ULTRASOUND METHOD AND APPARATUS FOR TUMOR ABLATION,

CLOT LYSIS, AND IMAGING

TECHNICAL FIELD

[0001] The technology described herein generally relates to methods and apparatus for noninvasive tumor ablation, clot lysis, and imaging. In particular the technology described herein relates to production and use of non-linear ultrasonic vibrations.

BACKGROUND

[0002] Ultrasound has found many applications in medicine including, principally, in diagnostic imaging, but also in therapeutic techniques. The use of current ultrasound technology in diagnostic imaging of human tissues has many limitations however, not least of which are resolution and quality of image. There are still further limitations on the application of ultrasound in therapeutic areas that include the fact that ultrasonic energy cannot be delivered effectively to shielded areas of the body, and the fact that ultrasonic beams cannot be focused or made targeted enough for many tasks.

[0003] The technology of ultrasound is about seven decades old. Although many innovations have taken place during this period, such as better use of phase variation, and utilization of the Doppler effect, the underlying technology is still based on the use of linear wave propagation in the form of a sinusoidal wave or packets of waves. Current ultrasound is therefore adequate for soft tissue diagnostic imaging and certain therapeutic applications, but is not so suitable for other medical needs.

[0004] A major area where ultrasound has proved ineffective is in treatment of stroke where higher frequency waves that would be required to break down blood clots cannot pass through a patient's skull. Additionally, clots in the brain often have varying physical dimensions and irregular shapes and are thus difficult to target with ultrasound as used today. Therefore, ultrasound, although effective in principle for clot lysis in other parts of the body, cannot be readily applied to mechanical dispersal of clots within the brain. For example, U.S. Patent Application Publication No. 2006/0184070 describes a device for protecting the skull from effects of over-heating during application of ultrasound, but does not improve the effectiveness of transmission of ultrasonic energy into the cranium. Currently, then, alternative methods of treating stroke are used. For example, intravenously administered tissue plasminogen activator

(tPA) - a lytic agent - can assist in dissipation of small clots. Invasive procedures that use intraarterial devices to carry out thrombolysis within a cerebral artery are still in the trial phase, however (see, e.g., Zoler, Mitchel L., Internal Medicine News, 15th November, 2005).

[0005] Another drawback of current ultrasound technologies is cavitation, because of local damage that is caused. Although cavitation has been used advantageously in some chemical reactions, it is not desired in biomedical applications. Cavitation is particularly likely for higher frequencies.

[0006] Beyond simple considerations of efficacy of a procedure are logistical and economic factors, however. Because there are so few qualified neuro-interventionists, a principal limitation on effective treatment is whether a qualified person is available locally to carry out the necessary procedure. Since time is of the essence in treatment of stroke, this limitation can often be critical. At present, a patient who is suspected of having a stroke is usually given a CT scan by a first emergency responder. If a clot is discovered, it can be treated with intravenous tPA if small enough, or intra-arterial tPA if more sizeable. Of course, damage to an area of the brain caused by deprivation of oxygen from a blocked vessel may be irreversible if the vessel is not opened soon enough.

[0007] Accordingly, there is a need for a method of treating stroke non-invasively, and that can be applied routinely and promptly as soon as an occurrence of stroke has been identified in a patient.

[0008] The discussion of the background to the invention herein is included to explain the context of the invention. This is not to be taken as an admission that any of the material referred to was published, known, or part of the common general knowledge as at the priority date of any of the claims.

[0009] Throughout the description and claims of the specification the word "comprise" and variations thereof, such as "comprising" and "comprises", is not intended to exclude other additives, components, integers or steps.

SUMMARY

[0010] The present technology uses solitonic acoustic waves in longitudinal, torsional, and shear forms, for a diagnostic imaging modality for the human body, as well as for therapeutic

applications. The various forms, longitudinal, torsional, and shear, can be created by controlling the oscillations of the output device.

[0011] Non-linear solitonic acoustic waves are sent from a probe to, and received from, a patient, to thereby produce ultrasonic images that have very high pixel-level resolution without much distortion. Moreover, the imaging process is not significantly impeded by dense bone, or air, or metal hardware. The acoustic waves are able to travel through tissues of any characteristics to produce images of high resolution, in particular at the cellular level (approx. 1 - 10 μ). Thus the wavelengths of the solitonic waves are comparable to the dimensions of human cells, if required. On occasions such high levels of resolution are not required. The waves can be focused in all three spatial dimensions to produce high quality spatial images for subsequent manipulation, display and analysis. Time-varying, real-time imaging is also possible, just as with other ultrasound imaging techniques used today. Because Doppler effects can be additive with this technology, high spatial angiography through all the human body can be achieved and combined in 3-D, by using maximum intensity projection (MIP), or multi-planar reconstruction (MPR) in the same way that such techniques are used in today's other ultrasonic imaging technologies. Thus the techniques herein, using Doppler effects, create an angiogram, revealing images of blood- flow. Because of the different densities and molecular structures of each type of tissue, another feature of the waves used herein is to facilitate presentation of images in which different tissues are represented in different colors where, for example, different colors or shades are applied according to the shift in frequency of the wave as it passes through a particular region. This makes imaging of adjacent tissues of different types easier.

[0012] Additionally, sites of infection, tumors, and other pathologies can be represented in contrasting colors for ease of analysis by a medical professional. The characteristic waves described herein that are received from various tissue planes can be used to differentiate tumors from cysts, infections, or other pathologies in a non-invasive way, thereby avoiding need for biopsy to determine the nature of a given pathology.

[0013] The imaging device described herein can be used in conjunction with intravascular or intracavity probes to produce composite images that are superior to any given existing probe alone. The device can also be combined with CT, MRI, angiography, PET to give images that are supplementary or complementary to those techniques. With the techniques herein, one can obtain images of histological architecture, thereby avoiding the need for a biopsy.

[0014] Endobronchial use of the technology can make the identification of endobronchial lung tumor and hilum, and mediastinal tumor possible. It is also possible to image deep-situated tumors that could not previously be seen because of surrounding structure or air, such as in the lungs (sinusoidal ultrasound travels poorly through air). Endoscopic and colonoscopic probes suitably configured with a device as described herein can improve tissue characterization.

[0015] The methods and apparatus described herein can also be used for surgical planning, i.e., deciding an avenue of best approach for a surgeon to access, e.g., a tumor.

[0016] Accordingly, the technology described herein comprises at least the following:

• A medical device comprising a generator of solitonic waves;

• A medical device, comprising: a generator of solitonic waves; an amplifier configured to accept solitonic waves from the generator and to create amplified solitonic waves; a transducer configured to convert the amplified solitonic waves into mechanical waves; and an applicator for transmitting the mechanical waves into a subject;

• A method of producing an image of an internal region of an organism, the method comprising: transmitting a mechanical wave into the organism, wherein the mechanical wave is generated by a generator of solitonic waves; detecting the mechanical wave after it has been transmitted through the region of the organism, thereby producing an image of the region;

• A method of ablating a tumor in an organism, the method comprising: generating at least one mechanical wave from a generator of solitonic waves; focusing the at least one mechanical wave to create at least one focused mechanical wave; and transmitting the at least one focused mechanical wave into the organism in such a manner that the at least one focused mechanical wave is directed on the tumor thereby destroying the tumor;

• A method of lysing a blood-clot in an organism, the method comprising: generating a mechanical wave from a generator of solitonic waves; focusing the mechanical wave; and transmitting the focused mechanical wave into the organism in such a manner that the wave is directed on the blood-clot and lyses the blood-clot; and

• A method of carrying out angiography using solitonic pressure waves.

BRIEF DESCRIPTION OF THE DRAWINGS

[0017] FIGs. IA and IB show exemplary solitonic waves;

[0018] FIG. 2 shows a schematic diagram of a device as described herein;

[0019] FIG. 3 shows, schematically, application of technology as described herein to a patient;

[0020] FIG. 4A shows peeling of an epithelial cell from an artery wall; FIG. 4B shows a model for an adhesive calculation.

DETAILED DESCRIPTION

Introduction

[0021] To remedy various shortcomings of current ultrasound-based technology in imaging and therapeutic applications, including that the frequencies of current ultrasound technologies are not high enough for many of the purposes described herein, a nonlinear wave propagation technique has been adopted. This technique permits creation of a waveform that is different from the purely sinusoidal waves as currently used. The waves described herein can pass through the bone structure of a human skull with little or no attenuation in comparison to the heavy attenuation experienced by sinusoidal signals. Attenuation, i.e., a decrease in amplitude of a vibration, occurs when the wave encounters an impedance that obstructs its passage. Such an impedance may be a solid material such as bone, or a boundary between two media of different densities.

Background on Solitary Waves or Solitons

[0022] Solitons are stable solitary waves in solutions of certain non-linear equations. Many model equations of nonlinear phenomena are known to possess soliton solutions (see for example, Kanehisa Takasaki, Kyoto University, http : //www.math.h.kyoto-u. ac . jp/~takasaki/soliton- lab/'ga 1 lery /solltons/i ndex-e . h tml ). Solitary waves behave like "particles" in a linear medium. Exemplary behavior is shown in FIG. IA. When they are located mutually far apart, each of them is approximately a traveling wave with constant shape and velocity. As two such solitary waves get closer, they gradually deform and finally merge into a single wave packet; this wave packet, however, soon splits into two solitary waves with the same shape and velocity as those waves before the "collision". Thus the waveforms are preserved in both amplitude and frequency despite the collision, but experience only a phase shift. The fact that the amplitude and frequency, i.e., shape, of the original waves is preserved is why the waves are thought of as having a particulate

nature. This phenomenon is important because, in imaging, it is often beneficial to use many waveforms that originate from differently located sources; their superposition within the region to be imaged leads to the resulting waveform that is detected and from which the image is derived.

[0023] The stability of solitons stems from the delicate balance of "nonlinearity" and "dispersion" in the model equations. Nonlinearity drives a solitary wave to concentrate itself; dispersion is the effect of spreading such a localized wave. If one of these two competing effects is lost, solitons become unstable and, eventually, vanish. In this respect, solitons are completely different from "linear waves" such as sinusoidal waves. In fact, sinusoidal waves are rather unstable solutions to some model equations for which soliton phenomena are stable. Computer simulations show that such sinusoidal solutions soon break into a train of solitons. See e.g., FIG. IB.

[0024] The technology described herein is based on the use of an equation such as the Korteweg-de Vries (KdV) equation, which is an exemplary model equation describing nonlinear waves, and is a non- linear partial differential equation of the third order having the following form:

u _t + 6uu _x + Uχχ _X = 0

[0025] wherein u is an amplitude of the wave, and subscript x represents a partial derivative with respect to distance, and subscript t represents a partial derivative with respect to time.

[0026] One solution of this equation describes a solitary wave having the following characteristics: permanent form, i.e., not decaying; localized, so that the wave decays or approaches a constant at infinity; and the waves can interact strongly with other solitons, but emerges from a collision unchanged apart from a phase shift.

[0027] It is the ability of these waves to propagate with small dispersion which can be used as an effective means to transmit the generated waves over a long distance. It is this unique characteristic which makes this type of wave more suitable than the sinusoidal waves that have been used in ultrasound applications to date. Accordingly the ultrasound waves generated based on the technology described herein are subjected to far less attenuation, if any, when passing through a non- linear medium such as human tissues and bones, than are sinusoidal waves.

[0028] In addition, when using more than one source of waves, as a solitonic ultrasound wave, also referred to herein as the Solitary Ultrasound Wave (SUW), enters human tissues, exhibits a

phenomenon which is different from that found in existing imaging and therapeutic applications, and is due to its non-linear characteristics. Using current ultrasound technology, when the pressure waves enter the body, (the focal point of transmitted waves), the frequency remains the same at the point of collision while the amplitude changes linearly. In contrast, when focusing several SUWs, at the collision point the amplitudes are summed up nonlinearly, and consequently a frequency change takes place. When soliton waves collide in a non-linear medium such as human tissue, the amplitude significantly increases and causes a corresponding increasing frequency. This new frequency, which is totally dependent on the characteristics of the medium where the collision is taking place, can be used to generate an image similar to existing imaging technology but with two major differences. First, the resolution can be significantly improved as there is basically no limit to how high the frequencies can be pushed up. Frequencies with wavelengths comparable to the size of a human cell are achievable with the technologies described herein. Second, every cell which is chemically and mechanically (biologically) different will be refracting with a different frequency. This physical phenomenon can be used to obtain a color coded image with photographic clarity.

[0029] A further advantage of solitonic waves is that they do not bring about cavitation. A drawback of normal sinusoidal ultrasonic waves is that the oscillating pressures induced by the vibrations cause separation of adjacent regions of the medium from one another. This process, known as cavitation because it creates voids within the material, is undesirable because of the associated local heating that occurs.

Apparatus

[0030] FIG. 2 shows, in schematic form, an exemplary apparatus for creating a single source of solitonic ultrasonic waves, in a form suitable for delivery to a patient. The waves are typically generated in packets. Wave generator 10 is configured to generate a solitonic wave. Wave generator 10 may be modified from a commercially available, off-the-shelf, piece of hardware that has been so configured, and typically comprises at least an oscillator 4 and a filter 6. Wave generator 10 may be a digital wave generator and thus may be configured by programming it, e.g., by using computer 2. A user or programmer programs computer 2 with a mathematical description of the soliton waveform. Computer 2 then transmits a representation of the waveform to oscillator 4 in wave generator 10.

[0031] As understood by one of ordinary skill in the art, one parameter that is important in determining properties of the solitonic wave is the pulse length. Many standard digital wave

generators have lower limits on the pulse length, e.g., 10 ns, and therefore are unable to generate a wavefunction with features finer than 10 ns. The pulse length for the technology used herein should be such that the wavelength is comparable to the dimensions of human cells. The relationship between wavelength (λ), velocity (c), and frequency (v) is given by λ = c/v for any wave; the appropriate λ for a solitonic wave is known in the literature.

[0032] Oscillator 4 transmits an oscillating form, optionally superimposed on a carrier wave, to filter 6, which translates the signal into an analog output.

[0033] In an alternate embodiment, an analog wave form generator is used instead of a digital wave form generator.

[0034] The analog wave that is output from the wave generator is directed to amplifier 20, which has been suitably configured to accept a solitonic wave as input. As would be understood by one of ordinary skill in the art, the amplifier's filter circuitry may be changed in order to achieve this. Amplifier 20 also will typically only accept inputs having a slew rate within a certain range. The slew rate for the solitonic wave can be calculated if the pulse width, and the frequency of the carrier wave are known. Amplifier 20 produces, as output, an amplified solitonic wave.

[0035] Transducer 30 accepts an amplified solitonic wave output from amplifier 20, and converts it into ultrasonic form, i.e., to a mechanical, or "pressure" wave. Transducer 30 has been suitably configured to accept an amplified solitonic wave. Transducer 30 can achieve the conversion by use of a piezo-electric crystal of appropriate size and shape. An appropriate piezoelectric crystal can be selected from tabular data on commercially available crystals, available to electrical engineers and others of ordinary skill in the art.

[0036] The vibrations output from the transducer may be adjusted in frequency and amplitude according to the application in question. Typical frequencies are in the range of low MHz to mid- GHz. In clot lysis applications, the wavelengths of the soliton waves are adjusted to be comparable to the physical dimensions of the clot.

[0037] By using multiple sources of solitonic waves, and by focusing those waves at a single point and with sufficient amplitude, the characteristic vibrations received at a focal point can be changed.

[0038] FIG. 3 shows, in schematic form, a device 40 as described herein, in operation. Device 40 emits an ultrasonic soliton wave 104, which is directed into subject 104. The manner in which the wave is directed into subject 102 may not be through-space as depicted in FIG. 3, but may be through use of an applicator such as a wand, or a piece that is shaped to fit a part of the anatomy. For example, the applicator may be in a helmet shape to fit on the head of a stroke victim. The applicator may also be contoured to fit a patient's chest, stomach, or a limb. Vibrations that have passed through a region of the subject 104 are received by detector 110.

[0039] In diagnostic applications, detector 110 receives signals from the patient, corresponding to the parameters of the solitonic waves after they have passed through the patient. In certain embodiments, detector 110 is configured to receive and detect both wavelength (or frequency) and amplitude of the vibrations. A detector is not required for, but may still be present in, therapeutic applications such as clot lysis.

[0040] It is further to be understood that, although FIG. 3 shows a single source of solitonic waves that is directed into a subject, multiple such sources may additionally be utilized. Thus, such multiple sources may simultaneously direct multiple solitonic waves, for example from different angles, into a subject, focused on a particular location such as a clot, a tumor, or a region for which images are desired. Focusing of various numbers of beams of solitonic waves can be achieved using standard triangulation methods. The waves from different sources typically collide at the point where they are focused and produce a wave of higher amplitude and higher frequency than either of the inputs. By focusing an additional carrier wave at the same point, the wave generated by superposition of the solitonic waves is picked up by the carrier wave and sent to the detector. The carrier wave can be a frequency modulated wave, or a random wave, such as white noise with appropriate spectral characteristics. The carrier wave is typically a sinusoidal wave and not of solitonic form prior to its interaction with the solitonic waves. Thus, detection of superposed waves can likewise be achieved with ultrasound detection technology presently used in the art.

[0041] Detector 110 may be configured to direct signals that it detects, in either raw, or processed form, to a display device 120, which may be viewed by a medical professional 130 as shown. Although the connection between detector 110 and display 120 is shown in FIG. 3 as a dedicated cable 121, it would be understood that the connection could be wireless, or via a computer network having multiple connections and nodes. Display 120 may be a computer or TV monitor as shown in FIG. 3, or may be situated on a handheld or portable device such as a laptop,

dedicated handheld peripheral, or personal digital assistant. It is also consistent with operation herein that detector 110 and display 120 are integrated into a single unit. Furthermore, the monitor or display may additionally be equipped with capability to store detected data in magnetic form and/or to direct the same to an output device such as a printer.

[0042] The technology described herein can be configured to be available at any hospital emergency room and thereby can dramatically increase the number of locations that are able to properly and timely treat patients such as stroke victims.

EXAMPLES

[0043] There are at least two principal categories of applications that are based on the ultrasonic technology described herein. A first area of application is medical devices, which includes both diagnostic/imaging as well as therapeutic applications. A second area includes industrial applications where both ultrasonic SUWs (pressure waves) as well as standard SUWs (electromagnetic waves) can be used, according to the nature of the application.

Example 1: Medical Applications

[0044] Medical applications the technology described herein can be categorized as imaging and diagnostic applications, or as therapeutic applications. In diagnostic and imaging applications, the generated SUWs from one to N sources, where N can be 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 50, or 100 sources, will be used with wavelength resolutions comparable to the size of cell in the desired area of investigation. When N=3 or greater, a three dimensional image of the selected area can be achieved in color as further described herein. The x, y and z coordinates of the desired area compared to a bench mark are identified and recorded.

Therapeutic Applications

[0045] The SUWs output from two or more sources will be focused on a identified area of tissue (e.g., inside the skull in case of stroke, or in the spinal cord). Both longitudinal as well as torsional pressure waves with appropriate wavelengths to match the clot size (in case of stroke), as well as phase shaping of each packet of input will be used to create a mechanical amplification of the clot, thereby bringing about its final disintegration and dispersion. Since clots are held together by fibrins, it is useful to use different wave forms to disrupt them. Different phases of waves, such as may be obtained by torsional or shear waveforms, can provide an appropriate impetus. In other therapeutic applications such as tumor ablation, the desired amplitude can be achieved with the selection of a proper number of SUW sources, and focusing them on the desired

area. Again, phase shaping of each packet of signals will be employed as a secondary technique to fine tune the amplitude. Since the desired amplitude is achieved at a very local level (nonlinear summation of all SUWs at their focal point and at a high resolution (cell size or bigger), any collateral damage (i.e., damage to surrounding healthy tissue/cells) is basically eliminated.

[0046] The use of the solitonic ultrasound waves as described herein will also have a myriad of biomedical applications as follows:

[0047] Central nervous system: by devising a prototype such as a helmet, the waves can be focused on a thrombus within a vessel of a stroke victim, not only by the use of imaging as described herein, but also by combination with current technology such as MRI, angiography and CT scans. Focusing of the waves on the tumor result in mechanical disruption of the clot, and restore blood flow within the vessel. This application can be combined with intravascular probes or probes placed intracavity. Also, pharmacological agents may be used in conjunction with the application of solitonic wave energy to permit pharmaco-mechanical thrombolysis.

[0048] Tumor ablation: ablation of a tumor in any organ can be achieved with high intensity focused solitonic ultrasound waves, without any destruction of the surrounding tissues. This technique can also be coupled with intravascular or intra-cavity probes (e.g., an endoscopic, intravascular, endorectal, and endovaginal probes) to achieve better results due to proximity to the site of interest. Whereas clot lysis is achieved principally through mechanical disruption caused by the soliton waves, tumor ablation is achieved principally through local and precise heating of the tumor that is caused by the waves. The technology described herein is applied particularly effectively to tumors that are located in regions that are difficult to access via surgical methods, such as the uterus.

[0049] Cardiovascular-acute myocardial infarction: this is a common cause of death. By the use of the imaging described herein, blood clots in the coronary vasculature can be identified and therefore treated to restore patency. The technology can be used to revascularize carotid arteries, visceral arteries, and the aorta, as well as extremities. The energies deployed - typically ~ 1 W/crrf ² so as not to increase the tissue temperature by more than 1 ⁰ F - will be used to treat atherosclerosis and to restore luminal patency.

[0050] Pulmonary-endobronchial use for treatment of tumor. For example, an endobronchial probe, fitted with the ultrasonic technology described herein, can be used.

[0051] Gastrointestinal-endoscopic and colonoscopic probes equipped with the technology described herein can be used to ablate polyps, early tumors, and active bleeding sites.

[0052] Treatment of kidney stones: application of the technology described herein will be more effective for kidney stones than current lithotripsy because the vibrations used herein are more focused and of higher energies than those used in lithotripsy.

[0053] Treatment of gall stones: similar to treatment of kidney stones, but without removal of the gall bladder.

[0054] Treatment of dysfunctional uterine bleeding, ablating the endometrium, polyps: the technology described herein can be attached to an endometrial probe, for cauterization.

[0055] Treatment of cystitis and polyps: the technology described herein can be used to treat or cauterize the bladder from within.

Example 2: Industrial Applications

[0056] The solitonic wave technology can be used in conjunction with a laser, such as a high power laser, for improved levels of penetration.

[0057] The technology described herein, when used at high power, can be used in various security applications. The technology described herein can further be applied to screening of cargo and shipping containers, as an alternative to X-rays as presently used.

[0058] The technology described herein can also be used in materials science, for example, for obtaining very high quality of images of materials assisting in evidence of fatigue, etc.

Example 3: Model of an arterial clot

[0059] Using typical material parameters for an artery:

• Artery length=0.1 m,

• Artery radius=0.001 m,

Artery Young's Modulus, E=I MPa,

• Artery Poisson Ratio, v = 0.4,

• Artery thickness, d=0.008 m,

Blood Hydrostatic pressure, P ₀ = 10 kPa, Blood Viscosity, μ = 0.004,μPa/s

• Initial blood Density, p ₀ = 1060,kg/m

[0060] The boundary conditions to be modelled are a controlled pulsing at the left of the artery, and a "leaky" clot at the right end. The boundary conditions can be modeled as follows. The left end has a prescribed velocity according to

v(z = 0, t) = v _o + V _o sm(2Ukj), (1)

where V ₀ is the initial condition for the interior, V ₀ is an amplitude, k is a wave number, t is time and T is the total simulation time.

[0061] For the right hand side

where v(L - AzJ) is the velocity just to the left of the clot, A^(L - AzJ = 0) is the artery cross- sectional area just to the left of the clot and A® is the clot cross-sectional area. When the clot cross-sectional area is the same as the artery cross-sectional area, the artery is plugged, at least initially. IfA^(L - Az, t) grows, the artery can begin to "leak". In addition to the velocity boundary conditions, we need either the pressure or density boundary data. If either of theses are known, the other can be computed from an equation of state.

P = Po + ζ (p/po - l) (3)

[0062] It is customary to specify the pressure, thus, at the left end

P(z = 0j) = P _{o + Po} sm(2Ukj), (4)

where P ₀ is the initial condition for the interior, p ₀ is an amplitude. At the right end,

P(Z = LJ) = P ₀ . (5)

[0063] The corresponding densities at these endpoints are computed from

p(z = LJ) I (6)

[0064] Note that the velocity profile can be approximated via

v(rj) = V(ZJ)(I - r l Rf) , (7)

where v(z,t) is the centerline velocity, r is the distance away from the centerline, R is the radius of the artery, and 2 < q is an exponent that grows with Reynolds number. This helps visualize the flow in a more realistic manner.

Example 4: Breaking and debonding of clots

[0065] Near the clot, there are two sources of damage (a) debonding of the artery wall and the clot and (b) direct damage to the clot.

(a) Debonding

[0066] Debonding of the artery wall from the clot would allow for dissolving medication to attack the clot (see, schematically in FIG. 4A). Crack growth rates are typically given by equations of the form:

where a is the length of the crack, C _d is a debonding constant (> 0), and W" abs ^s is the amount of energy delivered by the pulse. Alternatively, the growth rate can be written as a function of the (positive) pressure induced at the end of the tube. The debonding damage parameter can be calibrated by: (i) knowing the amount of energy per unit area needed to debond two materials, denoted as γ, (ii) realizing that Equation 8 implies

Aa = C _d AW ^abs , (9)

and (iii) defining a _o as the original crack length, this yields

a(t + δt) = a(t) = C _d AW ^abs . (10)

[0067] The computational algorithm is as follows, starting at t = 0 and ending at t = T:

(1) COMPUTE PULSE CONTRIBUTION

(2) COMPUTE ENERGY ABSORBED BY THE CLOT: δW° ^bs (11)

(3) COMPUTE CRACK GROWTH: a(t + At) = a(t) + C _d δ W" ^hs

(4) GO TO (1) AND REPEAT WITH (t = t + δt).

[0068] Cd can be experimentally determined. For example, a standard peel test can be used to determine the amount of energy absorbed in making a unit area of crack, which is a standard measure of the strength of an adhesive. The amount of energy associated with stripping off the cells can be determined as follows. Suppose an interface, which one can consider as a crack of

length a, with thickness d, advances by an increment δα, then it is required that: (work done by the loads) > (change in elastic energy) + (energy absorbed by the crack tip) or mathematically

SW ≥ U + GdSa , (12) where W is the work done, f/the elastic stored energy, G is the energy absorbed per unit area of crack (FIG. 4B). G is the amount of energy absorbed in making a unit area of crack (a material property), and it is usually called the toughness, and is usually used as a measure of the strength of an adhesive. A high toughness means it is hard to make a crack. Usually U is small in comparison to the other terms, thus δW~ Gdδa. Thus, if a constant force is used to pull the strip upwards:

SW = FSa , (13) then F = Gd or G = F/d. For a one centimeter wide strip and a force of 10 Newtons, G = IO Jm ^"2 . This is within the range of most industrial adhesives. For stronger bonds, enough to strip cells off, one should expect G ~ 10 ⁴ Jm ^"2 . This should serve as a guide to the type of materials.

(b) Direct pulse-induced damage on the clot face

[0069] The direct impact of the pulse to the clot face will also induce damage within the clot. The following is a model from which one can determine the damage to the clot. In many applications, it is important to simulate the properties/behavior of materials comprised of hard agglomerated granules, such as necrotic tissue in a clot, bound together by a binder under shock- type loading. For example, consider damage to be the debonding of material as a function of the amount of energy absorbed. In other words, the amount of energy absorbed is available to break bonds that bind the granules to the matrix. It is reasonable to assume that the rate of damage increase is proportional to the rate of energy absorbed:

a ∞ W ^abs . (14)

[0070] Here W ^abs is the rate of energy absorbed from the fluid interacting with the clot, and a value of a(t = 0) = 1 indicates an undamaged material (perfectly bonded), whereas a(f) = 0 indicates a completely damaged material. One may simply write

a = C W ^abs => a(t + At) = a(t) + CAW ^abs , (15)

where C represents the damage per unit energy. A computational algorithm is as follows, starting at t = 0 and ending at t = T:

(1) COMPUTE PULSE CONTRIBUTION

(2) COMPUTE ENERGY ABSORBED BY THE CLOT: δW° ^bs

(3) COMPUTE DAMAGE: a(t + At) = a(t) + Cδ W" ^hs (16)

(4) GO TO (1) AND REPEAT WITH (t = t + At).

[0071] The damage parameter was calibrated by: (i) knowing the amount of energy per unit area needed to debond two materials, denoted as γ, (ii) realizing that Equation 7.8 implies

Aa = CAW ^abs , (17) and (iii) defining for a perfectly bonded granule a = 1 and for a completely debonded granule a = 0. This yields

Aa = (0 - l) = C/4πb ² ^ C = ^ . (18)

[0072] The chosen value for γ was γ = 10 ² J/m ² , which is in the range of values for lower end (in terms of strength) industrial adhesives. The amount of damage incurred in the system scales linearly with C (which depends inversely on γ), thus making it a relatively natural parameter to use in such modeling.

(c) Optimizing system parameters

[0073] Ultimately, there are many parameters to vary in such a system: length of tube, ambient pressure, initial pulse shape, frequency of pulses, fluid properties such as viscosity, density, etc. The search for an appropriate set of system parameters to break a clot can set up as a minimization problem where II is a cost function: π = |(Desired pulse position) - (computed pulse position)! + ((Desired pulse strength) - (computed pulse strength)!, (19) and the parameters are varied accordingly to find minima. This can be done with, for example, extremely efficient genetic algorithms.

[0074] The foregoing description is intended to illustrate various aspects of the present invention. It is not intended that the examples presented herein limit the scope of the present invention. The invention now being fully described, it will be apparent to one of ordinary skill in the art that many changes and modifications can be made thereto without departing from the spirit or scope of the appended claims.