Medical Engineering & Physics
Volume 34, Issue 1 , Pages 17-27, January 2012

Analysis of flow and wall shear stress in the peroneal veins under external compression based on real-time MR images

  • Ying Wang

      Affiliations

    • Department of Chemical Engineering, Imperial College London, South Kensington, London SW7 2AZ, UK
    • Corresponding Author InformationCorresponding author. Tel.: +44 2075895111x55701.
    • ,
  • Iain Pierce

      Affiliations

    • NHLI, CMR Unit, Royal Brompton and Harefield NHS Trust, Imperial College London, UK
    • ,
  • Peter Gatehouse

      Affiliations

    • NHLI, CMR Unit, Royal Brompton and Harefield NHS Trust, Imperial College London, UK
    • ,
  • Nigel Wood

      Affiliations

    • Department of Chemical Engineering, Imperial College London, South Kensington, London SW7 2AZ, UK
    • ,
  • David Firmin

      Affiliations

    • NHLI, CMR Unit, Royal Brompton and Harefield NHS Trust, Imperial College London, UK
    • ,
  • Xiao Yun Xu

      Affiliations

    • Department of Chemical Engineering, Imperial College London, South Kensington, London SW7 2AZ, UK

Received 6 April 2011; received in revised form 14 June 2011; accepted 19 June 2011. published online 18 July 2011.

Article Outline

Abstract 

As a widely accepted prophylaxis for deep vein thrombosis, the underlying mechanism of compression stocking still remains unclear. In this study, computational fluid dynamics was applied to in vivo data to provide quantitative insight into the hemodynamic response of the deep venous system to static external compression. The geometry and flow information of deep veins before and after compression was acquired from ten healthy volunteers using magnetic resonance imaging.

Our results indicated that application of the compression stocking led to a small reduction in blood flow rate but a significant reduction in cross-sectional area of the peroneal veins in the calf, resulting in an increase in wall shear stress (WSS), but the individual effects were highly variable. The mean volume reduction of the deep veins was 58%, while the time-averaged WSS showed an average increase of 398% after compression (median 98%). The analysis also showed a strong linear correlation between the time-averaged WSS and mean blood velocity, suggesting that flow in the deep veins under the level of compression examined here can be approximated by Poiseuille's law despite local geometric variations. It is hoped that quantitative analysis of WSS in the deep venous system will aid in the future design and optimisation of the compression stocking.

Keywords: Peroneal veins, Deep vein thrombosis, Magnetic resonance imaging, Hemodynamics, Numerical simulation

 

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1. Introduction 

Deep vein thrombosis (DVT) is a common post-operative complication, and a serious threat to the patient's general recovery. In recent years, there has been an increasing awareness of the risk of DVT in healthy individuals after prolonged immobility, such as taking long-haul flights or sitting at a computer. Mechanical methods such as compression stockings and intermittent compression devices have been developed as prophylaxis for DVT [1], [2], [3], but their effects on blood flow and the resultant shear stress in deep veins in the calf have not been elucidated.

Under the assumption that fast flowing blood may help to flush away thrombi, early design of compression devices aimed at generating high peak velocity. However, evidence to date has supported wall shear stress (WSS) as a factor that regulates blood vessel structure and influences the development of vascular pathology [4], [5], [6], [7]. DVT has a propensity to occur in areas where blood flow is slow and changes direction, such as venous valve pocket [8], [9], [10]. In these susceptible areas, the endothelial monolayer is exposed to very low WSS. Conversely, steady flow and moderate levels of WSS have been shown to be important in keeping the health of the vascular system [11], [12], [13]. The biological responses of endothelial cells to WSS suggest another aspect of the working mechanism of the compression devices.

Calf veins are the most susceptible sites for DVT, while a thigh vein is less commonly affected. The other deep veins in the human body are less affected by DVT. Previous studies [14], [15], [16], [17] have been devoted to the exit velocity and volumetric flow rate in the femoral (thigh length compression) or popliteal (knee length compression) vein rather than the deep calf veins. Although analysis of downstream hemodynamic conditions can provide some useful information about the upstream flow, it may not capture the exact effects of the calf compression stocking.

It has been demonstrated that magnetic resonance imaging (MRI) is able to provide more accurate anatomical data than ultrasound [18]. Avril et al. [19] constructed a finite element model of a calf section based on MRI data to investigate the transmission of external compression through the soft tissue of calf. Using anatomical information obtained from MRI and pulsed Doppler ultrasound flow data, a computational fluid dynamics (CFD) analysis was performed to estimate the effect of static compression on WSS in the major deep and superficial veins of the calf [20]. However, the blood flow data used in this study were obtained from the downstream popliteal and great saphenous veins owing to the difficulty in measuring blood flow in the deep calf veins using ultrasound.

In this study, real-time blood flow data of the deep calf veins were acquired using phase contrast MR velocity mapping, together with anatomical images of the calf, before and after the application of a compression stocking. Ten young healthy volunteers participated in this study and all scans were performed in the supine position.

3D geometries of the deep veins were reconstructed from the MR images, and CFD was employed to analyse blood flow in the deep vessels under subject-specific flow conditions based on MR flow measurement. To the best knowledge of the authors, this is the first use of flow data directly measured within the reconstructed deep vessels in the calf, in order to provide matching geometry and flow boundary conditions.

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2. Materials and methods 

2.1. MRI imaging protocol 

In this study, ten healthy volunteers (24–35 years old) without any history of venous disease were included. The study was approved by the local research ethics committee, and informed consent was obtained from all participants. Scans were performed at the CMR Unit at the Royal Brompton Hospital. All scans were performed with the subject in the supine position. A cushion was used to support the subjects’ ankles which were lifted by about 10cm to avoid compressing the calf muscles against the table (Fig. 1).

None of the subjects was on any medication. The compression devices employed in this study were knee-length grade 1 static compression stockings (T.E.D.™ Covidien Inc.), which were designed to generate a pressure pattern of 18mmHg at the ankle, 14mmHg at the calf and 12mmHg at the knee. According to the manufacturer's instructions, the length and circumference of each subject's calf were measured (Fig. 2) and the stocking of appropriate size was selected for each subject. The following MRI scan procedure was adopted:

1.The subject lay on the patient table in a supine position without wearing any compression stockings. Short localiser scans (∼15s each) were performed to determine the location for the full MR examination.

2.A 19cm section of the calf was scanned using a 3D balanced steady state free precession (bSSFP) sequence. The echo time (TE), repetition time (TR) and full acquisition time (TA) were 1.86ms, 4.29ms and 3min 51s, respectively. Fat suppression pulses were applied during interruptions of the bSSFP every 172ms. The field of view (FOV) covered an area of 200mm×200mm and the spatial resolution was 0.625mm×0.625mm×2mm. A total of 96 images were acquired along the calf length for each subject.

3.The subject was given 2–3min to become accustomed to the metronome-guided respiration [21], before real-time phase contrast velocity mapping was performed and blood flow data were recorded over a period of approximately 38s to ensure at least 5 complete respiratory cycles were captured. MRI sequence parameters, TE/TR/TA=5.2ms/39.8ms/954.7ms, were employed. The FOV was 150mm×150mm with 320 primary phase encoding steps and readout samples, which led to spatial resolution of 0.5mm×0.5mm.

4.The compression stocking was put onto the subject's right leg, while the subject remained in a relaxed supine position.

5.A period of approximately 5min was allowed to elapse before any subsequent images were acquired. Then a further set of images and velocity data were acquired following the same procedure as described above.

The real-time phase contrast velocity mapping sequence used in this study was specially optimised for use in the lower leg. Details of the imaging sequence have been reported elsewhere [22] at lower spatial resolution, hence only a brief summary will be given here. It utilised a spiral k-space trajectory, split into 12 interleaves, each repeated for ‘symmetric’ velocity encoding achieving a final velocity range (VENC) of ±5cm/s. A parallel saturation band was used to suppress signal from the arterial blood entering the image slice, and slice-selective water excitation (using a spatial-spectral (1, 1) binomial RF pulse series) was used in order to reduce ‘off-resonance blurring’ artefact due to fat signal. The slice thickness was 5mm and acquired in-plane resolution was 0.5 by 0.5mm reconstructed to 0.3mm×0.3mm.

Velocity measurements were taken from the images using CMR Tools (Cardiovascular Imaging Solutions Ltd, London, UK). Regions of interest (ROI) were drawn around the peroneal veins on the real-time anatomical images that showed greatest in-flow enhancement of the veins (and compared with an ROI drawn on the corresponding slice from the 3D sequence). This ROI was then transferred to all the velocity maps of that series, keeping the ROI static throughout. Spatial mean velocities were recorded, multiplied by the ROI area for calculations of the volume flow. An ROI was placed within the muscle mass, also assumed to be stationary throughout the image series, to obtain background offset error corrections for the velocity images.

The real-time data were reconstructed using an in-house Matlab (Mathworks) programme with a sliding data window to achieve a final (interpolated) temporal resolution of 79.6ms.

2.2. Venous flow data 

The main deep vessels include peroneal veins, posterior tibial veins and anterior tibial veins, also known as the axial veins (Fig. 3). To some extent the architecture of the deep venous system is a mirror of the local arterial network, with vessels running alongside their corresponding arterial branches. In many cases, including the vessels mentioned above, the artery is accompanied by two or more veins.

Compared with the peroneal veins and the posterior tibial veins, the anterior tibial veins are much smaller in diameter. The spatial resolution of whole-body MRI scanners is insufficient for an accurate flow measurement in such small vessels, unless acquired over a longer timescale. On the other hand, the peroneal veins involve fewer bifurcations than the posterior tibial veins. For these reasons, in this study, blood flow rates in the peroneal veins were measured. Although flow data in both the lateral peroneal vein (LPV) and medial peroneal vein (MPV) was acquired, the LPV is very close to the fibula, which can affect the LPV deformation significantly. The deformation of the MPV is believed to be less subject-dependent compared with the LPV; hence the MPV was selected for the CFD analysis. For all the subjects, flow velocity was measured at about 5cm below the popliteal vein bifurcation. The measured flow rates in the MPV of all subjects before and after compression are shown in Fig. 4.

For each subject, a representative flow waveform was calculated by taking an ensemble average of 5 cycles from the actual flow data acquired (Fig. 5). This subject-specific representative flow rate waveform was applied as an inlet boundary condition in CFD simulations.

  • View full-size image.
  • Fig. 5. 

    Comparison of sample representative waveforms (continuous lines) and the MRI flow data (dashed lines). Data are taken from the medial peroneal vein in subject 1, before (top) and after (bottom) compression induced by the static compression stocking.

2.3. CFD modelling 

The geometry of MPV was reconstructed using Mimics 13.0 (Materialise Group, Belgium). The inlet of the reconstructed MPV corresponded to the section where the MR flow rate was acquired, but in order to avoid the inclusion of bifurcations, the position of the inlet was varied slightly (±6mm) depending on the architecture of the MPV. Because at any given time, blood flow rate should remain approximately constant within a section of vessel without any bifurcation, it is reasonable to assume that the slight variation in inlet position will have little effect on the subsequent flow analysis.

ICEM CFD (Ansys Inc., USA) was employed to generate the computational mesh for each reconstructed geometry (physical domain). The physical domain was divided into hexahedral structured grids. Increasing the nodes number from 310,000 to 2,480,000 resulted in a difference of less than 1% in terms of the spatial mean time averaged wall shear stress. A mesh size of 310,000 nodes was therefore selected. Spatial discretisation of the governing equations was performed via a hybrid 1st/2nd order scheme while temporal discretisation was performed via a fully implicit second order backward Euler scheme. The algebraic multigrid method was used to solve the resulting discretised equations.

The vessel wall was assumed to be rigid with a no-slip condition. The subject-specific representative venous flow rate waveform was applied at the model inlet which was extended upstream by 6 times the inlet diameter, and a relative static pressure of 0Pa was specified at the outlet. Blood was treated as a Newtonian fluid with density 1060kg/m3 and viscosity 3.5mPas. For the subjects included in this study, the peak Reynolds numbers at the inlet ranged from 30 to 162 and therefore, laminar flow assumption was made.

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3. Results 

Results for time-averaged wall shear stress (TAWSS) obtained from the CFD simulations are shown in Table 1. In terms of the spatial mean TAWSS, 9 out of 10 subjects showed increase after compression. Only subject 2 showed lower TAWSS with compression stocking than that before compression. The overall result showed an average increase ((TAWSSc−TAWSSu)/TAWSSu) of 398%, but individual results varied from −17% to 1934% (median 98%).

Table 1. Time-averaged wall shear stress for all subjects before and after compression.
SubjectUncompressed (Pa)Compressed (Pa)
MinMaxSpatial meanMinMaxSpatial mean
10.0320.2190.0980.1103.0350.740
20.1910.5480.3580.2060.4020.295
30.2971.1060.6340.5281.6501.035
40.0240.1030.0550.0370.2000.094
50.0100.0520.0290.0732.5960.590
60.0240.1360.0810.0710.2030.136
70.0720.7860.2840.4611.9540.956
80.0330.1580.0770.0800.2760.173
90.0850.3310.1900.1270.3300.204
100.0090.1180.0390.0840.8670.363
Mean0.0780.3560.1850.1781.1510.459
Median0.0330.1890.0900.0970.6350.329

The spatial distributions of TAWSS also varied significantly among subjects (Fig. 6), although in general uncompressed MPV had more uniform TAWSS than the compressed vessels. The deformation patterns of MPV under external compression were found to be highly variable among subjects, which was mainly responsible for the large variation in wall shear stress distribution. Nevertheless, the results from the ten subjects had some features in common. As shown in Fig. 6, higher TAWSS always occurs at locations with smaller diameter owing to local flow acceleration as a result of area reduction. This is consistent with the findings of a previous study [23]. Since the magnitude of wall shear stress depends on vessel geometry (shape and size) and flow rate, it would be useful to compare measured flow rates in the MPV before and after compression. Previous studies [24], [25] showed that external compression could reduce the flow rate in the femoral veins, but no direct measurement was made on flow in the deep veins in the calf. Table 2 shows the comparison of time-averaged volumetric flow rates in the MPV before and after external compression. These data were obtained from the MR flow measurements presented earlier. Our results showed a small reduction (mean 7%; median 7%) in MPV flow rate after compression, with 6 out of 10 subjects experiencing a reduced flow rate and 4 subjects experiencing an increased flow rate. The MPV flow rate in subject 7 was significantly higher than the mean over all subjects (2.60ml/s vs. 0.60ml/s before compression and 2.48ml/s vs. 0.56ml/s after compression).

Table 2. Comparison of time-averaged volumetric flow rate in the MPV before and after compression.
SubjectUncompressed (ml/s)Compressed (ml/s)
10.27560.3814
20.42910.2949
30.70210.3332
40.33420.1868
50.34280.6109
60.20900.2120
72.60112.4787
80.26180.1354
90.42720.3871
100.44790.5956
Mean0.60310.5616
Median0.38500.3573

Although external compression reduced (albeit slightly) the volumetric flow rate in the deep veins on average, it also caused the deep veins to collapse which could negate the influence of flow reduction and result in a increase in blood velocity. The volumes, before and after compression, of the 4cm sections of MPV examined are shown in Table 3. An average volume reduction of 58% was found after compression.

Table 3. Comparison of the reconstructed MPV volume before and after compression.
SubjectUncompressed (mm3)Compressed (mm3)Volume reduction
171425564%
240134215%
338717056%
4118257252%
5203760171%
668444635%
7180575358%
883533160%
965150822%
10222859173%
Mean109245758%

The effect of flow rate and cross-sectional area on wall shear stress in the deep veins was further investigated by examining the axial variation of the cross-sectional mean velocity which is defined as:

(1)
where Vu and Vc are the volumetric flow rates and Au and Ac are the cross-sectional areas, before and after compression respectively.

The cross-sectional mean velocity ratio after and before compression, as well as the corresponding ratio of TAWSS are shown in Fig. 7. Obviously, the axial variation of the TAWSS ratio followed a very similar trend to that of the mean velocity ratio, suggesting that the correlation between circumferentially averaged TAWSS and mean velocity in MPV is approximately linear. However, the quantitative relationship between mean velocity and TAWSS is subject dependent, since cross-sectional geometry of the MPV, which is highly variable among the subjects, plays an important role in determining WSS distribution.

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  • Fig. 7. 

    Axial variation of the ratio of cross-sectional mean velocity after and before compression (dashed lines), compared with the axial variation of the ratio of circumferentially averaged TAWSS after and before compression (continuous lines).

Variations of circumferentially averaged WSS and cross-sectional mean velocity with time also exhibited high level of linear correlation, as demonstrated by an example shown in Fig. 8.

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  • Fig. 8. 

    Variation of cross-sectional mean velocity (solid line) with time before (top) and after compression (bottom), compared with the corresponding WSS variation (dash line).

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4. Discussion 

In this study, grade 1 compression stockings were employed to investigate the effect of static external compression on flow in the deep veins in the calf. MRI images and flow data were acquired from 10 healthy subjects before and after the application of the stockings. Real-time flow measurement in the deep veins was performed using a newly developed MR phase contrast velocity mapping sequence. The architecture of the deep venous system in the calf is highly variable among subjects. In order to have a common ground for comparison, all the flow data were measured at approximately 5cm below the popliteal vein bifurcation, but only the medial peroneal vein (MPV) which is larger than the other deep veins at the same location, was chosen for detailed flow and wall shear stress analysis. Because observations from the acquired real-time phase-contrast images suggested that there was hardly any change in the shape and size of the veins during a respiratory cycle especially when the compression stocking was on (an example is shown in Fig. 9, Fig. 10), a CFD model with rigid wall was employed for the flow analysis. A similar study was performed by Downie et al. [20], but the corresponding venous flow data were estimated from Doppler ultrasound measurement made in the popliteal and great saphenous veins above the level of the stocking, which was the main limitation of the study as stated by the authors. The present study is an improvement over the previous study in that real-time flow measurements in the reconstructed deep vessels within the calf were made and used in the subject-specific analyses of flow and wall shear stress.

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  • Fig. 9. 

    Anatomical MR images at different time points of the diaphragmatic controlled breathing cycle generated by using the real-time phase contrast velocity mapping sequence without compression stocking. MPV: medial peroneal vein.

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  • Fig. 10. 

    Anatomical MR images at different time points of the diaphragmatic controlled breathing cycle generated by using the real-time phase contrast velocity mapping sequence with compression stocking. MPV: medial peroneal vein.

A reduction in femoral vein flow rates as a result of static external compression was observed in previous studies [24], [25]. In this study, compression stocking reduced the flow rate in MPV in 6 out of 10 subjects, with the mean (and median) MPV flow rate being reduced by 7%. The effect of compression on flow rate in other veins in the calf was not evaluated since accuracy of flow measurement could not be guaranteed for veins that are non-perpendicular to the imaging slice and for small veins due to insufficient spatial resolution. Although it is expected that the total flow rate in the calf veins would remain unchanged after compression, the effect of compression on the deep and superficial systems could be different. For cases where compression reduced the flow rate in the deep veins, it is possible that more venous flow was carried by the superficial system. In a previous study where the effect of elastic compression on vessel deformation was evaluated for both the superficial and deep veins, it was found that the mean cross-sectional area reduction was greater in the deep veins (64%) than in the superficial veins (39%) after the application of a flight stocking [18].

The measured waveforms of subjects 5 and 10 suggested the presence of significant reverse flow in the deep vein before compression. It is interesting that subjects 5 and 10 also showed the largest volume reduction among the 10 subjects. The collapse of the deep vein induced by the application of the stocking ceased when a balance between the external and internal pressure was resumed. Increase in the local blood pressure caused by external compression has been found in human calf arteries [26], [27] and femoral veins of dog [24], [25]. The implication of the information is not quite straightforward, but it is possible that under the same external pressure profile, the internal pressure of the deep veins should rise to a similar magnitude after compression, suggesting that the vessels experiencing larger deformation might have lower internal pressure before compression. Although dysfunction of the venous valve at the measurement location could be a reason, considering the age and the medication history of the subjects, and the elimination of the reverse flow after the application of the compression stocking, this would be highly unlikely. Perforator veins can induce disturbances to the flow, but none of them was observed at the velocity measurement location. However, the observed architecture of the deep venous system was highly variable. At a short distance from the location where velocity measurement was taken, overlapping of small veins with the MPV was recorded. It is possible that these small branches, either leaving or joining the MPV, provided an alternative path for the venous flow, which might have led to the observed retrograde flow at the measurement section.

Since the cross-sectional area reduction of the deep veins, in response to the application of the stocking, outweighed by far the reduction in venous flow rate, the overall effect of compression was to increase blood velocity in the deep veins. In a previous study of four subjects, it was found that the application of the compression stocking reduced the level of pulsatility in the velocity waveform and increased the time averaged blood velocity in the popliteal veins [20]. In the present study, results for the MPV of ten subjects showed that mean velocity was increased in nine subjects and the pulsatility of the waveform was reduced in only six subjects (two examples are shown in Fig. 11). The influence of external compression on increasing the deep venous blood velocity was consistent with the previous findings, but its effect on the pulsatility was not as significant as indicated before.

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  • Fig. 11. 

    Measured blood flow waveforms in the medial peroneal veins of 2 subjects before (dashed lines) and after (continuous lines) compression. In both cases, an increase in the mean velocity and reduction in the waveform pulsatility were observed after compression.

It has been demonstrated that DVT mostly arises in calf veins where most of the venous valves are located and is usually initiated from a venous valve pocket. In these susceptible areas, the venous flow is slow and eddies are present. Previous studies have shown that a steady and high level of wall shear stress is important for the health of the vascular system [11], [12], [13], [28]. In this study, the application of the static compression stocking increased the wall shear stress (WSS) in MPV in nine out of ten subjects and by an average of 398% (median 98%). The general trend is consistent with the previous study [20], although the latter overestimated the increase in WSS by assuming there was no change in flow rate before and after compression owing to the lack of direct measurement of flow rate in the deep veins.

While the overall results showed that the application of the stocking led to positive influences on the venous flow, the magnitude of the effect was highly variable among subjects. Disregarding the subject on whom the stocking generated a negative effect, the increase in time-averaged WSS ranged from 7% to 1934%. The reconstructed geometry of the MPV before and after compression showed that the deformation of the MPV as a result of the static external compression was also very subject-dependent. Although the selection of the location of the reconstructed segment was based on the same anatomic landmark, other factors such as the shape and location of the bones, the architecture and mechanical properties of the muscles and other soft tissues, are highly variable and can significantly affect the deformation of the deep veins, which will in turn affect the flow rate in the deep veins. All these factors act together to influence the level of WSS experienced in the deep vessels.

Although the time-averaged WSS distribution is highly variable among subjects, our flow analysis showed that variations of circumferentially averaged WSS followed those of the cross-sectional mean velocity almost linearly. This was because the Reynolds number of the flow was low (<200) and the Womersley parameter was also low (1–2), so that blood flow in the MPV under the conditions examined was quasi-steady, and behaved like fully developed laminar flow although the effect of local geometrical features (such as non-circular cross-section and curvature) was still present.

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5. Conclusion 

In this study, ten subjects were involved in the investigation of the effect of grade 1 compression stocking on deep venous flow. All the subjects were scanned in supine position, and performed diaphragmatic breathing during the MR flow measurement. Our combined MR imaging and computational fluid dynamics analysis showed that the application of the stocking resulted in an average of almost 4-fold increase in wall shear stress in the medial peroneal veins, but the magnitude of the effect was highly variable among subjects. Although our results demonstrated an overall positive influence of the stocking on flow in the medial peroneal veins in the calf, the response of other deep veins to external compression was not examined, which should be performed for a more complete evaluation of the benefits of the stocking.

Our results also indicated that reduction of the deep vein volume was an important consequence of the application of static external compression, which led to a higher blood velocity even though flow rate in the medial peroneal veins reduced slightly. The large individual variability observed in this study prompted us to suggest that the procedure used for selection of a suitable compression stocking for a given individual needs to be refined, and more sizes and ranges of stockings should be made available. In the future, it would be desirable to design personalised compression devices based on individual anatomical features the calf in order to achieve optimal therapeutic effects.

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Conflict of interest statement 

There are no conflicts of interest that could inappropriately influence this research work.

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PII: S1350-4533(11)00149-4

doi:10.1016/j.medengphy.2011.06.012

Medical Engineering & Physics
Volume 34, Issue 1 , Pages 17-27, January 2012

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