Solution of the linear bio-heat transfer equation

Nonlinear derating of high-intensity focused ultrasound beams using Gaussian modal sums

A method is introduced for using measurements made in water of the nonlinear acoustic pressure field produced by a high-intensity focused ultrasound transducer to compute the acoustic pressure and temperature rise in a tissue medium. The acoustic pressure harmonics generated by nonlinear propagation are represented as a sum of modes having a Gaussian functional dependence in the radial direction. While the method is derived in the context of Gaussian beams, final results are applicable to general transducer profiles. The focal acoustic pressure is obtained by solving an evolution equation in the axial variable. The nonlinear term in the evolution equation for tissue is modeled using modal amplitudes measured in water and suitably reduced using a combination of "source derating" (experiments in water performed at a lower source acoustic pressure than in tissue) and "endpoint derating" (amplitudes reduced at the target location). Numerical experiments showed that, with proper combinations of source derating and endpoint derating, direct simulations of acoustic pressure and temperature in tissue could be reproduced by derating within 5% error. Advantages of the derating approach presented include applicability over a wide range of gains, ease of computation (a single numerical quadrature is required), and readily obtained temperature estimates from the water measurements.

Improving image quality of diagnostic ultrasound by using the safe use time model with the dynamic safety factor and the effect of the exposure time on the image quality

Resolution and penetration are primary criteria for image quality of diagnostic ultrasound. In theory (and usually in practice), the maximum depth of imaging in a tissue increases as power (pressure) is increased. Alternatively, at a particular effective penetration, an increased power may be used to allow a higher ultrasound frequency for higher resolution and tissue contrast. Recently, Karagoz and Kartal proposed a safety parameter for thermal bioeffects of diagnostic ultrasound; that is, SUT (safe use time). The SUT model is constructed to determine how long one piece of tissue can be insonated safely according to a threshold exposure. Also, Karagoz and Kartal suggested that an increase in acoustic intensity beyond the current US Food and Drug Administration (FDA) limit of intensity can be theoretically possible by using SUT model while staying within the safe limit. The present study was motivated particularly by the goals of higher resolution and/or deeper penetration by using SUT model. The results presented here suggest that the safe use of higher exposure levels than currently allowed by the FDA may be possible for obtaining substantial improvements in penetration depth and/or resolution. Also, the study reveals that image quality can be functionally related to exposure time in addition to acoustic energy and frequency.

Preliminary ex vivo feasibility study on targeted cell surgery by high intensity focused ultrasound (HIFU)

High intensity focused ultrasound (HIFU) has become a new noninvasive surgical modality in medicine. A portion of tissue seated inside a patient's body may experience coagulative necrosis after a few seconds of insonification by high intensity focused ultrasound (US) generated by an extracorporeal focusing US transducer. The region of tissue affected by coagulative necrosis (CN) usually has an ellipsoidal shape when the thermal effect due to US absorption plays the dominant role. Its long and short axes are parallel and perpendicular to the US propagation direction respectively. It was shown by numerical computations using a nonlinear Gaussian beams model to describe the sound field in a focal zone and ex vivo experiments that the dimension of the short and long axes of the tissue which experiences CN can be as small as 50μm and 250μm respectively after one second exposure of US pulse (the spatial and pulse average acoustic power is on the order of tens of Watts and the local acoustic spatial and temporal pulse averaged intensity is on the order of 3×10(4)W/cm(2)) generated by a 1.6MHz HIFU transducer of 12cm diameter and 11cm geometric focal length (f-number=0.92). The concept of thermal dose of cumulative equivalent minutes was used to describe the possible tissue coagulative necrosis generated by HIFU. The numbers of cells which suffered CN were estimated to be on the order of 40. This result suggests that HIFU is able to interact with tens of cells at/near its focal zone while keeping the neighboring cells minimally affected, and thus the targeted cell surgery may be achievable.

A feasibility study of temperature rise measurement in a tissue phantom as an alternative way for characterization of the therapeutic high intensity focused ultrasonic field

The feasibility that temperature field measurements in vitro as an alternative way to characterize the high intensity focused ultrasound (HIFU) field used in therapeutic applications has been explored in a phantom study. Thermocouples (copper-constantan, diameter 0.125 mm) are embedded in a phantom filled with tissue mimicking material that simulates the thermal and acoustic properties of soft-tissue. The temperature rises as a function of ultrasound exposure time near the focus of a HIFU transducer (1.1 MHz, active radius a=32 mm, geometric focal length=62 mm) of various acoustic powers up to 30 W are measured and compared with predicted values using a simple nonlinear Gaussian model. The experimental results can be explained well by the model if no acoustic cavitation takes place. When the acoustic power become higher (>5 W) and the local temperature elevation >15 degrees C and the local temperature is >40 degrees C at the focal point, cavitation vapor bubbles appear. The presence of the cavitation bubbles may increase the temperature rise rate initially. The bubble aggregates may form along the beam axis under sonication and then eventually makes the temperature elevation reach a saturated value. When acoustic cavitation occurs, the bubble-assisted enhancement of the initial temperature rise (exposure time t<2s) can still be predicted by the theory.

Temperature modes for nonlinear Gaussian beams

In assessing the influence of nonlinear acoustic propagation on thermal bioeffects, approximate methods for quickly estimating the temperature rise as operational parameters are varied can be very useful. This paper provides a formula for the transient temperature rise associated with nonlinear propagation of Gaussian beams. The pressure amplitudes for the Gaussian modes can be obtained rapidly using a method previously published for simulating nonlinear propagation of Gaussian beams. The temperature-mode series shows that the nth temperature mode generated by nonlinear propagation, when normalized by the fundamental, is weaker than the nth heat-rate mode (also normalized by the fundamental in the heat-rate series) by a factor of log(n)/n, where n is the mode number. Predictions of temperature rise and thermal dose were found to be in close agreement with full, finite-difference calculations of the pressure fields, temperature rise, and thermal dose. Applications to non-Gaussian beams were made by fitting the main lobe of the significant modes to Gaussian functions.

A new safety parameter for diagnostic ultrasound thermal bioeffects: safe use time

It is widely accepted that diagnostic ultrasound has the potential to elevate the temperature of tissue being scanned. Because both the maximum value of the temperature rise and the temporal profile of that rise are necessary to estimate the risk correctly, the temperature rise [DeltaT(t)] at an observation point for an exposure condition is presumed to have two components, that is, DeltaT(t)=DeltaT(max)X(t). The amplitude component DeltaT(max) is the maximum value of DeltaT(t), and the exposure time component X(t) represents the time dependency of that DeltaT(t). Ninety-six cases were investigated to obtain the proposed DeltaT(t) model at six frequencies, four source diameters, and four f-numbers. Then, using the relative change in the rate of induction of a thermal effect due to ultrasound exposure that produces DeltaT(t) different from a threshold exposure, the safe use time (SUT) model was constructed. SUT informs the user of the maximum duration of exposure in a region at a particular output level that would be no more hazardous than scanning at the threshold exposure. Using the SUT model, high power ultrasound can be applied for a short time so that the user can improve imaging performance while staying within safe limits.

Ultrasound-induced thermal elevation in clotted blood and cranial bone

Ultrasound thermal effects have been hypothesized to contribute to ultrasound-assisted thrombolysis. To explore the thermal mechanism of ultrasound-enhanced thrombolysis with recombinant tissue plasminogen activator (rt-PA) for the treatment of ischemic stroke, a detailed investigation is needed of the heating produced in skull, brain and blood clots. A theoretical model is developed to provide an estimate for the worst-case scenario of the temperature increase in blood clots and on the surface of cranial bone exposed to 0.12- to 3.5-MHz ultrasound. Thermal elevation was also assessed experimentally in human temporal bone, human clots and porcine clots exposed to 0.12 to 3.5-MHz pulsed ultrasound in vitro with a peak-to-peak pressure of 0.25 MPa and 80% duty cycle. Blood clots exposed to 0.12-MHz pulsed ultrasound exhibited a small temperature increase (0.25 degrees C) and bone exposed to 1.0-MHz pulsed ultrasound exhibited the highest temperature increase (1.0 degrees C). These experimental results were compared with the predicted temperature elevations.

Long-time temperature rise due to absorption of focused gaussian beams in tissue

An analytical technique previously developed to study tissue displacement due to acoustic radiation force is extended to analyze temperature rise in tissue for exposure times that are comparable to, or longer than, the tissue perfusion time. A focused transducer with Gaussian amplitude shading is assumed to radiate into a perfused tissue medium with constant thermal and acoustic properties. A simple closed-form expression is derived for the steady-state temperature rise, and a transient correction term is constructed that allows for computation of the equilibrium time of the medium. Comparisons with temperature calculations for non-Gaussian transducers show that the model may be applied to more general intensity profiles.

Evaluation of nonscanned mode soft-tissue thermal index in the presence of the residual temperature rise

Previously, the temperature rise (deltaT) caused by diagnostic ultrasound and the AUIM/NEMA-defined thermal indices were examined to evaluate whether these indices were reasonable indicators of potential bioeffects due to ultrasound heating in the absence of a residual temperature rise (RTR). In our study, deltaT induced by diagnostic ultrasound exposures was estimated in the presence of an RTR using the Bioheat Transfer Equation. To evaluate deltaT/TIS in the presence of an RTR, 11 frequencies, eight cooling times, eight insonation times for the second ultrasound examination, and three source powers for a circular aperture (A(aprt)< or = 1 cm2) were investigated. In our comparison of the ratios of deltaT/TIS in the absence and presence of an RTR, a higher deltaT/TIS value was obtained in the examination with the RTR. We showed that the deltaT/TIS value is equal to 2.88 in the presence of an RTR, whereas the deltaT/TIS value without the RTR equals 1.90. In the presence of the RTR, although the TIS does not inform the user of higher ultrasound heating due to TIS values that do not exceed 1.00, deltaT reaches 2.62 degrees C, and the deltaT without the RTR reaches 1.68 degrees C in the case of a TIS value that does not exceed 1.00. These results suggest that, for nonscanned mode situations where soft tissue is insonated, the TIS should not be regarded as a reliable indicator of potential bioeffects due to ultrasound heating in the presence of the RTR. Our study also indicates the necessity for a new indicator that provides the clinical user with accurate in vivo temperature rise feedback (possibly even true deltaT), and includes adding an exposure time component to the Bio-Heat Equation model.

The effects of residual temperature rise on ultrasound heating

In recent theoretical studies, the temperature rise produced by diagnostic ultrasound was estimated by solving the Bioheat Transfer Equation (BHTE) but ignoring the initial temperature rise. The temperature rise was determined in our study by the BHTE including an initial temperature rise. We discuss how the initial temperature rise occurs during an ultrasound examination, and how the initial temperature rise affects subsequent ultrasound heating. We theoretically show that the temperature rise produced by the ultrasound examination (exposure time of 500 s) in a tissue sample having an initial temperature rise was higher than that in a tissue sample with no initial temperature rise that was exposed to ultrasound (exposure time of 1200 s). The theoretical results for these two cases were 5.64 degrees C and 3.58 degrees C, respectively. In our experimental study, the highest temperature rise was measured in the presence of an initial temperature rise as in the theoretical study under the same exposure conditions. Mean temperature rises for tissue without an initial temperature rise and for tissue with an initial temperature rise were 2.42 +/- 0.13 degrees C and 3.62 +/- 0.17 degrees C, respectively. Both theoretical and experimental studies show that unless the initial temperature rise produced by the first ultrasound examination decreases to 0 degrees C, the next ultrasound examination on the same tissue sample may cause the temperature rise to be higher than expected.

Temperature rise generated by ultrasound in the presence of contrast agent

Temperature elevation vs. time generated by a focused Gausssian ultrasound beam in the presence of contrast agents has been calculated using a perfect absorbing disc model. The results suggest that, if the contrast agent (Albunex) is introduced into the body intravenously, the temperature rise in the heart, which is 4.5 cm from the transducer, generated by 110-mW (the corresponding acoustic intensity at the transducer front surface is 0.4 W/cm2) 2-MHz ultrasound is about 2 degrees C in 10 s. The relationship between temperature rise and the blood perfusion, acoustic power and focal length is discussed.

Temperature rise generated by diagnostic ultrasound in a transcranial phantom

Temperature rises generated by diagnostic ultrasound from a modified commercial system (Sonos 1000 Hewlett Packard) in a transcranial phantom that consists of human temporal bone and tissue-mimicking material are measured. Significant temperature rises were found at the external and internal temporal bone surfaces. The experimental results are compared with cranial thermal indices (TIC) developed by the American Institute of Ultrasound in Medicine and the National Electrical Manufacturers Association for various modes. For all the modes compared, TIC underestimated temperature rise at the external temporal bone surface. The differences between the data and temperature rises predicted by TIC can be attributed to transducer surface heating.