A patient specific lumped parameter model of the upper limb

Transcription

1 A patient specific lumped parameter model of the upper limb Hanneke Gelderblom BMTE Internship to Supervisors: Carole Leguy Frans van de Vosse

2 Abstract Alterations of vessel wall properties indicate an increased risk of cardiovascular diseases at an early stage. Ultrasound measurements and models of the circulation can be used to determine these properties. In this study, a patient specific lumped parameter model is used in combination with non invasive ultrasound measurements of wall distension and blood flow velocity to investigate wave propagation phenomena and estimate mechanical properties of the large arteries of the upper limb. Ultrasound measurements of vessel wall distension and centerline blood flow velocity at several locations along the arterial tree of the upper limb were obtained within a group of 11 healthy volunteers. The wall distension was rescaled into a pressure waveform using local measurements of systolic and diastolic blood pressure (BP) in the brachial artery. Blood volume flow (BVF) was estimated from the centreline blood flow velocity using the velocity profiles given by Womersley. The results of these measurements were used to obtain initial input parameters for a lumped parameter model that simulates the BVF and BP in the main arteries of the upper limb, e.g. the brachial, ulnar and radial artery. The BVF computed from measurements at the more proximal site of the brachial artery was used as input flow for the model. The lumped parameters R, L and C (resistance, inertance and compliance) along the arm were estimated from the blood pressure and WD measurements assuming that arteries can be modelled as thin walled linear elastic tubes. Time averaged BVF and wall distension measured at the distal site of the radial and ulnar arteries were used to determine the end impedance of the extremities. Simulated BVF and BP curves were compared to the in vivo results. The model parameters were adapted to fit the simulations to measurements. It is assumed that the parameters corresponding to the best fitting form the most accurate approximation of the mechanical properties of the measured arteries. The shape of the simulated BVF along the arm was comparable to the in vivo estimations after the fitting. However, large differences were observed between simulated and in-vivo estimated BP curves. It is hypothesized that those differences are due to the non-linear and visco-elastic properties of the arterial wall that are not described by the model. 2

3 Introduction Cardiovascular diseases are a major cause of death in the western world. Therefore, early diagnosis is of great importance. Alterations of vessel wall properties indicate an increased risk of cardiovascular diseases in an early stage [5]. Arterial compliance is affected by those alterations of vessel wall properties. In vivo measurements of the arterial compliance can therefore lead to a predictor of a patient s risk of cardiovascular diseases [8]. Ultrasound and tonometry are frequently used noninvasive methods to determine arterial compliance [5]. The pulse wave velocity (PWV) can be used as a measure for arterial compliance using the Moens-Korteweg relation. It is usually measured using the foot (where the steep rise of the wave front begins) to foot time delay of pressure or blood flow velocity waveforms measured at two different locations. The actual PWV is estimated by dividing the distance between the recording sites by the calculated time delay. However, it is difficult to measure the distance between the recording sites accurately, since the surface distance between the two locations has to be used. Also, by measuring the time between the two pulses as the foot to foot delay, the effects of wave reflection on the shape of the curves are not taken into account. Furthermore, the resulting PWV represents an average for the complete arterial branch, while arterial compliance is know to decrease significantly towards the periphery and is therefore a local property [5]. Wall distension curves measured with ultrasound can be used to determine the local arterial compliance, assuming the vessel wall to be a linear elastic, thin walled circular tube. The local arterial compliance can be estimated by dividing the difference in lumen area by the pulse pressure measured in the brachial artery. The problems with this method are that the vessel wall non-linear visco-elastic properties are neglected and that the use the pulse pressure measured in the brachial artery as a surrogate for the local pulse pressure is not accurate. The amplitude of the pressure pulse increases towards the periphery because of wave reflections [5]. To get a better understanding of the influence of arterial wall properties on pressure and flow wave propagation and to consider the influences of wave reflection, models can be used. One of the simplest models of the vascular system is the windkessel model [12], which uses electric analogies for pressure (voltage) and flow (current). The arteries are represented by a compliance, modelling the arterial storage of blood, in series with an arterial characteristic impedance, parallel to a peripheral resistance, modelling the pressure drop in the vascular bed. The main limitation of this model is that travelling of pressure and flow waves through the arteries is not taken into account. Therefore, a model in which transmission phenomena are present was developed: a lumped parameter model. In such a model the analogy between the linearised Navier-Stokes equations describing the motion of blood and the continuity equation on one hand and equations describing propagation along a transmission line in the electrical domain on the other hand is used. The entire arterial tree is divided into short segments consisting of a resistance in series with an inertance, representing respectively the viscous and inertial properties of the moving blood, and a compliance mimicking the wall behaviour (the transverse impedance). All segments are connected to form the complete model, which shows realistic wave propagation behaviour and input impedance [12]. 3

4 A lumped parameter model can be used to simulate the influence of arterial properties on the wave propagation, but could also provide estimates of local arterial properties by using the results of in-vivo measurements as an input for a patient specific model. The goal of this study is to investigate the feasibility of a patient specific lumped parameter model to estimate local wall properties of the upper limb arterial tree. Ultrasound measurements of vessel wall distension and max-line blood flow velocity at several positions along the arterial tree of the upper limb were obtained within a group of 11 healthy volunteers. The wall distension was rescaled into a pressure waveform using local measurements of systolic and diastolic pressure in the brachial artery, assuming linear elastic vessel wall behaviour. Blood volume flow was estimated from the centreline blood flow velocity using the velocity profiles given by Womersley. A patient specific lumped parameter model of the upper limb arterial tree including the brachial, radial and ulnar arteries was constructed with parameters estimated from in-vivo measurements. Then, these parameters were adapted to obtain the best fitting between the simulated and in vivo estimated pressure and flow waveforms. The resulting parameters are assumed to be the most accurate estimates of the mechanical properties of the arterial tree considered. 4

5 Materials and methods In vivo measurement protocol A set of local ultrasound measurements was obtained within group of 11 healthy volunteers (male, average age 27 years (21-34), weight 82 kg (69-96), height 1.90m ( )), using Ultrasound scanner Ultramark 9 plus (Advanced technology Laboratories, Bellevue, WA, USA). The vessel wall distension (WD) and centreline blood flow velocity (CBFV) were assessed in time at several positions in the left arm (see Figure 1). The blood pressure (BP) in the brachial artery was measured at the start and end of each measurement session using a cuff (Omron 705 CP). The QRS peak of the electrocardiogram (ECG), which was measured continuously throughout the session, was used to trigger the measurements. The measurements started after the volunteer had rested for ten minutes in supine position to allow normalisation of the cardiovascular function. The complete session lasted for two hours. First, the position of the brachial artery bifurcation (see Figure 1) was identified in echo B-mode. Then WD and CBFV were measured at five or six locations: two locations in the brachial artery (BA), two in the radial (RA) and one or two in the ulnar artery (UA) (Figure 1). All measurements were performed at least 5 cm up- or downstream from the bifurcation of the brachial into the radial and ulnar arteries, to avoid influence of this bifurcation on the velocity profile. The position of the measurement locations with respect to the bifurcation was measured using a tape measure. The WD waveform was recorded in M-mode with a linear array transducer, followed by a CBFV measurement at the same location using a curved array transducer. B-mode was used to determine the centre of the artery, while the actual velocity profiles at this location were measured in Doppler mode, with an angle of 70. A cross correlation method was used to obtain the blood flow velocities from the radio frequency signals [1]. Each measurement covered 4 consecutive heart beats and was repeated at least three times. Details about the measurement protocol can be found in the document Protocol ultrasound measurements [2]. Estimation of blood pressure from the wall distension measurements The wall distension curves obtained from the ultrasound measurements were used to estimate the blood pressure waveforms. It was assumed that the vessel wall behaves linear elastically, so a linear relation between the lumen area and the blood pressure could be used. Furthermore, it was assumed that systolic and diastolic blood pressures remain constant over the entire arterial tree, so that the systolic and diastolic blood pressures measured in the BA could be used to rescale the wall distension at all locations. The resulting blood pressure waveform, p(t), can be written as: psys pdias 2 2 p( t) = pdias + ( d ( t) dmin ) 2 2 d d max min (1) with d(t) the vessel diameter in time obtained from the wall distension curve, d min the minimum and d max the maximum diameter, p dias the diastolic and p sys the systolic blood pressure measured in the BA. 5

6 BA, Position 2 BA, Position 1 Bifurcation RA, Position 2 RA, Position 1 UA, Position 2 UA, Position 1 Figure 1: Measurement positions along the upper limb arterial tree Estimation of blood volume flow from the centreline velocity measurements Direct calculation of the BVF from the measured velocity profile was not possible, since velocities measured near the walls of the arteries are not accurate due to wall movement. Therefore, only the velocity waveform at the position of the maximum velocity measured during systole was used to estimate the actual blood volume flow. The position of this maximum was assumed to be located in the centre of the artery, which means that the large arteries of the arm are assumed to be straight tubes. BVF was estimated from the measured maximum velocity using the Womersley relation between flow and axial velocity in the centre of a straight tube [13], as given by eq. 2 to 5. Equation 2 describes the Womersley profile for each velocity harmonic v z : vˆz (r ) = i pˆ J 0 (i 3 / 2αr / a) 1 ρω z J 0 (i 3 / 2α ) (2) ˆp the harmonic pressure gradient in axial z direction and ω the angular frequency. The Womersley number is defined with J0 the zeroth order Bessel function, as α = a ω, with ν the kinematic viscosity of blood (3.8*10-6 m2/s). The time ν averaged vessel radius a was computed from the wall distension waveform at each assessed location. The velocity harmonics in the centre of the tube (at r=0), v c, are given by: 6

7 i pˆ 1 vˆ = ˆ c vz ( r = 0) = 1 3 / 2. ρω z J0( i α) (3) and are found by decomposing the measured v c (t) into harmonics. The flow harmonics are found by integrating the velocity harmonics over the cross section of the tube and become, with use of relation (3): = a 2 3 / 2 3 / 2 3 / 2 πa pˆ 2 i αj ( ) 2 ( ) 0 αi J1 αi qˆ vˆ 2 = [ 1 ( )] = ˆ z π rdr i F10 α πa vc 3 / 2 3 / 2 z i α( J ( ) 1 ) (4) ρω 0 0 αi with J 1 the first order Bessel function and F 10 the Womersley function. The blood volume flow in time is then obtained by a summation of the flow harmonics qˆ : N h q( t) = Re qˆ f exp( i2π ft) (5) f = 0 with N h the number of harmonics taken into account (here N h =30 was used). The BVF calculated from the maximum velocity measured in the brachial artery (proximal to the armpit, BA position 2 in Figure 1) was used as input flow for the model. Construction of the lumped parameter model The ultrasound data sets were used to obtain a patient specific lumped parameter model of the upper limb arterial tree. The complete model, ranging from the armpit to the wrist, contained the brachial, radial and ulnar arteries and was constructed using 36 segments. The bifurcation of the UA was not considered. Every arterial segment consisted of an arterial resistance R, a compliance C, representing the arterial storage of blood and an inertance L (see Figure 2). The ulnar and radial arteries were terminated by a three-element windkessel model (Figure 3) with a compliance C in series with an arterial characteristic impedance Z, parallel to a peripheral resistance R v, modelling the pressure drop in the capillaries. This end segment represents the entire arterial branch distal to it. Figure 2: Arterial segment Figure 3: Three element end segment 7

8 Arterial segment parameter estimation The lumped parameters R, L, C along the arm were estimated from diastolic and systolic BP measurements in the BA and WD measurements at each measurement position (see Figure 1), assuming the arteries are straight circular tubes, using equation 6 to 8. The Poiseuille resistance was used as an estimate for arterial resistance R: 8η R = (6) 4 π a with η the dynamic viscosity of blood (4*10-3 Pa.s) and a the mean vessel radius. The inertance L is defined as: ρ L = (7) A with ρ the density of blood (1.05*10 3 kg.m -3 ) and A the mean vessel area (obtained from mean radius a). To calculate the compliance of every arterial segment, it was again assumed that the vessel wall behaves linear elastically and that systolic and diastolic blood pressures remain constant over the entire arterial tree, so that the diastolic and systolic pressure measured in the BA could be used to calculate the compliances. A Amax A C = = p p p min BA_ syst BA_ diast C is the linearized, real valued compliance, A max the maximal and A min the minimal vessel area (calculated from a max and a min ), p BA_syst the systolic and p BA_diast the diastolic blood pressure measured in the BA. Linear tapering of the arteries between the segments was assumed, so the R, L and C parameters could be calculated for every arterial segment using a linear interpolation of the vessel radius between the measurement locations. End segment parameter estimation The parameters of the three-element windkessel end segment were estimated using equation 9 to 12 (obtained from Huberts [3]): pmean Rp = (9) qmean 1 pmean = pdias + ( psys pdias ) (10) 3 R p the peripheral resistance, p mean the mean pressure calculated from the BA pressure measurements, using relation (10), q mean the mean flow in the RA obtained from the time average BVF estimated from the maximum velocity measurements. L Z = (11) C Z the characteristic impedance of the branch that is cut off by the end segment, L the inertance and C the compliance of the previous segment. Z is chosen such that it is equal to the input impedance of the previous segment, see [7]. This ensures a perfect impedance match between the end segment and the final arterial segment for higher (8) 8

9 frequencies. Reflection occurs when there is an impedance mismatch, so only low frequency components will lead to reflections at the end segment [12]. R = R Z (12) v p τ C = (13) R v C the compliance of the branch that is cut off, τ the time constant (1.5s [3]), R p the total peripheral resistance, resulting from the series arrangement of Z and R v (see Figure 3). Model optimisation The initial parameters estimated from the measurements were used for the first simulation with the model. Simulated BVF and BP curves were compared to the invivo results. Then, the model parameters were adapted to obtain more physiological results which are comparable with the measurements. First of all, the three-element windkessel end segment model was fitted to the in-vivo results. The fitting was performed analogue to the method of Stergiopulos et al [11]. The three-element windkessel model was fitted in the time domain with use of the measured flow as input by adjustment of the model parameters to minimise the root-mean-square deviation between the measured pressure and the windkessel predicted pressure. The time averages of the BVF and BP curves over four heart beats were calculated from the measurements of the RA proximal to the wrist (RA position 1 in Figure 1). A transfer function (eq. 13) was determined to express the relation between blood pressure and flow at this location in terms of the windkessel parameters: pˆ Rv = Ztot = Z + (14) qˆ 1+ iωcrv with pˆ and qˆ the pressure and flow harmonics. With the use of eq. 14 and the harmonics of the BVF determined flow the maximum velocity measurements (eq. 4), an expression for the BP obtained from the windkessel model in the frequency domain, ˆp, can be derived: mod totq ˆ p ˆ = mod Z (15) The pressure time signal can be reconstructed from the sum of all harmonics: N h pmod ( t) = Re pˆ f exp( i2π ft) (16) f = 0 Only the first 10 harmonics (N h =10) appeared to be important for reconstruction of the pressure time signal. The model pressure time signal was fitted to the measured time averaged BP signal, by adapting the parameters R v, C and Z until the least squares estimates of those parameters were obtained. With these new parameters, the second simulation was performed. 9

10 Results CBFV and WD in the subclavial artery appeared to be too difficult to measure and therefore the upper limb arterial tree was modelled starting from the brachial artery. For five volunteers, measurements at five or six locations, two in the BA, two in the RA and one or two in the UA, were performed. For the other volunteers less complete, but still usable datasets were obtained. For 4 volunteers the complete dataset was acquired in one session of 2 hours, but for the other volunteers more sessions were necessary. In the brachial artery, typical mean vessel diameters of 4 to 5 mm and wall distensions of 1 to 2 % were measured (Figure 4). Maximum velocities of 0.55 m/s were observed (Figure 5). In the radial and ulnar arteries, typical diameters of 3 mm, distensions of 1 to 2% and maximum velocities of 25 cm/s were measured. The flow waveforms reconstructed from the measured centreline velocities are depicted in Figure 6. Measurements in the radial and ulnar arteries were less accurate and difficult to perform because those arteries are located very close beneath the skin and hard to get in the focus of the ultrasound beam. Therefore a lot of transmission gel was necessary, which made it difficult to stabilise the ultrasound probe during the measurement. D [mm] Time [s] Figure 4: A typical wall distension curve measured in the brachial artery (straight line representing the mean vessel diameter) 10

11 Figure 5: A velocity profile measured in the brachial artery. The black line is indicating the centreline which is used for reconstruction of the velocity profile using Womersley BA (52 cm) BA (30 cm) RA (10 cm) RA (1 cm) UA (10 cm) UA (1 cm) q [ml/min] Time [s] Figure 6: Flow waveforms reconstructed from the measured centreline velocities at different positions in the arm arterial tree of volunteer 6. The data set of only 1 volunteer (volunteer 2) was used for the current lumped parameter model, but for the other datasets the procedure will be similar. For this volunteer, the measurements of the UA at 2 positions and the RA at 1 position were performed on a different day. Those WD measurements were not used for the vessel radius interpolation because there was too much deviation in the measured UA and RA radii between the days. Instead, it was assumed that UA and RA have equal radii and that the area of the UA and RA after the bifurcation equals 1.2 times the area of 11

12 the BA before the bifurcation. The multiplication factor was obtained from the data of Westerhof [13]. The results of the first simulation, with the roughly estimated parameter values, are depicted in Figures 7 and 8. There is some similarity between measured and modelled flow, but the shape of the modelled pressure curve differs significantly from the one that is estimated from the measurements. The systolic, diastolic and mean pressures in the model are much higher than the measured ones. To acquire better pressure modelling, the end impedance was fitted to the measurements. The result of this fitting is depicted in Figure 9. The estimated parameters with which the first simulation was performed and parameters resulting from the least square fit between the measured and modelled pressure curve can be found in table 1. After the fitting procedure, C decreased with 81%, Z with 84% and R v increased with 16%. It is known that the windkessel model is capable of describing the gross features of the arterial pressure and flow pulse, which are contained within the first few harmonics [10]. This is also observed in the plot of the modulus and phase of the fitted and measured input impedance (Figure 10 and 11). The magnitude and phase of the impedance are very well described by the windkessel model up to 4 Hz. For the higher harmonics, a large deviation in the phase and a smaller deviation in magnitude appear which cannot be described by the model. The same features were also found by Stergiopulos [10]. Figure 7: Simulation 1, without fitting of the end impedance 12

13 Figure 8: Simulation 1 (dashed lines) compared with the measurements (solid lines), (pressure in mmhg) 1.5 x measurement model 1.3 pressure (Pa) time (s) Figure 9: Measured time average BP and fitted model BP Parameter First estimate Least squares estimate C 1.02* *10-11 m 4.s 2.kg -1 Z 2.47* *10 8 m -4.s -1.kg R v 1.47* *10 10 m -4.s -1.kg Table 1: Estimated and fitted end segment parameters 13

14 18 x model measurement 14 magnitude Z [kg/s.m 4 ] frequency [Hz] Figure 10: Magnitude of the measured and windkessel impedance model measurement 0 phase Z [rad] frequency [Hz] Figure 11: Phase of the measured and windkessel impedance. With the new parameter values resulting from the fit, the second simulation was performed. The results are depicted in Figures 12 and 13. From Figure 12, it can be seen that there are some higher frequency components present in the signals compared to the first simulation, especially in the BA segments (see Figure 7). With the new parameters, the modelled pressure curves are in better agreement with the measurements: the systolic, diastolic and mean blood pressures are comparable with the measured ones. In the model, a clear increase in pulse pressure towards the periphery is observed, which is not present in the BP curves estimated from the measurements, using only the BA pulse pressure. Note that the measured pressure curves in Figures 8, 9 and 12 are not periodic, which can be explained by the fact that the depicted curves represent an average of several measurements with different heart rates. 14

15 Figure 12: Simulation 2, with fitted end impedance Figure 13: Simulation 2 compared with measurements (pressure in mmhg) 15

16 Discussion and conclusion In this study, a patient specific lumped parameter model was used, in combination with ultrasound measurements of vessel wall distension and blood flow velocity, to estimate local wall properties of the upper limb arterial tree. To obtain good estimates of the arterial wall properties from the fitting between the simulations and the measurements, it is important that measurements are accurate and reproducible. However, the reproducibility and accuracy of the measurements depends highly on the skills of the investigators. It was found that a lot of practice is necessary and even then it was very difficult to obtain complete data sets for some of the volunteers. To avoid influences of different heart rate and blood pressure, it is important to perform all measurements on the same day, during one measurement session. The BP curves resulting from the rescaled WD measurements that were used for comparison with the simulations and fitting of the end segments are not periodic. The reason for this is that these curves are an average of multiple WD measurements at the same location. The duration of the shortest heart beat was used, so all the other signals were cut off. A better way of taking the average of different curves would have been to calculate the average frequency components and reconstruct the mean signal using the first harmonics. BP curves were reconstructed from the WD measurements assuming a real valued, constant arterial compliance, while it is know that the compliance is dependent on the blood pressure and that there is a phase difference between the BP and wall distension curve [6]. Furthermore, systolic and diastolic pressures measured in the BA were used to rescale the WD measurements while in reality especially the systolic pressure will increase towards the periphery due to wave reflections [4, 5, 12]. Therefore, it would have been better to use the diastolic and mean pressure to rescale the measurements. The increase of pulse pressure towards the periphery was observed in the simulations, but not in the measurements, since only one blood pressure measurement was used to rescale all the wall distensions. So this rescaling of WD instead of using the actual local pressure can be a cause of the observed differences between the modelled and the measured pressure curves. These differences between modelled and measured pressure might also be due to the non-linear and visco-elastic properties of the arterial wall and to the fact that the model adaptation was done by fitting the end impedances only. The fitting should be extended to a fit of all arterial segments. This can be done by first calculating the input impedance of the complete modelled arterial tree, using transmission line theory, see [7], and then performing a fitting of the measured and the model BP curves, as was done for the end segment. This fitting will result in estimates of the arterial compliance in all segments along the arm arterial tree, the final goal of this study. Another method would be to decompose the measured and modelled waveforms in forward and backward travelling waves according to the method of Parker and Jones [9] and determine the arterial compliance from the travelling speed and attenuation of the waves. 16

17 The end segment fitting method used is based on the fitting of the pressure time signals, according to Stergiopulos [10, 11]. As explained before, the windkessel model can only describe features of the impedance for the first few harmonics, up to 4-5Hz. Apparently, these harmonics are also the most important ones for the dynamic features of the pressure curve, since the modelled and measured time signals agree very well. The behaviour of the impedance for higher harmonics (with an increase in magnitude of the impedance, see Figure 10) cannot be obtained using the current end segment model. In the results of the second simulation, with the fitted impedance, some high frequency components can be seen in the pressure and flow waveforms. This can be the result of the fact that the impedance of the fitted windkessel model is too low for the higher harmonics and therefore insufficient attenuation of these components takes place. To overcome these problems, a four-element windkessel could be used, as suggested by Stergiopulos [11] which uses an inertance L parallel to the resistance Z. Using this four-element model, Z will be bypassed for very low frequencies while for high frequencies all the flow goes through Z. It was hypothesized that the observed differences between measured and modelled BP are partially due to the non linear and visco-elastic properties of the arterial wall. Therefore, a continuous wave propagation model that takes these properties into account will be used in future work. Furthermore, future models should include the ulnar artery bifurcation and an option to model leakage of blood. In the model used for this research, all the input flow goes to the end segments of the RA and UA, which is not correct because a large amount of flow will go to the muscles of the upper and forearm. This increased flow in the end segments will also lead to higher blood pressures in the RA and UA. So including leakage and visco-elastic wall properties should provide a more physiological modelling of the pressure/flow relationship and therefore more accurate estimates of the arterial wall properties. In this study a method to estimate the arterial compliance of the upper limb was developed. The upper limb was chosen, since it is relatively easy to perform ultrasound measurements along the complete arterial tree ranging from armpit to wrist, the arteries are approximately straight tubes and blood pressure can be measured directly at the brachial artery. In the future, this method could be extended to for example the femoral arteries, to obtain more information about a patient s cardiovascular condition. 17

18 References 1. P.J. Brands, A.P.G. Hoeks, L. Hofstra, R.S. Reneman. A non invasive method to estimate wall shear rate using ultrasound. Ultrasound Med & Biol, 21(2): , H. Gelderblom and C.A.D. Leguy. Assessment of arterial properties of the upper limb in a healthy volunteers group: protocol ultrasound measurements. Internal report. Maastricht, Academic Hospital Maastricht, W. Huberts. The hemodynamical effects of arteriovenous fistula. Msc.Thesis. Eindhoven: Eindhoven University of Technology, M. Karamanoglu, M.P. Feneley. On-line synthesis of the human ascending aortic pressure pulse from the finger pulse. Hypertension 30: , S. Laurent et al. Expert consensus document on arterial stiffness: methodological issues and clinical applications. Eur Heart J. 27: , B.M. Learoyd, M.G. Taylor. Alterations with age in the viscoelastic properties of human arterial walls. Circ Res 18, , R.E. Matick. Transmission lines for digital and communication networks: an introduction to transmission lines, chapter 1. IEEE Press ISBN Mattace-Raso et al. Arterial stiffness and risk of coronary heart disease and stroke: the Rotterdam study. Circulation, 113(5): , K.H. Parker, C.J. Jones. Forward and backward running waves in arteries: analysis using the method of characteristics. J Biomech Eng, 112(3): N. Stergiopulos, J.J. Meister, N. Westerhof. Simple and accurate way for estimating total and segmental arterial compliance: The pulse pressure method. Ann of Biomed Eng, vol.22: , N. Stergiopulos, B.E. Westerhof, N. Westerhof. Total arterial inertance as the fourth element of the Windkessel model. Am. J. Physiol. 276 (Heart Circ. Physiol. 45):H81-H88, N. Westerhof, F. Bosman, C.J. de Vries, A. Noordergraaf. Analog studies of the human systemic arterial tree. J Biomechanics, vol.2: , J.R. Womersley. Method for the calculation of velocity, rate of flow and viscous drag in arteries when the pressure gradient is known. J Physiol, 127(3): ,

19 Assessment of arterial properties of the upper limb in a healthy volunteers group: PROTOCOL ULTRASOUND MEASUREMENTS Authors: Hanneke Gelderblom and Carole Leguy Contact c.a.d.leguy@tue.nl Last update: 06/07/2007 Maastricht, AZM 1 Introduction General set up...20 Blood pressure measurement...20 ECG...20 Measurement positions...20 Machine and computer settings Measurements on the carotid artery...23 Wall distension...23 Machine set up...23 Position of patient and investigators...23 RFDAPP adjustment...25 Results...26 Velocity...26 Machine set up...26 Position of the transducer...26 RFDAPP adjustment...28 Results Measurements on the brachial artery...29 Wall distension...29 Machine setup...29 Position of patient and investigators...29 RFDAPP adjustment...29 Results...29 Velocity...29 RFDAPP adjustment...29 Results Measurements on the radial artery...30 Wall distension...30 RFDAPP adjustment...30 Results...30 Velocity...30 RFDAPP adjustment...30 Results General measurement protocol for the upper limb

20 1 Introduction The goal of this study is to evaluate the feasibility of a new method to determine arterial wall properties based on a 1D wave propagation model. A reverse method will be developed in order to estimate the arterial properties (young s modulus) given the best fitting between BVF and vessel wall distension estimated from the measurements and the one provided by the simulation results at several locations along the arterial tree. In order to get the best chances to obtain a good fit with the wave propagations model, it is very important that local parameters can be measured at the strategic places along the arterial tree. Geometrical aspects like bifurcation positions have to be assessed as well as dynamical properties of the vessel distension. Hemodynamic properties are also essential to be determined, so blood velocity profiles are assessed at several positions. Blood pressure will be assessed by standard cuff measurement (as well as tonometer measurements). 2 General set up Blood pressure measurement The blood pressure can be measured using a cuff (Omron 705 CP). The cuff must be wrapped around the upper arm, about two centimeters above the elbow, with the outlet tube at the lower side pointing in the direction of the brachial artery. The patient must be in supine position on the bed with his arm stretched. First put the apparatus on and then start the measurement by pressing start. Measure the blood pressure at least three times (do not use the first measurement). N.B.: Start the measurement after the patient has relaxed for at least 15 minutes. ECG Electrode positioning: The ECG of the patient must be measured to trigger the ultrasound measurements. Place three ECG stickers on the patient: one on left side of the chest (near the sternum), one near belly button (left side) and one beneath the lower one. Connect the red electrode to the sticker on the chest, the yellow electrode to the sticker near the belly button and the green one to the third sticker. N.B.: Use new stickers (do not re-use them) because there has to be enough salt solution on them for optimal conduction. Measurement positions Measure the length of the whole arm (from wrist to elbow to armpit with a tape measure). Use the ultrasound transducer to find where brachial artery bifurcates into the radial and ulnar artery and determine this position with respect to the wrist. Determine the positions where the measurements take place with respect to these points. E.g.: 60 cm armpit 35 cm location brachial artery measurement 28 cm bifurcation Brachial into Ulnar and Radial arteries 2 cm location radial artery measurement 0 cm wrist 20

21 Figure 1: Measurement of the investigation location on the arm. Machine and computer settings Tools: The Ultrasound scanner Ultramark 9 plus (Advanced technology Laboratories, Bellevue, WA) is used. Figure 2: Measurement room. On the left we can see the Ultrasound scanner Ultramark 9 plus 1. Starting: Switch on the acquisition computer; click cancel when a password is asked. After the startup is completed, select the program RFDAPP. In RFDAPP, select the usr button and select from the directory carole carol.usr. Click OK. 21

22 Turn on the ultrasound machine using the power switch on the right side. After the complete startup, push the set-up button. Select settings vascular by pressing set (button on top of the machine, below the screens) until vascular is selected on the first row on the right sight of the screen, then select user Jeroen. Press set. N.B.: 1 focal point should be used (more focal points are convenient for clinical purposes, morphology information, but not for measurements). The ECG must be visible on both screens now. Noise on the ECG can appear because of disturbance from power supply of the bed. If this is the case, disconnect the plug of the bed from the socket. Check whether the T-peak of the ECG is not too high (otherwise the machine could trigger twice, both on R top and T top, and you want to trigger on the QRS complex). If the T-peak is too high, move the red electrode and sticker to the left (use a new sticker for this). Check the trigger light on the left lower side of the machine (ECG trigger output) 22

23 3 Measurements on the carotid artery Wall distension Machine set up On the ultrasound machine go to XDCR to select the transducer L mm by touching the display. A linear array transducer is used to measure wall distension. The system will calibrate a few seconds. Switch the system to the 2D-mode. Figure 3: Linear array transducer L mm (here used to measure the radial artery wall distension). Position of patient and investigators (see figure 2) When moving the bed, use the wheels. When the patient is lying on it, it should be on the table-legs. Patient position: 1. He should be in supine position on the bed. 2. Don t use a pillow for the head. 3. The patient should rotate the head a little bit on the external side to stretch the carotid artery. Ask the patient if the position is comfortable. Investigators position: One investigator sits on the head of the bed to perform the measurement (hereafter called Investigator 1 ), the assistant sits behind the computer and ultrasound machine to control them (Investigator 2). Investigator 1 can use the foot pedals to operate the ultrasound machine (switch between 2D-, M- and Doppler-mode). Position of the transducer: 1. The lower arm of investigator 1 is positioned on the bed. 2. Use a small pillow to support the arm. 3. The transducer cable is placed around his neck, or around a cable that can hold the weight of the probe. 4. Try to feel where the artery is located with fingers first. 23

24 5. Put an amount of ultrasound transmission gel on the transducer (Aquasonic 100). 6. Position the transducer on the right location (the small light on the transducer must be in the direction of the heart). 7. Investigator 1 can switch to Doppler mode using the pedals (see the section velocity ), or investigator 2 can switch to Doppler mode using the buttons on the screen; if you hear the flow in the artery, you are in the right position. 8. When searching for the artery, Investigator 2 must make sure all amplification switches are adapted to obtain a clear view. NB: Do not pay much attention to the exact position of the measurement volume and angle when checking the location in Doppler mode; just use it to check if you are at the right position (in an artery), not to perform a measurement. Once the artery is found, Investigator 2 can optimize the view on the ultrasound machine. In 2D mode: adapt amplification (walls: high signal, lumen lower signal). Choose the focal point between the walls (using the button focal and the trackball on top of the machine and press set at the right location). Increase the gain if necessary. With the amplification switches, Investigator 2 can locally change amplification, with the 2D/M-mode gain rotary knob he can in- or decrease the overall gain. Zoom in or out is possible by changing the depth using the depth rotary knob (increasing the depth is zoom out and vise versa). Once a correct view is obtained, switch to M-mode. A wall distension measurement is performed in M-mode. 1. The transducer must be positioned in such a way that the artery is perpendicular to the M-line. 2. The intima must be visible as a small line below the media to make sure the measurements are performed in the centre of the artery. 3. Investigator 1 must be careful he doesn t press too much on the artery (check it in the measurement results later on). 4. The patient should hold his breath during the measurement (5s) to avoid influences of pressure differences caused by the respiration. 5. Investigator 1 tells Investigator 2 when he s ready. Investigator 2 counts to 3 and then (both) the patient (and Investigator 1 if necessary) stops breathing for 5 seconds. 6. Investigator 2 counts from 1 to 6 and tells the patient when he can start breathing again. The investigators can see from the flashing light on the computer when the measurement has finished. N.B.: Investigator 1 can hold his breath as well to minimize the movement of the transducer during the measurement. During the measurement, investigator 2 watches the right screen of the ultrasound machine to check if the position of the transducer is constant during the measurement. If investigator 1 moves a little bit, the measurement must be repeated. A least 3 proper measurements of the distension should be performed, so when the settings are optimal, repeat the measurement at least 2 times before going to the velocity measurements. 24

25 RFDAPP adjustment 1. Investigator 2 adjusts RFDAPP. 2. Before starting up measurements: on the computer: make a folder per patient with name and measuring date in the folder DAS. 3. Go to offline. Adapt the offline acquisition parameters: - Depth (of the artery): 14 mm (it depends on the patient: take a look at the 2D image on the ultrasound machine to see where the artery is located) 4. Expected diameter (of the artery): 6 mm 5. Angle: Use option wall track 7. Open a measurement: go to Carole directory and fill in the name you want to give the measurement. Use CRT-c and CRTL-v to copy and paste the measurement names (to speed up the procedure). File name nomenclature example: 02_P03_CCA_D_03 1. Patient number: Position of the measurement: P03 3. Investigated artery: Common Carotid (CCA), Subclavial (SC), Brachial (BA), Radial (RA), Ulnar (UA) 4. Measurement type and measurement number: Wall Distension (D), Velocity (V) 5. Measurement number: 03 When the machine is tuned in M-mode, put the M-line in a right position for measurement using the trackball, and press the M-mode button again to see the distension over time on the right screen. Investigator 2 can open the measurement. Look at the computer screen to see if the window length is correct (you should see the reflection of both walls). Look at the left screen of the ultrasound machine to check which window length should be used. If necessary, adapt the size of the window (in RFDAPP you can see everything between depth and depth+ window length ). To do this, step back in RFdapp, go to settings and choose acquisition. Change the envelope setting (the length of the envelope and the window must be equal). e.g.: Envelope: 20mm Window: 20mm Open the measurement again (offline-wall track). If the peaks of the wall signal in RFDAPP are too high, lower the 2D/M mode gain on the machine. Make sure the peaks don t exceed the 90% boundary. Check the red dot on the acquisition screen overload. If the walls are not clearly visible, play with the position of the M-line on the screen and the transducer position. Before starting a measurement, check if the transducer is still positioned perpendicular to the M-line. To start a measurement in RFDAPP: Place mouse cursor in the middle between the 2 vessel walls. Click left mouse button between the walls to start the measurement. Investigator 1 should say when to start. N.B.: settings are only saved after a measurement is performed with these settings! 25

26 Results 1. The crosses in the distension curve (these are the indication of the ECG peak trigger) must precede the main distension peak (contraction of the heart precedes peak pressure in the artery). 2. If the main distension peak is flattened in stead of sharp, probably investigator 1 compressed the artery too much with the transducer. Redo the measurement with less pressure. 3. Check the measured diameter (is this value reasonable?), distension and the standard deviations. The relative distension must be around 10% for the carotid artery of a healthy (young) subject. When strange results are obtained, check whether the walls are clearly measured using the option wall in RFDAPP and selecting the measurement. Velocity Machine set up Use the XDCR button on the ultrasound machine to switch to the C9-5 curved array transducer. The system calibrates during a few seconds. Switch the system to the 2Dmode. Figure 4: Curved array transducer C9-5 (here used to measure blood velocity in the brachial artery). Position of the transducer 1. It is convenient for investigator 1 to hold the transducer with both hands: one hand to hold the quite heavy top of the transducer and one hand on the tip to accurately position the transducer (the small light on the transducer must be in the direction of the heart). 2. Try to stay at more or less the same location as where the distension measurements were performed. 3. First try to get a good view of the artery in 2D mode. 4. Investigator 2 can adjust depth, local amplification and gain. 26

27 5. Switch to Doppler-mode by pressing the Doppler-mode button on the machine once. Two lines appear (see figure 5): one long line (line 1) with a small rectangle on it (the measurement volume) and a small line (line 2) that makes an angle of 70 with line Investigator 2 can change the position of line 1 by using the trackball. 7. Use the options change angle and angle correction on the display of the ultrasound machine to make sure the angle between both lines is Place line 2 parallel to the artery; with the measurement volume exactly in the centre of the artery (perhaps Investigator 1 must turn the transducer a little bit to accomplish this). 9. Adapt the measurement volume (make sure you don t measure the walls; their movement disturbs the centre line velocity) using change measurement volume on the ultrasound machine display. Figure 5: Line 2 and the measurement volume should be positioned in the artery according to this figure 10. Once an optimal set-up is obtained, the measurement can start by pressing Doppler-mode on the ultrasound machine or using the pedals again. On the right screen of the machine the Doppler signal is visible. If the signal is inverted (negative peaks), Investigator 1 holds the transducer back to front. This can be changed by pressing spectral invert on the display of the machine. When the Doppler signal is to low, Investigator 2 can increase the signal using the Doppler gain button on the machine. 11. Once the settings are correct, investigator 1 can switch to the actual situation on the left screen again by pressing Doppler-mode with the pedals or investigator 2 can use the buttons on the ultrasound machine, to check if the position of the transducer is still correct. Investigator 2 can change the position of the measurement volume/ lines if necessary. Investigator 1 or 2 can switch to Doppler mode again to start the measurement. 12. The patient should stop breathing during the measurement (5s) to avoid influences of pressure differences caused by the respiration. Investigator 1 must tell the patient when to stop and start breathing, and investigator 2 when to start the measurement. Investigator 2 counts from 0 to 5 (seconds) during the measurement. He can see from the flashing light on the computer when the measurement has finished. 27

28 13. Investigator 2 checks the sound and shape of the waves on the left screens of the ultrasound machine, to check whether the position of the transducer is kept constant during the measurement. If investigator 1 moves, the measurement must be repeated. At least 3 proper measurements of the velocity should be performed. RFDAPP adjustment 1. Investigator 2 adjusts RFDAPP. 2. Go to offline. Adapt the offline acquisition parameters: 3. Depth (of the artery): 14 mm (check ultrasound machine for artery depth) 4. Expected diameter (of the artery): 6 mm 5. Angle: Use the option velocity distribution. 7. Open a measurement: go to Carole and fill in the name of the measurement. File name nomenclature example: 02_P03_CCA_V_03 1. Patient number: Position of the measurement: P03 3. Investigated artery: Common Carotid (CCA), Subclavial (SC), Brachial (BA), Radial (RA), Ulnar (UA) 4. Measurement type and measurement number: Wall Distension (D), Velocity (V) 5. Measurement number: 03 Click between the walls to start the measurement. Once the measurement is started, the sound of Doppler signal tones down a bit, but the frequency should not change! Results Check the velocity spectrum (one peak from the sender and a spectrum of peaks from the blood flow velocity). Check if the wall diameter corresponds more or less to the diameter measured during the measurement of the wall distension. It is convenient to perform calculations of the velocity of some measurements to check whether the measurements are correct. To calculate velocities: -go to comp ; estimate velocity and distension -check the velocity profile. Expected maximum velocity in the carotid artery: about 90 cm/s 28