Detecting the Process of Blood Coagulation and Clot Formation with

Journal of Medical and Biological Engineering, 25(4): 171-177
171
Detecting the Process of Blood Coagulation and Clot
Formation with High Frequency Ultrasound
Chih-Chung Huang1
2
Shyh-Hau Wang1,*
Po-Hsiang Tsui1,2
Chun-Yi Chiu1
1
Department of Biomedical Engineering, Chung Yuan Christian University, Chung Li, Taiwan, 320 ROC
Department of Biomedical Engineering, Yuan Pei Institute of Science and Technology, Hsin Chu, Taiwan, 300 ROC
Received 31 Aug 2005; Accepted 17 Oct 2005
Abstract
High frequency ultrasounds, up to 50 MHz, were applied to assess changes of blood properties during coagulating
and clotting. Experiments were performed using calcium chloride solution to induce the blood coagulation (BC) and
clot formation (CF) in porcine whole blood of various hematocrits ranged from 25 to 55 %. The ultrasonic signals
backscattered from the whole blood were digitized at a 500 MHz sampling frequency and collected for 30 minutes at
one A-line per second temporal resolution. The corresponding M-mode images and integrated backscatters acquired
from four transducers of different frequencies were processed to characterize blood properties. Two parameters,
denoted as Sr and tc respectively in response to the rate of change and duration between the onset of blood coagulation
and the end of clot formation, were derived from the integrated backscatter as a function of time to further evaluate the
sensitivity and accuracy for measurements. Results showed that backscattered signals acquired from different
frequencies and their relative analysis may be applied to effectively detect the process of BC and CF. In particular,
measurements using high frequency ultrasound tended to exhibits a better sensitivity to detect the coagulation, with
larger average Sr and shorter tc respectively corresponding to 0.23 dB/sec and 756 seconds measured from a hematocrit
of 35 % using a 50 MHz transducer. The discrepancy between results of tc measured by different frequencies may be
readily associated with the resultant size of the resolution cell of the transducer and the pulse duration. Both ultrasonic
M-mode image and integrated backscatter in this study were validated to monitor the process of BC and CF and
specifically with those quantitative parameters, Sr and tc. It enables a potential to further apply high frequency
ultrasounds for early detecting BC and CF in clinical diagnoses.
Keywords: Blood coagulation, Clot formation, High frequency ultrasound.
Introduction
The blood clot is a meshwork of fibrin fibers running in
all directions that composed of a part of blood cells and
entrapped plasma. Normally the formation of clot provides a
protective mechanism to stop bleeding from a wounded tissue.
However, an abnormal clot, called thrombus, could be
developed and attached inside the vessel wall. As there is an
adequate force of blood flow exerting the thrombus, it could be
come off from the attachment site to form an embolus and to
flow in a blood vessel [1]. The emboli developed in a large
artery or the left heart is severely hazardous for that it could
flow downstream into peripheral vessels to further occlude
blood supply in arteries or arterioles such as the brain, kidneys,
or other vital organs [1]. A vulnerable embolus originated in
the venous system or in the right heart could subsequently flow
into vessels in the lung leading to such a dreadful syndrome as
the pulmonary arterial embolism [2]. In addition, those
* Corresponding author: Shyh-Hau Wang
Tel: +886-3-2654504; Fax: +886-3-2654599
E-mail: [email protected]
immobile patients confined to bed frequently suffer from the
formation of the intravascular clot corresponding to the
obstructed flowing blood in any vessel for a few hours.
Consequently, it is crucial to develop techniques capable of
detecting the process of the blood coagulation and clot
formation in blood vessels for early diagnosing the formation
of any embolism.
To date, the simplest method to qualitatively characterize
the process of BC and CF is to withdraw a certain amount of
blood that is subsequently placed in a testing tube for
observing and recording the transient time of BC and CF [3].
Further typical modalities developed to quantitatively detect
the BC are based on three of the following principles:
mechanical impedance, electromagnetism, and photometry [4].
Most of these modalities however are not appropriate for
continuous and dynamic monitoring of the changes of blood
properties as well as remain invasive sampling of the blood.
Other feasibility studies by ultrasound techniques were carried
out due to low cost and real-time capability with the involved
ultrasound technique. Jacobs et al. [5] utilized two frequency
172
J. Med. Biol. Eng., Vol. 25. No. 4 2005
Table 1. Characteristics of employed transducers in the experiment. The
-6 dB bandwidth and pulse length were estimated from the
pulse echo response of transducers. The corresponding
F-number and diameter were obtained from the manufacturer’s
specifications.
Figure 1. Block diagram for the experimental arrangement.
scanning ultrasonic spectrographs that allow measurements to
be implemented continuously over a frequency range from 1 to
10 MHz. The instrument was applied to monitor changes of
blood property in sound velocity as a function of frequency
during BC in the purified human fibrinogen solution and
human plasma. Grybauskas et al. [6] developed a digital
ultrasonic interferometer of a fixed path that used only a small
amount of testing blood sample for investigating the
coagulation, retraction, and clot melting processes in the whole
blood. Machado et al. [7] employed the acoustic streaming to
assess BC, in which a 2.7 MHz transducer was applied to
measure ultrasonic scattering associated with moving spherical
glass particles, with an average size of 200 µm diameter
immersed in a 0.1 ml of plasma, driven by the incident
ultrasonic energy. The amplitude of varying backscattered
signals associated with the motion of these particles was
gradually reduced in response to the formation of clot. Alves et
al. [8] employed ultrasonic shear wave of a 2 MHz frequency
to measure the prothrombin time and activated partial
thromboplastin time by two AT-cut quartz crystal transducers.
Hartley [9] utilized a 20 MHz pulsed Doppler ultrasound to
evaluate the characteristics of acoustic streaming during BC
and found that the acoustic streaming decreased with the
increase of blood viscosity during BC.
Alternatively, the variation of ultrasonic quantitative
parameters, including sound velocity, attenuation, and
scattering, was known corresponding to the elastic properties
of media where the acoustic wave was propagated. Shung et al.
[10] indicated that ultrasound backscattering may be used to
determine the onset of the formation of fibrin clot in plasma
and whole blood. They later measured ultrasonic attenuation,
acoustic velocity, and backscatter of the human blood as a
function of time for up to 24 hours following the onset of BC
with a 7.5 MHz ultrasound [11]. These parameters were found
to increase significantly with the clot formation. Voleišis et al.
[12] measured the sound velocity in the coagulating whole
blood by a 5 MHz ultrasound and observed that a fine change
of ultrasonic velocity was registered corresponding to the very
Frequency
5 MHz
10 MHz
Manufacturer
Panametrics
Panametrics
Model
Diameter
F-number
-6 dB
bandwidth
Lateral
profile
Pulse length
Resolution
cell
V309
12.7 mm
1.5
A311R
12.7 mm
1.6
2-8 MHz
6-13 MHz
1.21 mm
0.55 mm
0.35 mm
0.26 mm
3
0.4022 mm
3
0.0617 mm
35 MHz
50MHz
Penn
state
5.0 mm
2.0
22-43
MHz
Penn
state
2.5 mm
2.0
32-62
MHz
0.21 mm
0.14 mm
0.15 mm
0.0052
mm3
0.11 mm
0.0017
mm3
beginning of the clotting to lysis. Ultrasonic attenuation
coefficient of coagulating blood was measured by Wang et al.
[13] using a 4.5 MHz ultrasound. The results were consistent
with those of measurements for blood viscosity as a function
of time using a viscometric method [14].
Among those ultrasonic parameters, backscattered signals
has been shown dependent on the size, shape, concentration,
density, and other elastic properties of the scatterers in a
biological tissue as well as the employed ultrasonic frequency
[15]-[20]. Accordingly, ultrasonic backscattered signals may
be sensitive to detect the local variation of scattereres in the
microstructure for early detecting the process of BC and CF.
To further explore a better sensitive and accurate ultrasonic
backscattering technique to detect BC and CF, measurements
by high frequency ultrasounds up to 50 MHz were carried out
from porcine blood of different hematocrits ranged from 25 to
55%. The process of BC and CF was detected and assessed by
both the M-mode backscattering image and its corresponding
integrated backscatter. Results were analyzed and discussed to
better elucidate the effects of ultrasonic frequency on the
sensitivity and accuracy of detecting the process of BC and CF
from different hematocrits of blood.
Materials and Methods
The experiments were performed with the porcine blood.
The acid citrate dextrose (ACD) solution was immediately
added to the porcine blood at a volume concentration of 15%
to prevent the coagulation. The blood was processed by
filtering out impurity contents and subsequently was
centrifuged to separate into the blood cells and plasma.
Different hematocrits of whole blood ranged from 25 to 55%
were made by reconstituting certain volume of separated
erythrocytes and plasma. The experimental arrangement is
shown in Figure 1 in which the blood sample was placed in a
rectangular plexiglass container in a water bath where
temperature was regulated at 32oC using a thermocirculator.
Four focused transducers with frequencies centered at 5, 10, 35,
and 50 MHz were used. The pulse-echo test of 50 MHz
transducer is shown in Figure 2. The pulse length, bandwidth,
and other characteristics of each transducer are listed in Table I.
Detecting the Process of Blood Coagulation
173
(a)
(b)
Figure 2. Pulse echo (a) and associated spectrum (b) of 50 MHz transducer used for measurement.
A pulser/receiver (5900PR, Panametrics, Waltham,
Massachusetts, USA) was used to drive transducers for
transmitting and receiving ultrasound. The received
radio-frequency (RF) signals backscattered from blood were
respectively amplified and filtered with a 54 dB variable gain
amplifier and a bandpass filter built-in in the pulser/receiver.
RF signals were subsequently digitized with a 8-bit
analog-to-digital (A/D) converter (PDA500, Signatec, Corona,
California, USA) by a maximum of 500 MHz sampling
frequency.
Measurements were performed by the procedure
described as follows. (1) The sample volume was located near
the focal zone of the transducer which was positioned
perpendicularly to the side wall of a container. (2) A 5 ml
blood of a specific hematocrit was placed in the container,
which was stored for 3 minutes to achieve thermal equilibrium
with the surrounding water in the tank. (3) The RF signals was
acquired at a 1 A-line per second temporal resolution. (4) One
minute after the acquisition of signals, a drop of 2.5 ml 0.2 M
CaCl2 solution was delivered into blood to induce BC and CF.
(5) The total data acquisition was lasted for 30 minutes.
A total of five measurements for each hematocrit of blood
samples were carried out with the employed ultrasound at
frequencies ranged from 5 to 50 MHz. The M-mode image for
monitoring the process of BC and CF was obtained from
envelopes calculated by the Hilbert transform for each A-line
of RF backscattered signals. Moreover, the integrated
backscatter (IB) for better quantifying the variation of
ultrasonic backscattering was calculated by the following
equation [21]-[22],
IB =
1
f 2 − f1
2
f2
Sr ( f )
f1
S ref ( f )
∑
2
(1)
where f1 and f 2 respectively denote the lower and upper
frequencies of the –6 dB bandwidth of the ultrasonic spectrum
and those of S r ( f ) and S ref ( f ) represent the spectra
acquired from backscattered signals of blood and echoes
reflected from a stainless steel reflector in the distilled water,
respectively. A five-point moving average filter was
subsequently applied to smooth out the integrated backscatter
as a function of time.
Results
Figures 3 and 4 respectively are typical M-mode image
and integrated backscatter as a function of time measured from
a 35% porcine blood with different ultrasonic frequencies from
5 to 50 MHz, which correspond measurements to the whole
process of BC and CF. The echogenicity demonstrated that the
M-mode image progressively increased toward the region in
the axial direction away from the transducer within the first
minute of the measurement, which is partially due to the
combination effect of red cell aggregation and sedimentation
[23]. The highest variation of both echogenicity and integrated
backscatter corresponds to measurements carried out using a
50 MHz ultrasound, shown in Figures 3(d) and 4(d), and which
agrees with the frequency dependency of ultrasonic scattering
described in Rayleigh scattering theory [23]-[24]. At the first
minute after the beginning of measurement, the addition of
CaCl2 solution into the blood led both the echogenicity and
integrated backscatter gradually decrease to a minimum owing
to partially the disruption of red cell aggregation and decrease
of hematocrit in the blood. As the effect of CaCl2 solution
induced the BC, the echogenicity and integrated backscatter
tended to increase dramatically.
To better elucidate the whole process of BC and CF,
typical results of Figures 3 and 4 were divided into five phases
with dashed line indicated in figure 4(a). These phases may be
empirically applied to differentiate variation of blood
properties during BC and CF, in which show phase I of the
original blood, phase II of the addition of CaCl2 solution,
phase III of the increase of blood coagulation, phase IV of the
variation with coagulating blood, and phase V of the clot
formation. The process of BC mainly correlates to phases at III
and IV, in which both M-mode image and integrated
backscatter tend to be fluctuating with results measured from
ultrasounds of all different frequencies. As the clot was formed,
those backscattered signals become less fluctuated, indicated
in phase V.
Two additional parameters defined to characterize and
assess the sensitivity and accuracy of detecting BC and CF
were respectively denoted as Sr, derived from the rate of
integrated backscatter as a function of time within the phase III
of Figure 4, and tc of the clotting time for assessing the
duration between the addition of CaCl2 solution and the
J. Med. Biol. Eng., Vol. 25. No. 4 2005
174
(a)
(b)
(c)
(d)
Figure 3. Ultrasonic M-mode images acquired from a 35% hematocrit of porcine blood during the blood coagulation and clot formation
measured by ultrasonic frequencies as: (a) 5 MHz, (b) 10 MHz, (c) 35 MHz, (d) 50 MHz.
(a)
(b)
(c)
(d)
Figure 4. The integrated backscatter as a function of time during the process of blood coagulation and clot formation obtained from a 35%
hematocrit of porcine blood measured by ultrasonic frequencies as: (a) 5 MHz, (b) 10 MHz, (c) 35 MHz, (d) 50 MHz.
Detecting the Process of Blood Coagulation
Figure 5. Sr as a function of ultrasound frequency associated with
different hematocrits of blood.
175
and IV, shown in Figure. 4. The overall results of tc as a
function of ultrasonic frequency are summarized in Figure. 6
in which data demonstrated a decrease of tc with the increase
of ultrasonic frequency including blood samples of different
hematocrits. Specifically, measurements from a 35%
hematocrit of blood exhibited the decrease of average tc from
1040 to 756 seconds corresponding to the increase of the
applied ultrasonic frequencies from 5 to 50 MHz. The tc was
also found to be dependent on hematocrit with the increase of
average tc from 758 to 1030 seconds relative to the increase of
hematocrits from 25 to 55 %. The tc dependency on the
ultrasound frequency becomes steady for the applied
ultrasound higher than 35 MHz, which is similar to results in
Figure. 5. These results consistently demonstrated that high
frequency ultrasound is capable of accurately and sensitively
detecting BC and CF.
Discussion and Conclusion
Figure 6. tc as a function of ultrasound frequency associated with
different hematocrits of blood.
instant clot was formed indicated by that the variation of
integrated backscatter as a function of time finally approached
to steady state. Higher value of Sr corresponds to faster
reaction for blood coagulation which could be detected. Figure
5 summarizes Sr measured with ultrasonic frequencies ranged
from 5 to 50 MHz and with blood of various hematocrits
ranged from 25 to 55 %. The tendency of Sr was found to
increase with the increase of ultrasonic frequency, which is
consistent with measurements in blood of all hematocrits. An
example adopted from results measured from blood of 35%
hematocrit demonstrated that the average Sr increased from
0.12 to 0.23 dB/S in accordance with the increase of ultrasonic
frequencies from 5 to 50 MHz. This also indicates that the
higher the applied ultrasonic frequency was used, the higher
sensitivity for the detection of blood coagulation can be
achieved. Furthermore, Sr is not linearly dependent on the
ultrasonic frequency, where Sr tends to approach steady state
with the employed ultrasonic frequency higher than 35 MHz
validated for all measurements from each hematocrit of blood.
Specifically, the average Sr obtained by a 35 MHz ultrasound
tended to decrease from 0.26 to 0.2 dB/S with the hematocrits
increased from 25 to 55%, in which the tendency is consistent
with measurements by other ultrasonic frequencies shown in
Figure. 5.
The tc is calculated from the duration between phase II
The development of blood coagulation in a vessel could
lead to the fatal formation of blood clot. It therefore is crucial
to develop techniques capable of early detecting the BC and
CF in clinical applications. Among those ultrasonic techniques,
ultrasonic backscattered signals from blood have shown to be a
great potential able to early detect variations of scattering
properties in a local tissue [13],[25]. This enables a feasibility
of applying ultrasonic backscattering to characterize the
process of BC and CF.
Present studies have demonstrated that both M-mode
image and integrated backscatter measured from ultrasonic
frequencies ranged from 5 to 50 MHz are able to effectively
quantify the process of BC and CF in porcine blood of
different hematocrits ranged from 25 to 55 %. The variation of
blood properties corresponds to the initial stage of the
development of BC associated with the addition of CaCl2
solution due to that the induced plasma protein prothrombin
was firstly converted to enzyme thrombin. The thrombin
would catalyze a subsequent reaction leading several
polypeptides to be separated from molecules of the large
rod-shaped plasma protein fibrinogen to be bound to each
other to form fibrin fibers [26]. Accordingly, the varying size,
shape, and density of scatterers in whole blood corresponding
to the progress of BC may be discerned by the gradual change
of both M-mode image and the integrated backscatter. As
described in previous section, the sensitivity for detecting BC
may be fairly evaluated with Sr. During the progressive
development of BC, a great quantity of fibrinogens was
subsequently converted to fibrin fibers tending to bind
numerous red blood cells. This response corresponds to
fluctuating M-mode image and integrated backscatter shown in
phase IV. As the clot was formed, considerable erythrocytes
were trapped in the fibrin meshwork firmly [26] leading to a
fair stable M-mode image and integrated backscatter in the
phase V of Figure. 4. The clotting time, tc, calculated from the
duration between BC and CF provides as a quantity to
characterize variations blood properties measured from various
hematocrits of blood sample by different ultrasonic
frequencies.
J. Med. Biol. Eng., Vol. 25. No. 4 2005
176
The summations of Sr and tc with respect to different
measurements by ultrasonic frequencies from 5 to 50 MHz in
blood of different hematocrits are respectively given in Figures
5 and 6. These results showed that the BC can be more
sensitively detected with high frequency ultrasound, discerned
with higher Sr. The Sr dependency on ultrasonic frequency
behaves as a nonlinear relationship in which Sr approaches to
steady state as that the applied frequency is higher than 35
MHz. Moreover, the clotting time tc is also
frequency-dependent, which is shorter as the applied frequency
is higher. These results could be largely due to such factors as
the pulse duration, beam width, and frequency-dependent
scattering that allow high frequency ultrasounds to be more
sensitive to detect BC than those of low frequency ultrasounds.
Moreover, due to that the composition of plasma in blood is
hematocrit dependent, the process of BC and CF tends to be
affected indicated by slightly different values of Sr and tc from
different hematocrits of blood [10]. The higher Sr corresponds
to measurements with higher ultrasonic frequencies due to
primarily that the high frequency ultrasound is with smaller
size of wavelength and resolution cell defined by the pulse
length and lateral beam profile of a transducer [27]. Assuming
an ideal cylinder is with the resolution cell of a transducer [28],
the sample volume of an applied 50 MHz transducer is
approximately equal to 0.0017 mm3. The high frequency
ultrasound with such small resolution cell and wavelength
enables a better sensitivity for detecting the instantaneous
change of blood properties during BC, verified by results in
Figure. 5. Similar reason may be directly applied to account
for shorter tc obtained using high frequency ultrasound in
Figures 4 and 6. In summary, this study applied both ultrasonic
M-mode image and integrated backscatter to monitor the
process of blood coagulation and clot formation and were
quantified by defined parameters Sr and tc. With both smaller
wavelength and resolution cell, high frequency ultrasound
tends to be more sensitive to detect BC and CF than those of
by ultrasonic frequencies lower than 10 MHz. Fresh porcine
whole blood collected from a local slaughterhouse was used in
this study. A lot of studies indicate that many blood properties
of pig are similar to human. Those blood properties include the
shape of red blood cell (RBC), RBC mean diameter, packed
cell volume, hematocrit, mean corpuscular hemoglobin, and
thrombocyte [23]. Consequently, many studies used porcine
blood to simulate human blood to explore the relationship
between ultrasound and blood properties [17],[19-20]. In
addition, the component of porcine plasma is different from
human blood, however, blood plasma is an important factor
that can influence the process of blood coagulation and clot
formation. Consequently, we consider that the results from
porcine blood may different from human blood but the
difference is limitation. Current study showed that ultrasonic
backscatter parameter might be applied for detecting the blood
coagulation and clot formation. However, we think it is still
difficult to implement the in vivo measurement.
Acknowledgements
This work was supported by the National Science Council
of Taiwan, ROC, of the grants: NSC 93-2213-E-033-035 and
NSC 94-2213-E-033-039.
References
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
[17]
[18]
[19]
[20]
[21]
[22]
D. J. Kuter and R. D. Rosenberg, Hemorrhagic disorders III.
Disorders of Hemostasis. Hematology 5th ed. MIT Press, 1991.
G. Murano and R. L. Bick, Basic concepts of hemostasis and
thrombosis. CRC Press, 1980.
J. M. Thomson, Blood coagulation and haemostasis. Churchill
Livingstone, 1991.
L. A. Geddes and L. E. Baker. Principles of applied biomedical
instrumentation. John Wiley & Sons, c1989.
J. E. Jacobs, A. V. Malinka, P. Haque, and M. D. Jhabvala,
“Ultrasound spectroscopy applied to blood coagulation
studies,” Ultrasonics, 3: 84-90, 1976.
P. Grybauskas, K Kundrotas, V Sukackas, and E. Yaronis,
“Ultrasonic digital interferometer for investigation of blood
clotting,” Ultrasonics, 16: 33-36, 1978.
J. C. Machado, A. Lenzi, and W. G. Silva, “An ultrasonic
method to measure human plasma coagulation time,” J. Acoust.
Soc. Amer., 90(4): 1749-1753, 1991.
C. H. F. Alves and J. C. Machado, “Measurement of plasma
clotting time using ultrasonic shear waves,” Physio.l Meas., 15:
309-316, 1994.
C. J. Hartley, “Characteristics of acoustic streaming created and
measured by pulsed Doppler ultrasound,” IEEE Trans. Ultrason.
Ferroelect. Freq. Contr., 44: 1278-1285, 1997.
K. P. Shung and R. A. Sigelmann, “Ultrasonic measurement of
blood coagulation time,” IEEE. Trans. Biomed. Eng., 22:
334-337, 1975.
K. K. Shung, D. Y. Fei, Y. W. Yuan, and W. C. Reeves,
“Ultrasonic characterization of blood during coagulation,” J.
Clin. Ultrasound, 12: 147-153, 1984.
A. Voleišis, R. Kažys, L. Mažeika, R. Šliteris, B. Voleišienè,
and P. Grybauskas, “Ultrasonic method for the whole blood
coagulation analysis,” Ultrasonics, 40: 101-107, 2002.
S. H. Wang and P. H. Tsui, “Ultrasonic techniques to assess the
properties of hard and soft biological tissues,” Key Engineering
Material, 247-273: 2055-2060, 2004.
Y. H. Wang, T. W. Chung, J. Y. Lai, J. J. Hsu, and Y. S. Lin, “A
viscometric method to study the effects of hematocrit of blood
and different surfaces of biomaterials on blood clot formation,”
J. Chin. Inst. Chem. Engrs., 31: 27-32, 2000.
J. C. Bamber and C. R. Hill, “Acoustic properties of normal and
cancerous human liver-I dependence on pathological
condition,” Ultrasound Med. Biol., 7: 121-133, 1981.
J. C. Bamber, C. R. Hill, and J. A. King, “Acoustic properties of
normal and cancerous human liver-II dependence on tissue
structure,” Ultrasound Med. Biol., 7: 135-144, 1981.
K. K. Shung, “On the ultrasound scattering from blood as a
function of hematocrit,” IEEE Trans. Sonics. Ultrason., 29:
327-311, 1982.
Y. W. Yuan and K. K. Shung, “The effect of focusing on
ultrasonic backscatter measurements,” Ultrason. Imaging, 8:
121-130, 1986.
S. H. Wang and K. K. Shung, “An approach for measuring
ultrasonic backscattering form biological tissues with focused
transducers,” IEEE Trans. Biomed. Eng., 44: 549-554, 1997.
S. H. Wang and K. K. Shung, “In vivo measurements of
ultrasonic backscatter in blood,” IEEE Trans. Ultrason.
Ferroelec. Freq. Contr., 48: 425-431, 2001.
M. O’Donnell, D. Bauwens, J. W. Mimbs, and J. G. Miller,
“Broadband integrated backscatter: An approach to spatially
localized tissue characterization in vivo,” IEEE Ultrason. Symp.
Proc., 175-178, 1979.
S. H. Wang, P. H. Chang, K. K. Shung, and H. B. Levene,
“Some considerations on the measurements of mean frequency
Detecting the Process of Blood Coagulation
[23]
[24]
[25]
shift and integrated backscatter following administration of
Albunex®” Ultrasound Med. Biol., 22: 441-451, 1996.
K. K. Shung and G. A. Thieme, Ultrasonic scattering in
biological tissues. CRC Press, 1993.
J.F. Greenleaf, Tissue characterization with ultrasound- volume
II. CRC Press, Boca Raton, 1986.
P. H. Tsui and S. H. Wang, “The effect of transducer
characteristics on the estimation of Nakagami parameter as a
function of scatterer concentration,” Ultrasound Med. Biol., 30:
1345-1353, 2004.
[26]
[27]
[28]
177
A. Vander, J. Sherman, and D. Luciano. Human Physiology:
The mechanisms of body function- 8th ed. McGraw-Hill. New
York. 2001
J. A. Zagzebski, J. F. Chen, F. Dong, and T. Wilson,
“Intervening attenuation affect first-order statistical properties
of ultrasound echo signals,” IEEE Trans. Ultrason. Ferroelec.
Freq. Contr., 46: 35-40, 1999.
D.A. Christensen. Ultrasonic bioinstrumentation. New York,
Wiley, 1988.