d Original Contribution CORRELATION BETWEEN CLASSICAL RHEOMETRYAND SUPERSONIC SHEAR WAVE IMAGING IN BLOOD CLOTS MIGUEL BERNAL,* JEAN-LUC GENNISSON,* P ATRICE FLAUD, y and MICKAEL T ANTER* *Institut Langevin – Ondes et Images, ESPCI ParisTech, CNRS UMR 7587, INSERM U979, Paris, France; and y Matiere et Systemes Complexes, CNRS UMR 7057, Universit e Paris VII Denis Diderot, Paris, France (Received 18 December 2012; revised 19 April 2013; in final form 23 May 2013) Abstract—The assessment of coagulating blood elasticity has gained importance as a result of several studies that have correlated it to cardiovascular pathologic conditions. In this study we use supersonic shear wave imaging (SSI) to measure viscoelastic properties of blood clots. At the same time, classical rheometry experiments were carried out on the same blood samples taken within the first few seconds of coagulation. Using SSI, phase velocities of the shear wave indicated increasing dispersion with time. In all cases, the frequency bandwidth of propagating shear waves changed from 20–50 Hz at the first few min of coagulation to around 300 Hz toward the end of experiments. Using the values of G 0 and G 00 from the rheometry studies, the theoretical shear wave velocities were calculated and correlated with SSI measurements. Results of the two techniques were in very good agreement, confirming that SSI provides accurate measurements of viscoelastic properties as corroborated by conven- tional rheometric measurements. (E-mail: [email protected]) Ó 2013 World Federation for Ultrasound in Medicine & Biology. Key Words: Deep venous thrombosis, Coagulation, Viscoelasticity, Dispersion, Rheometry, Supersonic shear imaging. INTRODUCTION Blood and its coagulation process have been studied for thousands of y. In the past few decades, the importance of the elastic and viscous properties of the coagulating blood has been recognized and correlated with increased coronary atherothrombosis, myocardial infarction (MI) and hypofibrinolysis (Collet et al. 2006; Fatah et al. 1996). It has been shown that blood samples from patients with premature coronary artery disease (CAD) produce ex vivo fibrin clots that are stiffer and resistant to fibrinolysis. Other studies have focused on the effect of blood clot elasticity on diseases like deep venous thrombosis (DVT) and pulmonary embolism (PE). Assessment of the age of thrombi has been shown to be critical for risk stratification and patient manage- ment in these conditions. Because the major risk occurs when the thrombus, or part of it, breaks, blocking the pulmonary veins and creating a pulmonary embolism, prediction of this event is of great importance. New or ‘‘acute’’ thrombi have been shown to be more likely to detach than ‘‘mature’’ and stable clots (Xie et al. 2005; Zwiebel and Pellerito 2004). In addition, by using mechanical testing (stress- strain relationships), Emelianov et al. found blood clot elasticity to be closely related to clot age (Emelianov et al. 2002; Rubin et al. 2006). To this end, multiple techniques have been devel- oped to provide blood elasticity. Some of these tech- niques have been developed to measure the microscopic properties of blood clots, whereas others have been focused on the blood clots as homogeneous masses. Studies using optical tweezers and atomic force micro- scopes have identified fibrin as the primary structural molecule of blood clots (Weisel 2008), the mechanical properties of which were studied as early as the 1940s (Ferry and Morrison 1944). Nowadays, it is known that viscoelasticity of fibrin determines whether a thrombus will tend to become occlusive or break off into clots, causing blockage of smaller conduits (Weisel 2008). Studies at the macroscopic level have used multiple approaches to measure the mechanical properties. Thromboelastography was first described by Hellmut Hartert in 1948 (Whitten and Greilich 2000). This technique used a small blood sample placed in a bowl, which is moved back and forth while a sensor (pin) is in contact with the blood and registers the resistance to Address correspondence to: Jean-Luc Gennisson, 1 Rue Jussieu, 75005 Paris, France. E-mail: [email protected]1 Ultrasound in Med. & Biol., Vol. -, No. -, pp. 1–14, 2013 Copyright Ó 2013 World Federation for Ultrasound in Medicine & Biology Printed in the USA. All rights reserved 0301-5629/$ - see front matter http://dx.doi.org/10.1016/j.ultrasmedbio.2013.05.014
Transcript
Ultrasound in Med. & Biol., Vol. -, No. -, pp. 1–14, 2013Copyright � 2013 World Federation for Ultrasound in Medicine & Biology
Printed in the USA. All rights reserved0301-5629/$ - see front matter
/j.ultrasmedbio.2013.05.014
http://dx.doi.org/10.1016
d Original Contribution
CORRELATION BETWEENCLASSICAL RHEOMETRYAND SUPERSONIC SHEARWAVE IMAGING IN BLOOD CLOTS
MIGUEL BERNAL,* JEAN-LUC GENNISSON,* PATRICE FLAUD,y and MICKAEL TANTER**Institut Langevin – Ondes et Images, ESPCI ParisTech, CNRS UMR 7587, INSERM U979, Paris, France; and yMati�ere et
Syst�emes Complexes, CNRS UMR 7057, Universit�e Paris VII Denis Diderot, Paris, France
(Received 18 December 2012; revised 19 April 2013; in final form 23 May 2013)
A75005
Abstract—The assessment of coagulating blood elasticity has gained importance as a result of several studies thathave correlated it to cardiovascular pathologic conditions. In this study we use supersonic shear wave imaging(SSI) to measure viscoelastic properties of blood clots. At the same time, classical rheometry experiments werecarried out on the same blood samples taken within the first few seconds of coagulation. Using SSI, phase velocitiesof the shear wave indicated increasing dispersion with time. In all cases, the frequency bandwidth of propagatingshear waves changed from 20–50 Hz at the first few min of coagulation to around 300 Hz toward the end ofexperiments. Using the values of G0 and G00 from the rheometry studies, the theoretical shear wave velocitieswere calculated and correlatedwith SSImeasurements. Results of the two techniques were in very good agreement,confirming that SSI provides accurate measurements of viscoelastic properties as corroborated by conven-tional rheometric measurements. (E-mail: [email protected]) � 2013 World Federation for Ultrasoundin Medicine & Biology.
Blood and its coagulation process have been studied forthousands of y. In the past few decades, the importanceof the elastic and viscous properties of the coagulatingblood has been recognized and correlated with increasedcoronary atherothrombosis, myocardial infarction (MI)and hypofibrinolysis (Collet et al. 2006; Fatah et al.1996). It has been shown that blood samples frompatients with premature coronary artery disease (CAD)produce ex vivo fibrin clots that are stiffer and resistantto fibrinolysis. Other studies have focused on the effectof blood clot elasticity on diseases like deep venousthrombosis (DVT) and pulmonary embolism (PE).Assessment of the age of thrombi has been shown tobe critical for risk stratification and patient manage-ment in these conditions. Because the major riskoccurs when the thrombus, or part of it, breaks,blocking the pulmonary veins and creating a pulmonaryembolism, prediction of this event is of greatimportance. New or ‘‘acute’’ thrombi have been shownto be more likely to detach than ‘‘mature’’ and stable
ddress correspondence to: Jean-Luc Gennisson, 1 Rue Jussieu,Paris, France. E-mail: [email protected]
1
clots (Xie et al. 2005; Zwiebel and Pellerito 2004).In addition, by using mechanical testing (stress-strain relationships), Emelianov et al. found blood clotelasticity to be closely related to clot age (Emelianovet al. 2002; Rubin et al. 2006).
To this end, multiple techniques have been devel-oped to provide blood elasticity. Some of these tech-niques have been developed to measure the microscopicproperties of blood clots, whereas others have beenfocused on the blood clots as homogeneous masses.Studies using optical tweezers and atomic force micro-scopes have identified fibrin as the primary structuralmolecule of blood clots (Weisel 2008), the mechanicalproperties of which were studied as early as the 1940s(Ferry and Morrison 1944). Nowadays, it is known thatviscoelasticity of fibrin determines whether a thrombuswill tend to become occlusive or break off into clots,causing blockage of smaller conduits (Weisel 2008).Studies at the macroscopic level have used multipleapproaches to measure the mechanical properties.Thromboelastography was first described by HellmutHartert in 1948 (Whitten and Greilich 2000). Thistechnique used a small blood sample placed in a bowl,which is moved back and forth while a sensor (pin) isin contact with the blood and registers the resistance to
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the displacement when the blood coagulates. Even thoughthis technique has been used for many y, its use in clinicalsetting is limited because it only provides qualitativemeasurements. Other techniques have used moreclassical approaches such as controlled stress and/orcontrolled strain to characterize the elastic behaviorof clot (Emelianov et al. 2002; Rubin et al. 2006;Xie et al. 2005). Another approach uses ultrasound(compressional) waves to study the change in acousticproperties as the blood coagulates. In 2009, Calle et al.published a study in which, by measuring the changes inspeed of longitudinal ultrasound waves, researchers wereable to identify different stages in the coagulationprocess that could be associated with biochemicalchanges (Call�e et al. 2009). Unfortunately, these changeswere not found to be large enough to extract bloodmechanical properties from compressional waves. Ultra-sound radiation force has also been used to generatemotion either on the clot itself (Viola et al. 2010) or on asphere embedded within the clot (Huang et al. 2011). Bymeasuring the generated displacement, qualitative infor-mation about the stiffness of the clot was inferred. Despitemany efforts, there is still a need for an in vivo and quanti-tative technique for blood clot elasticity assessment.
Shear waves have been used to study the elastic prop-erties of biologic soft tissues since the 1990s (Bercoff et al.2004a; Chen et al. 2009b; Muthupillai et al. 1995;Sarvazyan et al. 1998). This technique has been shownto be very useful in characterizing a variety of tissues,such as breast (Tanter et al. 2008), liver (Chen et al.2009a; Muller et al. 2009) and muscle (Gennisson et al.2010; Nenadic et al. 2009). By measuring the speed ofthe propagating waves at multiple frequencies, it ispossible to recover the viscoelastic properties usingdifferent rheologic models. In 2006, Gennisson et al.used a mechanical actuator to generate shear waves incoagulating blood at a specific frequency (25 Hz). Bymeasuring the speed and the attenuation of such wavesand using the Voigt model, they were able to recovervalues of shear elasticity and viscosity. Deffieux et al.demonstrated that the frequency dependence of theshear wave speed and attenuation can be assessedquantitatively and in real time by combining acousticradiation force and very high frame rate ultrasonicimaging (Deffieux et al. 2009). Interest in this ‘‘shearwave spectroscopy’’ approach lies in the fact that it canbe easily applied in vivo because it uses conventionalultrasonic probes. This technique has been appliedin vivo in breast (Tanter et al. 2008), liver (Bavu et al.2011) and muscle (Gennisson et al. 2010). Similarly,Schmitt et al. in 2011 used an external vibrator for theshear wave generation and to evaluate different rheologicmodels for the recovery of the storage (G0) and lossmoduli(G00) values between 50 and 150 Hz (Schmitt et al. 2011).
Our motivation with this study was to assess the riskof PE by providing a quantifying tool of DVT. Normally,DVTs are treated by using anti-coagulation drugs thatmodify mechanical properties of blood clots. However,this treatment presents an increased risk of severe andspontaneous bleeding (Landefeld and Beyth 1993). Wehypothesize that by knowing the viscoelastic propertiesof blood clots, the diagnosis and the choice of treatmentcan be improved. In the current work, our goal is twofold.First, we aim to demonstrate the feasibility of usingsupersonic shear wave imaging (SSI) to study the visco-elastic properties of blood clots in clinical practicewithoutthe use of any rheologic models. Second, we wanted todemonstrate the validity of SSI quantitative estimationsby correlating it with more conventional ‘‘gold standard’’rheometry techniques. For this purpose, we used twodifferent systems to cover the frequency spectrumbetween0.25 and 300 Hz. The low-frequency range (0.25–25 Hz)was tested using the gold standard (rotational rheometrywith a Haake Mars II), and the higher frequency range(20–300 Hz) was explored using radiation force and shearwave spectroscopy analysis provided by SSI. The fre-quency course of G0 and G00 estimated by both approachesduring coagulation reveals a very good agreement.
MATERIAL AND METHODS
Blood samplesIn our present study, blood from three healthy pigs
was used for experimentation. The blood was collectedfrom Institute Montsouris (Paris, France) in accordancewith the French Fair and Responsible Animal Researchguidelines and approved by the Montsouris Instituteethics committee. We collected 100 mL of blood fromeach animal. Immediately after the collection the bloodwas anticoagulated using a EDTA-saline solution at0.83% (Ethylene-diamine-tetra-acetic acid, E-9884,Sigma Chemical, St. Louis, MO, USA). This solutionwas added to the containers before the collection, de-pending on the amount of blood that was expected, inorder to achieve 2 mg EDTA per mL of blood. One ofthe blood samples (sample 1) was used within 2 h aftercollection, whereas the other two (samples 2 and 3)were refrigerated overnight at 4�C and used the nextday. During the experiments, coagulation was initiatedby adding calcium ions to the blood (CaCl2, C 5080,Sigma Chemical, St. Louis, MO, USA). The calciumwas diluted in saline solution at a concentration of 5%,and 4 mL of this solution were added to 100 mL of bloodfor each experiment.
SSI and shear wave spectroscopy analysisThe SSI technique was first described in 2004 by
Bercoff (2004b). The technique combines two different
Classical rheometry and shear wave imaging in blood clots d M. BERNAL et al. 3
kinds of waves; shear mechanical waves and ultrasoundcompressional waves. Based on the concept ofmultiwaveimaging, the interaction of these two waves allows thequantification and mapping of the shear properties oftissues with the spatial resolution of classical ultrasound(Fink and Tanter 2010). It combines quasi plane shearwaves generated by ultrasound radiation force (Bercoffet al. 2004) with ultrafast ultrasonic imaging, whichallows the tracking of the generated shear waves(Tanter et al. 2008).
The setup for the ultrasound part of the study is de-picted in Figure 1a. The radiation force was applied atdifferent depths (z direction) in order to create a quasiplane wave. The transition time between the push loca-tions (10, 15, 20 and 25 mm from the array) was shortenough that the medium ‘‘felt’’ a long push rather thanseparate pushes. Consequently, it generated a Machcone whose intersection in the imaging plane corre-sponded to two planar shear waves. The lateral localiza-tion (x-axis) of the excitation pushes was set at element64, so that the dispersion analysis could be done betweenelements 110 and 250 (majority of the 2-D field). Thepush at each depth was generated by 100 ms tonebursts
Fig. 1. Experimental setup. (a) The SSI setup, in which the ultra(100 mL for each experiment). Shear waves were generated byusing ultrafast imaging. The data were recorded in a computer awhich 2.9 mL of blood (same used in the SSI experiment) was pplane and a 6-cm diameter titanium rotating plate. The gap betwe
sonic shear wav
at a center frequency of 8 MHz. The resulting tissuemotion as a result of the radiation force generated thepropagation of shear waves. Using the same ultrasonicprobe, a plane ultrasound wave was used to produceimages of the field of interest at 2 kHz pulse repetitionfrequency in order to capture this shear wave propaga-tion. For each element in the transducer, all the back-scatter radio frequencies (RF) echoes were recordedand stored in memory. The beam-forming process wasdone in receiving mode, enabling the reconstruction ofone ultrasonic image for each plane wave transmission.The dimensions of the field studied in this case were25 mm deep by 51.2 mm wide. The spatial resolutionof the SSI technique was of the order of 1 mm.
Using cross-correlation algorithms between succes-sive speckle images acquired by the ultrafast imagingsequence, we were able to recover the shear wave propa-gation (Fig. 2). Shear displacements as small as 1 mm canbe measured with our system (Walker and Trahey 1994)in a frequency bandwidth ranging between 20 and400 Hz. The total acquisition time, including shear wavegeneration and ultrafast sequence, lasted 50 ms and wasrepeated every min for 120 min.
sound probe was placed in contact with the blood sampleradiation force and the propagation of these was trackednd further analyzed. (b) The classical rheometry setup, inlaced between a fixed and thermoregulated (Pelletier cell)en the plane and the platewas fixed at 1mm. SSI5 super-e imaging.
Fig. 2. Shear wave propagation at different coagulation time points and at different times during the acquisition. The firstcolumn shows the wave propagation at min 8, where panels a, d and g represent different acquisition times (3, 10 and20ms). Panel j shows the corresponding B-mode image at this coagulation time point. Similarly, the second column showsthe wave propagation series after 30 min of coagulation. In the same fashion, the third column shows the propagation atthe end of the experiment (120 min of coagulation). The dotted white lines represent the bottom of the plastic beaker in
which the blood samples were held.
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For the dispersion analysis, the propagating shearwave was averaged along depths between z 5 10 mmand z5 20 mm (Fig. 2). The resulting matrix representeda shear wave propagating in time and space. To avoid anyinterference from reflected waves, a directional filter wasapplied before the frequency analysis and shear wavespeed calculation (Deffieux et al. 2011). By taking thetwo-dimensional discrete fast Fourier transform (2-DDFFT) of the propagation, we transferred the time-space into the k-space, where the x-axis represents thefrequency and y-axis the wavenumber (k) or 1/wave-length (Fig. 3). The dispersion analysis was done byinvestigating the energy of the system, finding the peak
at each frequency (between 20 and 400 Hz) and the cor-responding k number and calculating the phase velocity(v) using eqn (1) (Bernal et al. 2011).
v5 lf (1)
where l is the wavelength (1/k) and f is the frequency.Because of the limited measuring distance (element
110 to 250, which is equivalent to 2.8 cm), we limited thefrequency analysis to those waves with a wavelengthsmaller than 1.4 cm. This would guarantee an appropriatemeasurement of the wave speed in the measuring field.We calculated the threshold velocity for each frequency
Fig. 3. k-Space plots for the different time points of coagulation. In this graph the x-axis represents the frequency and they-axis the wave number. Panels a, b and c show the frequency components of the propagating waves at min 8, 30 and 120
of coagulation.
Classical rheometry and shear wave imaging in blood clots d M. BERNAL et al. 5
using eqn (1) with a l 5 1.4 cm. Using these velocityvalues, we filtered the results to eliminate the diffractionbias caused by the out-of-plane diffraction occurring inthe near field of the radiation force location (Fig. 4).This filtering reduced the bandwidth of the SSI techniquefrom 20–400 Hz to 50–300 Hz.
Classical rheometryRheologic experiments were performed using
a Haake Mars II rheometer (Thermo Fisher ScientificInc, Waltham, MA, USA), as shown in Figure 1b. A2.9 mL sample of the blood prepared for the supersonicimaging experiments was placed between the fixed andthermoregulated (Pelletier cell) plane and a 6-cm diam-eter titanium rotating plate (PP 60 Ti). The gap betweenthe plane and the plate was fixed to 1 mm.
In order to characterize the blood rheologic behaviorduring the clotting experiment, an oscillatory shear wasimposed with sufficiently low amplitude (5% deforma-tion) to ensure the linearity of the viscoelastic response
of the blood. The frequency range of variation wasbetween 0.25 and 25 Hz, logarithmically varying with 5values per decade. Inertial effects of the oscillating platewere corrected and the temperature of the Pelletier cellwas set to the same value used in US measurements.
As in the ultrasound experiment, the measurementswere performed every minute. The results by the rheom-eter were given as G0 (storage modulus) and G00 (lossmodulus) as a function of frequency every minute (shownin Fig. 5). With these values, we calculated the phasevelocity (v) for a plane wave (rheologic model free) usingeqn (2):
where, u is the angular frequency and r is the density ofblood (1060 kg/m3).
Fig. 4. Three dimensional (3-D) dispersion plot for blood sample 1 (hematocrit of 30%). Panel a shows the dispersionwithout the 14-mm wavelength filter described in the methods section, whereas panel b shows the effect of this filterin the lower frequencies. In panels a and b, the x-axis represent the time of coagulation (min), y-axis the frequency(Hz), and z-axis the phase velocity (m/s). Panel c and d show the top views of panels a and b, respectively. The x-axisrepresents the frequency, y-axis represents the time, and phase velocity is given by the color code, which corresponds
to the color bars presented in panel a and b.
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Therefore, we obtain a dispersion curve for eachminute of coagulation between 0.25 Hz and 300 Hz usingboth techniques. Using these curves we fitted Maxwell,Voigt and Zener models using eqn (3), (4) and (5),respectively. The fitting was done by minimizing theleast mean square error (LMSE) for values of m and h inthe Maxwell and Voigt model and m1, m2 and h in theZener model. The frequencies (u) were chosen in thesame range as the experimental bandwidth. By doing so,we were able to recover the values of shear elasticityand viscosity for the coagulating blood at different timesof the experiment.
where r is the density of the blood, in this case 1060kg/m3.
RESULTS
The supersonic shear imaging experiments indicatedthat the shear wave velocity increases as the blood clotstiffens. Figure 2 shows the difference in wave propaga-tion for the same blood sample at different coagulationtimes (8, 30 and 120 min after adding the calcium solu-tion). As mentioned in the Methods section, the totalacquisition for each push was 50 ms. In Figure 2, thewaves are depicted at 3, 10 and 20 ms after the push (first,second and third rows, respectively). The last row shows
Fig. 5. Dispersion analysis for blood sample 1. Panels a and c show the 3-D representation of the dispersion curve after thewavelength filter. Panel a shows selected frequencies (30, 50, 100, 200 and 300 Hz) along the whole time of the exper-iment. Panel b shows these frequencies as a function of coagulation time. Panel c, similarly, shows the 3-D representationwith selected coagulation times (min 15, 30, 80 and 120 of coagulation). Panel d shows all the frequency components at
those times points.
Classical rheometry and shear wave imaging in blood clots d M. BERNAL et al. 7
the corresponding B-mode images at 8, 30 and 120 min.The dotted lines in all the panels represent the bottomof the plastic beaker in which the experiments wereconducted.
Figure 3 shows the corresponding k-space plots for8, 30 and 120 min of coagulation (panels A, B and C,respectively). In panel A, where thewave only propagatesa few millimeters (column 1 of Fig. 2), the k-space showsvery little energy mostly located at lower frequencies(20 Hz or less). As the medium hardens and the shearwaves begin to propagate, the contributing frequenciesof the shear wave increase. This can be observed in panelsB and C, where the energy distribution contains higherfrequencies as time increases. Also, notice the slightchange in the slope of the main energy peak for eachfrequency; this implies that the speed of propagationincreases. By finding the energy peaks from the k-spaceat each frequency and the corresponding wave number,we calculated the phase velocity every minute for the120 min of the experiment.
Figure 4 shows the dispersion curve as a function oftime for blood sample 1. Panels A (3-D view) and C (top
view) show the dispersion curve before applying the1.4 cm wavelength filter. Panels B and D show the effectof this filter on the lower frequencies (20–70 Hz), elimi-nating the error calculation of the phase velocity causedby diffraction and near-field effects. In panels A and B,the x-axis represents time (minutes), y-axis the frequency(Hz) and z-axis the phase velocity in (m/s). In panels Cand D (top view of panels A and B), the x-axis representsfrequency and the y-axis represents time in minutes. Thecolor bar represents the phase velocity values for anygiven frequency at any given time. In this figure, noticehow the frequency components tend to be at very lowfrequencies (around 20–50 Hz) in the initial momentsof coagulation. As time increases, the frequency compo-nents increase as well, up to 300 Hz.
Figure 5 shows the phase velocity behavior for thewaves generated by the ultrasound radiation force. PanelA and B show selected frequencies (30, 50, 100, 200 and300 Hz) along the 120 min that the experiment lasted.Panels C and D show the phase velocity dispersion atselected time points (15, 30, 50, 80 and 120 min) acrossall the frequencies that were measured during the
Fig. 6. Classical rheometry results for blood sample 1. Thex-axis represents the time of coagulation (min) and the y-axisthe storage and loss moduli (Pa). Three representative frequen-cies were selected for this plot: 0.25 Hz, 10 Hz and 25 Hz.
G0 5 storage modulus; G00 5 loss modulus.
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experiment. In this figure it is also possible to see thatthere is very little to no dispersion in the blood clot inthis frequency range, because all the curves in panel Blie on top of each other. Also in Panel D, there is no signif-icant change in the phase velocity as a function offrequency.
The results from the classical rheometry analysis areshown in Figure 6. During the experiments, the HaakeMars rheometer provided values of G0 and G00 everyminute for 120 min. Using eqn (2), which calculates themodel-free theoretical phase velocities, we were ableto obtain these values for the low-frequency range(0.25–25 Hz). Figure 6 shows the G0 and G00 values atthree frequencies: 0.25, 10 and 25 Hz.
The theoretical phase velocities (classical rheome-try) and experimental velocities (SSI) are displayed inFigure 7, where the agreement between the two tech-niques for blood sample 1 is shown. Panels A and Cshow the 3-D plot with selected frequencies (panel A)and time points (panel C). Panel B shows multiplefrequencies from both techniques as a function of thecoagulation time (0.25, 10 and 25 Hz from classic rheom-etry and 30, 50, 100, 200 and 300 Hz from the SuperSonicimaging technique). In contrast, Panel D shows all thefrequencies evaluated with both techniques (rangingfrom 0.25 to 300 Hz) at selected times (15, 30, 50, 80and 120 min). The gap observed between the two tech-niques increases with time. This gap is in part due tothe upper limit frequency of the rheometer (25 Hz) andthe difficulty of SSI to measure velocity values at suchlower frequencies. At the beginning of coagulation, thevelocity measurements are around 0.4 m/s. Thus, forlower frequency shear waves with a bandwidth between
30 and 70 Hz, the wavelength are between 1.3 and0.57 cm, respectively. Moreover, toward the end of theexperiment when the speed of propagation has increasedto around 1 m/s, shear waves in the same frequency rangehave wavelengths of 3.3–1.43 cm. Given that the lengthover which we can measure the wave propagationis limited by the size of the array transducer (28 mm),estimating the shear wave speed at wavelengths thatare longer than half our measuring distance (14 mm)becomes a challenge. Nevertheless, a good agreementcan be appreciated between the two modalities inFigure 7.
Tables 1, 2 and 3 show the results from the threeblood samples used in the experiments at 8, 30 and120 min after initiation of coagulation. We reported sixrepresentative frequencies from the classical rheometryexperiments (0.25, 1, 6.31, 10, 15.8 and 25 Hz) and fivefrom the SSI experiments (30, 50, 100, 200 and300 Hz). The values marked as ‘‘NaN’’ (not a number),which are mostly present in Table 1, are due to the soft-ness of the medium at that point (minute 8 of coagula-tion). Although the rheometry was able to recover thevalues of G0 and G00, the dispersion analysis needed thewaves to propagate several millimeters and because atthis stage the attenuation in the medium was very high,it was not possible to recover those values. NaN valueswere also assigned when the signal-to-noise ratio wasnot high enough to determine the velocity values withsufficient certainty.
The results of fitting the Maxwell (panel A), Voigt(panel B) and Zener (panel C) models are shown inFigure 8 for blood sample 1. For each time point (minutes10, 30, 50, 80 and 120) an LMSE minimization was doneto find the optimal values of m and h for Maxwell andVoigt and m1, m2 and h for Zener. The color symbolsrepresent the experimental data and the solid lines ineach of the panels represent the model for each time.Notice that the Zener model seems to do better at match-ing the low frequency values, whereas the Maxwell andZener models do a fair job at the high frequencies.
Table 4 shows the values found during the fitting andminimization process. For each coagulation time, wefound the mMaxwell (Pa) and hMaxwell (Pa$s) that mini-mized the LMSE. Similarly, the process was repeatedfor the Voigt and the Zener models, were we found mVoigt(Pa) and hVoigt (Pa$s), and m1 Zener (Pa), m2 Zener and hZener(Pa$s). In the table we also report the lowest LMSE foundin the minimization procedure for each model.
DISCUSSION
As mentioned previously, the speed of the shearwaves increased with time, which is expected as a resultof the stiffening of the clot during coagulation. In
Fig. 7. Comparison of the SSI and the classical rheometry results. Panels a and c show the 3-D dispersion plot of bothdispersion curves (classical rheometry and supersonic shear wave imaging). The characters in panel a represent selectedfrequencies from both techniques, whereas in panel c the characters show different time points along the frequency range(0.25–300 Hz). Panel b shows the behavior of the selected frequencies in the coagulation time, whereas panel d shows all
the frequencies at the selected time points.
Classical rheometry and shear wave imaging in blood clots d M. BERNAL et al. 9
Figure 2, we can notice the differences between the threecolumns (8, 30 and 120 min of experiment) and that thewave travels longer distances as the coagulation timeincreases, revealing increasing shear wave speeds. Inthe first column, the clot has just hardened enough tosupport shear waves (in our study, we determined thistime as coagulation time). Notice that the propagationoccurs after 20 ms on only a few millimeters (panel G).After 30 min of coagulation, the wave propagates signif-
icantly more. At the same time it is possible to appreciatethe ‘‘quasi’’ planar wave generated by the multiple pushesin the z direction. Similarly, after 120 min of coagulation,the shear wave exhibits a faster velocity propagating over20 mm in the first 20 ms of the acquisition after the push(panel I).
The stiffening of the blood clot indicated an increasein the bandwidth of the shear waves generated by the SSItechnique. This was to be expected because the hardening
Sample 1 (m/s) 0.51 0.52 0.53 0.54 0.56 0.62 0.66 0.72 0.70 0.1 NaNSample 2 (m/s) 0.55 0.6 0.57 0.58 0.6 NaN 0.54 0.52 0.52 NaN NaNSample 3 (m/s) 0.71 0.75 0.75 0.76 0.77 NaN 0.93 0.94 0.86 0.87 NaN
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of the blood clot decreases the damping of the higherfrequency components, allowing their propagation. It isalso worth mentioning the very low energy—less than20 Hz or more than 300 Hz—which explains why itwas not possible to recover phase velocities outside thisfrequency range. Figure 4 shows the progression of thephase dispersions recovered from the k-space, and it isevident that as time progressed, the bandwidth increased(panels C and D), starting with low-velocity values (0.4–0.5 m/s) in the first few minutes of coagulation and atfrequencies between 20 and 100 Hz. These valuesincreased toward the end of the experiments to 0.8 or0.9 m/s for samples 1 and 2 and to 1.1–1.2 m/s for sample3. In all the cases, the bandwidth increased to around300 Hz. One interesting thing to note is the high-velocity bump that can be appreciated at low frequencies(20–75 Hz) in panels A and C of Figure 4. This phenom-enon starts to develop after 20 min of coagulation andpersists until the end of the experiment. We believe thisis due to the diffraction effect, because the ‘‘quasi’’ planarwave is a circumferential wave diffracting outside theimaging plane (out-of-plane diffraction). This phenom-enon tends to affect the lower frequencies more dramati-cally than the higher frequencies, because in the lattercase, the circumferential front is perceived by themedium as a plane wavefront (small wavelengthcompared with the radius). This behavior was describedby Catheline et al. (1999) using spherical waves in gelatinphantoms. By using the wavelength as a parameter, wewere able to avoid this phenomenon. In this case, weeliminated the frequency components that gave a wave-length longer than twice the measuring distance that wehad—in our case, 28 mm. Therefore, we disregardedwavelengths above 14 mm.
Figure 5 shows the resulting dispersion curve forblood sample 1, where we follow some frequencies intime (panel B) and all the frequency components andgiven time points (panel D). This figure shows that therewas very little to almost no dispersion at each time point(panel D). Even though there was a change in phasevelocity with time, there was no change in this velocitywith frequency. This is seen in panel D, where acrossall the frequencies, all time points are almost flat. Thesame can be seen in panel B, where all frequency compo-nents followed the same curve in time, showing anincreased phase velocity in time that is the same for allthe frequencies. Nevertheless, it is important to notethat not all the frequencies are present during the wholeexperiment. For 30 and 50 Hz there are only a few pointsat very low velocities as a result of the wavelength limit.Beyond 100 Hz it is possible to see well-behaved curveswhose velocities increase with time. Similar results,showing little phase velocity dispersion in blood clots,were observed by Schmitt et al. (2011) using amechanicalvibrator. This behavior has also been shown in agar-gelatin mixtures during the blood transition from liquidto solid (Gennisson and Cloutier 2006).
The results obtained by classical rheometry were ingood agreement with those obtained with the SSI tech-nique. Figure 6 shows a similar dynamic behavior ofthe mechanical properties of the blood clots as that shownin Figure 5, panel B. It is important to mention the lowsignificance of the loss modulus (G00) compared withthe storage modulus (G0) for the three frequencies dis-played. The difference in magnitude was more than 18-fold at 0.25 Hz, 8-fold at 10 Hz and 7-fold at 25 Hz. Thesedifferences were more significant toward the end of theexperiment when the clot was fully formed. This marked
0.74 0.84 0.93 0.84 0.86 0.9NaN 0.81 0.88 0.82 0.84 NaNNaN NaN NaN 1.17 1.14 1.17
Fig. 8. Fitting of Maxwell, Voigt and Zener models to theexperimental dispersion curves at selected times of coagulation(10, 30, 50, 80 and 120 min) for blood sample 1. The solid linesin each panel represent best fit (least mean square error minimi-zation) of each model at the given time point. The values forelasticity and viscosity for the three models are shown in
Table 4.
Classical rheometry and shear wave imaging in blood clots d M. BERNAL et al. 11
difference in the two moduli suggests that the blood clotis mostly an elastic material with very little viscosity. Thisis also supported by the results of the SSI techniquewherevery little dispersion was observed. Comparison of ourrheometry results to those presented by Schmitt et al.
(2011) indicated good agreement in the values for G0
and G00 as well as in their progression in time. Similarly,using thromboelastography studies, Burghardt et al.(1995) also found very similar values of G0 and G00 tothose found in our study.
The good agreement between the two modalitiesexplored in this work was shown in Figure 7. Wecompared the phase velocities results obtained from theSSI technique between 30 and 300 Hz with those ob-tained with classical rheometry between 0.25 and25 Hz. It is possible to observe that in the first min ofcoagulation (15–30 min) the two techniques are in excel-lent agreement, showing a proper continuity (panel D).After 40 min the two curves produced a wider gap, whichcan be explained by the near-field effect and the wave-length filtering. Nevertheless, the trend observed by therheometry results (panel D, traces for 0.25, 10 and25 Hz) indicated an increase in velocity with frequencyat each time point, which agrees with the results fromthe SSI technique after the frequency gap (panels Band D). It is important to note that the dispersionobserved in this figure is not related to the viscous compo-nent but to the inherent rheologic model that governs theblood coagulation process, as was suggested by Schmittet al. (2011).
In Tables 1 to 3, it is also possible to appreciate thetransition between the two techniques. Except for thevalues from sample 2 at minute 30, which jumped from0.6 at 15.8 Hz (classical rheometry) to 0.54 at 30 Hz(SSI), all the other values produced a well-behaved tran-sition between the two techniques. The results presentedin Table 1 (minute 8 of coagulation) for the three samplesusing the SSI technique did not provide measurements forthe dispersion analysis. The medium was just beginningto coagulate and the clot was not sufficiently solid tosupport shear waves for more than a few millimeters;therefore, it was not possible to perform a dispersion anal-ysis. The values of shear wave speed shown in Table 1correspond to those measured by the classical rheometryat min 8. The values in Table 3 (120 min of coagulation)show a good agreement with the values reported by Gen-nisson et al. in 2006. In their study they reported phasevelocity values around 1 m/s after 100 min of coagulationfor blood samples with a hematocrit between 28% and48% (Gennisson et al. 2006). Recently, Viola et al.(2010) described a new methodology to study the haemo-static function of whole blood. In their work, they usedradiation force to move the blood around and determinethe relative stiffness by the displacement generated byultrasound push. Their study allowed them to identifydifferent stages of the coagulation process. They noticethat fibrin polymerization began around 5 min after addi-tion of a calcium solution. These values are not far fromthose found in our study, between 8 and 10min. The small
Table 4. Values of shear elasticity (m and m1, m2) and viscosity (h) found by fitting the Maxwell, Voigt and Zener model to theexperimental data at different time points. The LMSE error found during the minimization process is reported for each model
12 Ultrasound in Medicine and Biology Volume -, Number -, 2013
discrepancies could be attributed to the differences inhematocrit, which has been shown to play an importantrole in the coagulation process (Gennisson et al. 2006).Similar times of coagulation were also reported byRanby et al. (2003) using a oscillation rheometry method-ology. The values found in that study were between5.2 and 12.5 min after the recalcification of the blood(R�anby et al. 2003).
The differences in shear velocity and times of coag-ulation of the three samples can be attributed to multiplefactors. As was reported by Gennisson et al. (2006),hematocrit plays an important role in coagulation. Inour samples, hematocrit was 30% in sample 1, 24% insample 2 and 26% in sample 3. Another factor thatcould have influenced the results was whether the bloodwas tested the same day of collection or refrigeratedovernight. Samples 1 and 2 were refrigerated at 4�C over-night, whereas sample 3 was tested within hours of itscollection.
In our study the results for the shear wave dispersionare rheologic model free, meaning we did not assume thatthe blood clot had a viscoelastic behavior that followeda specific rheologic model. The only assumptions madein our study were the linear elasticity theory and localhomogeneity. Nevertheless, given the dispersion curves,we evaluated the fit by Maxwell, Voigt and Zener models(Fig. 8). Even though the Maxwell and Voigt models canbe easily related to the physical properties of tissuesbecause of the two parameters (elasticity and viscosity),we found that the Zener model was much better at char-acterizing the coagulation process in a frequency band-width that ranged from 0.25–300 Hz. Similarly, in 2011Schmitt et al. conducted a study modeling the rheologicbehavior of blood clots, in which they determined thatthe Zener model was the best to describe the rheologicproperties of blood in a frequency range from 50–170 Hz (Schmitt et al. 2011). In our study, the Maxwellmodel was shown to do a fair job describing some ofthe low frequencies, as well as the high ones (Fig. 8, panelA). Its disadvantagewas the model’s constraint of an elas-ticity of zero at zero frequency, which is not the case insoft tissues. In this case, we were able to measurethe quasi-static (zero frequency) shear elasticity using
the rheometry measurements at frequencies as low as0.25 Hz. From the three models, the Voigt presented theworst fit. Even though this model is widely use in thecharacterization of soft tissues, in the study of bloodcoagulation it proved to be a poor choice. It failed to char-acterize the low-frequency elasticity values as well as theplateau shear wave speeds. Even though toward the end ofthe experiment (time points 80 and 100 min) the Voigtmodel seems to do better than the Maxwell (LMSE of1.73 and 1.48 compared with 1.92 and 1.80, respectively),this was due to constraint of zero phase at zero frequency.The Zener model solves this disadvantage by providinga static shear elasticity value (m2), which allowed themodel to better characterize the coagulation process.Even though the Zener model performed much betterthan the Maxwell and Voigt models, it is important tokeep in mind that this model has the advantage of oneextra parameter. At the same time, the two values for elas-ticity (m1 Zener, m2 Zener) and the one for viscosity (hZener)make the physical interpretation of the rheologicbehavior a little bit more complex. Nevertheless theresults presented in Figure 8, panel C, proved an excellentfit between the model and the experimental data, asshown by the low LMSE values in presented in Table 4.These findings suggest that the coagulation process is infact described by this three-parameters model (Zener).If this is the case, as was also suggested by Schmitt in2011, the overall results of this study let us concludethat the agreement between the classical rheometry andthe SSI technique is also very good in the frequency rangeexplored. A study by Vappou et al. (2007) in brain tissuefound a similar agreement between rotational rheometryand shear wave analysis using magnetic resonance elas-tography (MRE). However, in this study the relationshipfound did not follow the Zener model but a power law(Vappou et al. 2007). This was to be expected becausethe nature of these two tissues is very different.
One of the disadvantages of our method was theamount of blood used in each experiment. Although ob-taining 100 mL of blood from a pig was possible, anyexperimentation on human blood would require theamount of blood to be significantly reduced. We arecurrently working on the translation of our methodology
Classical rheometry and shear wave imaging in blood clots d M. BERNAL et al. 13
into a setup at higher ultrasonic frequency that includesblood flow and a reduced amount of blood in order totransition to a non-invasive and in vivo setting for thecharacterization of coagulopathies. Another difficultyobserved during the experiments was due to syneresis.This phenomenon describes the expulsion of free serumfrom the blood clot (Pickering and Hewitt 1923). Duringsome of the classical rheometry experiments, the syner-esis generated a detachment of the top plate from theclot. This leads to a sudden drop of shear applied to thesample and was indicated in the results as an abruptplateau of the G0 and G00 measurements. Another impor-tant constraint of our method is the difficulty in character-izing the phase velocity at the low frequencies (0–50 Hz).This is due to the long wavelengths at such frequencies(i.e., at a speed of 1 m/s, the wavelength is on the orderof 2 cm at 50 Hz). And because the measurements aredone using a 5-cm ultrasound array, these long wave-lengths are not properly detected. Therefore, our methodis most reliable at higher frequencies—in the case ofcoagulating blood, 75 Hz and greater.
Nevertheless, the application of the SSI technique inthe study of blood clots could potentially provide a quan-titative, non-invasive and real-time approach to studyingthe mechanical properties of thrombi. The techniquemust be refined in order to overcome the constraints ofin vivo testing, such as clot size, flow and geometry.However, we are confident that translation into a clinicalapplication can be accomplished in the near future.
CONCLUSION
In this article, we described our study of the changesin the mechanical properties of coagulating blood withtime and frequency. To do this, we used two differenttechniques to explore a frequency range from 0.25 Hzup to 300 Hz. The first technique, used as the gold stan-dard, was classical rheometry using a Haake Mars II.Using this machine we obtained values for G0 and G00
for the coagulating blood at each minute for 120 min ina frequency range between 0.25 and 25 Hz. These valueswere used to calculate the theoretical phase velocity andto create a dispersion curve. The second technique, super-sonic shear wave imaging, used radiation force togenerate a shear wave and ultrafast imaging to measureits propagation. In this study we applied this techniqueto coagulating blood and retrieved the shear wavevelocity at every minute for 2 h. By doing this we wereable to produce a dispersion curve in time and frequency(30–300 Hz). The two techniques produced results thatwere in very good agreement, which validates the useof SSI to study the rheologic properties of soft solids aswell as materials with changing mechanical properties.By fitting the Maxwell, Voigt and Zener models to the
dispersion curves, we were able to retrieve values ofelasticity and viscosity by minimizing the LMSE. Thecomparison of the experimental results with the modelsseemed to suggest that the coagulation process isdescribed by a Zener rheologic model. Currently we areworking toward translating this technique to in vivo appli-cations such as diagnosis, risk assessment and treatmentof deep venous thrombosis and pulmonary embolisms.
Acknowledgment—The authors would like to thank Luc Behr and theInstitute Mountsouris, Paris, for providing the blood samples necessaryto perform these studies.
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