1. Field of the Invention
This invention relates to methods and systems for measuring mechanical property of a vascular wall and a method and system for determining health of a vascular structure.
2. Background Art
The following references are referenced herein:
A. J. Bank et al., “In Vivo Human Brachial Artery Elastic Mechanics Effects of Smooth Muscle Relaxation,” 1999; C
D. H. Bergel, “The Static Elastic Properties of the Arterial Wall,” J. P
C. Bilato et al., “Atherosclerosis and Vascular Biology of Aging,” A
O. Bonnefous et al., “Non Invasive Echographic Techniques for Arterial Wall Characterization,” IEEE U
J. Blacher et al., “Carotidarterial Stiffness as a Predictor of Cardiovascular and All-Cause Mortality in End-Stage Renal Disease,” H
J. Blacher et al., “Impact of Aortic Stiffness on Survival in End-Stage Renal Disease,” C
O. Bonnefous et al., “New TDI Developments for Vascular and Cardiac Applications,” IEEE U
A. Bruel et al., “Changes in Biomechanical Properties, Composition of Collagen and Elastin, and Advanced Glycation Endproducts of the Rat Aorta in Relation to Age,” A
D. Buprez et al., “Relationship Between Periventricular or Deep White Matter Lesions and Arterial Elasticity Indices in Very Old People,” A
A. Eriksson et al., “Arterial Pulse Wave Velocity with Tissue Doppler Imaging,” U
G. Faury, “Function-Structure Relationship of Elastic Arteries in Evolution: From Microfibrils to Elastin and Elastic Fibres,” P
Y. C. Fung, “Biomechanics: Mechanical Properties of Living Tissues,” 2nd Ed., Spring-Verlag, 1993: 321-391;
G. Guerin et al., “Arterial Stiffening and Vascular Calcifications in End-Stage Renal Disease,” N
Hardung V., “Propagation of Pulse Waves in Visco-Elastic Tubing,” A
D. R. Kaiser et al., “Brachial Artery Elastic Mechanics in Patients with Heart Failure,” 2001; H
K. Konner et al., “The Arteriovenous Fistula,” J. A
G. J. Langewouters et al., “The Static Elastic Properties of 45 Human Thoracic and 20 Abdominal Aortas In Vitro and the Parameters of a New Model,” J. B
M. A. Lubinski et al., “Speckle Tracking Methods for Ultrasonic Elasticity Imaging Using Short Time Correlation,” IEEE T
A. J. Luik et al., “Arterial Compliance in Patients on Long-Treatment-Time Dialysis,” N
J. J. Mai et al., “Strain Imaging of Internal Deformation,” U
M. Persson et al., “Estimation of Arterial Pulse Wave Velocity With A New Improved Tissue Doppler Method,” P
H. Taniwaki et al., “Femoral Artery Wall Thickness and Stiffness in Evaluation of Peripheral Vascular Disease in Type 2 Diabetes Mellitus,” A
S. Timoshenko et al., “Theory of Elasticity,” 3rd Ed., M
Arterial compliance has been shown to be a strong indicator of vascular disease; cardiovascular disease, peripheral vascular occlusive disease, diabetes, and renal failure. Changes in the ratio of collagen to elastin in the extracellular matrix of the arterial media is believed to be one of the causes of arterial stiffness (Faury 2001; Bilato and Crow 1996; Bruel and Oxlund 1996). By measuring mechanical properties of tissue, elasticity imaging could non-invasively monitor vascular pathologies developing within the vascular wall. Previous attempts at non-invasive vascular elastic imaging include arterial wall motion estimation (Bonnefous et al., 1996; Taniwaki et al., 2001; Luik et al., 1997; Guerin et al., 2000), intraparietal strain imaging (Bonnefous et al., 2000) and pulse wave velocity measurement (Eriksson et al., 2002; Persson et al., 2001). Arterial compliance measurement was also conducted by monitoring internal pulsatile deformation in tissues surrounding the normal brachial artery (Mai and Insanna 2002). With some limits, these measurements have been correlated with clinical events including stroke (Buprez et al., 2001) and claudication symptoms (Taniwaki et al., 2001) in non-ESRD (End Stage Renal Disease) patients and adverse cardiovascular events in patients with ESRD (Blacher et al., 1998; Blacher et al., 1999), as well as length of time on dialysis (Luik et al., 1997).
One factor limiting the success of previously used methods is that arteries normally distended under physiologic pressure produce only small strain. The normal arterial wall, however, is a highly non-linear elastic medium, as illustrated by the solid curve in
Another factor limiting the success of previous methods is that properties of the vessel as a whole or in cross-section are measured. In the previous reports on the arterial compliance over a wide range of intraluminal pressure (Bank et al., 1999; Kaiser et al., 2001), the compliance was inferred from the geometrical changes such as artery diameter and lumen cross-section based on a numerical model (Langewouters' model; Langewouters et al., 1984).
A phase-sensitive, two-dimensional speckle-tracking algorithm has been used by one of the co-inventors herein to determine displacements and strains (Lubinski et al., 1997).
An object of the present invention is to provide improved methods and systems for measuring mechanical property of a vascular wall and a method and system for determining health of a vascular structure wherein local deformation of a vessel wall resulting from physiologic pressures with altered transmural forces is measured.
Using local measures of strain, highly localized measurements can be made. These local measurements can be used individually or compiled into a “map” or “image” of the mechanical properties of the vessel wall. Consequently, the methods and systems have the capability of being “high resolution.”
In carrying out the above object and other objects of the present invention, a method for measuring a mechanical property of a vascular wall which deforms in response to a transmural force under usual physiologic pressures is provided. The method includes altering the transmural force to obtain an altered transmural force. The method also includes measuring local deformation of the vascular wall resulting from physiologic pressures with the altered transmural force, and determining a value for the mechanical property based on a measured amount of local deformation.
The mechanical property may be a non-linear elastic property of the vascular wall.
The step of measuring may include the step of non-invasively, ultrasonically imaging the vascular wall.
The step of altering may include the step of reducing the transmural force to obtain a reduced transmural force.
The step of reducing may include the step of applying an external pressure to the vascular wall.
The external pressure may be substantially equal to a baseline internal pressure, and the vascular wall may deform by pulse pressure during a cardiac cycle.
The step of reducing may include reducing an internal pressure to the vascular wall.
The vascular wall may deform a relatively small amount in response to a transmural force under usual physiologic pressures and a relatively large amount in response to physiologic pressures with the altered transmural force.
The step of determining may include the step of directly estimating strain of the vascular wall.
Further in carrying out the above object and other objects of the present invention, a method for measuring a mechanical property of a vascular wall is provided. The vascular wall is characterized by a relationship of arterial pressure versus strain that exhibits a relatively large slope under physiologic pressure caused by an arterial pressure pulse having a first mean arterial pressure and that exhibits a relatively small slope under physiologic pressure caused by an arterial pressure pulse having a second mean arterial pressure. The method includes altering the first mean arterial pressure to obtain the second mean arterial pressure. The method further includes measuring local deformation of the vascular wall at the second mean arterial pressure, and determining a value for the mechanical property based on the measured amount of local deformation.
The step of measuring may include the step of non-invasively, ultrasonically imaging the vascular wall.
The step of altering may include the step of reducing the first mean arterial pressure to obtain the second mean arterial pressure.
The step of reducing may include the step of applying an external pressure to the vascular wall.
The external pressure may be substantially equal to a baseline internal pressure, and the vascular wall may deform by pulse pressure during a cardiac cycle.
The step of reducing may include reducing an internal pressure to the vascular wall.
The step of determining may include the step of directly estimating strain of the vascular wall.
Still further in carrying out the above object and other objects of the present invention, a method is provided for determining health of a vascular structure which includes a vascular wall which deforms in response to a transmural force under usual physiologic pressures. The method includes altering the transmural force to obtain an altered transmural force. The method further includes measuring local deformation of the vascular wall resulting from physiologic pressures with the altered transmural force, and determining the health of the vascular structure based on the measured amount of local deformation.
The step of measuring may include the step of ultrasonically imaging the vascular wall.
The step of altering may include the step of reducing the transmural force to obtain a reduced transmural force.
The step of reducing may include the step of applying an external pressure to the vascular wall.
The external pressure may be substantially equal to a baseline internal pressure, and the vascular wall may deform by pulse pressure during a cardiac cycle.
The step of reducing may include reducing an internal pressure to the vascular wall.
The vascular wall may deform a relatively small amount in response to a transmural force under usual physiologic pressures and a relatively large amount in response to physiologic pressures with the altered transmural force.
The step of determining may include the step of directly estimating strain of the vascular wall.
Yet still further in carrying out the above object and other objects of the present invention, a system for measuring a mechanical property of a vascular wall which deforms in response to a transmural force under usual physiologic pressures is provided. The system includes means for altering the transmural force to obtain an altered transmural force. The system further includes means for measuring local deformation of the vascular wall resulting from physiologic pressures with the altered transmural force, and means for determining a value for the mechanical property based on the measured amount of local deformation.
The mechanical property may be a non-linear elastic property of the vascular wall.
The means for measuring may include means for non-invasively, ultrasonically imaging the vascular wall.
The means for altering may include means for reducing the transmural force to obtain a reduced transmural force.
The means for reducing may include means for applying an external pressure to the vascular wall.
The external pressure may be substantially equal to a baseline internal pressure, and the vascular wall may deform by pulse pressure during a cardiac cycle.
The means for reducing may include means for reducing an internal pressure to the vascular wall.
The vascular wall may deform a relatively small amount in response to a transmural force under usual physiologic pressures and a relatively large amount in response to physiologic pressures with the altered transmural force.
The means for determining may include means for directly estimating strain of the vascular wall.
Still further in carrying out the above object and other objects of the present invention, a system is provided for measuring a mechanical property of a vascular wall. The vascular wall is characterized by a relationship of arterial pressure versus strain that exhibits a relatively large slope under physiologic pressure caused by an arterial pressure pulse having a first mean arterial pressure and that exhibits a relatively small slope under physiologic pressure caused by an arterial pressure pulse having a second mean arterial pressure. The system includes means for altering the first mean arterial pressure to obtain the second mean arterial pressure. The system further includes means for measuring local deformation of the vascular wall at the second mean arterial pressure, and means for determining a value for the mechanical property based on the measured amount of local deformation.
The means for measuring may include means for non-invasively, ultrasonically imaging the vascular wall.
The means for altering may include means for reducing the first mean arterial pressure to obtain the second mean arterial pressure.
The means for reducing may include means for applying an external pressure to the vascular wall.
The external pressure may be substantially equal to a baseline internal pressure, and the vascular wall may deform by pulse pressure during a cardiac cycle.
The means for reducing may include the means for reducing an internal pressure to the vascular wall.
The means for determining may include means for directly estimating strain of the vascular wall.
Still further in carrying out the above object and other objects of the present invention, a system for determining health of a vascular structure including a vascular wall which deforms in response to a transmural force under usual physiologic pressures is provided. The system includes means for altering the transmural force to obtain an altered transmural force. The system further includes means for measuring local deformation of the vascular wall resulting from physiologic pressures with the altered transmural force, and means for determining the health of the vascular structure based on the measured amount of local deformation.
The means for measuring may include means for non-invasively, ultrasonically imaging the vascular wall.
The means of altering may include means for reducing the transmural force to obtain a reduced transmural force.
The means for reducing may include means for applying an external pressure to the vascular wall.
The external pressure may be substantially equal to a baseline internal pressure, and the vascular wall may deform by pulse pressure during a cardiac cycle.
The means for reducing may include means for reducing an internal pressure to the vascular wall.
The vascular wall may deform a relatively small amount in response to a transmural force under usual physiologic pressures and a relatively large amount in response to physiologic pressures with the altered transmural force.
The means for determining may include means for directly estimating strain of the vascular wall.
The local deformation for the above methods and systems may be an intramural deformation.
The above object and other objects, features, and advantages of the present invention are readily apparent from the following detailed description of the best mode for carrying out the invention when taken in connection with the accompanying drawings.
a and 6b are graphs of radial strain and strain rate, respectively, of a healthy volunteer with continuous external compression;
a and 7b are graphs showing strain rate over one cardiac cycle; under physiologic pressure (i.e.,
a and 8b are schematic diagrams showing scanning of an upper arm without (i.e.,
in semi-log scale and strain represents
As previously mentioned, one of the significant obstacles of measuring mechanical properties of blood vessels is that vascular wall deformations under physiologic pressures only exhibit small deformations with the usual (physiologic) forces applied. By altering the forces across a vessel wall (transmural=across the vessel wall), the deformations induced from physiologic pressure across the arterial wall is altered with the methods and systems of the present invention. By measuring the local deformations, which may be intramural deformations, with altered transmural forces, new and detailed measurements can be made about the mechanical properties of the vessel.
In other words, one of the significant obstacles of measuring mechanical properties of blood vessels (arteries, veins, fistulae or other blood transporting structures hereafter referred to as “vessel” [noun] or “vascular” [adjective]) in the body (in-vivo) is that vascular wall deformations under physiologic pressures only exhibit small deformations with the usual (physiologic) forces (or pressures) applied. By altering the transmural forces across a vessel wall (transmural=across the vessel wall), the changes induced (deformation=changes in position of at least one location within the vessel wall) from physiologic pressure across the arterial wall is altered. By measuring the deformations with altered transmural forces, new and very detailed measurements can be made about the mechanical properties of the vessel. These measurements are derived from deformations induced by the altered forces. In particular, non-linear elastic properties of the vessel wall can be measured with great accuracy and precision if large wall deformations (e.g., 20%) are induced. Non-linear elastic properties are directly related to many pathologies altering vascular compliance and, so, there should be numerous applications of a truly non-invasive method to monitor this physiologically significant parameter.
The measurements include an parameter that can be derived from (1) altering the transmural forces (or pressures), and (2) measuring the local deformation that results from physiologic forces. These measurements include, but are not limited to: displacement, strain, elastic moduli (e.g., Young's modulus), time derivatives (e.g., strain rate) or other mathematical operations or manipulations used to derive values from the measured local deformation. Consequently, an important aspect of the invention is measuring the local deformation of the vessel wall resulting from physiologic pressures with altered transmural force.
The means of altering the transmural forces may be highly variable and include: external pressure applied to the vessel directly or applied to tissues overlying or surrounding the vessel such as, but not limited to: (1) manual compression (e.g., external compression with the hand, or the hand holding an object), (2) other-methods of external compression such as a cuff inflated to apply pressure (such as, but not limited to a blood pressure cuff around an arm or leg), (3) internally “pressing” with a balloon or other internal structure that change geometry in such a way as to alter the transmural forces of a vessel, (4) maneuvers that alter forces such as straining against a closed airway (Valsalva maneuver) or blowing or sucking air against resistance, all of which change intra-thoracic pressure, alter blood flow in blood vessels with the thoracic cavity as well as blood entering and leaving the thoracic cavity, and thereby may change the transmural pressure (forces) of the vessel and allow the necessary measurements to be made, and (5) pharmacologic agents may be administered that alter blood pressure and thereby may be used to alter the transmural pressure, or (6) any other means of altering transmural vascular forces.
The preferred means of measuring the local deformation uses data generated from ultrasound imaging. However, other means of measuring the deformation will allow calculation of the mechanical properties of the vessel. These other means of measuring the deformation may include, but are not limited to: (1) visual inspection, (2) manual measurement either directly or indirectly from images generated of the deformations from any imaging system, (3) sensing any location within the vessel wall with any method or device (such as, but not limited to, any wavelength electromagnetic radiation including, but not limited to, X-ray, CT, or measuring other physical parameters that allow the movement or position of the vessel wall to be measured such as MRI, or any imaging modality). All that is important is to measure the location of the vessel wall to determine the local deformation from baseline (physiologic) pressures (forces) while the altered forces are generated.
As described herein, the mean arterial pressure is lowered to reduce the preload so that the arterial pressure pulse creates much larger strain (
By lowering mean arterial pressure, it is much easier to differentiate diseased from normal arterial wall. Almost all arterial pathologies decrease compliance, as illustrated qualitatively by the dashed curve in
Arterial elasticity can be more accurately determined by measuring localized intramural strain. As described herein, the intramural radial normal strain is directly estimated using a phase-sensitive, two-dimensional speckle-tracking algorithm to determine displacements and strains (Lubinski et al., 1997). In a clinical setting, larger arterial strains with corresponding higher strain signal-to-noise ratio (SNR) are demonstrated using free-hand deformation to induce transmural pressure equalization and reduce preload. Strain and strain rate measurements at maximum pulsation correspond to the compliance of the artery under the same condition that blood pressure is taken with a blood pressure cuff. The feasibility of this technique is demonstrated using ex- and in-vivo measurements, and a straightforward elasticity reconstruction algorithm is presented to quantitatively assess the results.
An example of preferred method of performing the measurement and resulting tenfold change in mechanical property (strain) measured is now described.
Peripheral Arterial Strain Imaging Using External Pressure Equalization
Non-invasive peripheral arterial ultrasound strain imaging was performed while applying external pressure to induce changes in the baseline pressure difference across the arterial wall. By equalizing the baseline internal and external arterial pressure during the ultrasound measurement, increased arterial strains are induced by the relatively stable pulse pressure (pulse pressure=systolic pressure—diastolic pressure) during the cardiac cycle. The brachial and radial arteries of a 43 year old man were imaged with a 7.2 MHz linear ultrasound transducer while external deformations were continually increased over several cardiac cycles. External pressure was increased until the arteries collapsed during diastole, but distended during systole when the applied force exceeded the internal reference pressure of 80 mmHg (subject's diastolic pressure). Correlation-based, phase-sensitive, two-dimensional speckle-tracking algorithm was employed to calculate strain and strain rate from the internal displacement of the artery wall.
Imaging of the arteries without external deformation resulted in measured strains up to 2% over the cardiac cycle. When applied pressure matched the internal baseline diastolic pressure of 80 mmHg, the strains increased by a factor of 10 with peak strains of 20% over the cardiac cycle. In addition, the peak strain rate under physiological conditions ranged from 0.1 sec−1 during diastole to -0.2 sec−1 during systole. After arterial pressure equalization, the peak strain rate increased to 1.0 sec−1 during diastole and −2.5 sec−1 during systole, similar to the increase in peak strains. By applying external pressure, the pressure difference across the arterial wall at baseline (diastole) is reduced, while the pressure change from diastole to systole remains stable. As a result, the preload on the arterial wall can be decreased to near zero, leading to maximal strain during the cardiac cycle. By varying the external pressure, the range of measured strains vary over a cardiac cycle, and the non-linear properties of the arterial wall may be better characterized. Methods such as this that elicit the non-linear properties of the arterial wall could be used to better characterize vascular pathologies such as vessel hardening, neointimal hyperplasia, and vulnerable plaques.
As shown in
By lowering mean arterial pressure, it is much easier to differentiate diseased from normal arterial wall. Almost all arterial pathologies decrease compliance, as illustrated by the dashed curve in
Arterial elasticity can be more accurately determined by intramural strain. Preferably, the intramural radial normal strain is directly estimated.
As described hereinbelow, in a clinical setting, larger arterial strains with corresponding higher strain signal-to-noise ratio (SNR) is demonstrated using free-hand deformation to induce transmural pressure equalization. Strain and strain rate measurements at maximum pulsation correspond to the compliance of the artery under the same condition that blood pressure is taken with a blood pressure cuff. The feasibility of this technique is demonstrated using ex- and in-vivo measurements.
Like any other tissue, arteries exhibit non-linear elasticity (Fung 1993). To demonstrate and quantify arterial non-linearity with respect to internal loading, a controlled experimental protocol was designed. The intramural strain of an ex-vivo bovine artery was measured when the internal pressure was increased by a fluid-filled syringe pump.
Experimental Set-Up. A closed-loop compression system was designed to pressurize an artery sample while simultaneously scanning with ultrasound. A programmable commercial syringe pump (Cole-Parmer) serves as a pressure source. An acoustic window is designed to hold an arterial sample between inlet and outlet ports. The outlet is sealed so that the internal pressure develops while the syringe pump compresses. A pressure gauge is placed between the syringe and artery sample close to the artery to measure intraluminal pressure. The acoustic window is placed in a water tank with anechoic material at the bottom to suppress possible reverberation, and the tank is placed underneath an ultrasound transducer positioning device. A PC-based RF data acquisition system is connected to a commercial ultrasound scanner (Siemens Elegra). A block diagram is presented in
Bovine Arterv ex-vivo. A 50 mm-long bovine carotid artery segment preserved in 30% ethanol (Artegraft, Brunswick, N.J.) was placed in the middle of the acoustic window connected to the flow path filled with degassed water. A commercial (Cole-Parmer) syringe pump was programmed to pump water at a fixed rate over a fixed period (70.5 ml/min. for 13 seconds) to build intraluminal pressure to 120 mmHg. While the artery distended from the resting position, a 12.0 MHz linear ultrasound array connected to a commercial ultrasound scanner (Siemens Elegra) imaged the arterial cross-section at a rate of 22 frames per second for 13 seconds. RF data from every frame in the sequence were captured. The intraluminal pressure over time was also recorded. Data were subsequently processed using a phase-sensitive, two-dimensional speckle-tracking algorithm to determine displacements and strains (Lubinski et al., 1997). Correlation-based algorithms were used to track internal displacements. Frame-to-frame lateral and axial displacements were estimated from the position of the maximum correlation coefficient, where the correlation kernel size equaled the speckle spot for optimal strain estimation and axial displacements were refined using the phase zero-crossing of the complex correlation function. Frame-to-frame displacement estimates were integrated from and registered to the initial coordinate system (i.e., Lagrangian presentation). Spatial derivatives of the displacements were computed in one region of the artery to estimate the radial normal strain (i.e., the radial derivative of the radial displacement). As described hereinbelow, the radial normal strain is called simply the strain, where appropriate.
Humian Artery in-vivo. Two subjects were tested. The first was a 43 year old healthy male volunteer and the second was a 48 year old male with ESRD secondary to diabetes mellitus, on hemodialysis, and a history of peripheral vascular occlusive disease, with prior right below the knee amputation.
A 7.2 MHz linear array was used with continuous freehand compression performed on the surface of the right upper arm close to the brachial artery. While imaging the cross-section of the brachial artery at a rate of 107 frames per second and collecting ultrasound data frame-by-frame, surface compression was performed by the investigators. The applied external force produces internal pressure comparable to that generated in measuring a subject's blood pressure. The compression was increased until brachial artery pressure exceeded diastolic pressure, as evidenced by viewing B-scan images. Collected RF data were processed off-line in the same way as described above.
Results
Bovine Arteiy ex-vivo. The accumulated displacement and axial normal strain within the artery wall were referenced to a frame where the artery was at rest. Representative image frames over the full pressure range are presented in
where a is the lumen radius, b is outer radius of the artery, and r is the strain measurement point. Using this relation, E can be estimated as a function of ε. In this experiment, outside pressure, po can be ignored because the artery sits less than 2.5 cm from the surface of the water. As illustrated in
Human Artery in-vivo. The accumulated radial displacement of the brachial artery wall was estimated relative to the original frame, as illustrated in
Based on the displacement information depicted in
The radial normal strain and strain rate of the diseased subject are compared with those of the normal, over approximately one cardiac cycle in
Elastic Modulus Reconstruction. For an isolated artery, Equation (1) can be used to reconstruct the arterial elastic modulus over the entire strain range, as illustrated in
To reconstruct the modulus, this equation must be inverted,
As a first step in solving this equation, a, b, and r must be estimated from B-scan images. In this study, the constants were computed by hand, but in real-time clinical operation it is very feasible to design automatic lumen detecting algorithms to define both intimal and advential boundaries (i.e., a and b). To determine a, b, and r, the averaging procedure was used in this study because artery was not perfectly circular over the entire pressure equalization procedure. This averaging should not introduce significant error into the estimated modulus as long as a and b change at the same rate for the reasonably small deformation.
Given a and b and the coordinates of the strain measurement position, the radius r can also be captured automatically. Consequently, Equation (3) can be written as:
where
are geometric factors computed from B-scan images. Δp is pulse pressure and Δε is inter-cardiac strain (i.e., change in strain from systole to diastole). The strain (
where ΔN0 is the maximum original strain at the pressure equalization frame (
Inter-cardiac strain of varying amplitude developed over each cardiac cycle Δε and corresponding mean strain
from Equation (4) is plotted on a semi-log scale versus mean strain at each cardiac cycle,
The nonlinear coefficient can serve as a strong indicator of arterial stiffness. To estimate this parameter with optimal accuracy, all image frames from high preload to low must be used. One limitation of the present study was that all image frames for the diseased subject were not of high enough quality to contribute to this accumulation. Consequently, high precision intramural strain was computed over several non-consecutive cardiac cycles in the image sequence. An absolute geometric reference was established between isolated segments by tracking changes in arterial wall thickness over the entire sequence using B-scan images. These lower precision measurements only provided the geometrical reference for high precision intramural strain measurements. Nevertheless, the results presented in
Discussion and Summary
The intramural strain range in peripheral arteries produced by the pulse pressure can be significantly extended by simply applying pressure comparable to a subject's blood pressure. Intramural strain can be monitored directly with high precision using phase-sensitive ultrasonic speckle tracking algorithms developed for elasticity imaging. By combining pressure equalization with phase-sensitive speckle tracking, new diagnostic information may be gathered about the non-linear elastic properties of the arterial wall. As demonstrated experimentally herein, the radial strain and strain rate increased ten-fold in a healthy artery when mean arterial pressure is reduced from physiologic levels. The deformation in a diseased artery, however, changed comparatively little as the pressure was equalized. Consequently, a diseased artery was easily differentiated from normal simply by observing radial normal strain and strain rate during the compressed phase of the examination. These very preliminary ex- and in-vivo results suggest that even small changes in arterial stiffness accompanying vascular disease may be sensitively monitored with elasticity imaging.
In addition to qualitative assessment of vascular compliance, the non-linear elastic modulus of the vascular wall can be quantitatively estimated using a simple reconstruction procedure. If surrounding tissue can be modeled as a continuous medium with elastic modulus E2, the elastic modulus E1 of the artery wall can be reconstructed using Equation (4). Within an offset proportional to E2, it is possible to reconstruct the arterial elastic modulus as a function of mean arterial strain from the ratio
at the following different levels of sophistication:
Both ex- and in-vivo measurements presented herein, as well as a large body of previous literature, suggest that the non-linear change in arterial elastic modulus with preload can be modeled as an exponential function. Consequently, a simple linear least squares fit to the natural log of the estimated elastic modulus as a function of preload can fully characterize the vessel wall's non-linear mechanical properties. A major advantage of this fit procedure is that only a few points are needed over a limited range of preloads to estimate the elastic modulus of the undistended artery. This may be very valuable in applications such as assessment of carotid compliance where it may be difficult to equalize the pressure all the way to the diastolic limit. Again, the elastic properties of the background medium will influence the fit, but they should not significantly alter the results except in the small preload limit of highly compliant arteries. In any event, both the intercept (i.e., the elastic modulus of the undistended artery) and the non-linear parameter (i.e., the slope of the fit) can assess the vascular compliance. Because of the large non-linear parameter in arterial tissue compared to most soft tissues, the slope should not be greatly affected by the surrounding medium. This hypothesis, as well as the predictive value of each parameter, can be tested in controlled ex-vivo studies.
External force measurement provides additional information about the elastic modulus of the surrounding muscle to further refine the reconstruction procedure. A commercial blood pressure cuff has been modified to have an acoustic window through which an ultrasound scan can be performed. A monometer attached to the cuff monitors the external force (
Reconstruction procedures presented herein focus on the static elastic properties of the arterial wall. It is well known that the arterial wall is a viscoelastic medium (Hardung, 1962). Consequently, additional information can be obtained by comparing strain rate measurements with the arterial pressure pulse to derive time constants related to viscoelastic parameters.
Assessing arterial elasticity has many important clinical applications. This method allows localized assessment of vascular elasticity that may reflect the degree of both local and general vascular disease. It may be useful in pre-operative assessment for certain vascular surgery procedures, since the elastic properties of the vessel may reflect the capacity of the artery to remodel, influencing clinical outcomes. For example, in surgically creating an arterial-venous anastomosis in hemodialysis fistula creation, the artery dilates to create a manifold increase in volume flow through the fistula to accommodate hemodialysis (Konner et al., 2003). Inelastic, diseased arteries, so prevalent in end-stage renal disease, may greatly influence the outcome of the procedure (Konner et al., 2003). Assessing the elasticity of arteries preoperatively may favorably influence site selection, prevent the development of peripheral ischemia and improve clinical outcomes. The ease of collecting data reliably, such as with a modified blood pressure cuff (
Referring now to
where A and B are constants related to the material characteristics and geometry.
The corresponding radial and tangential strains are:
Stress-strain relations for this problem are:
where σ1 is the ith component of the stress tensor and v is Poisson's ratio.
Since εz=0 for a plane strain case, Equation (A-6) becomes:
σz=v(σr+σθ). (A-7)
With this expression, Equations (A-5) and (A-6) can be rewritten as:
Combining Equations (A-8) and (A-9) to eliminate σθyields:
Substituting Equations (A-2) and (A-3) and applying boundary conditions at inner (σr=−po, at r=b, where po is the external pressure) surfaces lead to:
Combining Equations (A-11) and (A-12) determines the unknown coefficients, A and B. The radial strain of interest herein can be expressed as:
Assuming incompressibility, v=0.5, Equation (A-13) reduces to:
Referring now to
Note that D=0 to satisfy the boundary condition at infinity, i. e., no displacement. Using the same procedure as in Appendix A, radial stresses in medium I and II can be expressed as follows:
where E1 is the arterial elastic modulus and E2 is the modulus of the surrounding medium. Applying a boundary condition at the inner surface (σI,r=−pi, at r=a), and two boundary conditions at the outer surface (σII,r=−po, σII,r=σI,r, at r=b) yields:
Combining Equations (B-9), (B-10), and (B-11) determines A, B, and C:
Assuming incompressibility, v=0.5, radial strain in medium I can be reduced to:
While embodiments of the invention have been illustrated and described, it is not intended that these embodiments illustrate and describe all possible forms of the invention. Rather, the words used in the specification are words of description rather than limitation, and it is understood that various changes may be made without departing from the spirit and scope of the invention.
This invention was made with Government support under NIH Grant Nos. DK-47324, HL-47401, HL-67647 and HL-68658. The Government has certain rights in the invention.
Number | Name | Date | Kind |
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5265612 | Sarvazyan et al. | Nov 1993 | A |
5524636 | Sarvazyan et al. | Jun 1996 | A |
6165128 | Cespedes et al. | Dec 2000 | A |
Number | Date | Country | |
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20050124892 A1 | Jun 2005 | US |