure times, as has been suggested already elsewhere [ 16, 19]. The two limiting biochemical processes may describe a situation where the activation energy for protein denaturation shifts to a lower value when the temperature is increased above a certain temperature [ 16]. Alternatively, the short exposure process 2 may represent the primary protein denaturation dynamics, and the long exposure process 1 describes a combined effect of the primary process together with the slower cellular repair mechanism [ 11, 16, 19, 27].
We further assume, based on the similarity with parallel resistor circuits, that the effective VHS (variable heat shock) damage integral Ω VHS can be calculated for any exposure time t exp from the combined effect of the damage integrals Ω 1 ( t exp) and Ω 2 ( t exp) belonging correspondingly to processes 1 and 2, as follows:
$$ {\left(1/{\varOmega}_{\mathrm{VHS}}\right)}^p={\left(1/{\varOmega}_1\right)}^p+{\left(1/{\varOmega}_2\right)}^p $$
(3)
where p is the transition coefficient that determines the transition between the two limiting processes. For example, the dashed line in Fig. 1 represents an imaginary VHS critical temperature curve for a transition coefficient of p = 0.15.
The effective critical temperature ( T crit) of the combined processes is then determined by the following VHS relation:
$$ {t}_{\mathrm{exp}}=\left(\right(\exp {\left({E}_1/\left(R{T}_{\mathrm{crit}}\right)/{A}_1\right)}^p+{\left(\exp {\left({E}_2/\left(R{T}_{\mathrm{crit}}\right)/{A}_2\right)}^p\right)}^{1/p} $$
(4)
The effective damage rate A VHS and the effective activation energy E VHS, representing the VHS coefficients for the combined effect of the two processes for a thermal exposure time t exp can then be obtained from:
$$ {T}_{\mathrm{crit}}={E}_{\mathrm{VHS}}/\Big(R\ln \left({A}_{\mathrm{VHS}\cdot }{t}_{\mathrm{exp}}\right) $$
(5)

Physical model of tissue resurfacing

Mid-IR lasers, such as carbon dioxide (10,640 nm) and Er:YAG (2940 nm), are selectively highly absorbed by tissue water, with optical penetration depths ( δ) in the range of 1–30 μm, and are thus the most effective for non-ablative or ablative heating of superficial tissues in a very precise fashion [ 20, 28]. In our study, we applied a numerical model of the physical process of tissue resurfacing as originally developed to study thermo-mechanical ablation with mid-IR lasers. The details of the model are described in [ 25] and will not be repeated here.
In the model, a single wavelength ( λ) pulsed laser radiation is delivered to the surface of the treated tissue with a total pulse fluence F (in J/cm 2). Since we were interested in mucous tissue resurfacing, we modeled the tissue as a water-containing homogeneous media characterized by a single absorption coefficient of k = 1/δ, for the delivered laser wavelength λ. For simplicity, a square-shaped laser pulse with a duration, t in, was assumed. Since the main focus of our study was on laser wavelengths with short penetration depths, the effects of the scattering of the laser light within the tissue were not included. Similarly, it was taken that the laser spot size is much larger than the penetration depth (δ), and therefore, the diffusion of dissipated heat was treated in one dimension using a finite-difference scheme.
The model enabled calculation of the temporal evolution of the superficial tissue temperature during and following laser irradiation for different depths, z, within the tissue. As an example, Fig.  2 shows a simulated temporal temperature profile at the tissue surface for a CO 2 laser radiation ( λ = 10,640 nm) with a pulse duration of t in = 1 ms. For comparison, an experimentally measured temporal temperature profile is also shown, as obtained in a study of the viability of mammalian fibroblast cells exposed to heat shocks under similar conditions ([ 16], Fig.  7). For the monolayer cell culture used in the experiment, we assumed a CO 2 laser penetration depth of δ = 17 μm [ 16]. In all our calculations, we used the physical parameters of the irradiated media as published in [ 25].
As can be seen from Fig. 2, for short laser pulse durations and penetration depths, the temperature pulse shape resembles more a quasi “triangular” shape than a square shape. The heat shock pulse consists of the temperature ramp-up heating phase during which the temperature reaches its maximal value ( T max) and of the temperature ramp-down cooling phase during which the temperature returns back to its initial temperature T 0. The heating phase lasts approximately for the duration of the laser intensity pulse ( t in), while the cooling phase is determined predominantly by the rate of the heat flow away from the heated tissue volume. We shall define the maximal value T max of such a pulse during which the cell damage characterized by Ω = 1 occurs, as the damage threshold temperature T thr.
Since we were interested in the coagulation dynamics for fluences below and above the threshold for ablation, the model also included the microscopic physical model of the micro-explosion process, which combines the thermodynamic behavior of tissue water with the elastic response of the solid tissue components [ 25]. As an example, Fig.  3 presents the dependence of the maximal temperature T max on the delivered laser fluence F for the CO 2 laser wavelength and pulse duration t in = 1 ms.
As shown in Fig. 3, the maximal temperature T max grows approximately linearly with fluence until the ablation temperature T abl for confined tissue boiling is reached at the ablation threshold fluence F abl, above which the ablation of the superficial tissue layers by means of micro-explosions keeps the surface temperature at T abl. The calculated ablation temperature is equal to T abl = 256 °C, in good agreement with other reports [ 25, 28, 29]. The ablation threshold fluence is higher for larger δ and longer t in. On the other hand, T abl depends only on the tissue’s physical properties and is therefore the same for all predominantly water-absorbed lasers, providing that no tissue desiccation occurs during irradiation [ 30].

VHS damage integration method

It is important to note that Eqs. ( 1)–( 5) describe damage characteristics for square-shaped temperature pulses. For long exposure times, approximately square-shaped temperature pulses are relatively easy to achieve. However, this becomes exceedingly more difficult for exposure pulse durations shorter than approximately 1 s, as can be seen from Fig. 2.
A standard approach for calculating the damage caused by a non-square-shaped thermal exposure pulse has been to numerically calculate the integral of Eq. ( 1) over the duration of the pulse, by dividing the pulse into equidistant time segments ∆ t, and by adding the contribution of each temporal segment i to the overall damage using the experimentally measured time-dependent values of temperature ( T i), and by assuming A and E to be constant [ 16, 17]:
$$ {\varOmega}_{\mathrm{stand}}={\sum}_iA\exp \left(-E/R{T}_{\mathrm{i}}\right)\varDelta t $$
(6)
However, as can be concluded from Eqs. ( 3)–( 5), a “triangularly”-shaped pulse cannot be characterized by a fixed set of Arrhenius coefficients. The exposure time to low temperatures present at the base of a heat shock pulse is relatively long, while the exposure time to higher temperatures is increasingly shorter towards the peak of the “triangularly”-shaped temperature pulse. Therefore, the integration over time (Eq. ( 6)) is not adequate for calculating damages under variable heat shock response conditions. For this reason, we introduced an alternative “VHS” integration algorithm that is based on the integration over temperature instead of over time.
In the VHS damage integration method (depicted in Fig.  4), it is assumed that a single-peak temperature ( T max) pulse, consisting of a monotonically increasing heating phase and a monotonically decreasing cooling phase, can be considered as consisting of a set of N =  T max/∆ T square-shaped temperature pulses, with their peak temperatures separated by equidistant temperatures ∆ T. Each of such rectangular pulses ( j) is characterized by the pulse temperature T j, where T j =  T j − 1 + ∆ T, and the exposure time ( t expj) spanning between two identical temperature values ( T j), one belonging to the heating phase and the other to the cooling phase (see Fig. 4). Taking into account that the Arrhenius coefficients A j and E j are not fixed but are functions of t expj, the tissue damage caused by a heat shock pulse can be calculated from
$$ {\varOmega}_{\mathrm{VHS}}={\sum}_j{A}_j\left(\exp \left(-{E}_j/R{T}_j\right)-\exp \left({E}_j/\mathrm{R}{T}_{j-1}\right)\right){t}_{\exp j}. $$
(7)
It should be noted that within the standard single-process Arrhenius model, where coefficients A and E are independent of t exp, the two integration methods, represented by Eqs. ( 6) and ( 7), can be considered equivalent since they yield identical damage integral values, regardless of whether the integration is made over time (Eq. ( 6)) or over temperature (Eq. ( 7)). The only difference is that the VHS integration algorithm is more time-consuming since it requires a numerical determination of t expj for each of the constituting rectangular pulses j. However, within the VHS model, where coefficients A and E are functions of t exp, the integration over time fails, and it is the VHS integration algorithm that is at an advantage since it takes into account that A and E are not constant during a heat shock pulse.

Clinical test

The influence of larger penetration depths and, consequently, of longer thermal exposure times on the damage threshold was preliminarily tested on a case of skin resurfacing. The clinical effect on the dorsal skin located between the thumb and the index finger of one of the authors was observed following a single pulse with 2940 nm Er:YAG laser ( δ ≈ 3 μm) (Dynamis, Fotona d.o.o., Slovenia) or with 1340 nm Nd:YAP laser (Dualis, Fotona d.o.o., Slovenia) ( δ ≈ 400–800 μm; [ 31]), both with the laser spotsize on the skin of approximately 1 mm. The single-pulse fluence was adjusted to be just below the ablation threshold, resulting in the maximal skin surface temperature during irradiation of T max ≈ 250 °C for both laser types. Photographs of the irradiated skin area were taken using an optical microscope immediately and one day after the irradiation. The irradiation procedure used in this test is cleared for use and thus regularly applied to treat patients. Informed consent was obtained from the volunteer, and the procedure was performed according to the Declaration of Helsinki.

Results

Variable heat shock model coefficients

In order to obtain the parameters for the variable heat shock response (Eq. ( 4)), we used threshold temperatures T thr for the measured heat shock temporal profiles T( t), as published by Simanovskii et al. [ 16, 17]. Simanovskii et al. studied the viability of mammalian fibroblast cells exposed to heat shocks generated with a CO 2 laser with laser pulse durations in the range of t in = 0.3–100 ms. An example of the published temporal temperature profile was already shown in Fig. 2 for t in  = 1 ms. The measured threshold temperature for this particular heat shock profile was T thr ≈ 121 °C [ 16].
For longer exposure times, we used the published threshold temperatures from Moritz and Henriques [ 4], assuming square-shaped temperature profiles.
Using the VHS model and the VHS damage integration algorithm (Eq. ( 7)), we calculated damage integrals for the published temperature temporal profiles (Fig. 7 in [ 16] and Fig. 3 in [ 17]), characterized by T max =  T thr. By varying A 1, E 1, A 2, E 2, and p and using the least squares method, we searched for the optimal coupling coefficient p and the Arrhenius coefficients defining the two limiting processes, for which the calculated damage integrals for all temperature profiles deviated the least from Ω VHS = 1. The resulting VHS relation for T crit versus t exp is represented by the VHS model line in Fig.  5. The fitted transition coefficient is equal to p = 0.161 ± 0.02. The short pulse and long pulse Arrhenius lines represent the dependence of the critical temperatures on the exposure time for the long exposure process 1, characterized by A 1 = (4.7 ± 1.4) × 10 89 s −1 and E 1 = (5.67 ± 0.11) × 10 7 J kmol −1, and for the short exposure process 2 characterized by A 2 = (1.45 ± 0.15) × 10 4 s −1 and E 2 = (1.03 ± 0.03) × 10 7 J kmol −1.
To compare the T crit versus t exp relation according to the VHS model, with the published data on the viability of cells [ 1618], we followed a similar procedure as in [ 16]. The “effective exposure time” for the “triangularly”-shaped heat shock pulse was defined as the duration of an imaginary rectangular temperature pulse of a constant temperature T crit, which produces the same amount of damage ( Ω VHS) as calculated for the actually measured “triangularly”-shaped temperature pulse with maximal temperature T max:
$$ {t}_{\mathrm{eff}}={t}_{\mathrm{exp}}\left({T}_{\mathrm{crit}}\right){\varOmega}_{\mathrm{VHS}} $$
(8)
Here, t exp is calculated from Eq. ( 4) and Ω VHS is calculated using Eq. ( 7), taking T crit =  T max. The obtained calculated effective times for the published measured heat shock temperature profiles and corresponding measured critical temperatures are in Fig. 5 depicted by squares [ 16] and triangles [ 17] for short exposures and by circles for long exposures [ 4]. Additionally, although not used for the fit, a published thermal damage data point for the endodontic pathogen Enterococcus faecalis bacteria exposed to a t in = 25 ms laser pulse is also shown (represented by the diamond) [ 18, 32].

VHS model of laser resurfacing

In the following, we modeled the temporal and spatial temperature evolution and the resulting damage integral Ω during non-ablative laser resurfacing of an optically and physically homogeneous water-containing tissue, approximately representing a mucous vaginal or oral tissue.
Figure 6 shows the temperature evolution at the tissue surface as simulated for a case of irradiation with a t in = 100 μs energy pulse for three energy penetration depths within the tissue, approximately representing Er:YAG ( δ = 3.3 μm [ 25], further in the text denoted by δ = 3 μm), CO 2 ( δ = 17 μm), and near IR lasers in the range of 1.2–1.6 μm ( δ ≈ 400 μm) [ 31, 33, 34]. An example of a laser with δ ≈ 400 μm is a 1.47 μm diode laser [ 34]; however, this penetration depth can also be considered to approximately represent tissue resurfacing with radiofrequency (RF) [ 35] or ultrasound [ 36] energy-based devices that are typically characterized by even deeper energy penetration depths. The laser pulse fluence was set to slightly below the threshold value as calculated for each of the three penetration depths.
As can be seen from Fig. 6, the duration of the cooling phase of a heat shock pulse depends strongly on the laser penetration depth. The conductive cooling of the interaction layer is more effective for smaller penetration depths characterized by larger temperature gradients. Consequently, for smaller penetration depths, the duration of the cooling phase is shorter, resulting in shorter effective exposure times and therefore also higher threshold temperatures. Similarly, the duration of the energy pulse ( t in) influences the duration of the heating phase, with shorter energy pulse durations resulting in higher T thr.
The dependence of T thr at the tissue surface on penetration depth and energy pulse duration can be seen from Fig. 7, which shows damage threshold temperatures ( T thr) as calculated using the VHS response model and simulated temporal temperature evolutions for different values of δ and t in.
As can be concluded from Fig. 7, there exists a range of “safe” fluences within which the maximal temperature does not exceed the threshold temperature. This range of safe fluences is defined by the energy device’s penetration depth ( δ) and pulse duration ( t in). As an example, Fig.  8 shows the dependence of T max on laser fluence for t in = 100 μs, and three penetration depths ( δ = 3, 17, and 400 μm), together with corresponding threshold temperatures. The safe fluence range lies below 0.15 F abl for δ = 400 μm (diode laser) and below 0.47 F abl for δ = 17 μm (CO 2 laser). On the other hand, for the Er:YAG laser ( δ = 3.3 μm), the maximal temperature never exceeds the threshold temperature, since T thr >  T abl, and the maximal temperature stops growing once the ablation threshold temperature has been reached.
The damage caused by a heat shock pulse depends on whether the maximal temperature reached during a heat shock pulse is below or above the threshold temperature. The calculated damage Ω VHS as a function of the depth z within the tissue for different laser pulse fluences is for δ = 3 μm (representing Er:YAG) and δ = 17 μm (representing CO 2) depicted in Fig.  9a, b, respectively.
As expected, the tissue damage is much higher for the δ = 17 μm penetration depth, where exposure times are longer. For the shorter penetration depth of δ = 3 μm, the damage never exceeds Ω VHS ≈ 0.8. Therefore, under appropriate energy source conditions characterized by T thr <  T abl, the safe fluence window extends up to and above the ablation threshold fluence, providing extremely safe operating conditions for tissue resurfacing.

Clinical test

Figure 10 shows the clinical effect on human skin following a single pulse with 2940 nm Er:YAG laser or with 1340 nm Nd:YAP laser. In spite of the same maximal temperature, the longer exposure time generated by the Nd:YAP laser resulted in a significantly higher damage to the tissue.

Discussion

It is not clear whether the two processes of the VHS model (Fig. 5) describe the actual situation or whether they represent only a useful tool for calculating the damage integral under different exposure conditions. An extrapolation of the imaginary Arrhenius curve 2 of the short exposure process 2 to longer exposure times reveals that the curve already intersects 37 °C at exposure times longer than approximately 6 ms (see Fig. 5), which is obviously not what is observed in nature. One explanation could be that at lower temperatures the activation energy shifts to higher values [ 16]. However, it is also possible that the observed cellular viability characteristics at short pulse durations represent the primary process of thermal damage, while the data at longer pulse durations represent a combined effect of the primary process together with the slower cellular repair mechanism becoming increasingly more effective at longer exposure times [ 16, 19]. This hypothesis appears to be supported by the observation that exposing cells to pre-conditioning heat shock pulses induces thermo-tolerance [ 11, 27], which could be explained by the cellular repair mechanism taking place during and following a heat shock pulse.
By taking into account the relatively high critical temperatures at extremely short exposure times, the VHS damage response model is potentially relevant for many laser medical procedures. For example, when attempting to damage a thin hair or a thin vessel with short laser pulses corresponding to the short tissue relaxation (TRT) time of these targets, the temperatures and/or exposure times required to achieve their protein denaturation are even higher than what would be expected by taking into account the standard Arrhenius relation [ 8].
When applied to the case of laser resurfacing, the VHS model demonstrates that under appropriate conditions, very intense (i.e., short-duration, high-temperature) heat shock pulses can be safely delivered to the epithelia without causing irreversible tissue damage. Based on this observation, we propose below an additional mechanism of action which may be responsible for the reported clinical regeneration effects of non-ablative Er:YAG resurfacing [ 22, 23, 3760]. This additional mechanism involves indirect triggering of tissue regeneration through intense heat shock to the superficial epithelia, in addition to the slower direct thermal injury to the connective tissues [ 20, 21, 47, 61, 62].
Non-ablative laser rejuvenation procedures typically focus on regenerating connective tissues, such as dermis or lamina propria, which are responsible for holding the skin, vagina, and other organs together. The regeneration mechanism is based on direct thermal injury (“coagulation”) to the connective tissue in order to cause a reactive inflammatory response resulting in the increase of the biosynthetic capacity of fibroblasts and other cells, inducing the reconstruction of an optimal physiological environment, the enhancement of cell activity, hydration, and the synthesis of collagen and elastin [ 63]. When using an energy-based medical device, such as a laser, radiofrequency [ 35], or an ultrasound device [ 36], to create a thermal exposure pulse within the connective tissue, the duration and the shape of the resulting thermal exposure pulse typically do not follow the duration and the shape of the delivered energy. This is because the volume of the heated connective tissue is typically relatively large, and the major mechanism by which this large volume can be cooled down is through the relatively slow diffusion of the deposited heat into the surrounding unheated tissues [ 25]. It is therefore the thermal diffusion rather than the temporal pulse length ( t in) of the delivered energy that sets the lower limit to the achievable duration of the exposure time. Typical cooling times of the connective tissues are on the order of seconds or longer. This limits the treatment temperatures for direct connective tissue regeneration to about 45–70 °C (see Fig. 5).
The technique employed to achieve direct heating of the deeper lying connective tissue using an Er:YAG laser involves delivering laser energy in one or several 0.1–1-s-long “SMOOTH” mode sequences, each consisting of several consecutive sub-ablative sub-millisecond Er:YAG laser pulses [ 20, 47, 61, 62]. Using this technique, the laser-generated heat is effectively “pumped” by means of heat diffusion away from the epithelia, several hundred microns deep into the connective tissue [ 47, 61, 62].
Since the Er:YAG laser wavelength is limited to its very shallow optical penetration depth, it has been hypothesized that instead of having to rely on the SMOOTH mode heat pumping technique, devices with a deeper penetration depth may represent a more suitable means for deep thermal remodeling [ 64]. However, the excellent clinical results obtained with the Er:YAG laser wavelength, with a small number of reported complications, warrant further investigation of the potential mechanisms of action that make this laser so effective not only for ablative but also for non-ablative resurfacing. The Er:YAG laser has been, for example, very successfully used for non-ablative resurfacing of vaginal [ 22, 3861] and oral tissues [ 23]. Histological studies have demonstrated neo-collagenesis and elastogenesis, foci of neo-angiogenesis, reduction of epithelial degeneration and atrophy, and an increase of the fibroblast population [ 3841]. The rejuvenation of the mucous tissue following Er:YAG non-ablative vaginal resurfacing has been shown to alleviate symptoms of atrophy [ 4247], stress urinary incontinence [ 4855], and vaginal relaxation syndrome [ 5661]. Similarly, non-ablative resurfacing of soft palate, uvula, and tonsillary regions has been reported to significantly reduce symptoms of chronic snoring-related sleep disorders [ 23].
It should be noted that it represents a considerable challenge to heat up the deeper lying connective tissue to appropriately high temperatures. This is because in order to reach the fibroblasts, the delivered energy must first traverse the epithelial layer located above the basement membrane. This means that the delivered energy may be predominantly absorbed by the superficial epithelium layers. Accordingly, the maximally allowed temperatures which apply to the epithelial layer limit the temperatures that can be generated within the connective tissue. In many cases, the physician is thus faced with a trade-off between using enough energy for effective therapy, while staying within the thresholds to prevent damage to the superficial tissue. In this regard, delivering laser energy in short laser pulses, and only to the thin superficial layer of epithelia, is an advantage according to the VHS model since it allows much higher epithelial temperatures than what would be considered safe if the energy was delivered over longer times and into a larger tissue volume.
As shown in Fig. 7, the damage threshold temperatures are much higher than the normally assumed safe temperatures of up to 65–70 °C [ 48], providing that the energy penetration depth ( δ) and the duration of energy delivery ( t in) are sufficiently short. The influence of larger penetration depths and, consequently, of longer thermal exposure times on the damage threshold was observed also during skin resurfacing. In spite of the same maximal temperature, the longer exposure time generated by the Nd:YAP laser resulted in a significantly higher damage to the tissue (see Fig.  10). It should be noted, however, that this is just one example which cannot be considered to be statistically significant.
We propose that intense heat shocks that can be safely delivered to the epithelium tissue using energy devices with short penetration depths, with shorter penetration depths allowing higher superficial temperature heat shocks, may represent an additional mechanism of action for the reported clinical effects of Er:YAG laser resurfacing. Our hypothesis is based on the understanding that it is not only fibroblasts but also the superficially located keratinocytes that are involved in the wound healing process. It is known that keratinocytes recruit, stimulate, and coordinate the actions of multiple cell types involved in healing [ 6567]. In particular, keratinocytes and fibroblasts communicate with each other via double paracrine signaling loops, known as cross-talk or dynamic reciprocity, that coordinate their actions to restore normal tissue homeostasis after wounding [ 67]. In response to paracrine signaling from keratinocytes and inflammatory cells, fibroblasts synthesize collagen and promote cross-linking to form an extracellular matrix. We therefore propose an additional, indirect tissue regeneration mechanism, which is complementary to the direct stimulation of fibroblasts and other cells, to respond to wound healing scenarios caused by relatively slow thermal pulsing of the connective tissue. The mechanism is based on stimulating signal transduction processes for transcription factor activation, gene expression, and fibroblast growth, thus leading to new collagen and extracellular matrix formation. A spatially localized, laser-generated supra-physiological level of heat is able to induce a transient heat shock response (HSR), characterized by the production of a family of proteins, termed the heat shock proteins (HSP), which are presumed to initiate temporary changes in cellular metabolism, resulting in the release and production of growth factors and thus in the increase of the rate of cell proliferation [ 27, 68, 69]. In addition, a controlled generation of reactive oxygen species (ROS) at very high local temperatures occurs within the shallow penetration depth of the Er:YAG laser, which was proposed to explain the healing effects exerted by the Er:YAG laser during rejuvenation treatments [ 70, 71]. Namely, low amounts of ROS have been found to stimulate wound healing via increased proliferation of keratinocytes and fibroblasts, which in turn generate collagen [ 7276]. Furthermore, the generation of ROS during resurfacing procedures has been found to be enhanced by the unique 2940 nm Er:YAG laser wavelength, which matches the exact vibrational oxygen-hydrogen (OH) stretch frequency of water, resulting in a resonant splitting of water molecules at high local temperatures [ 71].
Furthermore, for laser wavelengths with extremely short penetration depths, such as the 2940 nm wavelength of the Er:YAG laser, a safety window of laser pulse durations characterized by T abl <  T thr, exists within which the damage threshold temperature cannot be exceeded regardless of the laser pulse fluence delivered to the tissue. This characteristic potentially makes this type of device extremely safe for tissue resurfacing since once the epithelia temperature reaches T abl, the onset of minimally invasive, micron layer-by-layer ablation automatically prevents the epithelium surface temperature from getting heated above T abl <  T thr. Figure 10 demonstrates that the longest penetration depth of an energy-based device for which the safety window exists is about δ ≤ 6 μm. This applies for extremely short energy delivery times ( t in ≤ 10 μs). For more realistic energy delivery times ( t in ≤ 150 μs), the requirement for the penetration depth is δ ≤ 3.5 μm. This is important, for example, when treating body cavities, such as the vagina, where the internal surface may not be regularly shaped, and therefore the delivered fluence and consequently the generated heat may vary from one location to another. Also, the energy source may not always be kept at the optimal distance or optimal angle with regard to the tissue surface, again resulting in non-uniform heat pulse generation. Finally, human error can also occur. In all these cases, the laser ablation mechanism protects the patient from any irreversible injury and keeps the treatment within the safe resurfacing limits.
It should be noted here that our calculation of the VHS model coefficients was based on the available published experimental data for the fibroblast cell culture. Therefore, the results of the model should be considered to describe only the basic qualitative features of the variable heat shock response, with the exact quantitative features depending on the damage response characteristics of a particular type of the affected tissue. Also, in the model, it was assumed that the treated tissue is optically and physically homogeneous, which more closely applies to moist mucous tissues than to skin, where the water content has been found to vary considerably within the first approximately 50 μm of the epidermis [ 77].
It is interesting to note that the VHS model requirements limit the range of energy-based devices that are potential candidates for the proposed hypothetical indirect superficial triggering of tissue regeneration to short pulsed lasers with appropriately short penetration depth within the tissue. Other types of energy-based devices [ 78], such as radiofrequency or ultrasound devices, have too long energy delivery times and extremely deep penetration depths, and are therefore not suitable for epithelial heat shock signaling. The requirement for the penetration depth to be below about 6 μm further narrows the choice of energy devices primarily to lasers with a wavelength positioned close to or preferably at the water absorption peak at 2940 nm. The Er:YAG laser therefore appears to hold a unique position within the group of resurfacing lasers. We believe that this explains the extreme safety of Er:YAG lasers when used for ablative or non-ablative resurfacing.
The proposed superficial signaling mechanism resembles the effects of the micro-needling technique, which aims to not injure keratinocytes but to stimulate them with superficial punctures and without any injury to fibroblasts [ 79, 80]. Similarly to laser resurfacing, the mechanism of action of micro-needling appears to involve not only a direct inflammatory response to the localized “ablation,” but also indirectly induced cell proliferation by electrical signals [ 80]. Since with micro-needling only a relatively small percentage of the skin is being affected, the treatment outcome is expected to be accordingly limited. On the other hand, the Er:YAG laser-induced thermal triggering mechanism can be viewed as non-ablative thermal “needling” (i.e., triggering) of the total treated skin surface, with the action of the spatially sharp needles being replaced by the action of temporarily “sharp” but spatially extended heat shock pulses.

Conclusions

Published critical temperatures over a broad range of thermal exposure times indicate that tissue denaturation under elevated temperatures cannot be adequately described by a single biochemical process with fixed Arrhenius coefficients. In this paper, we propose a different, variable heat shock (VHS) response model that describes the tissue response as a combined effect of two limiting processes defining cell viability at very long and very short thermal exposure times. Based on the VHS model, the activation energy E and the damage rate A are not constant parameters but are functions of the thermal exposure time. In order to be able to calculate damage integrals for non-square-shaped temperature pulses under VHS conditions, a novel numerical algorithm for calculating the damage integral was developed. Instead of integrating the damage over time, the new algorithm is based on the integration of damage over temperature, which enables taking into account that Arrhenius coefficients are not constant during a heat shock pulse.
The proposed VHS model is potentially particularly relevant for understanding laser procedures involving targets with short thermal relaxation times, such as thin superficially heated tissue layers during tissue resurfacing, or thin hair follicles or blood vessels, where the VHS model predicts much higher damage threshold temperatures than what would be expected from the standard single-process Arrhenius model.
Our analysis of tissue resurfacing using the VHS damage model demonstrates that under appropriate conditions, intense heat shocks can be safely generated within the superficial epithelium tissue layer. A mechanism of action for tissue regeneration with Er:YAG lasers involving indirect triggering of tissue regeneration through intense heat shocking of epithelia is proposed. This mechanism of action is in addition to the commonly accepted mechanism of tissue regeneration by means of direct thermal injury to deeper lying connective tissues. Further research is needed to verify this hypothesis.

Compliance with ethical standards

The clinical example is from a study which was approved by the Slovenian national ethics committee (KME 120-365/2017-9).

Conflict of interest

Three of the authors (ML, TP, FB) are currently affiliated also with Fotona d.o.o.

Informed consent

The skin resurfacing was performed on a volunteer who is one of the authors (ML). Informed consent was obtained from the volunteer, and the procedure was performed according to the Declaration of Helsinki.
OpenAccess This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

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