In Search of Optimal Laser Settings for Lithotripsy by Numerical Response Surfaces of Ablation and Retropulsion

Even though ureteroscopic laser lithotripsy (URSL) has become the preferred treatment option for urolithiasis due to shorter operation time and a better stone-free rate, the optimum laser pulse settings for URSL with the shortest operative times remain unknown. In this chapter, two sets of design of experiments (DOE) were conducted with response surface methodology: 1) the quantitative responses of calculus ablation and retropulsion in terms of the pulse energy, pulse width, and the number of pulses of a prototype Chromium (Cr3+), Thulium (Tm3+), Holmium (Ho3+) triple doped yttrium aluminum garnet (CTH:YAG) laser system. The ablation or retropulsion is inversely proportional to the pulse width, and the pulse width has a higher impact coefficient for the ablation than for the retropulsion. The quadratic fit of the response surface for the volume of ablation has a nonlinear relationship with the pulse width and number of pulses. 2) the laser setting optimization of laser lithotripsy of a commercially available CTH: YAG laser system. The experimental setup is based on a benchtop model first introduced by Sroka’s group. Comparing to frequency, the laser pulse energy or peak power has a higher impact coefficient to stone retropulsion as compared to stone ablation in CTH: YAG laser lithotripsy. The most efficient way to curtail stone retropulsion during laser lithotripsy is to lower the laser pulse peak power.


Introduction
Urolithiasis, which is hard tissue (stone) formation in the urinary tract due to supersaturated body fluids, has risen steadily in recent decades. The leading causes of stone formation are the reduction of urine volume (or water intake), an increased calcium oxalate/calcium phosphate secretion, urine pH alteration, or urinary tract infections (urease forming bacteria) [1][2][3][4]. The prevalence in western countries is estimated at 10%-15%, and the recurrence rate is averaging up to 50% [5][6][7]. And according to Charles D. Scales [8], the prevalence of kidney stones nearly doubled in about 17 years from ~1995 to 2012. The prevalence of urolithiasis has been rising internationally over recent decades because of population growth, predicted obesity During laser-calculus interaction, the urinary calculus is subject to retropulsion forces caused by the combined effects of ablated particle ejection, interstitial water vaporization, and bubble expansion/collapse [39][40][41]. And an asymmetric collapse of the bubble near a solid boundary can generate a water jet in the time scale of milliseconds [30]. Therefore, because of the recoil momentum, the calculus is moved away from the end of the laser fiber. The calculus motion prolongs the procedure time because of the burdensome procedure needed to reorient the laser fiber to the new calculus locality. Earlier retropulsion studies quantified calculus retropulsion distance by altering laser pulse energy, pulse frequency, and fiber core size [42][43][44]. Retropulsion boosted with the laser pulse energy and the laser fiber core size. Moreover, Charles D. Scales et al. reported that a longer pulse width reduced calculus retropulsion distance during a procedure without diminishing ablation efficiency significantly [45].
Although laser lithotripsy is now the preferred treatment option for urolithiasis because it is capable of fragmenting calculus of all known composition, including hard calcium oxalate monohydrate, brushite, and cystine calculus [22,24,25,29], and the rising prevalence of calculus disease has led to similarly increasing efforts to optimize ureteroscopic treatment [43,[45][46][47][48][49][50][51][52], the operative time for the stone procedure can be well above the one hour mark. According to Levi A. Deters et al. [53], URSL management of renal stones and ureteral stones were markedly different, with a significant increase in operative time (60% more) for renal stones and a significant lower stone-free rate (27% lower). And of the 213 cases, the average operative time for the renal group (98 cases) is 112 min and range up to 245 min, and the average operative time for the ureteral group (115 cases) is 70 min and range up to 185 min.
The response surface methodology (RSM) is a powerful statistical tool that can generate the numerical relationship between some key performance variables (responses) and device control parameters (control inputs). Although the model is only an approximation most of the time because of limited knowledge of the process, the RSM plus design of experiments (DOE) can produce analytical models (equations) that can depict 1) the relative impact of the control inputs on the responses by comparing their coefficients in the coded equations; 2) optimization of the responses with proper control inputs.
In this chapter, two sets of DOE experiments were conducted with response surface methodology: 1) the quantitative responses of calculus ablation and retropulsion in terms of the pulse energy, pulse width, and the number of pulses of a prototype CTH: YAG laser system. This step is to understand the dominant laser parameters that control the lithotripsy outcome, so that preferred laser settings can be derived for the next generation of laser lithotripter; 2) the laser setting optimization of laser lithotripsy of a commercially available CTH: YAG laser system. This experiment is to identify a series of laser settings for relatively efficient laser lithotripsy in terms of laser pulse energy and peak power.

Experimental method and setup
2.1 The quantitative responses of calculus ablation and retropulsion in terms of the pulse energy, pulse width, and the number of pulses of a prototype CTH:

YAG laser system
In this study, the key components of the setup of the experimental materials are listed in Table 1.
A prototype CTH:YAG laser had pulse energy from 0.2 J to 3.0 J with variable pulse width from 150 μs to 1000 μs at 2.13 μm. This range of pulse duration is Response Surface Methodology in Engineering Science known to generate a photothermal effect to fragment the calculus [51]. Each data point is the average of 10 sample measurements. Figure 1 is the pictures of the test setup, (a) ablation test setup, and (b) retropulsion test setup. In the ablation test setup (a) submerged in the distilled water, the fiber was held vertically by a clamp with its tip in contact with the calculus phantom underneath the fiber inside a holder. The stone was held fixed during the ablation study.
The laser ablation crater volume in the phantom due to the laser pulse and calculus interaction was measured by a digital microscope (VHX-900F, Keyence, Elmwood Park, NJ, USA). In the retropulsion test setup (b), the fiber was held horizontally, pointing to an underwater pendulum phantom cube with a dimension of 10 × 10 × 10 mm3. The pendulum length was ~200 mm, and the phantom was held by 2 strings with a separation of ~10 mm in a clear plastic basket. The retropulsion motion of the calculus phantom was recorded and analyzed by a high-speed camera. Figure 2 is a screenshot of DOE by Design-Expert®10. There are three categories of the laser parameter settings: energy, number of pulses, and electrical pump pulse widths (not the optical output pulse width). The ten-pulses range was selected since the typical retropulsion of a 10 × 10 × 10 mm3 will reach its maximum amplitude after ~1 s of 10 Hz 1 J pulse train from the fiber tip [52]. There are 5 × 3 × 3 = 45 data points with the combination of all the laser parameters.

The laser setting optimization of laser lithotripsy of a commercially available CTH:YAG laser system
It is challenging to characterizing the URSL performance (ablation and retropulsion) in one setup that can mimic the clinical situation, especially measuring retropulsion [55][56][57][58][59][60][61]. In this study, in vitro investigations of Ho:YAG laser-induced stone ablation and retropulsion were performed with a benchtop model first introduced by Sroka's group [55,60]. It is a test that can be performed in a highly reproducible manner using a hands-free setup and measuring the effects of multiple pulses which are mimicking the clinical situation. The advantage of this setup has two folds: 1) No human factor, hands-free, independent repetitive experiments; 2) Providing measurement results for both ablation rate and retropulsion speed. Although the stone moves during the test, which means the distance between the fiber tip and the stone is not a constant, which will report a lower ablation rate, it is still an efficient way to generate meaningful data in terms of ablation and retropulsion for comparing different laser modes. Table 2 is a description of the list of the key components of the setup. The setup, an acrylic cylinder with a drill hole mimicking the ureter ending in a conical base, is illustrated in Figure 3. The diameter of the drill hole can be adapted to the clinical situation (e.g., ureter diameter) or stone size. The stone phantom is a 5 mm cubic shape Bego stone with a composition of 15:3 [62]. The setup is in an upright position filled with the saline at a designated flow speed. The optical fiber is attached through a borehole at the base of the acrylic cylinder. Therefore, laser energy can be delivered to the stone phantom to produce vertical displacement. The gravity and the viscosity of the water are the steady resistances to this motion.
The ablation is quantified by the stone phantom mass deficit after the laser stone interaction by a scale with a resolution of +/− 0.0001 g (Entris 224-1S Sartorius Lab Instruments GmbH & Co. KG, Goettingen, Germany).  Response Surface Methodology in Engineering Science 6 The retropulsion is quantified by the vertical displacement velocity of the stone during the laser stone interaction. A high-speed camera, Sony RX100 IV (1000 fps), oriented perpendicular to the upright motion and aimed to the middle of the artificial ureter, registers the event for ~7 seconds. The video subsequently is analyzed in MATLAB, and a representative stone sample vertical displacement graph vs. video frame is illustrated in Figure 3 (B). Initial data assessment incorporates background rectification and color tracking algorithm, recognition of the   center of weight of the traced stone image in each frame and tracing the center of weight position as a function of time. Afterwards, each rising wing can be utilized to obtain the ascending vertical speed. The 1st Derivative of rising flanks displays the mean velocity of the stone = / (x-displacement, t-time), and the velocity of rising flanks is proportional to the applied momentum = * v (m-stone mass, v-stone velocity). The experiment is designed by Design-Expert® with randomized optimal (custom), two replicate points, and two lack-of-fit points. Figure 4 is a few screenshots of the DOE of laser pulse energy: 0.2, 0.4, 0.6, 0.8, 1.2, 1.5 J and frequency: 5, 10, 15, 20, 30, 40 Hz. A sample size of 14 is used for each data point, and each sample was applied with 15 seconds long laser dose.

The quantitative responses of calculus ablation and retropulsion in terms
of the pulse energy, pulse width, and the number of pulses of a prototype CTH:YAG laser system

Retropulsion amplitude data
The retropulsion videos taken by a high-speed camera at 10 k FPS were analyzed by a MATLAB program for the pendulum swing amplitude. Figure 5(a) is some sample curves of the retropulsion movement; each data point is the average of 10 measurements.    (1) Where A is the amplitude of retropulsion in mm, n is the pulse number, ε is the pulse energy in J, and τ is the pulse width in μs.

Volume of ablation data
The volume of the hole by laser ablation was quantified by a digital microscope. A representative picture is in Figure 7.

Volume of ablation response surface
According to the response surface information from the above section, the Design-Expert® -10 app can produce a response surface and the analytical equation.
Where V is the ablation volume in mm 3 , n is the pulse number, ε is the pulse energy in J, and τ is the pulse width in μs. Figure 9 is the pictures of the response surface of ablation volume under the quadratic fit with pulse width and the number of pulses at the pulse energy status of (a) 1 J; (b) 2 J; (c) 3 J. The analytical equation of the response surface of ablation volume, involving the polynomial terms of two factors interactions, is illustrated in Eq. (3). The ANOVA shows an insignificant lack of fit, acceptable agreement of the Predicted (0.9900) and Adjusted (0.9999) R-Squares, and acceptable precision (466.6, > 4.0).
Ln V 1.16 0.94n 3.46 -0.021 0.0031n 0.00048n 0.0014 -0.078n -0.77 0.0000093 Where V is the ablation volume in mm 3 , n is the pulse number, ε is the pulse energy in J, and τ is the pulse width in μs. Figure 10 is the ablation and retropulsion in percentages by 10 pulses of the 1000 μs pulses versus those of 333 μs. The variation of the volume of between long and short pulse is comparatively larger at 1 J and 2 J level contrasting to retropulsion. Namely, ablation declines more swiftly than retropulsion when expanding pulse width.

Response surface in terms of laser pulse energy
A P-100 -Ablation rate, R P-100 -Retropulsion velocity, A-Frequency, B-Energy From the coded equation, we can see the impact of the laser pulse energy is 1.4 times that of the frequency on the ablation rate, while for retropulsion velocity, the impact of the laser pulse energy is 5.8 times that of the frequency. This indicates the laser pulse energy setting has a vital impact on both ablation rate and retropulsion velocity.

Response surface in terms of laser pulse peak power
The laser pulse peak power is another way of evaluating the laser damage to the stone [63]. The peak power value is defined by the laser pulse energy over the full pulse width (full width of pulse at ~10% of max amplitude). The ANOVA shows an insignificant lack of fit, acceptable agreement of the Predicted and Adjusted R-Squares, and acceptable precision (> 4.0).   A P-100 is the Ablation rate, R P-100 is the Retropulsion speed, A is the Frequency, B is the Peak power, and C is the Pulse width.
From the Eqs. 8 and 9, we can see the peak power has roughly the same influence as the frequency on the ablation rate; and for retropulsion speed, the peak power's influence is 13 folds that of the frequency. Namely, the peak power parameter is crucial to retropulsion speed.
The actual analytical equation of ablation and retropulsion by laser pulse peak power is:

The quantitative responses of calculus ablation and retropulsion in terms of the pulse energy, pulse width, and the number of pulses of a prototype CTH:YAG laser system
In the coded formulas of the response surface (1) and (2), the pulse energy is the dominant control input factor for both the responses of retropulsion and ablation (1.42 and 1.11); while the control input pulse width has more than an order of magnitude less influence on the responses of ablation and retropulsion (−0.0083 versus −0.0021). And the two-factor terms have even lesser influence (a few times to an order of magnitude) than the first-order terms. The pulse number term seems to have some nonlinear effects between long and short pulses at pulse numbers ~7-8 from Figure 9. This effect could be due to the vapor bubble behavior of [47]. As it is shown in Figure 15(b) since the vapor bubble of the long laser pulse will have a much-elongated shape bubble which can be divided into two small bubbles which will collapse sequentially with the 2nd bubble collapses further away from the fiber tip as compared to the bubble of a short laser pulse. Therefore, the long laser pulse can make a deeper crater. This effect will be enhanced at higher pulse energy, and furthermore, since both fiber and calculus were fixed, the depth of the hole max out after ~7-8 pulses.

The laser setting optimization of laser lithotripsy of a commercially available CTH:YAG laser system
For the response of ablation rate, the coded formulas of the response surface reveal that the control input laser pulse energy is 1.4 times as impactful as that of the frequency, and the laser pulse peak power has the same impact as the frequency; while for the response of retropulsion, the control input laser pulse energy is 5.8 times as impactful as that of the frequency, and laser pulse peak power has 13 times  as impactful as the frequency. The laser pulse peak power is the dominant control input factor for the response of stone retropulsion during laser lithotripsy.
As for the optimal lithotripsy laser dosimetry (setting), there are conflict interests to deliver more energy per time (more power or fluence) and achieve faster lithotripsy but at the cost of more retropulsion and larger fragments. As concluded by Sea J et al. in Ref [47], the optimal lithotripsy laser setting depends on the individual case condition (calculus type, size, location, etc.) and the desired outcome. The response surfaces are generated by analysis of variance (ANOVA) of the tested data points, and a ranked list of the optimized laser settings can be generated by the criteria the user selected. If the least retropulsion is the desired, the most effectual method to curtail stone retropulsion during laser lithotripsy is to decrease the peak power (which has the maximum influential coefficient in the coded response surface equations). Dongyul C et al. investigated the ablation thresholds of stone sample by peak power density [63], which presents a recommendation of the lowest peak power for Bego calculus phantom ablation.

Conclusions
In this chapter, the application of RSM were conducted by two sets of DOE experiments: 1) with a prototype CTH:YAG laser system, the RSM reveals that the dominant control input laser parameters that influence the responses of lithotripsy outcome: the ablation or retropulsion is Inversely proportional to the pulse width, and the pulse width has a higher impact coefficient to the ablation than that to the retropulsion. The quadratic fit of the response surface for the volume of ablation has a nonlinear relationship with the pulse width and number of the pulse. 2) the laser setting optimization of laser lithotripsy of a commercially available CTH:YAG laser system: a series of laser settings for relatively efficient laser lithotripsy (maximize the ablation rate while minimizing the retropulsion as well as to improve the discharge of fragments via the urinary tract) in terms of control input laser pulse energy and peak power. Comparing to the control input frequency, the laser pulse energy or peak power has a higher impact coefficient to the response of stone retropulsion as compared to the response of stone ablation in Ho:YAG laser lithotripsy. The most efficient way to curtail stone retropulsion during laser lithotripsy is to lower the laser pulse peak power.
More detailed investigation of the optimal conditions for the ablation of other kinds of calculus samples and the fiber size/burn back effects will be conducted as a future study.