Upon absorption of laser energy, microparticles can convert the absorbed energy into temperature rises, pressure waves, and vaporization. All of these will affect the surrounding material as well as damaging the absorbing particle. The pressure signals display especially complex behavior because of two competing time scales: the duration of the laser pulse and the characteristic mechanical oscillation time of the absorber. As the pulse duration is lengthened, the pressure signals become increasingly more complicated. Using power spectra and Lyapunov exponents, we show that for pulse durations greater than the characteristic oscillation time, the pressure signals are chaotic. The chaotic nature of the pressure signal presents potentially dangerous uncertainty when using longer laser pulses in biomedical and engineering applications.
Resonance effects can occur upon laser absorption by micro and nanoparticles when a train of pulses is used. The pressure generated by the train of pulses may be significantly different than the pressure generated by a single pulse with the same total energy. For pulsed lasers with a gap duration between pulses that is an integer multiple of the characteristic oscillation time of the absorber, constructive interference occurs and the pressure is increased. For pulsed lasers with a gap duration between pulses that is an half integer multiple of the characteristic oscillation time of the absorber, destructive interference occurs and the pressure is significantly decreased. We present numerical computations showing the manifestation of this effect in gold particles with a radius of 100 nm. The resonance effects have implications for damage thresholds and therapeutic applications
of laser radiation.
We present initial results showing chaotic behavior in the pressure signals generated by laser absorption by a microparticle. Specifically, the system of a melanosome immersed in water is investigated. We describe how the system manifests chaos, and the implications for causing damage to the surrounding material. We also find that a characteristic acoustic time of the absorber, the time it takes a sound wave to traverse the absorber, known as the stress confinement time, defines an important time scale for laser pulse duration. For pulse durations shorter than the stress confinement time, the pressure response is periodic, while for pulse durations greater than the stress confinement time, chaotic pressure transients are observed.
Damage by pulsed lasers to the retina or other tissues containing strongly absorbing particles may occur through biophysical mechanisms other than simple heating. Shockwaves and bubbles have been observed experimentally, and depending on pulse duration, may be the cause of retinal damage at threshold fluence levels. We perform detailed calculations on the shockwave and bubble generation expected from pulsed lasers. For a variety of different laser pulse durations and fluences, we tabulate the expected strength of the shockwave and size of the bubble that will be generated. We also explain how these results will change for absorbing particles with different physical properties such as absorption coefficient, bulk modulus, or thermal expansion coefficient. This enables the assessment of biological danger, and possible medical benefits, for lasers of a wide range of pulse durations and energies, incident on tissues with absorbing particles with a variety of thermomechanical characteristics.
The concept of confinement is that if energy deposition into a system occurs during durations shorter than a confinement time, the response of the system depends only on the total energy deposited and not on the deposition time. For stress confinement, the relevant response is the pressure that is produced. We have shown previously that for laser absorption by a spherical absorber, stress confinement is not valid at the core of the absorber and the tensile stresses continue to grow as the pulse duration shrinks well below any characteristic response time of the system. We have now calculated the pressure response in the cellular medium outside the absorber. We find that for a variety of energies, stress confinement is valid. We find that the characteristic confinement time agrees well with that expected for pressure transmission across the absorber. We show that even though the peak pressure that is produced varies slowly as a function of pulse duration, there is a sudden onset of shock wave production when the pulse duration is shortened below the confinement time. Since damage results from pressure gradients, the sudden onset of shock waves implies a sharp increase in the potential for damage.
We study the response of a spherical absorber immersed in aqueous media. We investigate temporal resonant absorption and present initial numerical calculations of the same topic. Initial results indicate that, because of the dynamical characteristic of the system, the response after a sequence of energy pulses depends nonlinearly on the time between pulses. Specifically, the response exhibits resonant type behavior around a critical time, the time it would take a sound wave to traverse the absorber.
Theoretical work has been previously reported in which the full thermo-mechanical response of an absorber to an incident laser pulse has been calculated. For a laser pulse of any energy or duration, the temperature rise, explosive bubble formation, and shock wave generation in the surrounding medium can be predicted. This work allows the assessment of danger to biological or opto-electronic systems from laser pulses. The work also allows the thermo-mechanical properties of micro and nano particle absorbers, such as the thermal expansion coefficient and bulk modulus, to be calculated from measurements of the pressure waves generated in the medium. Previous results assumed a temporal profile for the laser pulse that was a square wave with infinitely fast rise and fall times. We report on new calculations that use a more realistic gaussian-like temporal profile for the laser pulse. We compare how the resulting thermo-mechanical responses are altered compared to the idealized temporal square wave laser pulse.
We have developed a detailed theoretical model that allows for the prediction of the shockwave strength and bubble size that are expected to result in the retina as a result of a laser pulse of any pulse duration or energy. The results of the calculations for the shockwave and bubble size depend on the absorption coefficient and unknown thermo-mechanical properties of the absorbing melanosomes. We discuss how the shock strength and bubble size depend on melanosome parameters such as absorption coefficient, thermal coefficient of expansion and bulk modulus. We also describe experiments that could be performed to measure these coefficients in spite of the difficulty presented by the small size of the melanosomes.
The generation of shock waves and bubbles has been experimentally observed due to absorption of sub-nanosecond laser pulses by melanosomes, which are found in retinal pigment epithelium cells. Both the shock waves and bubbles may be the cause of retinal damage at threshold fluence levels. The theoretical modeling of shock wave parameters such as amplitude, and bubble size, is a complicated problem due to the non-linearity of the phenomena. We have used two different approaches for treating pressure variations in water: the Tait Equation and a full Equation Of State (EOS). The Tait Equation has the advantage of being developed specifically to model pressure variations in water and is therefore simpler, quicker computationally, and allows the liquid to sustain negative pressures. Its disadvantage is that it does not allow for a change of phase, which prevents modeling of bubbles and leads to non-physical behavior such as the sustaining of ridiculously large negative pressures. The full EOS treatment includes more of the true thermodynamic behavior, such as phase changes that produce bubbles and avoids the generation of large negative pressures. Its disadvantage is that the usual stable equilibrium EOS allows for no negative pressures at all, since tensile stress is unstable with respect to a transition to the vapor phase. In addition, the EOS treatment requires longer computational times. In this paper, we compare shock wave generation for various laser pulses using the two different mathematical approaches and determine the laser pulse regime for which the simpler Tait Equation can be used with confidence. We also present results of our full EOS treatment in which both shock waves and bubbles are simultaneously modeled.
Laser energy absorbed in cells can affect the cellular materials through a variety of physical mechanisms. For pulses longer than a microsecond in duration, damage at threshold levels is due to thermal effects. However, for supra-threshold pulses, or for threshold levels at shorter pulse durations, other physical mechanisms may be the source of damage. The most likely mechanisms are the generation of large pressures, and the creation of bubbles. This is especially true for heavily pigmented cells, such as the retinal pigment epithelium, where large energy densities can be attained in the strongly absorbing pigments. We describe how the generation of large pressures depends on laser pulse duration and energy, as well as the properties of the absorbing pigment. Extremely large negative pressures can be generated in the core or the absorber, possibly resulting in the explosion of the absorbing pigment within the cell. We also discuss the conditions for which damaging bubbles are likely to be formed.
We have made a detailed theoretical investigation of the pressure generated in melanosomes upon absorption of laser energy. Our model treats the melanosome as a homogeneous absorber surrounded by a transparent water medium. The mechanical impedance mismatch between the absorbing melanosome and the surrounding medium is taken into account and has important ramifications. We have calculated the pressure profiles for pulses of microsecond duration down to picosecond duration. We show that the concept of stress confinement is not valid for this system. Though pressure amplitudes generated at the surface do reach a limit as the pulse duration is shortened below a nanosecond, no such pressure confinement occurs at the center of the absorber. As the pulse duration is shortened below a nanosecond, the tensile pressure at the center continues to rise without limit. This implies that explosive fracturing of the melanosome can occur due to the large tensile stresses, and accomplishing this fracturing requires smaller fluences as the pulse duration is shortened. We present quantitative results exhibiting how the core's tensile stress increases as the pulse duration is shortened.
As part of a research program to understand and model eye damage produced by exposure to cw and pulsed lasers, the U.S. Air Force has created a granular model of laser retinal damage. The Thompson granular model simulates absorption of light by melanosomes distributed in the retinal pigmented epithelium, melanosome heating, and subsequent photothermal damage from bulk tissue heating. Various biological input parameters required for the model, such as the density, size, spatial distribution, and absorption coefficient of melanosomes, are not well known, creating uncertainty in the results. This problem is being addressed both experimentally, through measurements of biological parameters for various species, and theoretically, through analysis of parameter sensitivity in the model. In the current study, the parameter sensitivity was analyzed using a technique known as 'design of experiments,' which allows statistical estimation of the relative importance of independent experimental variables. A matrix of 20 cases has been analyzed, using 7 input parameters as independent variables. Cases have been confined to the long pulse regime (greater than or equal to 10 microseconds), where photothermal damage is dominant. Results were assessed using both temperature rise and Arrhenius damage integral values. Corneal fluence was found to be the most important physical parameter and melanosome absorption the most important biological parameter.
We have computationally modeled the generation of high pressures in melanosomes resulting from the absorption of sub- nanosecond laser pulses. The melanosome is treated as a solid sphere characterized by a bulk modulus, specific heat, coefficient of thermal expansion, and a uniform absorption coefficient. Using a series of partial differential equations to represent how the absorbed laser energy is converted to thermal and mechanical energy, we can calculate expected pressures resulting from laser pulses of any duration or fluence. We find that for the same fluence, the maximum pressure generated increases as the pulse duration decreases. For sub-nanosecond pulses, kilobar pressures can be generated inside the melanosome. We examine how the pressures that are generated depend on pulse characteristics and melanosome properties.
Recent theoretical work has shown that damage to retinal pigment epithelium cells from nanosecond laser pulses is likely to occur by bubble formation at lower fluences than damage caused by thermal heating. The bubbles form around the strongly absorbing melanosomes and the bubbles remain within the cell in which they form. This suggests that damage due to bubbles will remain localized in cells containing the strong absorbing material, whereas thermal damage tends to affect surrounding cells. This same approach may be useful in treating pigmented skin which also contains strong absorbers. By killing cells with bubbles produced by nanosecond laser pulses, damage to surrounding healthy tissue may be minimized. Laser pulse lengths, fluence levels, and potential applications for treating melanoma and congenital nevi will be discussed.
For sub-nanosecond pulses incident on the retina, damage mechanisms arising from high pressure within the melanosome absorber become important. This paper investigates the formation of stress waves generated in tissue as a result of laser exposure. This will eventually lead to a determination of the manner in which thermomechanical waves cause damage in cellular material such as the retinal pigment epithelium. The first step in understanding how stress waves are generated within melanosomes requires determination of how energy `channels' into separate mechanisms. The present lack of an equation of state for the melanosome/cellular system limits our ability to determine how the absorbed energy is divided between thermal and mechanical processes. We will use the fundamental definition of the experimental Gruneisen parameter as an approach to get the necessary equation of state. This will lead to melanosome temperature and internal pressure at the end of an ultrashort pulse.
Bubble formation in the retinal pigment epithelium by submicrosecond laser pulses may be a source of laser induced retinal damage. Heat conduction away from absorbing melanin granules requires timescales on the order of microseconds. For pulses of shorter duration, all energy absorbed is effectively absorbed as a (delta) -function in time, and energy concentration may be high enough to cause vaporization of the surrounding medium. This occurs at lower fluences than required for thermal denaturation of a significant volume of cellular material. The adiabatic nature of the absorption and subsequent expansion is used to develop expressions for the calculation of maximum bubble size as a function of laser intensity and melanosome properties such as radius and absorption coefficients. We describe the analysis that went into the development of the bubble size expression and also present the results for representative calculations of maximum bubble radius. We find that our expression leads to a threshold for the formation of bubbles in the retinal pigment epithelium that is close to the ED50 experimentally measured for laser induced retinal damage.
The threshold radiant exposure [Hth (J/cm2)] at the retina which produces a minimal visible lesion (MVL) has been investigated as a function of the laser pulse duration (tp). By considering the optical absorption coefficient of the melanosomal interior, (mu) a.melanosome, one can calculate the threshold deposited energy, Qth equals (mu) a.melanosomeHth (J/cm3), for the MVL. The tp-dependence of Qth is adequately explained for tp > 16 microsecond(s) by the thermal relaxation of heated melanosomes in the retinal pigmented epithelium (RPE). However, at very short pulses (< 100 ps), there is an apparent on the order of 10-fold drop in the Qth which is possibly due to the onset of a photomechanical mechanism of damage. Thermoelastic expansion of the laser-heated melanin granules (approximately 10 nm in size) within the 1.5-micrometers melanosome is induced by laser pulses less than 50 ps in duration. This expansion occurs faster than the induced pressure can dissipate from the granules at the speed of sound. The stress relaxation time of a 10-nm melanin granule is about 7 ps. As the accumulated pressure attempts to propagate out of the granule as a pressure wave, the pressure wave suffers reflectance at the granule surface boundary due to the difference in acoustic impedances of the granule and surrounding intramelanosomal matrix. About 12% of the acoustic energy is estimated to be reflected back into the granule as a negative (tensile) pressure wave. This negative stress is hypothesized to elicit cavitation within the melanin granule. This mechanism of intragranule cavitation is a working hypothesis for the mechanism of the MVL in the sub- 50-ps regime. An experimental test of feasibility was conducted using a Q-switched laser and a liver/saline interface. A negative reflectance of about -22% was demonstrated at the liver/saline interface, indicating the ease with which negative stress can be generated at interfaces with mismatched acoustic impedances.
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