From Abe to MoXy™ and Beyond; Part 3 -- Moses' Math Works January 16 2017
Part 3 is a bit of a departure from my planned sequence for this series. A colleague has graciously permitted me to share a slow motion video that he produced of a generic side fire fiber delivering a single pulse of holmium energy into a beaker of water. Herein I hope to demonstrate that surgical fiber performance can be modeled/predicted, and quite accurately, and that there isn't anything mysterious or magical involved. Sure, some aspects of laser surgery are extremely complex, like laser-tissue interactions, but the tools that science provides do allow us to design devices intelligently. That's my company's motto, after all: Intelligent Designs for Superior Performance.
For new readers, the "Moses Effect" is how we describe the phenomenon, or mechanism, by which laser energy that is strongly absorbed by water, such as a holmium laser pulse, is able to pass through water to ablate tissue. Briefly, the energy front vaporizes a bubble pathway within the water, allowing the remainder of the pulse to pass through the steam bubble with minimal loss. All we lose is the energy required to "part the seas".
The annotated image below is taken from the slo mo video. The side fire fiber bevel tip is outlined in blue and the fiber is firing upward. The approximate beam divergence has been outlined in red. The mushroom cloud at the top is the laser energy/water interaction front: laser vaporized water that is driven outward faster than the rest of the bubble can expand. The rest of the sphere is smooth and represents the expansion front of steam that has already been produced.
The video is loaded with useful information, but you have to play it over and over to see everything. Please pardon the embedded youtube code and all the garbage that comes after the Moses Bubble video; it's all that I could figure out to get this thing to post. Hit the replay button at the bottom left.
First I need to deal with the credits and such...
The video comes from Glenn Yeik, President of Trimedyne (Irvine, CA), makers of the first holmium laser in medicine (OmniPulse™) and some of the most successful side fire fibers, ever.
This side fire fiber is not a commercial device. It is just a simple, pre-Abe design that was made for producing the video. It is a simple TIR bevel based on a 0.22 NA fiber that is housed within a homemade quartz capsule. It does appear to have significant wear -- as evidenced by the pit at the output -- probably due to the hundreds of laser shots prior to this one that were needed for setting the shot up. The scale at the left is millimeters. The laser was a VersaPulse™ with a pulse width of ~350 microseconds and the pulse energy was set to 2 joules.
Now comes the fun part: The Math...
At it's maximum, the roughly spherical bubble has about a 7 millimeters radius. This gives us a volume of ~1.44 cubic centimeters (or milliliters) from 4/3 π r^3 or 0.00144 liters. The volume of the side fire fiber within the sphere is about 0.1 ml, so the gas forming the bubble (steam) occupies about 0.00134 liters.
Note: All of this approximately, about and ~ stuff is related to "significant figures": a subject that a lot of my friends in high school just couldn't grasp. The concept is simple: the precision of any mathematical outcome is limited to the precision of the least precise datum. In this case, that is the 7 mm radius. It's about 7 mm, but it might be 7.25 mm or 6.75 mm. We just don't know, mainly because we don't know the absolute position of the ruler within the experimental setup and we don't know the precision and accuracy of the ruler itself. This is 'ballpark' science at about 7% uncertainty, regardless of the precision of the rest of the data used. Accordingly, the 0.00134 liters is technically incorrect since it implies a precision of 2 to 4 parts in 134. It should be rounded to 0.0013 but I like to carry excess precision until the end result.
Mass of Water Vaporized:
Using the Ideal Gas Law, PV = nRT, and inserting the volume (V) of 0.00134 liters steam, the Ideal Gas Constant (R) at 0.0821 liter-atmospheres/mol-K, a temperature (T) of 373 Kelvin and one atmosphere of pressure (P), we find we have about 0.044 moles (n) of steam in the bubble. Since the molecular weight of water is ~18.02 grams per mole, this steam came from vaporizing about 0.0008 grams of water.
It takes about 4.18 joules of energy to raise one gram of water one degree Kelvin. Assuming that this water was at room temperature, or ~298K (25C or 77F), and knowing that water boils at 373K (100C or 212F), that's a 75K increase. This means it takes about 0.25 joules to heat the water up to 100C, just shy of boiling. The bulk of the energy required to vaporize the water is consumed in the phase change from liquid to gas. This energy, or enthalpy of vaporization, is 2257 joules per gram or 1.78 joules for the 0.0008 grams involved. Add the energy expenses together and we get ~2 joules: that's what the laser was set to put out.
QED: science works.
We can get far more out of this video that just some confirmation that our science teachers weren't lying to us. I've selected a couple of frames to point out some things, but the first take home lesson is simple; the bubble does not take on a conical shape dictated by the fiber divergence. It's a sphere whose volume (or diameter) is dictated by the amount of energy consumed in vaporizing the water. This does not mean we can't compare divergences from different fiber designs using this method. We can. But it is not that a perfectly straightforward problem. We'll need something to "catch" most of the pulse energy that doesn't get hot enough to boil the water itself -- an beam absorber to catch the part of the pulse that does not boil water -- and that absorber will have to be closer to the fiber output than the radius of the Moses bubble in free space water. (We're working on filming this. Keep an eye out for a blog on this in the future.)
At about the bubble maximum (below), we can see that there was a bead of water adhered to the back of the side fire cap because the backscatter is starting to boil that bead. I've circled this feature in the image.
The next image points out evidence of some of the scatter in this generic side fire fiber is caught by the steel tube. A tiny source of turbulence is visible due to different refractive indices of cold and hot water.
Now, going back to the video, watch the beveled fiber tip inside the cap after the bubble collapses: it waggles within the cap bore. This could be very damaging if the laser pulses happened to fall on a harmonic of this 'waggle frequency'. (Of course, we have no idea where within the stainless steel tube the fiber is fixed, if it is fixed at all, so we can't assume that this occurs in surgical side fire fibers from this video alone. Even so, it's interesting and would explain a few things that I've seen in studying used fibers over the years.)
Well, that's it for this impromptu blog. I'll try to post what was to be Part 3 next week, as Part 4, but it has gotten insanely busy in the lab so it may not post until February.
As always, thanks for reading,
Stephen Griffin is @doctorsilica
OmniPulse is a trademark of Trimedyne and VersaPulse is a trademark of Lumenis.
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