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Injection of calcium phosphate pastes: prediction of injectionforce and comparison with experiments
Ahmed Fatimi • Jean-Francois Tassin •
Julia Bosco • Remi Deterre • Monique A. V. Axelos •
Pierre Weiss
Received: 21 November 2011 / Accepted: 29 March 2012 / Published online: 24 April 2012
� Springer Science+Business Media, LLC 2012
Abstract Calcium phosphate ceramics suspensions
(ICPCS) are used in bone and dental surgery as injectable
bone substitutes. This ICPCS biomaterial associates
biphasic calcium phosphate (BCP) granules with hydro-
xypropylmethylcellulose (HPMC) polymer. Different
ICPCS were prepared and their rheological properties
were evaluated in parallel disks geometry as a function of
the BCP weight ratio (35, 40, 45 and 50 %). The sus-
pensions show a strongly increased viscosity as compared
to the suspending fluid and the high shear rate part of
the flow curve can be fitted with a power law model
(Ostwald-de Waele model). The fitting parameters depend
on the composition of the suspension. A simple device
has been used to characterize extrusion of the paste using
a disposable syringe fitted with a needle. The injection
pressure of four ICPCS formulations was studied under
various conditions (needle length and radius and volu-
metric flow rate), yielding an important set of data.
A theoretical approach based on the capillary flow of non-
Newtonian fluids was used to predict the necessary
pressure for injection, on the basis of flow curves and
extrusion conditions. The extrusion pressure calculated
from rheological data shows a quantitative agreement
with the experimental one for model fluids (Newtonian
and HPMC solution) but also for the suspension, when
needles with sufficiently large diameters as compared to
the size of particles, are used. Depletion and possibly wall
slip is encountered in the suspensions when narrower
diameters are used, so that the injection pressure is less
than that anticipated. However a constant proportionality
factor exists between theory and injection experiments.
The approach developed in this study can be used to
correlate the rheological parameters to the necessary
pressure for injection and defines the pertinent experi-
mental conditions to obtain a quantitative agreement
between theory and experiments.
A. Fatimi � J. Bosco � P. Weiss (&)
INSERM, U791, Laboratoire d’Ingenierie Osteo-Articulaire
et Dentaire (LIOAD), 1 place Alexis Ricordeau,
BP 84215, 44042 Nantes Cedex 1, France
e-mail: [email protected]
A. Fatimi
e-mail: [email protected]
A. Fatimi � J. Bosco � P. Weiss
LUNAM Universite, Laboratoire d’Ingenierie Osteo-Articulaire
et Dentaire (LIOAD), 1 place Alexis Ricordeau, 44042 Nantes
Cedex 1, France
J.-F. Tassin
CNRS, Universite du Maine, UMR 6120, Laboratoire
Polymeres, Colloıdes, Interfaces (LPCI), avenue Olivier
Messiaen, 72085 Le Mans Cedex 9, France
R. Deterre
LUNAM Universite, IUT de Nantes, CNRS, GEPEA, UMR
6144, OPERP ERT1086, 2 avenue du Professeur Jean Rouxel,
BP 539, 44475 Carquefou Cedex, France
M. A. V. Axelos
INRA, UR1268 Biopolymeres Interactions Assemblages (BIA),
BP 71627, 44316 Nantes Cedex 3, France
Present Address:A. Fatimi
Ecole de Technologie Superieure, Mechanical Engineering
Department, Centre de Recherche du CHUM, Laboratory of
Endovascular Biomaterials, 2099 Alexandre de Seve, Y1604,
Montreal, QC H2L 2W5, Canada
123
J Mater Sci: Mater Med (2012) 23:1593–1603
DOI 10.1007/s10856-012-4640-4
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1 Introduction
Calcium phosphate (CaP) ceramics are the main raw mate-
rials used to elaborate granules for bone substitutes. These
ceramics are being increasingly used in orthopedic [1],
maxillofacial [2] and dental surgery [3]. CaP bone substi-
tutes, which are biocompatible with bioactive properties,
have been studied extensively within the last two decades
[4]. More than 10 years ago, a CaP aqueous suspension was
developed to obtain an injectable biomaterial [5]. This first
generation of injectable calcium phosphate ceramics sus-
pension (ICPCS) associates biphasic calcium phosphate
(BCP) particles (40–80 or 80–200 lm in diameter) with a
cellulose ether derivative polymer. ICPCS formulation is an
essential factor acting on rheological properties which are of
primary importance to control the injectability [6].
The BCP mineral phase is a combination of hydroxyap-
atite (HA) and b-tricalcium phosphate (b-TCP). The suitable
proportions of HA (60 %) and b-TCP (40 %) has provided
BCP ceramics with controlled bioactivity and biocompati-
bility [7, 8]. The viscous phase of ICPCS is a solution of a
biocompatible polymer. Cellulose ether derivatives regroup
among others: hydroxypropylmethylcellulose (HPMC),
methylcellulose (MC), hydroxyethylcellulose (HEC) and
carboxymethylcellulose (CMC). Several studies have been
focused on properties of cellulose ether derivatives such as
water affinity, gelation and rheological properties [9–12].
HPMC is an important cellulosic derivative used in bioma-
terial domain [13, 14]. It is an hydrophilic cellulose deriv-
ative and biocompatible polymer which can be use as a
suspending medium in ICPCS [5]. Apparent viscosity and
viscoelastic properties of ICPCS are based on different
characteristics (molecular weight and concentration of
polymer, sterilization, BCP particles size and BCP ratio).
Injectability of ICPCS is a key feature for the practical
development of this generation of bone substitutes. In
dental application, the size and the lack of accessibility of
the various endodontic sites required the development of
new injection systems [6]. Injectability is often addressed
as one of the most important properties of materials to be
used in minimally invasive surgery. Several works have
been reported on the injectability of CaP based biomate-
rials [15–26]. The definition of injectability is questioned
[15] and besides the injection force the ability of the paste
to remain homogeneous during injection must also be
considered. Indeed, most studies were carried out using
setting CaP cements and influence of additives to improve
the injectability has been the subject of several investiga-
tions [17–19, 23–26]. Khairoun et al. [16, 21] measured the
injectability of cement pastes which harden as a function of
time by measuring the percentage of paste that could be
extruded from a syringe fitted with a needle. Bohner and
Baroud [15] have already proposed a theoretical approach
of extrusion of CaP cement and have studied the effect of
geometry and solid content of the paste on injectability.
Their work is focused on the existence of phase separation
or filter pressing. More recently, Habib et al. [24] studied
the mechanisms underlying the limited injectability of
hydraulic CaP paste using rheological and injectability
measurements and came up with practical conditions of
both the injection system and the formulation of the cement
to improve the injectability. In all of these studies, the
phenomenon of filter pressing competes with the flow of
the suspension along the injection device. The addition of
hydrosoluble polymers at low concentrations can avoid this
phenomenon. This is precisely the case of our study where
neither sedimentation nor filter pressing were observed
during the experiments. We thus were motivated in pro-
posing an injection model which takes into account the
rheological behavior of the CaP biomaterial and the geo-
metrical parameters of the injection system and comparing
the theoretical prediction with experiments.
In the present study, a modeling of the injection of
viscoelastic fluids is developed and applied to non-setting
CaP biomaterials. The modeling is based on the flow
properties of the sample as well as the detailed injection
conditions (syringe and needle radii, needle length and
injection speed). This model will be first tested for model
fluids (a Newtonian oil and a shear thinning polymer
solution). The case of CaP biomaterials will be further
studied by comparing theoretical values of the extrusion
pressure with experimental data obtained under about 68
different conditions (extrusion and CaP concentration). The
main advantage of this approach is that a rheological
characterization of the considered fluids allows a prediction
of their injectability under various conditions. The com-
parison between experimental and predicted values is
based on the use of a power law behavior of the flowing
materials under the injection conditions. The parameters of
the model have been characterized using the rheological
data on these materials obtained in the first step. In this
paper, the terms ‘‘injection’’ and ‘‘extrusion’’ are used
indifferently.
2 Materials and methods
2.1 Materials
2.1.1 Vaseline oil
Vaseline oil provided by Prolabo� (France) was used as a
Newtonian fluid. Its viscosity was measured as 30 Pa.s at
25 �C.
1594 J Mater Sci: Mater Med (2012) 23:1593–1603
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2.1.2 HPMC solutions
The cellulose ether derivative used in this study was
HPMC MethocelTM
E4M, which was supplied by Color-
con� (Kent, UK). The characteristics of the samples are
given in Table 1. Aqueous solution of HPMC polymer was
prepared at 3 % w/w. Polymer powder was dispersed in
deionized water at room temperature during 24 h. Subse-
quently, polymer solutions were refrigerated during 3 days
at 4 �C to ensure a complete solubilization.
2.1.3 BCP particles
The CaP ceramics used in this study was BCP (60 % HA
and 40 % b-TCP) prepared in our laboratory (LIOAD,
INSERM U791) by precipitation of calcium-deficient
apatite (CDA) and sintering [27]. After sintering at
1,050 �C during 7 h, the BCP granules were obtained and
sieved to one range (40–80 lm in diameter) [28]. Image
observation and granulometry analysis of BCP particles
were realized using scanning electron microscopy (SEM)
at 15 kV (LEO 1450 VP, Oberkochen-Zeiss, Germany).
2.1.4 Injectable CaP paste
Different formulations of ICPCS were prepared by mixing
BCP particles (40–80 lm) with HPMC solution in water
(3 % w/w) at different ratios (35, 40, 45 and 50 % w/w).
Samples were sterilized by autoclave Alphaklave� 23
(HMCE, Taillis, France) according to the standard phar-
maceutical procedure (121 �C during 20 min). The rheo-
logical and injectability studies of different CaP pastes
were carried out 3 days after steam sterilization.
2.2 Methods
2.2.1 Rheological measurements
Rheological measurements of HPMC polymer solution
were carried out at 25 �C using the ‘‘Rheo Stress 300’’
rheometer (ThermoHaake�, Karlsruhe, Germany) with a
titanium cone-plate geometry (60 mm diameter, 1� cone
angle). Steady shear tests were carried out to determine
flow curve of HPMC solution (viscosity versus shear rate).
The operating shear rate ranged from 10-1 to 103 s-1 (100
points during 300 s). The flow curve of HPMC polymer
could be well described using the simplified Cross
equation [29].
g ¼ g0
1þ ðk _cÞn ð1Þ
where g is the viscosity at a given shear rate ( _c); g0 is the
limiting Newtonian viscosity; k is the relaxation time and n
is the exponent of the power law.
Rheological measurements of different CaP pastes (HPMC
polymer solution in water with BCP particles) were carried
out at 25 �C using the ‘‘Haake Mars’’ rheometer (Thermo-
Haake�, Karlsruhe, Germany) with a titanium parallel-plate
geometry (20 mm diameter, 1 mm gap). For suspensions, a
parallel-plate geometry with a sufficient gap was used to
ensure continuous mechanics conditions (i.e. a gap above ten
times the largest particles sizes). Furthermore, wall slip was
avoided by using plates equipped with emery paper. Since
thixotropic effects are often observed in suspensions, all
samples were pre-sheared at fixed shear rates (100 s-1) during
100 s before determination of the flow curves to allow for a
more rapidly obtained steady state. Flow curves of CaP pastes
(shear stress and viscosity versus shear rate) were obtained
over a limited number of shear rates by applying a given shear
rate during 120 s. The operating shear rate ranged from 10-1
to 102 s-1. Since parallel plates geometry does not yield a
constant shear rate throughout the gap, raw data (torque versus
angular velocity) have to be corrected to obtain flow curves.
The shear stress s is expressed as
s ¼ M
2pR33þ d ln M
d ln _c
� �ð2Þ
where M is the torque and R is the radius of the plate. The
shear rate _c is given by
_c ¼ R
hx ð3Þ
h being the value of the gap and x the angular velocity
Each rheological experiment was performed in tripli-
cates. Results are expressed as mean ± standard error of
the mean (SEM) of triplicate determinations.
2.2.2 Extrusion studies of the fluids (Vaseline oil, HPMC
solutions and CaP pastes)
Injectability was evaluated by extruding a certain amount
(*1 ml) of fluid or paste through a disposable BD Luer-
LokTM
Tip syringe (Fig. 1) (5 ml in volume and 11.5 mm
Table 1 Composition of HPMC polymer used in the present work
Polymer Methoxyl degree of substitution Hydroxypropyl molar substitution Methoxyl (%) Hydroxypropyl (%)
MethocelTM
E4M 1.9 0.23 29.0 9.7
Information supplied by Colorcon�
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inner diameter) (Becton–Dickinson, New Jersey, USA).
The measurements were realized using different needles as
far as their length or their inner diameter is concerned
(Becton–Dickinson, Madrid, Spain). To minimize the ends
effects, L/Rn ratios of the needle were chosen to be as high
as possible (L = 20, 40, 75 and 90 mm, Rn = 0.42, 0.68
and 0.77 mm). The necessary force to extrude the fluids or
CaP pastes was measured using a TA-HDplus Texture
Analyser (Stable Micro SystemsTM
, Godalming, UK) using
the compression test mode. Different displacement speeds
were applied (0.05, 0.1, 0.2 and 0.5 mm.s-1). Each exper-
iment was performed in triplicates. Results are expressed as
mean ± SEM of triplicate determinations. A Newtonian
fluid and a viscoelastic fluid were tested to check to validity
of the modeling and finally four formulations were studied
(HPMC at 3 % with different BCP ratios).
The necessary pressure DP to flow any fluid is given by
DPExtrusion ¼F
Ssð4Þ
where F is the measured force and Ss is the surface of the
syringe.
2.3 Theoretical approach of injectability
The injection of these materials implies the flow of a fluid
in a capillary. For any fluid, the shear stress at the wall sw,
assuming a non-wall slip condition is [30]
sw ¼Rn
2
DP
Lð5Þ
where DP is the pressure loss in the needle and L the length
of the needle.
The shear rate at the wall is easily calculated for New-
tonian fluids as [30]
_capp ¼4Q
pR3n
¼ 4VR2
s
R3n
ð6Þ
where Q is the volumetric flow rate, V, the speed of the
piston, Rs and Rn the inner radii of the syringe and of the
needle respectively. The Newtonian viscosity is readily
obtained by the ratio between Eqs. (5) and (6)
Although the flow curves in capillary flow can be
determined formally without any assumption on the rheo-
logical behavior of the fluid, calculations and use of inverse
methods, which will be required here, appears more easy
when the fluids obey a so called power law or Ostwald-de
Waele model [31] given by
s ¼ K _cn ð7Þ
where K is the consistency factor and the exponent n is the
flow index.
Indeed, in non-Newtonian fluids the velocity profile
(which is parabolic for Newtonian fluids) is unknown, but
can be analytically calculated when the fluid follows a
power law behavior. The Rabinowitsch procedure [32] was
used to take into account the non-Newtonian behavior of
the fluid. The volumetric flow rate Q of an Ostwald-de
Waele fluid is given by
Q
pR3n
¼ 1
s3w
Zsw
0
s2 sK
� �1n
ds ð8Þ
where Rn is the inner radius of the capillary (needle in this
study), s is the shear stress and sw is the shear stress at the
wall, which can be calculated by Eq. (5).
For non-Newtonian fluids, Eq. (6) does not yield the
true shear rate at the wall but the so called apparent shear
rate at the wall. The true shear rate at the wall involves
the exponent n of the power law and the apparent shear
rate as
_cw ¼ _capp
3nþ 1
4n
� �ð9Þ
Applying Eq. (7) at the wall, combining with Eqs. (5)
and (9) leads to the theoretical necessary pressure to inject
L 2Rn
F
2Rs
Fig. 1 Schematic view of the syringe using for injectability mea-
surements. F force, L length of the needle, Rs inner radius of the
syringe and Rn inner radius of the needle
1596 J Mater Sci: Mater Med (2012) 23:1593–1603
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the fluid or the CaP paste through the needle with given
experimental conditions as
DPRheology ¼ 2KLR2n
s
R3nþ1n
4nVn 3nþ 1
4n
� �n
ð10Þ
The measured extrusion pressure can be considered as
very close to the pressure drop inside the needle provide:
– that the pressure loss in the syringe is negligible in
comparison with the pressure loss in the needle,
– that the friction of the piston along the syringe is
negligible and
– that entrance and exit conditions of the capillary
(needle) lead to negligible pressure losses with respect
to those along the capillary.
The required pressure necessary to overcome the friction
of the piston along the syringe was checked and appeared
effectively negligible with respect to the paste’s extrusion
pressure. Of course, this procedure could not be applied to
low viscosity fluids for which the friction of the rubber part
along the piston contributes to a large part of the applied
pressure. The experimental conditions (diameter of the res-
ervoir ten times larger than that of the capillary and large
L/D values) where chosen in order to minimize the other effects.
Therefore, in the following the extrusion pressure
DPExtrusion is essentially equal to the pressure loss along the
needle and is predicted by Eq. (10).
3 Results
3.1 BCP particles
The HA and b-TCP percentage in BCP were 60 and 40 %
respectively. The Ca/P ratio of the BCP was 1.6 [27]. The
SEM observation and the size volume distribution of
the BCP particles are represented in Fig. 2. The SEM
image indicates that the BCP particles are not spherical.
The shape and size vary from one particle to another. The
particles size distribution indicates that distribution clearly
displays a maximum for this range of granulometry
(40–80 lm) and the mean diameter was 78 lm.
3.2 Rheological behavior of HPMC polymer solution
The flow curve of the 3 % water solution of HPMC is
shown in Fig. 3. The flow curve shows a Newtonian zone
at low shear rates followed by shear thinning at high shear
rates. The critical shear rate corresponding to the transition
from Newtonian to shear thinning behavior is 35 s-1. The
limiting Newtonian viscosity (g0) and the relaxation
time (k) were determined using Eq. (1). The values are
5.6 ± 1 Pa.s and 28.3 ± 3.5 ms, respectively. The power
law exponent (n) informs on the deviation from the New-
tonian behavior, for which n = 1. For the HPMC solution
(at 3 %) the exponent of the power law is 0.81 ± 0.08.
The rheological behavior of a 3 % solution of HPMC in
water is typical of an entangled polymer solution.
0
2
4
6
8
10
100010010
Particule size (µm)
Vo
lum
e (%
)
Fig. 2 SEM observation and particles size volume distribution of
BCP particles (40–80 lm)
0.1
1
10
100
0.01 0.1 1 10 100 1000
Shear rate (s-1)
Vis
cosi
ty (P
a.s)
Experimental dataCross model
Fig. 3 Flow curve of HPMC solution (3 %) at 25 �C. Viscosity as a
function of shear rate
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3.3 Rheological behavior of injectable CaP biomaterial
Concentrated suspensions are known to eventually display
a thixotropic behavior, which leads to long shearing times
before reaching a steady state under flow. Figure 4 illus-
trates the existence of thixotropy in a 50 % w/w suspension
of BCP in a 3 % HPMC solution in water (which is the
most critical case). The data were collected after 120 s
shearing time at each shear rate. The curve obtained on
increasing the shear rate lies above the one collected on
decreasing it. This is linked to a long (higher than the
waiting time) destructuration time of the suspension at the
low or moderate shear rates. This is why we decided to first
pre-shear the suspension at high shear rate (100 s-1) before
collecting the flow curve using increasing shear rates and
shearing time of 120 s at each shear rate. This method was
shown to lead to reproducible results.
The flow behavior of different CaP pastes was charac-
terized under these conditions and is shown in Fig. 5. As
compared to the suspending fluid, all the suspensions show
an increase in viscosity. For moderate concentrations of
fillers, a Newtonian plateau is observed at low shear rates.
The length of the plateau decreases by increasing the parti-
cles content. For 50 % w/w, measurements were not carried
out at sufficiently low shear rates to decide whether the
suspension shows a Newtonian behavior under these con-
ditions or is a yield stress fluid, as it can be expected at high
solid content.
Obviously, a power law can not accurately describe the
behavior of the materials over a large shear rates range.
The apparent wall shear rates under the different con-
ditions of extrusion were calculated using Eq. (9). Dis-
placement speeds (0.05, 0.1, 0.2, 0.5 mm.s-1) used in
extrusion experiments correspond to apparent wall shear
rates of 37, 75, 151 and 379 s-1, respectively. In this very
limited shear rate range, the Oswald–de Waele model (Eq.
(7)) was applied to the four last points corresponding to our
shear rate range (inset of Fig. 5a).
The change of the consistency factor, K, obtained from
the Ostwald-de Waele model reflects roughly the change of
viscosity. The flow index, n, was below 1 for all bioma-
terials pointing that the biomaterials were shear thinning at
high shear rates. The consistency of CaP paste, K,
increased with BCP ratio, while the flow index, n,
decreased strongly with BCP ratio (Fig. 6). Such a
behavior is commonly observed in suspensions [31].
Increasing BCP ratio (solid phase) leads to an increase
in the number of particles in the system. The increase of the
consistency can be attributed to an increase in particle–
particle interactions leading to an increased resistance to
10
100
1000
10000
0.01 0.1 1 10 100 1000
Shear rate (s-1)
Sh
ear
stre
ss (
Pa)
Fig. 4 Thixotropic behavior of the ICPCS: flow curve at 25 �C.
HPMC solution (3 %) was mixed with BCP particles (40–80 lm) at
fixed BCP ratio (50 %). The operating shear rate was
10-1?102 ? 10-1s-1 (20 points during 2,400 s), starting from rest
0.1
1
10
100
1000
10000
Shear rate (s-1)
Sh
ear
stre
ss (
Pa)
35%
40%
45%
50%
(a)
100
1000
10000
1 10 100 1000Shear rate (s -1)
Sh
ear
stre
ss (
Pa)
10
100
1000
10000
0.01 0.1 1 10 100 1000
0.01 0.1 1 10 100 1000
Shear rate (s-1)
Vis
cosi
ty (
Pa.
s)
35%
40%
45%
50%
(b)
Fig. 5 Flow curves of different ICPCS at 25 �C at different BCP
ratios (35, 40, 45 and 50 %). HPMC solution (3 %) was mixed with
BCP particles (40–80 lm). a Shear stress as a function of shear rate.
The inset shows the modeling of the flow curves. The Oswald-
de-Waeel model was applied to the four last points. b Viscosity as a
function of shear rate
1598 J Mater Sci: Mater Med (2012) 23:1593–1603
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flow [33]. Therefore, the determination of the suitable BCP
ratio to induce acceptable extrusion forces appears to be a
very important step in the formulation [15].
The chemical study of the ICPCS has been already carried
out and the results demonstrate that, under our experimental
conditions, there is no chemical interaction between the CaP
particles and HPMC polymer [34]. From the physical point
of view the polymer-particle interactions cannot be totally
ruled out. The addition of a polymer into the CaP biomaterial
can sometimes lead to a decrease of the viscosity of the paste
due to lubricating effects. This effect is observed in the
so-called ‘‘granular regime’’ where the flow behavior is
mostly controlled by direct interparticular contacts. In this
case, the paste cannot be sheared without volume expansion,
and hence intergrain friction occurs. The presence of a
polymer between the grains can in some conditions reduce
the friction coefficient between the grains, and hence
improve the paste injectability [15]. The rheological data
show that this regime is not observed here. In contrast, the
increase in viscosity is explained by an increase of the vol-
ume fraction of the solid phase, which might include poly-
mer particle interaction, namely adsorbed polymer chains
bridging several particles. However, in view of the scope of
this study, a detailed investigation of polymer-particle
interaction has not been carried out.
3.4 Injection of model materials
The vaseline oil was injected at 0.05, 0.075 and 0.1 mm.s-1
using 0.84 mm inner diameter needles, corresponding to
shear rates of 84, 127 and 169 s-1, respectively. The extru-
sion pressure is reproducible and increases linearly with the
flow rate. The predicted extrusion pressures at the corre-
sponding shear rates (using the measured viscosity) is com-
pared with the experimental ones (Table 2). A satisfactory
agreement (differences lower than 10 %) can be noted.
The 6 % HPMC solution was studied at 0.05, 0.1 and
0.2 mm.s-1 with the same needles. The concentration was
chosen in order to have extrusion pressures comparable
with CaP pastes. In this case of a non-Newtonian fluid, the
extrusion pressure increases with the extrusion speed
(volumetric flow rate) with a power law: DP � Q0:2. The
exponent is close to that obtained with the cone-plate
geometry in the same range of shear rates. The predicted
values of the extrusion pressure, assuming a power law
behavior in this range of shear rate are in good agreement
with experimental data (Table 2).
The reasonable agreement between predicted values of
the extrusion pressure from cone and plate data and
experimental ones obtained using capillary flow validates
the modeling and allows us to study the injectability of the
biomaterials.
3.5 Injection of CaP biomaterial
Extrusion curves whatever the diameter (Fig. 7) were char-
acterized by a very rapid increase of the force followed by a
plateau [15]. Filter pressing [15] and phase separation [35,
36] were not observed during measurements and the absence
of a final rapid increase of the force after the plateau confirms
these results. The injection force depends on needle length
(Fig. 7a), extrusion speed (Fig. 7b) and BCP ratio (Fig. 7c).
The injection force appears proportional to the needle length,
in such a way that entrance effects [37] can be neglected, or in
0
100
200
300
400
500
600
700
800
30 35 40 45 50 55
BCP ratio (%)
Co
nsi
sten
cy fa
cto
r (P
a.s
n) (
)
0
0.2
0.4
0.6
0.8
1
Flo
w in
dex
()
Fig. 6 Effect of BCP ratio on the consistency factor K (filled circle)
and the flow index n (filled square)
Table 2 Predicted pressure using the measured viscosity of Newtonian and non-Newtonian fluids
Fluid Type Injection
speed (mm.s-1)
Shear
rate (s-1)
DPExtrusion
(Pa)
DPRheology
(Pa)
Vaseline oil Newtonian 0.05 84.93 1.07 106 ± 4.10 104 1.14 106 ± 9.53 103
0.075 127.40 1.47 106 ± 1.07 104 1.62 106 ± 1.04 104
0.1 169.86 1.98 106 ± 1.66 104 2.09 106 ± 1.54 104
6% HPMC Non-Newtonian 0.05 145.58 3.94 105 ± 9.55 103 3.65 105 ± 1.12 104
0.1 291.17 4.58 105 ± 2.46 103 4.37 105 ± 9.13 103
0.2 582.35 5.04 105 ± 1.09 104 5.22 105 ± 1.51 104
J Mater Sci: Mater Med (2012) 23:1593–1603 1599
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other words, the apparent pressure gradient inside the cap-
illary is independent on the length of the needle.
The injection pressure increases by increasing the BCP
ratio of the suspension, as expected from the increase in
viscosity as seen in Fig. 5b. The influence of the extrusion
speed shows that the injection force increases by increasing
the shear stress on the sample, as it could have been
expected.
The necessary pressure (DPExtrusion) to inject the CaP
paste was determined from extrusion force using Eq. (4).
The theoretical injection pressure (DPRheology) can be
calculated (Eq. (10)) from the rheological parameters of the
suspensions and taking into account all experimental
parameters such as syringe radius (Rs), needle radius (Rn),
needle length (L) and injection speed (V). We recall that the
complex flow behavior of the suspension has been
approximated by a power law, the parameters of which
(consistency factor K and flow index n) have been adjusted,
in the considered shear rate range, from the flow data col-
lected independently under well defined shear conditions.
Figure 8 shows the comparison between the theoretical
pressure (DPRheology) and the experimental pressure
(DPExtrusion) obtained from extrusion experiments. It can be
seen from Fig. 8 that two sets of data can be distinguished.
For the needles with the largest diameters (1.36 and
1.54 mm) experimental and calculated values of the
extrusion pressure are in fair agreement. For the narrowest
needle (0.84 mm diameter), both data follow the same
trend, but the predicted extrusion pressure is systematically
higher than the experimental one, with roughly a factor 2.
In the following section, a discussion of possible expla-
nations of these results is presented.
0
10
20
30
40
50
60
70
Distance (mm)
Fo
rce
(N)
20mm
40mm
75mm
90mm
Extrusion speed = 0.1mm.s-1
BCP ratio = 50%
(a)
0
20
40
60
80
100
Distance (mm)
Fo
rce
(N)
0.5mm.s-1
0.2mm.s-1
0.1mm.s-1
0.05mm.s-1
Needle length = 90mmBCP ratio = 45%
(b)
0
10
20
30
40
50
60
0 2 4 6 8 10 12
0 2 4 6 8 10 12
0 2 4 6 8 10 12
Distance (mm)
Fo
rce
(N)
35%
40%
45%
50%
Extrusion speed = 0.2mm.s-1
Needle length = 40mm
(c)
Fig. 7 Typical extrusion curves obtained for ICPCS (40–80 lm
particles and HPMC at 3 %): a with different needle lengths at fixed
BCP ratio (50 %) and extrusion speed (0.1 mm.s-1); b with different
extrusion speeds at fixed needle length (L = 90 mm) and BCP ratio
(45 %); c with different BCP ratios at fixed extrusion speed
(0.2 mm.s-1) and needle length (40 mm). The displacement was
10 mm and the diameter of needle was 0.84 mm
0,01
0,1
1
10
0,01 0,1 1 10
PE
xtru
sio
n(M
Pa)
PRheology (MPa)
Needle 1: L=40mm ; Rn=0.42mmNeedle 2: L=75mm ; Rn=0.42mmNeedle 3: L=90mm ; Rn=0.42mmNeedle 4: L=40mm ; Rn=0.68mmNeedle 5: L=40mm ; Rn=0.77mm
Fig. 8 Comparison of experimental (DPExtrusion) and theoretical
(DPRheology) pressure obtained with needles of different diameters.
The experimental pressure was measured by extrusion of ICPCS
(40–80 lm particles and HPMC at 3 %) under different conditions:
BCP ratios (35, 40, 45 and 50 %), needle radii (0.42, 0.68 and
0.77 mm), needle lengths (40, 75 and 90 mm) and extrusion speed
(0.05, 0.1, 0.2, 0.5 mm.s-1)
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4 Discussion
As mentioned earlier, the rheological behavior of the fluid
can be approximated by a power law only on a limited
shear rate range. However, the derivations used to calculate
the theoretical injection pressure imply that the power law
behavior is followed within the capillary, i.e. over a much
larger range, since the shear rate is close to zero at the
centre of the capillary. Obviously, such an approximation
leads to an overestimation of the extrusion pressure.
However, since the power law has been adjusted at large
shear rates, under the extrusion conditions and since most
of the energy is dissipated close to the wall, the influence of
a poor approximation of the rheological behavior close to
the centre of the capillary does not lead to strong errors in
the prediction of the extrusion pressure. Moreover, this
explanation cannot account for the good quantitative
agreement with large needles and the systematic overesti-
mation for the narrowest one.
The calculations used in the rheological modeling
assume the so-called no-slip condition, i.e. that the velocity
of the fluid at the wall is equal to zero. It is known that in
concentrated suspensions a depletion of the particles often
occurs close to the wall. Of course, it might also occur in
the rheometer used to determine the flow behavior. How-
ever, as mentioned earlier, the plates were covered by
rough surfaces to prevent wall slip.
The existence of wall slip was checked using the
Mooney approach [38], which can be easily applied here
since measurements with needles having the same length
but different diameters were available. It is assumed that
the volumetric flow rate is increased by the slipping
(slipping velocity Vs, which depends only on the wall shear
stress) so that Eq. (8) is rewritten as
4Q
pR3n
¼ 4Vs
Rþ 4
s3w
Zsw
0
s2 sK
� �1n
ds ð11Þ
By plotting the apparent volumetric flow rate versus 1/R
for a given wall shear stress; one should obtain a linear
relationship from which the slip velocity and the flow rate
corrected for wall slip are obtained. Such a plot is
illustrated in Fig. 9, for several values of the applied
stress and a BCP concentration of 40 %. The same type of
data is obtained at other concentrations. The data are not
compatible with Mooney’s analysis since the intercept is
negative, resulting in a negative wall shear rate corrected
for slip which has no physical meaning. Such behavior has
already been reported [39].
In our case, due to the presence of particles that are
relatively large in the suspension, we do not attribute the
change in behavior with the radius of the needle directly to
slip, but to the fact that in the narrowest needle
(R = 420 lm) the radius is only equal to about five times
the size of the particles. Under these conditions, migration
of the particles away from the walls of the needle (deple-
tion) concentrates the particles in almost 3/5 of the capil-
lary diameter. The energy is thus essentially dissipated in
the high shear rate region, where the concentration of the
particles is less. This leads to a reduced viscosity as
compared to the theoretical prediction. For large needles,
this phenomenon might still be valid but the particles
concentrate in 8/10 i.e. 4/5 of the capillary diameter. In this
case, the depletion effect is proportionally less, so that the
energy dissipated in the depleted layer become smaller than
the one lost in the overall flow. Under these conditions, a
fair agreement between theory (which assumes no slip and
the same composition of the material along the radius) and
experiment is observed.
This leads us to conclude that a good agreement
between the measurement of the extrusion stress and the
prediction based on the rheological behavior can be
obtained provided a sufficiently large diameter needle is
chosen, so that particle depletion effects can be neglected.
Of course, in absence of particles, no wall effect is
observed and predicted data are in good agreement with
experimental ones.
The calculation developed in this paper can thus be
used, from a practical point of view, to adapt the dimen-
sions of the injection system to the viscosity of the mate-
rials to target a reasonable injection force.
5 Conclusion
The experimental and theoretical studies show that the flow
properties of ICPCS can be characterized by two ways:
0
200
400
600
800
1000
0 500 1000 1500 2000 2500
Ap
par
ent
shea
r ra
te (
s-1 )
1/Rn (m-1)
= 1178Pa
= 1418Pa
= 1970Pa
τττ
Fig. 9 Mooney plots (apparent shear rate as a function of 1/Rn at
fixed shear stress) for a BCP content of 40 %
J Mater Sci: Mater Med (2012) 23:1593–1603 1601
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conventional rotational rheometry or extrusion. Rheological
characterization of ICPCS showed that BCP ratio affects the
flow properties. Four formulations were chosen to study the
injection of the ICPCS. Experimentally, effects of the needle
length, the extrusion speed and the BCP ratio have been
observed. The injection force increases with increasing
extrusion speed and/or BCP ratio and/or length of needle.
The results obtained in this study suggest that, for a
Newtonian fluid and a non Newtonian polymer solution,
there is a quantitative agreement between the rheology and
injection force under the experimental conditions investi-
gated here. This validates the method for rather simple
fluids.
In the case of a non Newtonian suspension (CaP paste) a
fair agreement between the prediction of the injection force
and the rheologically predicted one is observed when suf-
ficiently large needle diameters are used, with respect to
the particle’s diameter. When the diameter becomes too
small, the injection force is less than expected from the
modeling. However, from a practical point of view, a
proportionality factor between experiment and predictions
applies. The disagreement of the method, when too narrow
needles are used has been ascribed to the existence of
depletion of particles close to the walls, in such a way that
the suspension is less sheared in the capillary than expected
and leads to lower extrusion pressures. One might note that
this can be quite useful in practice, since it decreases the
injection force.
The approach developed in this study allows us to cor-
relate the rheological parameters to the necessary pressure
for injection and/or eventually to predict the necessary
pressure for injection from rheological data.
Various studies have already shown possible strategies
to improve the injectability of CaP biomaterials. Among
them, several factors like viscosity of the polymer solution,
average particle size and shape of particles affect the in-
jectability. In our case, the same strategy to improve the
injectability of ICPCS could be applied to obtain an opti-
mum BCP ratio. This study also suggests that favoring a
slight particle depletion from the wall or eventually wall
slip using surface treatment of the inner part of the needles
can eventually also improve the practical injection condi-
tions. With the new paradigm, new avenues to understand
the microscopic correlation between rheology and injec-
tability, such as different particles size and shape, large
range of extrusion speeds, large rang of shear rates, will be
explored in future research activities.
Acknowledgments This study was supported by the regional pro-
gram BIOREGOS (Region Pays de la Loire, France). Authors extend
their sincere thanks to Colorcon� for the supply of the polymer
MethocelTM
E4M. The help of Paul Pilet for the image observations
and Jean-Michel Bouler for the BCP preparations is acknowledged
with gratitude.
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