A blood-mimicking fluid for particle image velocimetry with silicone vascular
models
Majid Y. Yousif 1
David W. Holdsworth2
Tamie L. Poepping3*
1. Biomedical Engineering Graduate Program, The University of Western Ontario, London ON,
N6A 3K7 CANADA
2. Robarts Research Institute, The University of Western Ontario, 100 Perth Drive, London ON,
N6A 5K8 CANADA
3. Department of Physics and Astronomy, The University of Western Ontario, London ON, N6A
3K7 CANADA
*Corresponding author: T.L. Poepping, Phone: +1-519-661-2111 ext 86431, Fax: +1-519-6612033, poepping@uwo.ca
ABSTRACT:
For accurate particle image velocimetry measurements in hemodynamics studies it is important
to use a fluid with a refractive index (n) matching that of the vascular models (phantoms) and
ideally a dynamic viscosity matching human blood. In this work, a blood-mimicking fluid
(BMF) composed of water, glycerol, and sodium iodide was formulated for a range of refractive
indices to match most common silicone elastomers (n=1.40-1.43) and with corresponding
dynamic viscosity within the average cited range of healthy human blood (4.4±0.5 cP). Both
refractive index and viscosity were attained at room temperature (22.2±0.2°C), which eliminates
the need for a temperature-control system. An optimally matched BMF, suitable for use in a
vascular phantom (n=1.4140±0.0008, Sylgard 184), was demonstrated with composition (by
weight) of 47.38% water, 36.94% glycerol (44:56 glycerol-water ratio), and 15.68% sodium
iodide salt, resulting in a dynamic viscosity of 4.31±0.03 cP.
KEYWORDS: velocimetry; PIV; blood mimicking fluid; silicone elastomer; refractive index;
vascular models; blood flow; Sylgard 184; blood viscosity
Introduction
Particle image velocimetry (PIV) is an engineering technique used to obtain quantitative flow
information. Typically, a flowing fluid is seeded with tiny particles and illuminated with a laser
sheet of light, while images are taken in consecutive pairs or series. The images are analyzed to
determine the distances traveled by particles, from which velocity vectors are calculated. To use
PIV for vascular research, blood vessels can be modeled in transparent phantoms fabricated from
different materials, such as glass (refractive index, n=1.47), acrylic (n=1.485-1.492), and silicone
(n=1.40−1.44) (Hopkins et al. 2000; Miller et al. 2006; Nguyen et al. 2004; Nishino and Choi
2006; Yip et al. 2004). Silicone is of particular interest due to its versatility, robustness, excellent
optical clarity, and ready availability in a two-component liquid form making it easily castable
into the required geometry and dimensions with high accuracy.
An optimal working fluid for PIV studies should exhibit a refractive index matched
accurately to that of the particular phantom material used. As well, for vascular research, a PIV
blood-mimicking fluid (BMF) should possess a dynamic viscosity (µ) similar to human blood at
normal arterial shear rates, so as to obtain realistic blood-flow modeling. Based on a literature
review (Yousif 2009) of recent studies of human blood viscosity, we found an average value
from the published viscosity values to be 4.4±0.5 cP (at 37°C) for normal control subjects and
moderate large-artery shear rates (Bor-Kucukatay et al. 2008; Carrera et al. 2008; Fehr et al.
2008; Galduroz et al. 2007; Rajzer et al. 2007; Vaya et al. 2008).
However, several difficulties arise in finding a PIV BMF with both suitable refractive
index and dynamic viscosity. First, the refractive index of the phantom is not always accurately
known a priori and can vary (between models or batches) for a given material. Second, the
viscosity is typically determined by the same component used to adjust refractive index and thus
can’t be adjusted independently. Therefore studies often compromise accurate matching of the
viscosity or use suitably scaled models and flow waveforms to achieve hemodynamic similarity.
Additionally, it is often desirable to do cross-modality comparison studies (Poepping et al. 2010),
thus requiring accurate matching of viscosity across studies; for example, in-vitro ultrasound
studies typically use a well-established BMF (Ramnarine et al. 1998; Teirlinck et al. 1997), with
dynamic viscosity of 4.1 cP achieved using ~10% (by weight) glycerol in water (to achieve an
appropriate acoustic velocity) plus dextran to increase the viscosity further. Finally, since
refractive index and viscosity are known to be temperature dependent, it is important to attain
both properties at the same working temperature. Unfortunately, a PIV BMF that demonstrates a
refractive index matching with silicone and a dynamic viscosity similar to blood, both at the
same temperature (and preferably room temperature), is not readily described in the literature.
A blood analogue commonly used in the PIV literature is a composition of glycerol and
water (Lim et al. 2001; Nguyen et al. 2004; Raz et al. 2007). However, to attain a refractive
index ≥1.40 requires at least 40% (by volume) of glycerol, which results in a dynamic viscosity
>5.0 cP at 20°C (i.e. >80th percentile of average human blood viscosity), and the higher
concentrations needed for larger refractive index will result in even higher viscosity.
Another possible fluid, which has been modeled empirically by Nguyen et al. (Nguyen et
al. 2004), uses combinations of diethyl phthalate (DEP) and ethanol for a BMF with a wide range
of refractive index and viscosity values at different temperatures. The model shows good results
for matching the refractive index of various silicone elastomers, but the resulting viscosity values
are again lower than human-blood viscosity. For example, the model shows a refractive index of
1.44 for a mixture (by vol.) of 55.6% DEP and 44.4% ethanol, but requires chilling to a
temperature of 16.9°C to achieve a kinematic viscosity of >3 cP (3.327 cSt). To obtain refractive
indices below 1.44 would thus require lowering the DEP ratio, but this will further decrease the
viscosity, as it represents the more viscous component (about 10x that of ethanol) (Nguyen et al.
2004). Furthermore, it requires a temperature-control system for chilling the fluid, with standard
room temperatures resulting in even lower viscosities, and a sealed system to avoid rapid
evaporation (and resultant cooling).
A three-component BMF composed of different relative quantities of water, glycerol and
sodium iodide (NaI) has been introduced in the literature, but the described formulations are for
use with high refractive-index models fabricated from acrylic (n = 1.485-1.492) or glass
(n=1.474) (Fontaine et al. 1996; Grigioni et al. 2001; Kadambi et al. 1990; Morsi et al. 2000;
Sankovic et al. 2004; Sastry et al. 2006; Yagi et al. 2006) and thus not directly suitable for
silicone elastomers (n = 1.40-1.44).
Consequently, the various PIV fluids of previous work mentioned in the literature
demonstrate either a match of refractive index with silicone models or a viscosity close to blood,
but none demonstrates a simultaneous match of the two properties. Here we introduce a method
for formulating a BMF for use at room temperature with a range of refractive indices matching to
most commonly used silicone elastomers, while simultaneously exhibiting acceptable dynamic
viscosity to mimic human blood.
Methods
In this work, Sylgard-184 silicone (Dow Corning Corp., Midland, MI, USA) was used to cast
anthropomorphic phantoms of vascular models (Fig. 1) for studying hemodynamics at the
bifurcation of the common carotid artery. Based on in vivo geometric characterization (Smith et
al. 1996), phantoms were manufactured with idealistic artery dimensions, using a lost-material
casting technique (Poepping et al. 2004; Poepping et al. 2010; Smith et al. 1999). A flow loop,
with temperature-controlled mixing bath and Abbe refractometer (ATAGO NAR-3T, ±0.0001
precision), was used to determine the refractive index of the silicone vascular phantom. An initial
solution was prepared with a refractive index around the lower bound of silicone elastomers at
1.40. This fluid was composed (by weight) of 50.21% water, 39.14% glycerol (5350-1, Caledon,
Georgetown ON, Canada), and 10.65% NaI salt (7920-1, Caledon). The resulting glycerol-towater ratio of 44:56 was held constant during the experiment. A peristaltic pump was used to
circulate the fluid from an in-line mixing container on a magnetic stirrer, through the silicone
phantom placed over grid paper, and then an Abbe refractometer (ensuring consistent
temperature for subsequent refractive-index measurements) before returning. Sodium iodide salt
was accurately weighed and added in regular increments (~0.5% by weight), allowing ~30
minutes for it to completely dissolve between increments, continuing until a formulation was
achieved with a refractive index matching to the specific phantom. For each new concentration,
images were recorded to monitor the distortion of grid lines (Fig. 2), and the refractive index was
precisely measured using the Abbe refractometer. A match in refractive index was visually
detected by way of elimination of discernible distortion of the grid lines. All measurements were
performed at 22.2±0.2°C.
Based on the experimental results for the above refractive-index measurement for the
phantom, five fluid samples were prepared with the same initial relative concentration of
glycerol-to-water (44:56 by weight) and five different concentrations of NaI in order to achieve a
range of refractive index values spanning ~1.40-1.43. For greater flexibility to select the
refractive index and dynamic viscosity independently, and considering that viscosity of glycerol
(1490 cP at 20°C) is a thousand times higher than that of water (1.002 cP at 20°C) (Weast 1969),
a second series with lower viscosity was prepared using a lower glycerol-to-water ratio (40:60 by
weight) and again with incremental NaI content to achieve the same range of refractive indices.
For each sample in the two series, refractive index was precisely measured using the Abbe
refractometer. Kinematic viscosity was measured using a Cannon-Fenske viscometer, and
density using a volumetric flask and digital scale. Dynamic viscosity was calculated from the
product of kinematic viscosity and density. All measurements of refractive index, kinematic
viscosity, and density were repeated five times for each concentration, with mean and standard
deviation calculated for each set. All measurements were performed at a temperature of
22.2±0.2°C. Finally, sensitivity to temperature change was investigated for the refractive index
and dynamic viscosity, such as might occur between or during experiments. Measurements were
made over a range of working temperatures from 20-25°C using a sample fluid composed (by
weight) of 47.38% water, 36.94% glycerol (44:56 glycerol-to-water ratio), and 15.68% NaI salt.
All data was fit using an N-dimensional regression model (D’Errico 2006) as a linear or secondorder polynomial function, as specified for each fit given in the results.
Results
Figure 2 demonstrates the visual monitoring of the distortion of underlying grid lines under
ambient lighting with different fluids in the phantom. Minor distortion, as demonstrated in Fig.
2B for a fluid refractive index of 1.4112±0.0001, was gradually eliminated with additional NaI
until the distortion was no longer visually discernible (Fig. 2C); this remained so for a range of
fluid refractive indices from 1.4132 to 1.4148 (i.e. 0.0016 or 0.1%), before distortion was again
apparent. Thus the refractive index of the Sylgard-184 phantom was indirectly determined to be
1.4140±0.0008, with uncertainty equivalent to approximately ±0.5% by weight of NaI. The
formulation with refractive index of 1.4140±0.0001, corresponding to the centre of the optimal
range, was composed of 47.38% water, 36.94% glycerol, and 15.68% NaI salt. The resulting
average fluid density was 1.244±0.002 g/mL, and the average dynamic viscosity was 4.31±0.03
cP, which lies within 2.0% of the target range (4.4±0.5 cP) to mimic human blood viscosity.
Figure 3 shows the dynamic viscosity as a function of NaI concentration for the two
series of fluid samples, corresponding to the two glycerol-to-water ratios. The average refractive
index value (from 5 measurements) is noted alongside each corresponding data point. For the
upper series, with 44:56 (by weight) glycerol-water, corresponding dynamic viscosity varied
from approximately 4.15 to 4.65 cP for NaI concentrations from 7 to 25% (by weight), thus
providing a BMF with acceptable viscosity values (±0.5 standard deviation of human blood
viscosity) for any material of refractive index between 1.40-1.43.
The dynamic viscosity (µ) was best fit to a second-order polynomial function with NaI
concentration (x1, % by weight) according to: µ= (6.674x10-4)x12+(7.008x10-3)x1+4.0808
(R2=0.9943) for 44:56 glycerol-water by weight and µ=(1.19x10-3)x12+(1.447x10-2)x1+3.597
(R2=0.9912) for 40:60 glycerol-water by weight. To enable greater extension to other
concentrations of NaI and glycerol (x2, % by weight), a 2-D second-order polynomial model is
given by: µ=(8.147x10-4)x12+(2.117x10-3)x22+5.127x10-2 (R2=0.9973).
It was noted that kinematic viscosity (not shown) was not significantly dependent on NaI
concentration and was mainly dependent upon the relative glycerol concentration. The five fluid
samples with varying NaI concentration in 44:56 glycerol-water had a kinematic viscosity of
about 3.51±0.04 cSt, and the seven with 40:60 glycerol-water had a kinematic viscosity of about
2.96±0.02 cSt. However, the increase in density with increasing NaI concentration, led to the
significant increase in dynamic viscosity seen in Fig. 3.
Refractive index was found to vary linearly (not shown) with NaI concentration,
according to n=(1.680x10-3)x1+1.3877 (R2=0.9981) for 44:56 glycerol-water and n=(1.791x103
)x1+1.3804 (R2=0.9985) for the 40:60 glycerol-water fluid. A linear 2-D regression fit was
described by: (1.728x10-3)x1 + (1.326x10-3)x2 + 1.3286 (R2=0.9973).
Figure 4 shows the variation of refractive index and dynamic viscosity with temperature,
along with the corresponding equations of best fit.
Refractive index decreased by 0.0005
(~0.04%) over a 5°C increase in temperature, which is less than the range of uncertainty
observed when visually matching the fluid and phantom refractive index (±0.0008). The change
in viscosity was more significant, decreasing by 0.75 cP (~17%) over a 5°C increase or 0.3 cP
(~7%) for a 2°C increase. Thus for precision better than 10% once the formulation has been
optimized for desired refractive index and dynamic viscosity, a temperature-control system
should not be needed for room temperature fluctuations less than ±1°C.
This BMF has the advantages of being inexpensive (~$20/L), non-volatile, and a low
safety risk (either no risk or only mild irritant, non-flammable, and non-reactive according to the
components’ Material Safety Data Sheets). One limitation to be noted is that the fluid exhibits a
discoloration (yellowing) over time, reportedly caused by the ionization of NaI (releasing of I3-
ion) after exposure to air or light for several hours (Narrow et al. 2000). This problem can be
treated by easily dissolving 0.1% (by weight) of sodium thiosulphate (Na2S2O3; 8460-1,
Caledon) in the BMF to retrieve the original colorless form of the fluid (Narrow et al. 2000).
However, phantoms should be rinsed after use to avoid potential staining from the iodide over
long-term use or storage.
Conclusion
A three-component BMF, composed of water, glycerol, and NaI, was characterized for use with
castable silicone elastomers of cited refractive index values range from 1.40−1.44 (Hopkins et al.
2000; Miller et al. 2006; Nguyen et al. 2004; Nishino and Choi 2006; Yip et al. 2004).
Characterization of the refractive index and viscosity as functions of the glycerol-water ratio and
NaI concentration enables the adjustment of the refractive index to accommodate either different
silicones, batch-to-batch variance for a given material, or even different types of materials, while
maintaining a consistent dynamic viscosity appropriate for modeling blood.
Acknowledgements
The authors would like to acknowledge Hristo Nikolov for phantom fabrication. Financial
support is acknowledged from the Heart and Stroke Foundation of Ontario (grant #T-6427). The
Natural Sciences and Engineering Research Council of Canada (TLP), Canadian Institutes of
Health Research Training Fellowship in Vascular Research (MYY).
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Fig. 1: Idealized model (A) and transparent phantom (B) of a common carotid artery (CCA, 8.0
mm ID) as it branches into the external (ECA, 4.62 mm ID) and internal (ICA, 5.52 mm ID)
carotid arteries. The model on the left shows a severe stenosis (diseased constriction) of the ICA,
whereas the phantom on the right has a normal (disease-free) ICA.
Fig. 2: Visual monitoring of the match in refractive index based on distortion of grid lines
beneath a phantom filled with (A) air, showing high distortion, (B) nearly matched fluid
(n=1.4112±0.0001), still showing minor distortion as indicated by the arrows, and (C) optimally
matched fluid (n=1.4140±0.0001) with no distortion, as indicated by the arrows. Note the
vertical white markers, denoting the flow lumen, and the unintentional stain at the bifurcation
apex, which provides a convenient landmark here.
Fig. 3: Dynamic viscosity for two series of fluids with different glycerol-to-water ratios (44:56
for upper curve and 40:60 for lower), as a function of percentage sodium iodide in solution,
along with curves and equations of best fit. Corresponding average refractive index (n) values
are shown as data labels, enabling inter. Error bars represent standard deviation based on 5
repeated measurements.
Fig. 4: Dynamic viscosity (dashed line) and refractive index (solid line) each as a function of
temperature for a solution with 44:56 (by wt) glycerol-water ratio and 15.68% (by wt) sodium
iodide. Corresponding lines and equations of fit are shown using a second-order polynomial fit
for viscosity and a linear fit for refractive index. Error bars represent standard deviation of 5
measurements.