Lasers in Surgery and Medicine 7512-519 (1987)

Energy Requirements for Osteotomy of Femora and Tibiae With a Moving

CW CO2 Laser Suleyman Biyikli, PhD, and Michael F. Modest, PhD

Department of Mechanical Engineering, University of Southern California, Los Angeles

This paper describes the laser cutting and the amount of laser energy needed to remove a unit mass of compact or cancellous human cadaveric bones (“heat-of- removal”) by using a COz laser. Data are collected under different operating conditions, such as laser power, scanning speed, and lens focusing for fresh and fixed human bones from male and female femora and tibiae samples with ages varying between 28 and 73 years old. The aim of the present experiments was to demonstrate the feasibility of laser osteotomy, to find the energy requirements for given groove depths or bone removal rates, and to shed some light on optimum conditions for laser osteotomy. Only cadaveric bones were used in this study, since the present aim did not include the investigation of heating rates and the extent and effect of thermal necrosis adjacent to the cut. In vivo properties may be somewhat different from those of cadaveric material. While blood circulation within the living bone may contribute to the laser cutting characteristics, it cannot be addressed here. Experiments showed that very deep cuts are difficult to achieve with a CO2 laser, as at high-power/low-scan-speed the groove becomes rather wide, with unacceptable thermal damage adjacent to the cut, while multiple passes do not easily attain large depths. There was no significant difference for the laser heat-of-removal for different age groups and for male and female samples. The laser heat-of-removal was found to be higher for compact bone than for cancellous bone samples. Comparison of cross-sections of the cuts with an existing model gave good agreement.

Key words: laser osteotomy, bone cutting, heat of removal, evaporation

INTRODUCTION

During the last few years the use of lasers has become more and more important in all aspects of every- day life as well as in scientific research. The number of investigations using the laser as an orthopedic surgical tool has also been increasing. The investigations have addressed bone drilling [Clayman et al, 1978; Allen and Adrian, 1981; Tauber et al, 19791 as well as cutting [Small et al, 1979; Mills et al, 1985, 19861. Clayman et a1 [1978] studied defects produced in ten rabbit femora using both continuous-wave (CW, 2-45 W) and rapidly super-pulsed (SP, < 20 W) stationary laser beams. Both types incised the bone readily and produced defects less than 2 mm in diameter. There was little damage to the bone more than three or four cell layers from the charred zone. Allen and Adrian [1981] did a similar experiment on a group of 40 rats, using a 30-W CW laser. Both experiments were successful but resulted in retarded healing of the laser-drilled holes. Tauber et a1 [1979]

compared osteotomies by gigli saw and CW laser (40 W) in the femora of 48 rabbits. Laser osteotomy was achieved by drilling a sequence of small holes, followed by break- ing the bone.

Actual bone cutting was carried out by Small et a1 [1979], who studied the effects of CW (10 W) and SP lasers (6 W) as compared to bone burs. They osteoto- mized the tibia of nine rabbits and concluded that the bur method healed faster initially due to minimal production of necrotic bone. In vivo experiments by Mills et a1 [ 1985, 19861 compared the healing rates of conventional and laser surgery using a total of 145 rats. In a first set of experiments [Mills et al, 19851 a COz laser was oper- ated in CW mode with a power output of 17 W and a

Accepted for publication October 9, 1987.

Address reprint requests to Suleyman Biyikli, Department of Mechan- ical Engineering, University of Southern California, Los Angeles, CA 90089-1453.

0 1987 Alan R. Liss, Inc.

CW CO2 Laser Energy Required for Osteotomy 513

Ver t ico I stepping motor

1.2 KW CO, loser ZnSe lense

Somple holder

- . Moving stoge

Hor izontol Computerized stoge stepping motors motion controller 9 Fig. 1. Experimental setup for laser bone cutting.

scanning speed of 0.5 cm/s, producing a 1.5-mm-deep incision in the ridge of the left tibia of an anesthesized rat. Conventional osteotomies 1.5 mm deep were pro- duced by a Dremel handsaw in the right tibia. In a second set of experiments [Mills et al, 19861 they used a high- power 100-W laser with a scanning speed of 4.5 cm/s to again achieve cuts of 1.5-mm depth, also using a nitrogen gas jet to reduce charring. In both experiments animals were killed at different time intervals. They concluded from the results of x-rays, histology, and breaking- strength tests that the healing rates of conventional and laser osteotomy were comparable. While it is clear that optimal laser surgery could overcome a number of prob- lems associated with conventional surgery, such as ther- mal necrosis, cracks, excessive bleeding, and heterotopi ossification, and that lasers could perform cutting of complex contours at remote locations, to date no work seems to have been done to optimize laser parameters, such as laser power, lens focal length, etc. Recently, a mathematical model has been developed by Modest and Abakians [ 1986a,b] and Biyikli and Modest [ 19871 that allows for a prior optimization of the laser cutting pro- cess by considering the influence of parameters such as laser power, scanning speed, focal length of lens, and focal point position. The model requires knowledge of thermal properties such as density, specific heat, thermal conductivity, and thermal diffusivity . These properties have been measured for human bones by Biyikli et al [1986]. Also needed for the model is the amount of energy required to evaporate bone material. Since bone is an anisotropic material consisting mainly of collagen fibers, mineral crystals resembling hydroxyapatite, small quantities of mucopolysaccharides, lipids, carbonate, magnesium, sodium, fluorine, citrate, and inorganic compounds [Zipkin, 19731, one may assume the laser evaporation process to take place as follows: laser energy is absorbed by solid bone material as well as bone fluid slightly below the surface; this causes internal evapora- tion, pressure buildup and microexplosive removal of still-solid bone material. Thus, for anisotropic materials such as human bone, the heat-of-evaporation used in a cutting model must be an effective value obtained from actual laser osteotomy experiments. The purpose of the

present paper is twofold: to provide some insight into the laser energy requirements for laser osteotomy and to study the effects of laser osteotomy parameters (lens focal length and position, scanning speed), and to provide data of an effective heat-of-evaporation to be used in the theoretical model for the optimization of laser surgery.

MATERIALS AND METHODS

All laser experiments were performed by using the experimental setup shown in Figure 1. The laser beam is generated with a Photon Sources C02 laser with an av- erage maximum power output of 1.2 kW at CW mode. The beam is directed with copper mirrors to the working stage and the beam is focused onto the surface of the bone samples by using ZnSe lenses with focal lengths of 2.5 and 13 inches. The C02 laser generates light at a 10.6-pm wavelength invisible to the human eye. A low- power HeNe laser generating visible light is aligned with the CO2 laser beam in order to follow the path of the C02 laser beam visually. The bone samples were located on top of a stage by using a specially designed sample holder. Stage velocity was controlled by a computer.

The compact and cancellous bone samples were obtained along the length of human cadaveric femora and tibiae. By using a band saw samples were cut to about 2 X 4 cm2 surface size for easy manipulation under the laser beam. The bone samples were positioned under the laser such that a flat bone surface was exposed to the laser in order to reduce variation of lens focus with respect to the moving surface. The samples were covered with an asbestos plate which had a slit approximately 1 cm wide. This allowed the scanning laser to reach steady state (avoiding the power spike which usually occurs after turn-on) before the beam hit the sample. Fresh bone samples were selected from both male and female speci- mens and from age groups varying between 28 and 73 years old. The fresh samples were taken from frozen cadavers which were thawed on the day of the experi- ment. Roentgenograms for some of the samples were taken in order to insure that none of the bones had osteoporosis.

After cutting the bone samples with the laser, they were sliced perpendicular to the laser cuts by a diamond saw to get a picture of the cross section. The cross- sectional views were photographed and magnified 50 times and were then used to calculate the cross-section areas with a planimeter. The amount of laser energy required to evaporate and remove a unit mass of bone material (termed here “heat-of-removal”) was obtained from

h, = PIpuA (1)

where h, is heat-of-removal, P is the laser power, u is scanning speed, A is the cross-sectional area of the cuts,

514 Biyikli and Modest

Fig. 2. Laser-cut cross sections for compact and cancellous bones with stage velocity 2.67 cm/s. ~ 5 0 . a: Compact bone, focal point on surface, 180 W. b: Cancellous bone, focal point on the surface, 180 W. c: Compact bone, focal point on the surface, 360 W. d: Cancellous bone, focal point on the surface, 360 W.

T- Fig. 3 . Effect of change in the focal point on laser cuts of human compact bone at 400 W and 2.0 cmls. X20. a: Focal point is 1.5 mm below surface. b: Focal point is on the surface of the bone. c: Focal point is 1.5 mm above the surface.

CW COz Laser Energy Required for Osteotomy 515

1 NO. O f

passes 2 3 4 5

Fig. 4. Effect of multiple passes on laser cuts of human compact bone without changing the focal position at 4.0 cm/s and 200 W laser power. X 2 0 .

p is the bone density which is obtained from reference [Biyikli et al, 19861, and puA is the removed mass per unit time. Since total power is used in equation (1) h, includes sensible heat (heating bone from room temper- ature to its evaporation point), latent heat (heat required for partial evaporation and microexplosive removal of liquid and solid remnants), and heat losses (convection to outside and conduction into the bone, both expected to be very small).

RESULTS AND DISCUSSION

Figure 2 shows some sample pictures of laser cuts on compact and cancellous bones at a constant stage velocity. As expected, increasing the laser power in- creases the sizes of the laser cuts for both compact and cancellous bones. At the same power level grooves in cancellous bone are always deeper than in compact bone, apparently because the higher fluid content and weaker solid matrix causes microexplosive removal at lower pressure. It is also seen that grooves in compact bone are more pointed, while the ones in cancellous bones have constant widths over much of the groove depth. Figure 3 shows the effect of the change in the focal length on the laser cuts of human compact bone. Three different cross- sectional cuts are shown, ie, one where the laser is properly focused and the other two with the laser focus far above or below the surface. As shown in the figure, when the laser is focused properly the laser cut is nar-

rower and deeper compared to the poorly focused cases. The curvature in Figure 3c cannot be easily explained but is probably due to some inhomogeneity in the bone leading to extensive beam guiding. Figure 4 shows the effect of multiple passes on laser cuts of compact bone. For all the passes the laser focus is kept on the surface of the bone samples. As can be seen from these pictures, wih increasing number of passes, the depths of the cuts do not increase proportionally. This is due to the increas- ing surface area struck by the laser beam causing more of the laser energy to dissipate as thermal conduction into the bones and by defocusing of the beam at greater depths away from the focal point. External views of laser cuts on a human compact femur are shown in Figure 5. These figures illustrate the effect of change in lens focal point position when a laser moves across the femur with a fixed focal position as indicated in the figure. At 200 W CW approximately ten passes are necessary with a 2.5- inch lens to cut through a human femur, resulting in a 1- mm-wide cut (as opposed to 0.25 mm for a single sweep).

In order to predict the depth and shape of a laser cut by using an analytical model [Biyikli and Modest, 19871 it is necesary to know the total energy required to remove a unit mass of bone material. This amount of energy consists of sensible heat (raising the temperature to the boiling point) and the heat of evaporation. How- ever, since bone is a complicated combination of mate- rials, no single boiling temperature exists [Lim and Liboff, 19721. Instead, the laser-bone interaction appears

516

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Biyikli and Modest

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Fig. 5 . External view of laser cuts on a human compact bone after different number of laser passes with 200 W and 4.0 cm/s without changing the laser focus. Also visible is the effect of change in the focal position over the bone surface. X6.5.

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Fig. 6. Laser heat of removal for compact and cancellous bones as a function of stage velocity at constant laser power P = 480 W for human tibia. human tibia.

Fig. 7. Laser heat-of-removal for compact and cancellous bones as a function of laser power at constant stage speed U = 2.67 cm/s for

CW COz Laser Energy Required for Osteotomy 517

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P/u =480 J/cm + : f 13" Lense o : f = 2.5" Lense

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Fig. 8. Laser heat-of-removal for compact and cancellous bones as a function of stage velocity at constant P/U = 180 J/cm for human tibia.

to be as follows: the bone at and near the surface under- goes a rapid rise in temperature; when the boiling point of low-boiling-temperature constituents (water, fats) is reached these substances will evaporate below the surface while the temperature continues to rise. While some of the vapor will escape through cracks, other vapor will build up internal pressure until microexplosion occurs- ie, part of the bone will be blown away in the form of tiny solid and liquid particles. Thus, the heat required to remove a certain amount of bone by a laser will be less than the sensible heat and heat of evaporation of all its constituents, making the direct measurement of these quantities unnecessary and useless. Therefore, we have measured the effective heat-of-removal of fresh human cadaveric femora and tibiae, ie, the actual energy re- quired to remove bone material by sensible heat, partial evaporation, and microexplosions. For simplicity we as- sume that all energy goes into the heat-of-removal; ie, the heat of removal includes sensible heat, heat of evap- oration, as well as small losses by conduction into un- evaporated bone. Unfortunately, unlike the heat of evap- oration for the constituents, the eflective heat of removal is not a material property, but rather depends also on cutting conditions: laser focal length and focal position, laser power, and scanning speed.

Figure 6 shows the laser heat of removal for com- pact and cancellous bones as a function of stage velocity at a constant laser power of 480 W for human tibiae. The data were obtained by using lenses whose focal lengths were 13 and 2.5 inches. There was no significant differ- ence for the removal rate obtained by using these very different focal-length lenses. The effective heat of re- moval for compact bone is considerably higher and ac-

Human Femora (Fresh) P = 4 8 0 W 2.5" Lense 0

\

E

2 40 s -

u- 0

'0 W 20 301 I I I I

-0 1.0 200 3.0 4.0 Stage Veloc i ty , u, cm/sec

Fig. 9. Laser heat-of-removal for compact and cancellous bones as a function of stage velocity at constant laser power P = 480 W for human femora.

companied by more scatter. Apparently the small pores in compact bones can withstand much higher pressures before microexplosions occur, so that more energy is used to heat, weaken, and partially evaporate other con- stituents. The datum scatter seems to indicate that pores outgas very irregularly through cracks and that tempera- tures and pressures at which microexplosions occur vary substantially from pore to pore. The heat of removal decreases somewhat with increased speed, due to lesser conduction losses. Lines drawn in Figure 6 (as well as Figures 7-11) are eye-approximate means of the datum points to show trends; they do not represent a theory or statistical analysis.

Figure 7 shows laser heat of removal for compact and cancellous bones as a function of laser power at a constant stage velocity for fresh human tibiae. The data for compact bone shows increasing heat of removal with increasing laser power. An increase is expected because, for higher power, a deeper groove is formed with a larger area, resulting in higher conduction losses. However, this is not corroborated by the data for cancellous bone. Indeed, checking the theoretical model below indicates that conduction losses are nearly negligible. This is due to microexplosive removal occuring at higher tempera- tures and pressures for a high-power beam, since such a beam penetrates deeper into the bone where it is very difficult for evaporated bone fluid to escape. Figure 8 shows laser heat of removal for compact and cancellous bones as a function of stage velocity at a constant power/ velocity ratio for human tibiae (resulting in constant total energy deposit per unit surface area). The data show

518 Biyikli and Modest

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somewhat unexpected behavior: for low speed/low power there is lots of time to diffuse heat into surrounding bone, which should result in little evaporation and a high heat of removal. As speed and power are gradually increased, conduction losses-and heat of removal-should gradu- ally decrease. Instead, heat-of-removal values increase with stage velocity to a maximum before decreasing. Again, apparently, the deeper-penetrating beam at higher power offsets much of the lesser conduction losses.

Figures 9 and 10 show laser heat-of-removal data for fresh human femora. Because femur bone material is generally more compact than tibia, the laser heat-of- removal data for femora are always higher than for tibiae but otherwise very similar in every respect. Figure 11 shows laser heat-of-removal for fixed human femora which have a relatively low water content as compared to fresh femora. Consequently, the heat-of-removal for fixed femora is even higher than for fresh femora because of decreasing water content on heat-of-removal (through decreasing material removal by microexplosions).

The depths and shapes of the experimental laser groove cross sections are compared with predictions from a mathematical model [Biyikli and Modest, 19871. The comparison is shown in Figure 12 for different laser powers at a constant stage velocity. The heat-transfer model incorporates a number of simplifying assump- tions-namely, constant properties, isotropic and homo- geneous medium, negligible beam channeling, and one- step evaporation (this would rule out microexplosive re- moval which can be modeled, however, if an effective heat of evaporation is employed as has been measured here). Fixed compact bone will be the closest among the bone samples to satisfy these requirements, and has been

0 0 E 30

0 0

0 8 0 h

Fig. 11. Laser heat-of-removal for compact and cancellous bones as a function of laser power at constant stage speed for fixed human femora.

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N e = 0 . 0 5 4 N k = 0.00007

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Exper iments u = 2.67 cm/sec + P = 1 8 0 W A P = 3 6 0 W 0 P = 6 0 0 W

30.0

0.0 iD 2.0 3.0 4 Y/RO

Fig. 12. fixed human femora with model predictions.

Comparison of experimental laser groove cross sections for

selected for comparison with the model predictions. Thermal properties were obtained from the reference [Biyikli et al, 19861 to be used in the model. There are no available data for evaporation temperature of the bone, and it is assumed here that bone evaporates when temper- ature is increased to 600°C. Since the thermal conductiv-

CW C02 Laser Energy Required for Osteotomy 519

ity of bone is very small, changing the evaporation temperature has little effect on the sizes and shapes of the grooves. For example, lowering the assumed evapo- ration temperature to 300°C will change the maximum groove depth by 0.46%. Employing the evaporation tem- perature, the sensible heat is subtracted from the heat-of- removal to calculate the heat of evaporation to be used as input data for the model. As can be seen in Figure 12, the agreement between the experimental points and the model predictions is very good.

CONCLUSIONS

The feasibility and power requirements for osteot- omy of human bones with a CW C02 laser have been investigated. The results may be summarized as follows: 1. C02 lasers can be used to cut human bones effec- tively. This is done partly by evaporating the bone ma- terial and partly by microexplosive removal of liquid and solid material. 2. Multiple passes do not readily result in large groove depths. 3. The laser energy required to cut compact bones is higher and less accurately predictable than for cancel- lous bones, apparently due to lesser microexplosive solid removal at higher pressures. 4. Depths and shapes of laser cuts can be predicted by a mathematical model prior to surgery.

ACKNOWLEDGMENTS

Support for this work under National Institute for Arthritis, Diabetes, Digestive and Kidney Diseases, grant No. AM30240, is gratefully acknowledged.

The laser facilities used in this research were made available by the University of Southern California Center

for Laser Studies. Diamond saw cutting and photography of the laser treated samples were carried out by the Bone Physiology Laboratory under B.G. Mills, MD, at the University of Southern California Orthopaedic Hospital. The support is gratefully acknowledged.

REFERENCES

Allen GW, Adrian JC: Effects of carbon dioxide laser radiation on bone, an initial report. Milit Med 146:120-123, 1981.

Biyikli S, Modest MF: Effect of beam focusing on evaporative cutting with a CW laser. Presented at the ASME/JSME Joint Meeting, Hawaii, March 1987.

Biyikli S, Modest MF, Tarr R: Measurements of thermal properties for human femora. J Biomed Mater Res 20: 1335-1345, 1986.

Clayman L, Fuller T, Beckman H: Healing of continuous wave and rapid superpulsed, carbon dioxide, laser-induced bone defects. J Oral Surg 36:932-937, 1978.

Lim JJ, Liboff AR: Therrnogravimetric analysis of dentin. J Dent Res

Mills BG, Biyikli S, Modest MF: Healing of laser vs. conventional osteotomy. Int Assoc Dent Res Annu Meet, Las Vegas, March 1985.

Mills BG, Biyikli S, Modest MF: Laser osteotomy in the rat vs increased power and nitrogen assist. Int Assoc Dent Res Annu Meet, New Orleans, March 1986.

Modest MF, Abakians H: Heat conduction in a moving semi-infinite solid subjected to pulsed laser irradiation. J Heat Transfer

Modest MF, Abakians H: Evaporative cutting of a semi-infinite body with a moving CW laser: J Heat Transfer 108:602-607, 1986.

Small IA, Osborn TP, Fuller T, Hussain M, Kobernick S : Observa- tions of carbon dioxide laser and bone bur in the osteotomy of the rabbit tibia. J Oral Surg 37: 159-166, 1979.

Tauber C, Farine I, Horoszowski H, Gassner S: Fracture healing in rabbits after osteotomy using C02 laser. Acta Orthop Scand

51:509-514, 1972.

108:597-601, 1986.

50:385-390, 1979. Zipkin I: “Biological Miseratization.” NY: J. Wiley & Sons, 1973.