A Technique for Estimating Sclerosis of Carotid Artery with Ultrasonic Echo F. Nogata1, Y. Yokota2, Y. Kawamura3, W.R Walsh4, H. Morita5, Y. Uno5 T. Kawamura6, M. Nagashima6, and N. Hotta6 1
Gifu University/Human and Information Systems, Faculty of Engineering, Gifu, Japan Gifu University/Information Science, Faculty of Engineering, Gifu, Japan 3 Gifu University/Post Doctorial Researcher, Faculty of Engineering, Gifu, Japan 4 University of New South Wales/Prince of Wales Hospital, Sydney, Australia 5 Gifu University/Graduate School of Medicine, Gifu, Japan 6 Chubu Rosai Hospital, Nagoya, Japan 2
Abstract— With aging, tensile strength, elongation and burst pressure of artery decrease, however its stiffness (stress/strain) increases. Also rate of arteriosclerosis progression depends on individual. It is an urgent task to establish inspection technique with those strength parameters for arteriosclerosis progression. The report proposes that a technique for estimating sclerosis of common carotid artery in vivo using ultrasound Bmode (Brightness-mode) imaging. The method is based on in vivo stiffness, Eth, calculated from variations in carotid diameter with changes in systolic and diastolic blood pressures. In addition, from the results of tensile and internal pressure tests by subjecting human and animal arteries specimens to step-bystep loads in vitro, we found a correlation between Eth and strength (Vu). Thus, using the correlation curve, in vivo Eth and Vu of the carotid artery can be predicted. To simplify the technique for routine medical examination, prototype software that is capable of measuring diameter changes by image processing based on 30-image/s and one pixel size data from an ultrasound device was developed. The total examination time for both sides of the common carotid artery was less than 300 seconds. To examine the validity of this technique, clinical data was used. The results indicated that stiffness (Eth), strength (Vu), and critical burst pressure (Bp) are useful symptom indices for arterial sclerosis, particularly for identifying the beginning of sclerosis in patients in their early twenties. Keywords—in vivo strength, stiffness, common carotid artery, arteriosclerosis, B-mode image.
I.
INTRODUCTION
With aging, property of artery wall changes both morphologically and mechanically. And the progression rate of sclerosis depends on individual. Mechanical changes include thickening of arterial walls, alteration of arterial elasticity, contraction of smooth muscle, increased sensitivity to pharmacological stimulation and increased arterial viscoelasticity, i.e., arteriosclerosis [1]. A report by the Japan Ministry of Health, Labor and Welfare indicated that cardiac and cerebrovascular diseases were the main cause of one-third of deaths in Japan in 2002 [2]. Cardiac
diseases, such as myocardial infraction, and cerebrovascular diseases are directly related to arteriosclerosis [3]. Arteriosclerosis is a disease of the arterial walls, in which clinical symptoms are typically only seen when the disease is advanced. Therefore, it is necessary to detect arteriosclerosis by early diagnosis methods in order to prevent the progression of this condition. In order to establish a noninvasive method for estimating sclerosis of in vivo arteries, we first examined the relationship between mechanical properties (stiffness and strength) and diameter changes in blood vessels due to heartbeats. Secondly, prototype software that is capable of measuring small diameter changes based on 30-image/s by ultrasound B-mode imaging (0.0713 mm/pixel, 7.5 MHz linear probe) was developed. The system was applied clinically during a feasibility study that may become a routine health examination item in the near future. II. ESTIMATION OF STRENGTH OF IN VIVO AERTERY A. Definition of elastic stiffness (Eth) of artery Hardening of blood vessels is a sign of aging in humans, and is the result of degradation of elongation and strength from a mechanical viewpoint. It is essential to establish simple and noninvasive techniques for measuring mechanical properties. Figure 1 shows a schematic stress-strain relationship of arteries. The curves, for both young and older adults, exhibit non-linear relationships due to the viscoelastic nature of blood vessels. In addition to strength reduction with increasing age, the curve becomes steeper. For this nonlinear relationship, the definition of a generalized mathematical expression for calculating stiffness, dV/dH, of the human artery is complex. Several reports describing the mechanical propertys of in vivo arteries have been published [4, 6-9]. In the present report, because the variations in blood vessel diameter are very small, 3~12% of the diameter (0.2~1.2 mm) due to systolic (Ps) and diastolic
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(Pd) blood pressures in the resting state, we defined a linear relationship between stress and strain, dV/dH =Eth, designated in vivo stiffness. The equation is based on a hollow thick-walled cylinder model subjected to internal pressure, as the ratio of thickness (t) and diameter (D) of the human artery, approximately t/D=0.1~0.15, is given by, (thҏ=(VTHTҗ) V
T
HT
^( R
2 i
җ 2 o
R ) p s (R
'Ri / Ri,
'Ri
R ) p d `/( R
2 i
R
2 o
i
2 i
2 o
R ),
Ri
From the condition of no volume-change between systolic and diastolic pressures, it is given as, ҏ ҏ ( Ri2 Ro2 ) ( R i2 R o2 ) ҏ җ where VT and ҏHTҏ are circumferential stress and strain at the inner wallѽ, Ri and Ro are the inner and outer radius of blood vessel respectively. Underline means the diameter at the systolic pressure, ps.
Bp=Vu(Ro2-Ri2)/(Ro2+Ri2)
(4)
In general size of the common carotid artery, Ri=3.5, Ro=4.0mm, i.e. Bp =0.133Vu, MPa. B. Strength of in vivo artery using B-mode image Since stiffness (Eth) was assumed between upper (Ps) and lower (Pd) pressures as a linear relationship, then we examined practical utility of Eq. (1) by comparing, mechanical properties by tensile and liquid-pressure tests using some materials. And the Eth was compared with other four equations (Ep,Einc,VE,andE*) in terms of stiffness reported in references [6-9]. Some kinds of materials including human common carotid [10] and artery of ox, big, tube of silicon and rubber specimens were tested. In determining 'Ri, the microscopic change in the specimen’s diameter due to inner-pressure was measured using opticalimage expanded.
Common carotid artery
Central position estimated. 'Ri=0.68 mm Figure 1. Schematic stress-strain curves showing change in mechanical properties of artery with aging; Eth increases and Vu decreases.
On the other hand, there is a non-dimensional equation known as beta parameter, E* expressing by natural logarithm of Ps/Pd. The equation [1] is
E*
ln( p s / p d ) /[( Ri Ri ) / Ri ] ln( p s / p d ) / 'Ri
(3).
The coefficients (Ri, Ro, Ri, and Ro) in Eq. (1) or (3) can be measured using ultrasound B-mode motion image. To establish an estimation technique of strength of in vivo artery, we examined the relation between ultimate strength (Vu) and Eth by tensile and liquid pressure tests for in vitro human and animal arteries specimens; step-by-step loading and rupture finally[5]. And critical burst pressure (Bp) of in vivo artery can be estimated as a hollow cylinder model subjected to inner pressure,
2Ri =7.43 mm at Ps 2Ri =6.75mm at Pd
1 sec. 1 mm Ri-variation with time, 22-year old
Figure 2. A system developed for estimating strength of in vivo artery using B-mode ultrasound image; variation of Ri wtith time is shown.
Figure 2 shows a trial system for estimating sclerosis of in vivo artery using B-mode image. For measurement of the common carotid artery, the patient lays down on a bed in a relaxed mood keeping their chin slightly upward and turning 30o approximately in a direction opposite to the side where carotid artery to be viewed. Ultrasound gel is applied on the skin surface of the subject’s neck and a linear-type ultrasound transducer (7.5 MHz) was placed. Subsequently, the B-mode image of the subject’s artery appeared on the monitor of the ultrasound equipment (540x420 pixel, 0.0713 mm/pixel in case of SonoAce PICO). The variation of Ri and Ro wtith time is measured from B-mode moving
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A Technique for Estimating Sclerosis of Carotid Artery with Ultrasonic Echo
image of a couple of heartbeats. And we assumed that Ro=Ri+wall thickness (t) =Ri+0.6 mm ( t=0.4~0.8mm; anatomical data for age of 40s~80s ). The trial software developed for analyzing the variation of Ri allows real-time measurement.
Bp
657
Vu (MPa)
, mmHg -0.1MPa d Eth d 4.0 MPa
III. RESULTS AND DISCUSSIONS Figure 3 shows a curve of stress vs. srain subjected to tensile and liquid-pressure loading for human common carotid artery,80s. Although a non-linear relation is observed, we fitted by a linear line between upper (Ps=150 mmHg) and lower (Ps=70 mmHg) blood pressures for the both loading tests. Thus, Eth of the artery was measured as 0.53 MPa and 0.46 MPa for tensile and pressure loadings, respectively. The beta value (E*) was 0.22 and 0.68 respectively. In addition, we examined other stiffness parameters, Ep, Einc, and VE in the references [6-9], and we confirmed that Eth estimated by Eq. (1) is only equivalent with tensile and internal pressure tests by comparing some viscoelastic materials[5]. We concluded that the Eth is reasonable as a strength index to express progression of arteriosclerosis. Figure 4 shows the correlation between in vivo Eth and Vu, which allows estimation of in vivo Vu of arteries ( a cylindrical model ) by B-mode imaging using the curve. rical model, which allows estimation of in vivo strength from the Eth. For example, Vu is 0.8 MPa (Bp=798 mmHg) when in vivo Eth is 0.5 MPa (average for age 60-70 years).. If tensile strength is below a lower threshold (Vu=0.2 MPa), the probable value of Bp is 200 mmHg when in vivo Eth is larger than 3~4 MPa, and this might indicated a potential risk to patient health.
Stiffness Eth, (MPa) Figure 4. Correlation between in vivo Eth and strength (Vu) obtained from tensile and internal pressure tests of the human common carotid artery specimens, which allows estimation of .Vu and Bp.
2
L R R advanced person
R
L
L
Male Female
Figure 5. Clinical investigation data showing dependence of age, gender and location ( right or left ) of common carotid artery on stiffness; special investigation is requrired if Eth is over 2.0 (under 400 mmHg). Burst pressure, Bp Strength, Vu
Figure 3. Relationship between stress and strain of the common carotid artery, 80s male ( Eth=0.46~0.53 MPa, ruptured stress Vu=0.56MPa.).
Figure 5 shows the dependence of Eth on the age of test subjects (159 males and 51 females) for right and left common carotid arteries. All experiments complied with the rules of the Ethics Committees of Gifu University Hospital and Chubu Rosai Hospitals. In this graph, the scale of critical burst pressure predicted from the relationship in Fig. 5 was confirmed. Differences in Eth for the right and left common carotid arteries are visible for both young adults and older adults, but the trend is prominent for the latter group. According to this figure, it cannot be demonsrated that Eth for a particular (right or left) artery is always larger; rather, it varies by individual. Similarly, it is not always true that the difference in magnitudes of Eth for the right and left common carotid arteries varies by gender (male or female)
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at the same age, but the difference in magnitude of Eth increases with age for both males and females. Thus, measuring Eth for both common carotid arteries during diagnosis of arteriosclerosis is necessary. Because sclerosis of the artery proceeds in localized areas, we measured stiffness distribution of the common carotid artery by moving the ultrasound transducer linearly with regular intervals of 3~5 mm for nine positions. Figure 6 shows the results for in vivo Eth in a 64-year-old female. From this figure, in vivo Eth has slight dependence on location, with the maximum Eth being 1.01 MPa. This suggests Bp=548 mmHg based on Eq. 4. This is the proposed procedure to estimate the strength of in vivo arteries. It is effective to use the mechanical strength of arteries as an index of sclerosis development.
1) In vivo Eth can be estimated using Eq. (1) and critical burst pressure (Bp) using Eq. (4). 2) In vivo Eth, tensile strength (Vu) and burst pressure (Bp) are useful symptom indices for arteriosclerosis, particularly for identifying the beginning sclerosis that during the early twenties.
ACKNOWLEDGMENT The authors are grateful to organizations for their contributions. were performed according to the Committees of Gifu University paricipating hospials.
to all cooperating Clinical investigations rules of the Ethics Hospital and other
REFERENCES 1.
ǍRi (mm)
ǍRi (mm) interval
Figure 6. Distribution of stiffness (Eth) showing sclerosis progression of the common carotid artery, measurement of 4~5-mm inerval.
IV. CONCLUDING REMARKS A new technique for investigating risk of arteriosclerosis by measuring in vivo stiffness (Eth) of the common carotid artery is proposed. This method is based on in vivo Eth, as calculated from the variations in carotid artery diameter at systolic and diastolic blood pressures by image processing using B-mode images. The technique was applied clinically to during feasibility study that could become a regular health examination item in a near future. It can be concluded as,
T. Matsumoto and K. Hayashi, “Response of arterial wall to hypertension and residual stress,” Biomechanics, Springer, 1996,pp.93-119. 2. Annual report of Ministry of Health, Labor and Welfare, Japan 2003. 3. G. Gamble, et al., “B-mode ultrasound image of the carotid artery wall, Correlation of ultrasound with histological measurement,” Arteriosclerosis, Vol. 102, 1993, pp.163-173. 4. T. Imura, et al., “Non-invasive ultrasonic measurement of the elastic properties of the human abdominal aorta,” Cardiovascular Research, Vol. 20, 1986, pp.208-214. 5. F.Nogata, Y.Yokota, Y.Kawamura, H.Morita and Y. Uno, ”Estimating of mechanical strength of in vivo common carotid artery using ultrasound echo images” Proceedings of ISBPE/The 22nd SICE Symposium. Harbin, China, 2007,pp.249-252. 6. R. H. Peterson, R. E. Jensen, R. Parnell: “Mechanical properties of arteries in vivo,” Circulation Research, Vol. 8, 622-639,1960. 7. A.G., Hudetz, “Incremental elastic modulus for orthotropic incompressible arteries,” J. Biomechanics, Vol. 12,1979, pp.651-655 8. F.Hansen, et al., “Diameter and compliance in the human common carotid artery variations with age and sex,” Ultrasound in Med. & Bio. Vol. 21,1995,pp.1-9 9. D. H. Bergel: “The Static Elastic Properties of the Arterial Wall. J. Physiol,”1961, 156,pp.445-457. 10. F.Nogata, Y.Yokota, Y.Kawamura, H.Morita Y. Uno, and W.R.Walsh, "A Technique for estimating arteriosclerosis using ultrasound images of the common carotid artery” Proceedings of EMBEC 08, Chania, Crete Island, Greek Author: Fumio Nogata Institute: Gifu University, Human and Information Systems, Faculty of Engineering Street: Yanagi-do City: Gifu Country: Japan Email:
[email protected]
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