The rate of heat flow from a rod of length W L, width d, thermal conductivity and a temper- K ature above the temperature of the tissue is T approximately:

Initial loaded position

Restoring force F=K X0

####### W

= (6) KTd²/L = (6) KTd²/L =

Velocity=0

where denoting the rods ‘flicking’ duration or vapor- t ization time duration, as well as the duration of deliv- ery of thermal energy from the rod to tissue. This implies:

End point of oscillation: Velocity zero; Upward acceleration a=F/M = kX0/M

–X0

Skin surface

t HL/KT. (7) t HL/KT. (7) H vaporiz

Figure 2. Model for analysing the dwelling time of vaporizing rods in tissue.

For ~ 400°C) For ~ 400°C) 650 micron, 400°C, (copper, 2 L T K = °C W/cm and 100 micron we obtain, H =

41/51/70 no ygolonhceT fo etutitsnI enolhtA .ylno yb moc.erachtlaehamrofni esu lanosrep roF morf dedaolnwoD rehT resaL temsoC J

decelerated prior to the backward acceleration, implying: 2Ö(2MH/F). dwelling (2) t =

~ 2 milliseconds.

####### t

These results lead to the following observations: The distal end of length 650 micron of a copper 400°C, rod, which is elevated to a temperature of can provide the necessary energy to vaporize a 100 ~2 micron deep crater in tissue within milliseconds. Shorter time durations are achievable with higher compression or smaller size copper blocks (smaller mass M).

As explained in the section ‘Experimental results’, our design parameters were: 150 g; 100 M H = = micron; KX, spring constant 8 kg/cm; F K = = = loading distance (spring compression) 10 mm. X = = According to Equation (2), this implied dwelling ~1 time milliseconds. Dwelling time duration is pro- ÖH portional to and can be adjusted by varying the initial compression (by varying the distance X). F

- iii) Treatment repetition rate

The treatment repetition rate has been analysed by solving the one dimensional heat Equation (7)

- ii) Thermal parameters

We hereby calculate the thermal parameters of the metallic rods, which can fulfil the stated above prerequisites.

¶²T/¶²X 1/a²¶T/¶t (a²= K/cr), (8) =

for the flow of heat in the treatment rods (of 10 mm 400°C length) with boundary conditions: T on the = 37°C proximal end of the treatment rod and on T = the 650 micron distal section each time rod is in

The energy needed to vaporize a crater with, for E example, a square shape of width and a depth is: d H d2H, (3) E H = vaporiz vaporiz where is the latent vaporization energy of 1 H vaporiz cm3 J/cm3) of tissue (approximately 3000 (6). The thermal energy E, which is stored in a distal length of the vaporizing metallic rod and may be L available for vaporizing tissue, is given by:

contact with tissue for a duration of 1 millisecond.

We assume that during that period of time, rod distal end is emptied from its thermal energy (heat has flown to tissue and vaporized a crater), and we use Equation (8) to find out how fast the rod distal end is recharged with heat for the next treatment. Figure 3 presents the solution to Equation (8) and shows that a repetition rate as high as 1 Hz is attainable with the ‘ThermiXel’ technology for an unlimited number of treatments.

= (4) = (4)

####### E

where where heat capacity, vaporizing rod material C = = (~400°C). density, rod temperature T = ~E Based on the first pre-requisite, namely E > vaporiz and equations (3) and (4):

- iv) Residual heat

L H/(CrT). (5) L H/(CrT). (5) > vaporiz ~ °C; In the case of a copper rod, 0.4 J/g density: C g/cm3, r ~ 9 implying that for a vaporization depth 100 micron. H =

In similarity to CO2 laser treatments, the heat accu- ~50–150 mulated in the micron width coagulated 100°C) zone (initially at which surrounds the vapor- ized craters, diffuses to surrounding tissue and ele- vates its temperature. By chilling the skin to a 10°C temperature of for a short time duration of ~0.5 ~0.5–1 seconds (depth of mm) with the protec- tive plate before each treatment pulse, we increase the number of epidermal cells between the craters

####### L

> micron. > micron.

Namely, the vaporizing energy flows into the skin from a distance of 650 micron in the rod.