All Holmium Laser Fibers are the Same, Right? Part 8: Moses and the Stones

In contrast to what you may have been told by sales people, energy lost to boiling water in holmium laser surgery matters, particularly in stone dusting, but even in fragmentation the losses are significant. Naysayers point to the ‘vanishingly small’ amount of water, or ‘mere nanoliters’, boiled as evidence that the effect is trivial. Such ploys exploit our inherent bias that all things “nano” must be exceedingly small, but in this choice of volumetric nomenclature, things can be extremely misleading at 1000-fold; one milliliter of water weighs one gram, not one milligram.

A couple of years ago I started reading and hearing reports like this one in the Journal of Urology: DOI: http://dx.doi.org/10.1016/j.juro.2014.02.780. As summarized in the red data rows in Table 1, 3 watts took almost twice as long to affect disintegration at lower pulse energy. Clearly the authors of such reports are not considering the loss of energy that is consumed in boiling irrigant.

A conclusion of this study was, “Stone dusting settings were inferior in the renal pelvis as they required longer fragmentation time compared to conventional settings.” I am personally no fan of dusting, but if the authors were aware of the content of this blog post, perhaps different “stone dusting settings” would be used, rather than dismissing the technique outright. Of course I’d be remiss in my duties if I failed to point out  the broader range of power settings available to urologists using ProFlex™ LLF, e.g. our true 200 micron fiber that permits 100% flexible ureteroscope deflection and is safe at 30 watts in, full deflection.

Allow me to add a new column to these data and tabulate them as Table 2; trust me, it’ll help us to understand the paper’s results.

Doesn’t that clear things up a bit?

After adjusting for predicted energy losses due to boiling water, the 0.6 joule setting is actually significantly higher than the 0.2 joule setting at the same laser output power.  In fact, the ratios of adjusted powers predict the results very well: 2.6/1.45 = 1.5 and 616/389 = 1.6. I need to do more work to figure out the 5.9 watt versus 2.6 watt results, but accounting for Moses bubble losses brings the results into much better focus.

This is the type of revelation available through Gedankenexperiment and it clearly has value. Of course, the proof will be in the pudding; the pudding being laboratory verification of the mathematical prediction. By the way, even though the math is but high school geometry and science, I’ll append my work for any skeptics who wish to check it. But for now, let’s get back to the other stones associated with Moses.

Holmium lasers’ output wavelengths (and Thulium lasers and some diode lasers) are strongly absorbed by water. In fact that’s the whole idea behind using these wavelengths: the most prevalent constituent of tissue is water. Stones absorb holmium and thulium laser energy strongly as well, in part because they also can contain a lot of water within a matrix of absorbing organic and/or inorganic salts. The obvious downside is that we're working within an aqueous environment that absorbs even more efficiently than our targets.

The same sales people who diminish the volumes of water boiled in surgery usually start with arguments that the fiber is in such close contact with the stone that there is no water involved. If this were true we’d see no water boiling but we do see bubbles. The fact is that it is simply impossible to keep a fiber in intimate contact with a target -- particularly any hard target – after you start blowing holes in that target. There will be gaps and any gap between the fiber and target harbors water and that water will absorb the laser energy and boil.

It’s estimated that the effective distance from the fiber to the stone in fragmentation is between 0.1 mm to 0.3 mm, depending on retropulsion issues. It can be less and can be more, but 0.2 mm average seems a reasonable place to base some calculations and that’s what I chose to do in approximating the actual power out the fiber in Table 3. (If one were to ignore the other losses involved, one could theoretically calculate the average fiber to phantom separation that existed in the experiments based upon the data provided.) In dusting, fiber to target separation is usually larger at about double; more on the order of 0.4 mm (at least for the cases I’ve watched, and the math works so I tend to cleave to this value and that's what I used to adjust the power in Table 2).

Some of my readers are likely familiar with the term “Moses bubble”, but for those who are not…

Because water absorbs holmium wavelengths so well, it boils along the beam path, “parting the seas” between fiber and target with a steam bubble. The steam bubble itself absorbs a little energy, but for all intents and purposes, the Moses bubble offers a clear path between the fiber and target. For obvious reasons, this effect is called the 'Moses Effect' (Isner, et al., in “Mechanism of laser ablation in an absorbing fluid field”, Lasers Surg. Med., 8(1988): 543–554.) We’ve extended this nomenclature to include the bubble, for consistency.

The energy absorbed in forming the Moses bubble is lost in each and every pulse (except for the second pulse in ‘double pulse mode’ for Trimedyne lasers, according to the manufacturer) and this loss can be a substantial portion of the total pulse energy, particularly for large core fibers or at low pulse energies (Table 3). Large fibers used at dusting settings suffer doubly.

The Moses bubble loss calculated for a typical “200 μm fiber”, as used in the paper cited above, comes to 0.082 joule per pulse for a non-IQ, true 200 micron fiber or 0.11 joule per pulse using most fibers calling themselves 200 micron (using 0.4 mm as the average separation). This loss is independent of pulse energy or repetition rate setting. I adjusted the ‘laser power’ to give the ‘actual fiber power’ by subtracting 0.082 joules from the pulse energy setting, for all settings, and multiplied the new pulse power by the repetition rate. In reality, the actual power is a bit lower, but we’ll not delve into those issues here; most of them have been discussed in terms of design issues within prior chapters, although they’ve not necessarily been quantified.

Geometry is not a controversial subject: larger subtended angles produce larger areas or volumes (Figure 2). Most holmium fibers are made from 0.22 NA fiber (where ‘NA’ is the numerical aperture – a quantity defining a fiber’s acceptance and divergence cones: the half angle of acceptance or divergence, in air, is the arcsine of the NA). Some smaller core fibers are made with higher NAs – up to 0.29 – as part of strategies for capturing more of the laser output within a small core. As with most small fiber design schemes, there is a consequence of using higher NA fiber that some designers may not fully appreciate: higher NA means higher divergence at the output and larger Moses bubble loss.

Table 3 is a handy tabulation of losses calculated for standard fiber designs, by fiber size, at nominal fragmenting and dusting distances.

Figure 2 is a graphic depicting the reduced losses for ProFlex™ LLF with the Pulsar™ HPC laser connector. IQ’s patented Pulsar HPC (High Power Connector) is the only holmium fiber connector that reduces Moses bubble losses by quasi-collimating the laser output within the fiber (see last installment of this blog for more information, or go to porflexfibers.com or drop me an e-line or give me an old-fashioned telephone call, if you want a personalized explanation).

When using ProFlex LLF holmium fibers, lithotripsy times are reduced in several ways. Only the highest quality optical fibers are used in making ProFlex, for lower intrinsic transmission losses. Pulsar HPC technology safely couples more of the laser output into the fiber so there is more energy available at the fiber and ProFlex LLF fibers may also be used at higher powers than standard holmium fibers. Finally, a smaller fraction of this higher power is wasted in boiling water; more of your laser’s output reaches the stone to do work.

Figure 2: Comparison of ProFlex LLF divergence with mode filled divergence

Next time in “All Holmium Laser Fibers are the Same, Right?” Part 9: Summing Up

• P.S. If you are an academic urological surgeon, IQ seeks disinterested third parties willing to perform experiments that are designed to prove or disprove the results of our Gedankenexperiments. While we prefer to minimize direct financial assistance for such activities (in preservation of impartiality), we can reimburse some costs, some of our equipment may available for loan and experimental design assistance is always available. In some cases it may be preferable to co-author papers. Contact me at steve@innovaquartz.com if interested.

Appendix: The Math

The red conical frustums in Figure 2 (above) depict the volume of space occupied by the laser output from the fiber face to a plane at about a half millimeter away. (A conical frustum is a cone with the pointy end lobbed off.) If the volume occupied by the red laser output is filled with water, and the laser light is highly absorbed by water as is holmium or thulium laser light, that water will block the light from reaching the target unless there is sufficient energy in the output frustum to boil the water away, producing a relatively clear path to the tissue.

In high school we learned about how much energy was required to heat things -- called specific heat capacity -- and that this is different depending state of matter a thing was, e.g. ice, water, steam. The specific heat for water is 4.187 kJ/KgK (or 4.187 Joules per gram for each Kelvin degree of temperature rise). We also learned that it typically took a lot more energy to change a state of matter – called enthalpy or latent heat – and that the amounts vary from material to material and which matter state change was involved, e.g. the enthalpy for vaporization (or condensation) of water is 2257 kJ/kg (2257 J/g).

From the volume of the water that interacts with the laser, we can therefore calculate the energy that is required to for the Moses bubble. To calculate that volume, we need to do a bit of geometry.

The fibers depicted in Figure 2 are chosen to illustrate two things simultaneously: the effect of using a false 200 fiber versus a true 200 fiber and the effect of reducing the divergence in the output of a fiber with the IQ Pulsar™ HPC connector. I’ll deal with these effects separately then combine them for the finale.

Figure 3: Area and volume equations for a conical frustum

Referring to Figure 1 (far above), the diameter of the base of the frustum is that measurement between the two vertical arrows: a function of the divergence (12.7°). We’ll assume equivalent divergence for both fibers, at first, and explain why the situation is actually worse that this suggests after. Most holmium fibers are 0.22 NA, meaning the maximum angle of emission is the arcsine of 0.22, in air (or steam). Divergence is significantly lower in water due to water’s higher refractive index, but this actually does not matter in holmium and thulium lasers because the Moses bubble always forms and, even if it does form in the frustum described at the lower divergence, first, once formed the divergence increases to include the balance of the maximum divergence. In short, while you may think you are operating in water, the fiber knows it’s actually steam. (This is another trick sale professionals will employ in effort to diminish the reality of the losses their fibers actually experience.)

The arcsine of 0.22 is 12.7 (degrees) so we can draw a triangle to get to the diameter through some simple relations. The diameter at half a millimeter distance is the fiber core diameter plus 2X in Figure 1. Assuming almost a half millimeter distance (0.04 cm for convenience in conversion to mass through density), from geometry we know that the side of a triangle opposite the angle, divided by the adjacent side, is the tangent of the angle so tan 12.7 = X/0.04 and X = 0.009. Where the fiber core diameter is 0.02 cm (200 micron), the diameter at a half millimeter distance is 0.02 + 2 x 0.009 = 0.038 cm (380 microns). Using the formula for the volume of the conical frustum then gives us the volume:

(π/3) x 0.04cm [(0.038cm/2)² + (0.02cm /2) ² + (0.038cm/2) x (0.02cm)/2] = 0.000027 cm³

Recalling that one cc (cm³) of water weighs one gram, excepting for small variances, means the weight of the water boiled is 0.000027 grams. This may not seem like very much water at just over 27 micrograms, but remember, we’re boiling this weight with every pulse and it takes a lot of energy to boil water for your afternoon tea….

Starting at 37°C and raising the water temperature to the boiling point (100°C) is a 63 °C (63 K) rise that requires 4.187 joules for every gram of water or, in this case a paltry 0.0072 joule. The phase change (boiling) requires about ten-fold as much energy; at 2257 joules per gram this is 0.062 joule. The total energy lost is therefore 0.069 J per pulse for a true 200 micron fiber at full divergence (mode filled). That’s a substantial amount, particularly under dusting conditions where pulse energies are low, i.e.  over a third of a 0.2 joule pulse that is lost to boiling water.

A false 200 fiber (273 micron core) is worse worse at 0.11 joule, and while this does not seem like too much of a difference, so far this comparison has ignored the quasi-collimation in IQ’s patented Pulsar™ HPC and beam shaping of the Smooth Passage™ output tip. As depicted in Figure 2, IQ’s Proflex™ fibers output diverges far less than a standard fiber, working out to be about 8 degrees (including the focal waist) instead of 12.7 degrees. Working through the math for the 8 degree divergence yields a spot diameter of just 0.0312 cm for a weight of water vaporized of 0.00002 g and the energy loss per pulse is reduced to 0.053 joule. The bottom line is that Moses bubble losses for the ProFlex 200 are half those of others’ “200 micron” fibers.

Moses bubble losses at about a half millimeter separation rise to levels that are likely far higher than you might suspect for larger core fibers: use the table I’ve provided above to avoid situations where too little energy reaches your target.

Next time in “All Holmium Laser Fibers are the Same, Right?” Part 9: Summing Up