878
Effect of elec~ostatic forces on the dynamic rheological properties of injectable collagen biomaterials Joel Rosenblatt Department of Chemical and Biochemical Baltimore, MD 21228, USA
Engineering,
University
of Maryland
-
Baltimore
County,
Brian Devereux De~rtment
of Chemical
Engineering,
University
of California
-
Berkeiey,
Berkeley,
CA 94720, USA
and Donald G. W&lace Celtrix Laboratories
Inc., 2500 Faber Place, Palo A/to, CA 94303, USA
Injectable collagen is a concentrated dispersion of phase-separated collagen fibres in aqueous solution used to correct dermal contour defects through intradermal injection. The effect of electrostatic forces on the rheology of injectable collagen was studied by observation of the birefringence of collagen fibres through a polarizing microscope as well as by oscillatory rheological measurements on dispersions of varying ionic strengths (0.06-0.30). The birefringence of fibres progressively increased as ionic strength was reduced from 0.30 to 0.06. The linear viscoelastic measurements displayed a logarithmic relationship between storage (and loss) moduli and frequency over oscillation frequencies of 0.1-100 rad/s. The associated relaxation time spectra, interpreted using the theory of Kamphuis et al. for concentrated dispersions, show that collagen fibres become more flexible as ionic strength increases. This result was analysed at the molecular level from the perspective that collagen fibres are a liquidcrystalline phase of rigid rod collagen molecules which have phase-separated from solution. Electrostatic forces affect the volume fraction of water present in the collagen fibres which in turn alters the rigidity of the fibres. Flexible collagen fibre dispersions displayed emulsion-like flow properties whereas more rigid collagen fibre dispersions displayed suspension-like flow properties. Changes in fibre rigidity significantly alter the injectability of collagen dispersions which is critical in clinical performance. Keywords: Received
Collagen, IO January
injection,
flow properties
1992; revised and accepted
Highly purified, injectable collagen has been successfully used as a biocompatible implant in the correction of dermal contour defects for many yearslV2. Injectable collagen is manufactured by solubilizing Type I collagen from cow hide and [following purification] reconstituting the soluble collagen into fibrils by precipitation at neutral pH. The purification of collagen has been described in detail elsewhere3. The thermodynamics and kinetics of precipitation of aqueous solutions of Type I collagen have been studied extensively4-*. Studies of the rheological properties of concentrated dispersions of reconstituted collagen fibres have not been extensive. Limited previous work includes creep compliance measurements on concentrated collagen dispersions7 and extrusion force measurements on cross-linked collagen suspensions’. Type I collagen molecules (300 nm long X 1.5 nm Correspondence Biomaterials
to Dr J. Rosenbfatt.
1992, Vol. 13 No. 12
20 April 1992
diameter rigid rod, 300 kD proteing] self assemble into phase-separated fibres at neutral pH and 288-310 K. In vitro collagen fibril assembly displays two different growth phases when studied by turbidity measu~ments”: a lag phase in which an as yet undefined nucleation or early assembly event occurs’; followed by a growth phase where striated fibres appear. The molecular architecture of these fibres has been studied by electron microscopy’l and X-ray diffractionI’. They possess a regular stagger of approximately l/4 of a rod length between each molecule and its axially aligned neighbour. Wallace and Thompson3 have quantitatively modelled the kinetics of fibre growth using a nucleation and growth model. An electron microscope study13 suggests that reconstituted collagen fibres can organize into higher-order structures when precipitation occurs in an unstirred system. The effect of electrostatic interactions on the kinetics Q 1992 Butterworth-Heinemann 0142-9612/92/120878-09
Ltd
879
Rheological properties of iniectable collagen biomaterials: J. ~osenb/aft et a/.
__---...-.._-
of fibril assembly has been extensively studied5% 6814.The data exhibit a strong decrease in the half-time for fibrillogenesis when prevailing ionic strength decreases. The amino acid sequence of Type I collagen is well characterizedI and the rod-like molecule contains ,258 positive and 232 negatively charged groups (at pH 7) which are distributed along the rod and can participate in electrostatic interactions. The model of Wallace” for the electrostatic contribution to collagen fibril stabilization predicts that the net electrostatic attractive energy is equivalent to one close charge-pair interaction per molecule (2 kcal/mol), suggesting that significant cancellation between attractive and repulsive interactions occurs when collagen molecules pack into fibres. The results suggest that electrostatic forces are complex yet important regulators of intra- and inter-fibre interactions in collagen fibre dispersions. The same study16 predicts that hydrophobic interactions contribute much larger stabilization energies to collagen fibres. In this study hydrophobic forces were kept constant (measurements performed at constant temperature) but electrostatic forces were varied (measurements performed on dispersions with varying ionic strengths) in order to define the effect of electrostatic interactions on the mechanical properties of collagen fibre dispersions.
EXPERIMENTAL Collagen was isolated from bovine hide by swelling in acid and pulverization followed by solubilization with porcine pepsin. The solubilized collagen was purified as previously described3. The pepsin digestion reportedly removes all the N-terminal extrahelical peptide and the distal end of the C-terminal peptide but the rod-like triple helix is not degraded’7. Fibrillar collagen was obtained by precipitating the purified collagen solution (approx. 3 mgiml protein in 10 mM HCl) in 20 mM sodium phosphate (final pH 7.2) as described elsewherel’. The precipitated collagen was centrifuged for 45 min at 15 OOOgto form a dense pellet (37.1 mg/ml protein cont.). The pellet was then divided into six equal portions which were diluted to 35 mg/ml with 20 mM phosphate (pH 7.2) and sodium chloride at varying concentrations giving ionic strengths of 0.057-0.30. Samples were allowed to equilibrate at 277 K for 1 month. The dispersions were examined through an Olympus polarizing microscope under cross-polarized light to observe the degree of birefringence in each sample. The dispersions were also examined through a phase-contrast microscope to observe fibre textures. Dynamic rheological measurements were performed on a Rheometrics Fluids Spectrometer for all samples using parallel plate geometry. The cone and plate geometry was not applicable to these dispersions as the largest fibre sizes (>lOO,~rn) exceed gap spacings at the tip of a cone and plate. Frequency response was measured in the linear viscoelastic spectrum over three decades of frequency (lo-‘-10’ rad/s) using 50 mm diameter parallel plates. The frequency response measurements were performed with gap spacings of approximately 2 mm. Rheological spectra were independent of gap spacing for gaps greater than 1 mm. The linear viscoelastic spectra were measured at a constant strain of 1%. This strain was well within the linear
viscoelastic limit as identical spectra were recorded for strains of less than 1% (G’ and G” independent of strain). Measurements were performed at 293 K using a hydrated chamber so that the dispersion did not dry out. Samples were loaded by radial squeeze flow of the dispersion between the plates. This induces an initial radial (r) fibre alignment. Dynamic measurements performed on samples that were presheared (initial angular, 0, alignment) gave slightly different spectra. All measurements reported here are for dispersions with presumably initial radial fibre alignment. Samples were allowed at least 2 h relaxation following loading before measurement. The time interval was arrived at from stress relaxation measurements. Samples were subjected to sudden large strain displacements (as would be encountered during sample loading) and the shear modulus [G(t)) was monitored over time. Figure 2 presents a plot of G(t) for a sample (Z = 0.20) subjected to an initial 100% strain displacement. The sample relaxed to its yield stress value after approx. 2 h. Non-linear dynamic spectra were also measured in the parallel plate geometry. The recorded G’ and G” are for nominal strains at the outer edge (radia1 direction) of the platen. For any given angular deformation of the sample the applied strain is a function of radial position in this geometry. Thus, values of G’ and G” computed from measured torques on the platen are rigorous only when G’ and G” are independent of strain (linear viscoelastic region). Since the computation of G’ and G” in the parallel plate geometry assumes G’ and G” are independent of strain, the computed G’ and G” values in the non-linear viscoelastic region become progessively more inaccurate as strains are increased
80
60
40
t I
0
2000
6000
4000 Time [s)
Figure 1 Shear stress relaxation measurement for 35 mg/ml collagen dispersion (ionic strength = 0.20) following the imposition of a sudden shear strain of 100%. The measurement was performed in a Rheometrics Fluids Spectrometer using a parallel plate geometry (50 mm diameter plate) with a gap spacing of approximately 2 mm. The measurement was performed in a hydrated chamber at ambient temperature (approx. 295 K).
--_--.__ Biomaterials
1992, Vol. 13 No. 12
880
Rheological properties of injectable collagen biomaterials: J. ~osenb/af~ et al.
beyond the linear viscoelastic limit. To circumvent this problem, measurements were attempted in a couette geometry (concentric cylinders). However, reliable data were difficult to obtain because the dispersions could not be uniformly loaded in this geometry. The non-linear spectra were recorded at 293 K in a humidified environment, Spectra of G’ and G” versus strain were recorded at 1 radfs (the selection of this frequency is discussed later).
RESULTS Figures 2 and 3 present photomicrographs of fibres from dispersions with ionic strengths [I) of 0.10 and 0.20 under cross-polarized light. Figures 4 and 6 present photomicrographs for the identical dispersions using phasecontrast optics. Figures 6a and 6b display the frequency response of G’ in the linear viscoelastic region for the series of ionic strengths prepared. Figures 7a and 7b present the plots of G” corresponding to those in Figures 6a and 6b. The data are near linear when plotted log G’ or G” versus log frequency (w). Parameters a’ and II’, defined by:
Figure 4 Photomicrograph using phase-contrast optics of collagen fibres from dispersion with ionic strength 0.10. Original magnification X40.
Figure 5 Photomicrograph under phase-contrast optics of collagen fibres from dispersion with ionic strength 0.20. Original magnification X40.
G’
Figure 2 Photomicrograph under cross-polarized light of a collagen fibre from a dispersion with ionic strength 0.10. Original magnification X100.
=
a’&
Ill
were calculated by linear regression of log G’ versus log 6.1over the range of I (Table 3). Similar linear leastsquares parameters, a” and II” defined by: G” = a’rWn” (2) were calculated by linear regression of log G” versus log w (Table 2). Non-linear rheological spectra of G’ and G” versus strain (w = 1 radis) measured in the parallel plate geometry [despite the previously discussed inaccuracies) are presented in Figures Ba and 8b and in Figures 9a and 9b respectively. Relaxation time spectra (H(t)) over three decades of frequency were computed from the linearly viscoelastic G’ data using the second-order approximation of Tsoegle? H(t) = {dG’/dlnw - 0.5[dZG’/dlnw2]] l/o = (tlzy(3)
Figure 3 Photomicrograph under cross-polarized light of a collagen fibre from a dispersion with ionic strength 0.20. Original magnification X100. Biomaterials 1992, Vol. 13 No. 12
and from the linearly viscoelastic G” data the second-order approximation of Schwarzl Stave~an”: H(t) = (2h)[G”
using and
- d2G”ldlnw2] l/w = t
(4
Rheological
properties
of injectable
collagen
biomaterials:
J. Rosenblatt
et a/.
881
+
+
lo4+ +
+ + + _
+
-
0
+
+ 0
0
+
0
I
0
0
+ 0
o”
+ +o
+
0
0
0
=
.
. .
0
. .
‘ I .
w
0
.
a
‘b
m . I
103 10-l
a
Frequency
b
(t-ad/s)
I
11.11
loo
10'
Frequency
1021 Frequency
b
(z-ad/s)
IO0
IO'
Frequency
H(t) = (a’n’(1 - n’/2)2”“2]t-“’
(51
H(f) = [(2/n)3”“‘2a”(1 - nrF)]fP”
(61
Values
of
K’
(=(a’n’(l - n’lZ]2y)
and
K”
lo*
conditions
10*
fradls)
Figure 7 Dynamic rheological measurements in the linear viscoelastic region for G” versus frequency. Measurement are described in the text. a: 0, I = 0.057; 0, I = 0.10; A, ! = 0.14. b: +, I = 0.20; 0, I = 0.25; n , I = 0.30.
By computing derivatives based on Equations 1 and 2 the respective functions for H(t) become:
,,,,,lJ
(t-ad/s)
Figure 6 Dynamic rheological measurements in the linear viscoelastic region for G’ versus frequency. Measurement are described in the text. a: 0, I = 0.057; 0, I = 0.10; A, I = 0.14. b: +, I = 0.20; 0, t = 0.25; n , I = 0.30.
to-'
1
conditions
(= [(Z/n)3 “““a”(1 - n”)]) (Table 3) show that the two approximations agree within about 25%. Note from 22zble 3 that H(t) declines with increasing t for all dispersions but the rate of decline is a function of I. FerryI discussed the significance of the slope of H(t) and showed that fluid-like viscoelastic materials have a steeper decline in H(t) versus t [larger n’ or II”) than more rigid viscoelastic materials. Biomaterials
1992. Vol. 13 No. 12
882
Rheoiogical properties of injectable collagen biomaterials: J. Rosen~/a~ et al.
Table 1 Effect of ionic strength on linear viscoelastic behaviour of storage modulus for collagen dispersions Ionic strength
a’
n’
P
0.057 0.10 0.14 0.20 0.25 0.30
5374.2 5215.4 6369.7 5880.2 4543.0 3442.1
0.130 0.140 0.157 0.196 0.230 0.247
0.998 0.998 0.997 0.999 1.ooo 1.ooo
Parameters a’ and n’ were computed from a linear least-squares analysis of the data in Figures 6a and b applied to Equation 1: G’ = a’o”‘. r is the correlation coefficient from the linear least-squares analysis. The units of G’ are dyne/cm*, and the units of OJare rad/s.
Table 2 Effect of ionic strength on linear viscoelastic behaviour of loss modulus for collagen dispersions Ionic strength
a”
n”
8
0.057 0.10 0.14 0.20 0.25 0.30
1275.8 1348.0 1612.8 1757.2 1641.6 1355.4
0.140 0.168 0.196 0.224 0.234 0.236
0.986 0.991 0.998 0.999 0.999 0.998
Parametersa”andn”werecomputedfrom a linear least-squaresanalysisof the data in Figures 7a and b applied to Equation 2: G” = a”&‘. r is the correlation coefficient from the linear least-squares analysis. The units of G” are dyne/cm’, and the units of f+ are radls.
DISCUSSION Collagen fibre formation kinetics’ 6xl4 decrease with increasing I since collagen intermolecular attractive forces also decrease with increasing I. Decreases in
tv
0
10
20
a Figure 8 described
30 Strain
(%I
40
intermolecular attractive forces would also be expected to decrease the molecular ordering in fibres. This is clearly demonstrated by the photomicrographs in Figures 2-5. There is a distinct decrease in the degree of phase separation at 1 = 0.20relative to 1 = 0.10as can be seen from the decrease in birefringence in Figure 3 as well as from the (volume) expansion and Ioss of texture in the fibres in Figure 5, Mechanically, this decrease in molecular organization would be expected to translate into enhanced fibre flexibility.
Relationship between rheological spectra and collagen fibre rigidity A mechanistic and quantitative interpretation of the dependence on the slope of the relaxation time spectrum on fibre rigidity may be obtained by considering the model of Kamphuis and Jongschaap”) ‘* for concentrated dispersions. Their model describes the mechanical properties of a network of interconnected .webs (or chains) with solvent trapped between the web junctions (points where chains intersect). For collagen fibre dispersions, each fibre would corrrespond to one chain. As derived in Ref. 20, the rheology is described by a statistical mechanics transient network model where the chains are idealized as linear springs. The model allows for non-affine deformation of chains by assuming that chains deform and chain junctions rupture so as to distribute forces equally throughout the network. Chain junction formation and rupture is described by a structure kinetics equation and the anisotropic contribution to the stress tensor is computed by averaging the dyad of the vectors of chain length and chain force over the distribution of chain lengths and orientations. Kamphuis et al. give the following expressions for the
50
b
Strain
(%I
Traces of measured G’ versus strain (at 1 radls) for dispersions of varying ionic strength. Measurement conditions are in the text. a: Cl, f = 0.057: @, I = 0.10; A, I = 0.14. b: +, I = 0.20; 0, / = 0.25; 8, f = 0.30.
Biomaterials
1992, Vol. 13 No. 12
Rheological -
properties
of injectable
collagen
lo21----0
20
10
30
Strain
Figure 9
described
J. Rosenblatt et al.
biomaterials:
40
50
(%)
Traces of measured G” versus strain (at 1 rad/s) for dispersions of varying ionic strength. Measurement in the text. a: 0, I = 0.057; 0, I = 0.10; A, I = 0.14. b: +, I = 0.20; 0, I = 0.25; n , I = 0.30.
Ionic strength dependence of linear viscoelastic time spectrum coefficients K’ and K” as defined in the text
Table 3
Ionic strength 0.057
0.10 0.14 0.20
0.25 0.30
K’
K”
883.3 712.8
754.3 783.0
973.1 1112.6 1001.4 811.8
919.3 981.2 910.3 749.3
G’(w) = j {H(t)oi2fF/(l
relaxation time (ti) and modulus (Gi) for the ith relaxation mode in a system of similar type chains: ti = l/(&J
(71
G, = nflq,/15{3f0 + (1 + f,lc)[cl(l ndo/15{(1+ f,/c)[c/(l i>l
+ A)]}
i = 1
+ Ac)][hz/(l + AC)]‘- ‘1 (81
where h, is the rate constant for chain rupture, no is the initial chain number density, qO is the initial average chain length vector, fO is the average initial force per chain, c is the chain spring constant and A is a parameter which describes the degree to which the deformation is non-affine. The rigidity of the fibres is reflected in c, the fibre elasticity constant. For non-affine flow, which most likely occurs in the highly concentrated dispersions studied here, the long time relaxation modes [smaller i from Equation i’] proportionately weight network configuration (no, qO) as well as chain elasticity (c). Shorter time modes (larger i) display an increasing importance of the chain elasticity (on Gi) as the [AC/(1 + dc)] term in
conditions are
Equation 8 (i > 1) is raised to the i - 1 power. This is particularly important for very short time modes. In contrast, the effect of network configuration (no, qO)on Gi is linear for all relaxation time modes. The relationship between Gi andH(t) can be seen from a comparison of the dependence of G’ (w) on both termslg: G’(w) = Zi{Gi~;t;/(l
The coefficients K’ and K” are defined in the textand have unitsof dyne/cm2. The exponents n’ and n” corresponding to H(f) in Equations 5 and 6 are tabulated in Jab/es 1 and 2 respectively.
’
883
+ wi”ti”)} + w,2t,2)}dlnt
@a) (gb)
Equations 9a and 9b show that both Gi and H(t) reflect the magnitude of specific time-dependent relaxation modes and that they differ only in that H(t) is a continuous representation of this functional dependence and Gi is a discrete representation. For a rigid solid (G’(w) constant) the only non-zero Gi occurs when ti becomes infinite [Equation 9a). The rigid solid corresponds to the case (from Equation I) where n’ goes to zero. Consequently, for the dispersions with smaller values of n’ only the long ti relaxation mechanisms are significant whereas for dispersions with larger values of n’ shorter ti relaxation mechanisms gain increasing significance. Rigid fibres correspond to c (in Equation 8) becoming very large. In this limit, the i = 1 [longest time mode] value Of Gi will be much greater than values of Gi for i > 1 (shorter time modes). Therefore rigid fibre dispersions correspond to the rheological spectra where n’ is small since both limits (n’ small, c large] require the longest time relaxation modes to dominate. Conversely, flexible fibre dispersions correspond to spectra with larger values of n’. In a dispersion, shorter time relaxation modes correspond to fast intrafibre relaxation (elastic fibre contractions) and longer time relaxation modes correspond to slower interfibre relaxation (fibres in unfavourable entanglement configurations rearrange to more favourable configurBiomaterials
1992. Vol. 13 No. 12
884
RheoloQical _
properties
ations]. This interpretation is based on the fact that shorter time relaxation modes are much more strongly weighted by chain elasticity (in Equation 8) whereas longer time modes more proportionately weight chain configuration. The effect of decreasing I in collagen fibre dispersions is a progressive rigidification of the fibres as can be seen from the data (measured values of n’) in Table 1.
Relationship between collagen packing of collagen molecules
fibre rigidity and in fibres
The effect of molecular packing on the rigidity of collagen fibres can be described by treating the collagen fibre as a liquid-crystalline phase of ordered rigid rod collagen molecules3. The relationship between collagen fibre rigidity and molecular packing in the fibres can be established by considering theories describing the rheology of rigid rod polymer liquid-crystalline phases (LCPs). Matheson” has developed a theory for the viscosity [Q)of monodisperse rigid rod polymers in a LCP where q is related to an order parameter (~1, the rod volume fraction in the LCP (41, and the maximum possible rod volume fraction at tight packing (@,,,] as: 17- YW0
- @~4&J
(10)
The order parameter, y is a function of the degree of rod alignment in the LCP. The theory predicts that at small rod volume fractions [@< 0.3) increased rod alignment in the LCP reduces the LCP viscosity; however, at 4 > 0.3, n begins to increase dramatically with increasing @. The effect of rod volume fraction becomes especially pronounced as 4 approaches &,,,. Collagen fibres become more rigid as n increases. The rigidification of collagen fibres is expected to correspond to collagen molecule packing conditions where 4 approaches Q,,,. The Matheson theory predicts that in concentrated LCPs [such as collagen fibres) the rigidity will be dominated by the volume fraction of solvent (water) remaining in the fibre. One complexity not considered in the Matheson theory is that the collagen fibres studied here contain a polydisperse rod (molecule) size distributior?. Aharoniz4 has developed a theory for q in LCPs composed of polydisperse rigid rods. The Aharoni theory predicts behaviour similar to the Matheson theory where at @ > 0.4, n increases precipitously with increasing @ due to close packing effects. Thus it is clear that the measured changes in collagen fibre rigidity as I increases must be accompanied by an increase in the water volume fraction in the fibres. This probably explains the observed changes in fibre structure between Figures 2 and 3 (as well as between Figures 4 and 5).
Relationship between ionic strength and molecular packing of collagen fibres Insight into the mechanism by which ionic strength alters the volume fraction of water in collagen fibres can be obtained by considering thermodynamic theories which describe the equilibrium compositions of LCPs created by the phase separation of rod molecules. The extended Flory-Matheson theoryI describes the effect of electrostatic contributions to the phase equilibrium compositions of collagen fibres. This theory applies the more general Biomaterials
1992, Vol. 13 No. 12
of injectable
collagen
biomaterials:
J. Rosenblatt
et a/.
Flory theoryz5 describing the equilibrium of phaseseparated rigid-rod polymers to collagen, The Flory theory predicts the volume fraction of solvent and rod polymer in the separated LCP as well as in the nonseparated solvent phase. The phase equilibrium predictions depend on the magnitude of the Flory x parameter which describes the interaction energies between solvent molecules and rod polymer molecules. The extended Flory-Matheson theory splits the contributions tax in a collagen-water system into electrostatic and hydrophobic components: x = -(Af,,
+ AfJRT
(11)
where Af,, and Af,i are the free energies of hydrophobic and electrostatic bonding per collagen polymer segment during fibril formation. Afh is shown16 to be sensitive to temperature but is very weakly dependent on I. Af,, is the sum of a smeared charge repulsion between neighbouring rods and discrete nearest neighbour point charge attractions and repulsions. At pH 7, collagen is nearly isoelectric so the smeared charge contribution is negligible. The discrete charge interactions (AFeldiscrete) are given by: AFeldiscrete = [e2/ZDR] {e-KR}Czizj
(12)
where D is the effective dielectric constant in the neighbourhood of the charges, R is the distance between nearest neighbour charges, e is the electronic charge (in units of esu), zi and zj are the charges of each nearest neighbour and K is the Debye-Huckel parameter. AF,, is equal to Af,, when AF,, is divided by the number of polymer segments (approximately 200) in a collagen molecule. In Equation 12, ZZiZjimplies summing over all nearest neighbour point charges. As is discussed in Ref. 16, this detailed accounting of charges was replaced by a net effective discrete charge made up of a small number of charge pairs which approximate the actual charge distribution. AFeldiscrete is dependent on I and T, since: K = {(8ne2N,1)l(1000 kD,T)}“’
(13)
where D, is the dielectric constant for the bulk electrolytic medium, iV, is Avogadro’s number, k is Boltzman’s constant and T is temperature. Since temperature was held constant in the experimental measurements conducted here, hfh is expected to be the same for all the dispersions. Equation 13 gives the following Af,, scaling with I: WI
- exp{-Z”‘]
(141
Thus, electrostatic attractive forces between collagen molecules in fibres are very sensitive to I, with small increases in Z expected to significantly diminish Af,,. Calculations of the volume fraction of water present in collagen fibres as a function of Z were performed for comparison with the measured rheological properties of the fibre dispersions. Since the collagen used in these experiments was pepsin digested, a variation of the Flory equilibrium theory was used” which could account for the presence of the residual portion of the C-terminal telopeptide of collagen which is not cleaved during enzyme digestion. Details of the phase equilibria calculations have been described elsewherez7. Computations of the solvent and rod volume fractions in collagen fibres corresponding to the range of conditions studied experi-
Rheolonical _
properties
of injectable
collaaen
biomaterials:
mentally are presented in Table 4. The results show that, based on thermodynamic principles, the variation in solvent volume fraction in the collagen fibres is minimal; however, since collagen volume fractions are nearly @max, the changes in Table 4 correspond (in Equation 10) to a range where 17[hence rigidity) of the fibres changes precipitously. These theories give a rational framework explaining how electrostatic forces alter the physical properties of collagen fibre dispersions. In these experiments electrostatic forces between collagen molecules in fibres were systematically altered by changing the prevailing ionic strength. Changes in electrostatic attractive forces alter the volume fraction of water present in the phaseseparated fibre phase. These changes in the water content of fibres then alter fibre rigidities which govern the physical properties of the dispersions. There are several practical complications in this system that might make the actual water volume fractions in collagen fibres different from those calculated in Table 4. The theoretical calculations were premised on a system composition of monodisperse rods which are linear. The collagen used in these studies is known to have significant polydispersitti3, containing rods which are double or triple the length of a collagen monomer (oligomers) as well as rod fragments which are shorter than a collagen monomer”. In addition, it is possible for higher-order oligomers to be branchedz3. In polydisperse rod systems, LCPs are known to grow by incorporating the rods of the largest length firstz4, “, Thus, with fibre-nuclei containing a high concentration of collagen oligomers it is unlikely that collagen fibres could grow with packings as dense as the theoretical predictions would suggest. This effect is further exacerbated by the presence of branched oligomers. Furthermore, there is dramatic evidence3’ that even small defects in collagen molecules significantly affect the structure of fibres which grow. In these studies, point mutations of amino acids in collagen monomers yielded fibres substantially less robust than fibres grown from non-defective monomers. An additional practical factor which can affect the actual volume fraction of water in collagen fibres is the storage history of the fibres following precipitation.
Table4 Phase equilibrium calculations of collagen volume fractions in both fibre and solvent phases in collagen fibre dispersions
0.02 0.04 0.08 0.12 0.16 0.20 0.28 0.30
-12.55 -10.92 -8.96 -7.70 -6.77 -6.05 -4.98 -4.76
-67.92 -67.92 -67.92 -67.92 -67.92 -67.92 -67.92 -67.92
1.58 2.67 4.99 7.46 9.98 1.26 1.75 1.87
x x x x x X x x
10m5 10m5 10-5 1O-5 lo-’ 1O-4 10-4 1O-4
0.930 0.928 0.926 0.925 0.924 0.923 0.922 0.922
Calculations are based on an initial dispersion of monodisperse pepsindigested collagen monomers. Collagen fibre dispersions are at pH 7.2 and 293 K. I is the ionic strength of the dispersion. Afe, and Af,, are the free energies (in calories) per mole of polymer segment used in computing the Flory X-factor in the phase equilibria calculations (there are 201 polymer segments in a pepsin-digested collagen monomer). Calculation of these terms is described in detail in Refs 16 and 27. @ is the volume fraction of soluble collagen in the solvent (water) phase and @’ is the volume fraction of collagen in the (phase-separated) fibre phase.
J. Rosenblatt
et al.
885
Here, experiments were performed on fibres which were disassembled by increasing the ionic strength of the solvent they were resuspended in, whereas the model predictions were based on soluble collagen molecules phase-separating into fibres. The process is not completely reversible because collagen molecules can undergo when in the fibrillar state. Partial crosscross-linking3’ linking would have a similar effect to oligomers in altering the equilibrium rod volume fractions which would be attained in collagen fibres. Storage of the fibres at 277 K is possibly too cold to permit equilibrium fibre in response to the ionic structural rearrangement3 strength of the buffer the fibres are resuspended in following precipitation. Decreasing the temperature has an effect analogous to increasing the I of the dispersions, in that colder temperatures significantly diminish Af,, (Ref. 3). Reassembly of fibres [at 293 K) in such a highly concentrated system could proceed very slowly from dispersions that were thermally disassembled at 277 K. It is possible that measurements here were performed on dispersions which were not at equilibrium, yet were kinetically trapped in a non-equilibrium state. Precipitating the fibres at specific ionic strengths and incubating the dispersions at 293 K might yield different results.
Non-linear
viscoelastic
bebaviour
Figures 8 and 9 show significant differences in the strainthinning behaviour of collagen dispersions as a function of ionic strength [measured at 1 rad/s). Dispersions composed of fibres of high ionic strength (more flexible] display less strain thinning than low ionic strength [more rigid] fibres. Thus the dispersion appears to undergo a transition from emulsion-like to suspension-like behaviour 33. The data in Refs 32 and as ionic strength decreases 32X 33 show that the frequency of 1 rad/s used in the experiments here is within a small frequency range which is sensitive to these different flow behaviours. This behaviour is consistent with the results of the polarized microscopy and linear viscoelastic measurements where high prevailing ionic strengths result in weaker intermolecular attractive forces (due to screening of the discrete charges interactions), a higher water content in the fibres, more flexible fibres, and a more emulsion-like dispersion. Dispersions at low ionic strengths, in contrast, are subject to greater intermolecular attractive forces which give more rigid fibres and result in a more suspension-like dispersion. The jump in the low strain value of G’ at ionic strengths of less than 0.25 is probably a result of the formation of a gel (three-dimensional network of fibres) due to the presence of sufficient fibre rigidity and sufficiently strong interfibre attractive forces to form a continuous soft solid. Similar gel-like behaviour has been reported for other rigid rod polymers which phase separate into LCPS~~.
CONCLUSIONS Electrostatic forces in collagen fibre dispersions mediate the dispersion rheological behaviour through changes in fibre rigidities. Fibre rigidities appear to be altered by changes in the water volume fraction of the fibres. Polydispersity, other defects in the collagen monomers, Biomaterials
1992, Vol. 13 No. 12
Rheological
886
properties
and non-equilibrium conditions can significantly affect the fibre structure and consequently the range of ionic strengths over which fibre rigidities change. From a practical standpoint, fibre rigidity and inte~ibre attractive forces define whether the dispersion flows like a suspension or an emulsion. The degree of emulsion- and suspension-like character in injectable collagen is crucial to its efficacy in clinical applications where it is injected intradermally through very fine gauge needles (25-30 gauge). A dispersion which is too emulsion-like does not thin sufficiently during flow and requires excessive injection pressure. Conversely, a dispersion which is too suspension-like is subject to occlusion of the mouth of the needle due to excessive fibre entanglement.
16
17
18
19 20
REFERENCES 21 1
2
3
4
5
6
7
8
9
10
11 12
13
14
15
Knapp, T.R., Kaplan, E.N. and Daniels, J.R., Injectable collagen for soft tissue augmentation, Plast. Reconsfr. Surg. 1977, 60, 398405 Stegman, S.T. and Tromovitch, T.A., Implantation of collagen for depressed scars, J. L?ennatol. Surg. Oncol. 1980, 6, 450-453 Wallace, D.G. and Thompson, A., Description of collagen fibril fo~ation by a theory of polymer c~stallization, ~io~olyme~ 1983, 22, 3793-1811 Gelman, R.A., Williams, B.R. and Piez, K.A., Collagen fibril formation, Evidence for a multistep processf. Biol. Cbem. 1979,254,180-186 Williams, B.R., Gelman, R.A., Poppke, PC. and Piez, K.A., Collagen fibril formation. Optimal in-vitm conditions and preliminary kinetic results, J. Biol. Chem. 1978, 253, 8578-8585 Veis, A. and Payne, K., Collagen fibrillogenesis, in Coiiagen, Vol. I [Ed. M. Nimni), CRC Press, Boca Raton, FL, USA, 1988, pp 114-137 Wallace, D.G., Rhee, W. and Weiss, B., Shear creep of injectable collagen biomaterials, J. Biomed. Mater. Res. 1987, 21, 881-880 Wallace, D.G., Rhee, W., Reihanian, H., Ksander, G., Lee, R.K., Braun, W.B., Weiss, B.A. and Pharriss, B.B. Injectable crosslinked collagen with improved flow properties, J. Biomed. Mater. Res. 1989, 23, 931-945 Woodhead-Galloway, J., Structure of the collagen fibril: an interpretation, in Collagen in Health and Disease (Eds J.B. Weiss and M.I. Jayson), Longman, Edinburgh, UK, 1982, Ch 3 Na, G.C., Phillips, L.J. and Freire, E.I., In-vitro collagen fibril assembly: thermodynamic studies, Bjocbemistry 1989, 26, 7153-7161 Smith, J.W., Molecular pattern in native collagen, Nature 1988, 219,157-158 Fraser, R.D.B., McRae, T.P. and Miller, A., Molecular packing in Type I collagen fibrils, J. Mol. Biol. 1987,193, 115-125 Bouligand, Y., Denefle, J.-P., Lechaire, J.-P. and Maillard, M., Twisted architectures in cell-free assembled collagen gels: study of collagen substrates used for cultures, Biol. Cell 1985, 54,143-161 Bensusan, H.B. and Hoyt, B.L., Effect of various parameters on the rate of formation of fibres from collagen solution, J. Am. Cbem. Sot. 1958, 60, 717-724 Chapman, J.A., Holmes, D.F., Meek, K.M. and Rattew, C.J., Amino and sequence of collagen, in Structural
Biomaterials
1992, Vol. 13 No. 12
22 23
24
25
26
27
28
29
30
31
32
33
34
of injectable
collagen
biomaterials:
J. Rosenblatt
et a/.
Aspects of Recognition and Assembly in Biological Molecules [Ed, M. Balaban), International Science Services, Rehovot, PA, USA, 1981, pp. 387-401 Wallace, D.G., The reiative contribution of electrostatic ~temctions to stabilization of collagen fibrils, ~jopo~~e~ 1990, 29,1015-1026 Capaldi, M.J. and Chapman, J.A., The C-terminal extrahelical peptide of Type I collagen and its role in fibrlllogenesis in-vitro, Biopolymers 1982, 21, 2291-2313 Wallace, D.G., Condell, R.A., Donovan, J-W., Paivinen, A., Rhee, W.M. and Wade, S.B., Multiple denaturational transitions in fibrillar collagen, Biopolymers 1986, 25, 1875-1893 Ferry, J.D., Viscoelastic Properties of Polymers 3rd Edn, John Wiley, New York, USA, Ch. 3, 4 Kamphuis, H., Jongschaap, R.J.J. and Mijnlieff, P.F., A transient network model describing the rheological behavior of concentrated dispersions, Rheologica Acta 1984, 23, 329-344 Kamphuis, H. and Jongschaap, R.J.J., The viscoelastic behavior of heat-set ovalbumin gels explained in terms of a transient network model, J. Rheol. 1985, 26, 685-708 Matheson, R.R., Viscosity of solutions of rigid rodlike macromolecules, Macromolecules 1980, 13, 643-648 Chow, A.W., Fuller, G.G., Wallace, D.G. and Madri, J.A., Rheo-optical response of rodlike chains subject to transient shear flow. 2. Two color flow birefringence measurements on coliagen protein, macromolecules 1985, 16, 793-804 Aharoni, SM., Rigid backbone polymers. XVII. Solution viscosity of polydisperse systems, Polymer 1980, 21, 1413-1422 Flory, P.J., Phase equilibriums in solutions of rodlike particles, Proc. Roy. Sot. Lond, Ser. A 1956, A234, 73-89 Matheson, R.R. and Flory, P.J., Statistical thermodynamics of mixtures of semirigid macromolecules: chains with rodlike sequences at fixed locations, Macromolecules 1981, 14, 954-960 Wallace, D.G., The role of extrahelical peptides in stabilization of collagen fibrils, Bjopo~ymers 1990, 30, 689-897 Chow, A.W., Fuller, G.G., Wallace, D.G. and Madri, J.A., Rheo-optical response of rodlike shortened collagen protein to transient shear flow, Macromolecules 1985,16, 805-810 Moscicki, J.K. and Williams, G., Model calculations of the phase behavior of rodlike particles in solution: polydisperse systems having asymmetric distributions of rod-lengths, Polymer 1983, 24, 85-90 Prockop, D.J., Mutations that alter the primary structure of Type I collagen. The perils of a system for generating large structure by the principle of nucleated growth, 1. Biol. Chem. 1990,256,15349-15352 Yamanuchi, M. and Mechanic, G., Collagen crosslinks, in Collagen, Vol. I, Biochemistry (Ed. M. Nimni), CRC Press, Boca Raton, FL, USA, 1983, Ch. 8 Onogi, S. and Matsumoto, T.. Rheological properties of polymer solutions and melts containing suspended particles, Polymer i&g. Rev. 1981, 1, 45-87 Komatsu, H,, Mitsui, T. and Onogi, S., Nonlinear viscoelastic properties of semisolid emulsions, Trans. Sot. RheoJ. 1973.17, 351-364 Cheng, S.Z.D., Lee, S.K., Barley, JS., Hsu, S.L.C. and Harris, F.W., Gel/sol and liquid-crystalline transitions in solution of a rigid-rod polyimide, Macromolecules 1991, 24, 1883-1889
Effect of elec~ostatic forces on the dynamic rheological properties of injectable collagen biomaterials Joel Rosenblatt Department of Chemical and Biochemical Baltimore, MD 21228, USA
Engineering,
University
of Maryland
-
Baltimore
County,
Brian Devereux De~rtment
of Chemical
Engineering,
University
of California
-
Berkeiey,
Berkeley,
CA 94720, USA
and Donald G. W&lace Celtrix Laboratories
Inc., 2500 Faber Place, Palo A/to, CA 94303, USA
Injectable collagen is a concentrated dispersion of phase-separated collagen fibres in aqueous solution used to correct dermal contour defects through intradermal injection. The effect of electrostatic forces on the rheology of injectable collagen was studied by observation of the birefringence of collagen fibres through a polarizing microscope as well as by oscillatory rheological measurements on dispersions of varying ionic strengths (0.06-0.30). The birefringence of fibres progressively increased as ionic strength was reduced from 0.30 to 0.06. The linear viscoelastic measurements displayed a logarithmic relationship between storage (and loss) moduli and frequency over oscillation frequencies of 0.1-100 rad/s. The associated relaxation time spectra, interpreted using the theory of Kamphuis et al. for concentrated dispersions, show that collagen fibres become more flexible as ionic strength increases. This result was analysed at the molecular level from the perspective that collagen fibres are a liquidcrystalline phase of rigid rod collagen molecules which have phase-separated from solution. Electrostatic forces affect the volume fraction of water present in the collagen fibres which in turn alters the rigidity of the fibres. Flexible collagen fibre dispersions displayed emulsion-like flow properties whereas more rigid collagen fibre dispersions displayed suspension-like flow properties. Changes in fibre rigidity significantly alter the injectability of collagen dispersions which is critical in clinical performance. Keywords: Received
Collagen, IO January
injection,
flow properties
1992; revised and accepted
Highly purified, injectable collagen has been successfully used as a biocompatible implant in the correction of dermal contour defects for many yearslV2. Injectable collagen is manufactured by solubilizing Type I collagen from cow hide and [following purification] reconstituting the soluble collagen into fibrils by precipitation at neutral pH. The purification of collagen has been described in detail elsewhere3. The thermodynamics and kinetics of precipitation of aqueous solutions of Type I collagen have been studied extensively4-*. Studies of the rheological properties of concentrated dispersions of reconstituted collagen fibres have not been extensive. Limited previous work includes creep compliance measurements on concentrated collagen dispersions7 and extrusion force measurements on cross-linked collagen suspensions’. Type I collagen molecules (300 nm long X 1.5 nm Correspondence Biomaterials
to Dr J. Rosenbfatt.
1992, Vol. 13 No. 12
20 April 1992
diameter rigid rod, 300 kD proteing] self assemble into phase-separated fibres at neutral pH and 288-310 K. In vitro collagen fibril assembly displays two different growth phases when studied by turbidity measu~ments”: a lag phase in which an as yet undefined nucleation or early assembly event occurs’; followed by a growth phase where striated fibres appear. The molecular architecture of these fibres has been studied by electron microscopy’l and X-ray diffractionI’. They possess a regular stagger of approximately l/4 of a rod length between each molecule and its axially aligned neighbour. Wallace and Thompson3 have quantitatively modelled the kinetics of fibre growth using a nucleation and growth model. An electron microscope study13 suggests that reconstituted collagen fibres can organize into higher-order structures when precipitation occurs in an unstirred system. The effect of electrostatic interactions on the kinetics Q 1992 Butterworth-Heinemann 0142-9612/92/120878-09
Ltd
879
Rheological properties of iniectable collagen biomaterials: J. ~osenb/aft et a/.
__---...-.._-
of fibril assembly has been extensively studied5% 6814.The data exhibit a strong decrease in the half-time for fibrillogenesis when prevailing ionic strength decreases. The amino acid sequence of Type I collagen is well characterizedI and the rod-like molecule contains ,258 positive and 232 negatively charged groups (at pH 7) which are distributed along the rod and can participate in electrostatic interactions. The model of Wallace” for the electrostatic contribution to collagen fibril stabilization predicts that the net electrostatic attractive energy is equivalent to one close charge-pair interaction per molecule (2 kcal/mol), suggesting that significant cancellation between attractive and repulsive interactions occurs when collagen molecules pack into fibres. The results suggest that electrostatic forces are complex yet important regulators of intra- and inter-fibre interactions in collagen fibre dispersions. The same study16 predicts that hydrophobic interactions contribute much larger stabilization energies to collagen fibres. In this study hydrophobic forces were kept constant (measurements performed at constant temperature) but electrostatic forces were varied (measurements performed on dispersions with varying ionic strengths) in order to define the effect of electrostatic interactions on the mechanical properties of collagen fibre dispersions.
EXPERIMENTAL Collagen was isolated from bovine hide by swelling in acid and pulverization followed by solubilization with porcine pepsin. The solubilized collagen was purified as previously described3. The pepsin digestion reportedly removes all the N-terminal extrahelical peptide and the distal end of the C-terminal peptide but the rod-like triple helix is not degraded’7. Fibrillar collagen was obtained by precipitating the purified collagen solution (approx. 3 mgiml protein in 10 mM HCl) in 20 mM sodium phosphate (final pH 7.2) as described elsewherel’. The precipitated collagen was centrifuged for 45 min at 15 OOOgto form a dense pellet (37.1 mg/ml protein cont.). The pellet was then divided into six equal portions which were diluted to 35 mg/ml with 20 mM phosphate (pH 7.2) and sodium chloride at varying concentrations giving ionic strengths of 0.057-0.30. Samples were allowed to equilibrate at 277 K for 1 month. The dispersions were examined through an Olympus polarizing microscope under cross-polarized light to observe the degree of birefringence in each sample. The dispersions were also examined through a phase-contrast microscope to observe fibre textures. Dynamic rheological measurements were performed on a Rheometrics Fluids Spectrometer for all samples using parallel plate geometry. The cone and plate geometry was not applicable to these dispersions as the largest fibre sizes (>lOO,~rn) exceed gap spacings at the tip of a cone and plate. Frequency response was measured in the linear viscoelastic spectrum over three decades of frequency (lo-‘-10’ rad/s) using 50 mm diameter parallel plates. The frequency response measurements were performed with gap spacings of approximately 2 mm. Rheological spectra were independent of gap spacing for gaps greater than 1 mm. The linear viscoelastic spectra were measured at a constant strain of 1%. This strain was well within the linear
viscoelastic limit as identical spectra were recorded for strains of less than 1% (G’ and G” independent of strain). Measurements were performed at 293 K using a hydrated chamber so that the dispersion did not dry out. Samples were loaded by radial squeeze flow of the dispersion between the plates. This induces an initial radial (r) fibre alignment. Dynamic measurements performed on samples that were presheared (initial angular, 0, alignment) gave slightly different spectra. All measurements reported here are for dispersions with presumably initial radial fibre alignment. Samples were allowed at least 2 h relaxation following loading before measurement. The time interval was arrived at from stress relaxation measurements. Samples were subjected to sudden large strain displacements (as would be encountered during sample loading) and the shear modulus [G(t)) was monitored over time. Figure 2 presents a plot of G(t) for a sample (Z = 0.20) subjected to an initial 100% strain displacement. The sample relaxed to its yield stress value after approx. 2 h. Non-linear dynamic spectra were also measured in the parallel plate geometry. The recorded G’ and G” are for nominal strains at the outer edge (radia1 direction) of the platen. For any given angular deformation of the sample the applied strain is a function of radial position in this geometry. Thus, values of G’ and G” computed from measured torques on the platen are rigorous only when G’ and G” are independent of strain (linear viscoelastic region). Since the computation of G’ and G” in the parallel plate geometry assumes G’ and G” are independent of strain, the computed G’ and G” values in the non-linear viscoelastic region become progessively more inaccurate as strains are increased
80
60
40
t I
0
2000
6000
4000 Time [s)
Figure 1 Shear stress relaxation measurement for 35 mg/ml collagen dispersion (ionic strength = 0.20) following the imposition of a sudden shear strain of 100%. The measurement was performed in a Rheometrics Fluids Spectrometer using a parallel plate geometry (50 mm diameter plate) with a gap spacing of approximately 2 mm. The measurement was performed in a hydrated chamber at ambient temperature (approx. 295 K).
--_--.__ Biomaterials
1992, Vol. 13 No. 12
880
Rheological properties of injectable collagen biomaterials: J. ~osenb/af~ et al.
beyond the linear viscoelastic limit. To circumvent this problem, measurements were attempted in a couette geometry (concentric cylinders). However, reliable data were difficult to obtain because the dispersions could not be uniformly loaded in this geometry. The non-linear spectra were recorded at 293 K in a humidified environment, Spectra of G’ and G” versus strain were recorded at 1 radfs (the selection of this frequency is discussed later).
RESULTS Figures 2 and 3 present photomicrographs of fibres from dispersions with ionic strengths [I) of 0.10 and 0.20 under cross-polarized light. Figures 4 and 6 present photomicrographs for the identical dispersions using phasecontrast optics. Figures 6a and 6b display the frequency response of G’ in the linear viscoelastic region for the series of ionic strengths prepared. Figures 7a and 7b present the plots of G” corresponding to those in Figures 6a and 6b. The data are near linear when plotted log G’ or G” versus log frequency (w). Parameters a’ and II’, defined by:
Figure 4 Photomicrograph using phase-contrast optics of collagen fibres from dispersion with ionic strength 0.10. Original magnification X40.
Figure 5 Photomicrograph under phase-contrast optics of collagen fibres from dispersion with ionic strength 0.20. Original magnification X40.
G’
Figure 2 Photomicrograph under cross-polarized light of a collagen fibre from a dispersion with ionic strength 0.10. Original magnification X100.
=
a’&
Ill
were calculated by linear regression of log G’ versus log 6.1over the range of I (Table 3). Similar linear leastsquares parameters, a” and II” defined by: G” = a’rWn” (2) were calculated by linear regression of log G” versus log w (Table 2). Non-linear rheological spectra of G’ and G” versus strain (w = 1 radis) measured in the parallel plate geometry [despite the previously discussed inaccuracies) are presented in Figures Ba and 8b and in Figures 9a and 9b respectively. Relaxation time spectra (H(t)) over three decades of frequency were computed from the linearly viscoelastic G’ data using the second-order approximation of Tsoegle? H(t) = {dG’/dlnw - 0.5[dZG’/dlnw2]] l/o = (tlzy(3)
Figure 3 Photomicrograph under cross-polarized light of a collagen fibre from a dispersion with ionic strength 0.20. Original magnification X100. Biomaterials 1992, Vol. 13 No. 12
and from the linearly viscoelastic G” data the second-order approximation of Schwarzl Stave~an”: H(t) = (2h)[G”
using and
- d2G”ldlnw2] l/w = t
(4
Rheological
properties
of injectable
collagen
biomaterials:
J. Rosenblatt
et a/.
881
+
+
lo4+ +
+ + + _
+
-
0
+
+ 0
0
+
0
I
0
0
+ 0
o”
+ +o
+
0
0
0
=
.
. .
0
. .
‘ I .
w
0
.
a
‘b
m . I
103 10-l
a
Frequency
b
(t-ad/s)
I
11.11
loo
10'
Frequency
1021 Frequency
b
(z-ad/s)
IO0
IO'
Frequency
H(t) = (a’n’(1 - n’/2)2”“2]t-“’
(51
H(f) = [(2/n)3”“‘2a”(1 - nrF)]fP”
(61
Values
of
K’
(=(a’n’(l - n’lZ]2y)
and
K”
lo*
conditions
10*
fradls)
Figure 7 Dynamic rheological measurements in the linear viscoelastic region for G” versus frequency. Measurement are described in the text. a: 0, I = 0.057; 0, I = 0.10; A, ! = 0.14. b: +, I = 0.20; 0, I = 0.25; n , I = 0.30.
By computing derivatives based on Equations 1 and 2 the respective functions for H(t) become:
,,,,,lJ
(t-ad/s)
Figure 6 Dynamic rheological measurements in the linear viscoelastic region for G’ versus frequency. Measurement are described in the text. a: 0, I = 0.057; 0, I = 0.10; A, I = 0.14. b: +, I = 0.20; 0, t = 0.25; n , I = 0.30.
to-'
1
conditions
(= [(Z/n)3 “““a”(1 - n”)]) (Table 3) show that the two approximations agree within about 25%. Note from 22zble 3 that H(t) declines with increasing t for all dispersions but the rate of decline is a function of I. FerryI discussed the significance of the slope of H(t) and showed that fluid-like viscoelastic materials have a steeper decline in H(t) versus t [larger n’ or II”) than more rigid viscoelastic materials. Biomaterials
1992. Vol. 13 No. 12
882
Rheoiogical properties of injectable collagen biomaterials: J. Rosen~/a~ et al.
Table 1 Effect of ionic strength on linear viscoelastic behaviour of storage modulus for collagen dispersions Ionic strength
a’
n’
P
0.057 0.10 0.14 0.20 0.25 0.30
5374.2 5215.4 6369.7 5880.2 4543.0 3442.1
0.130 0.140 0.157 0.196 0.230 0.247
0.998 0.998 0.997 0.999 1.ooo 1.ooo
Parameters a’ and n’ were computed from a linear least-squares analysis of the data in Figures 6a and b applied to Equation 1: G’ = a’o”‘. r is the correlation coefficient from the linear least-squares analysis. The units of G’ are dyne/cm*, and the units of OJare rad/s.
Table 2 Effect of ionic strength on linear viscoelastic behaviour of loss modulus for collagen dispersions Ionic strength
a”
n”
8
0.057 0.10 0.14 0.20 0.25 0.30
1275.8 1348.0 1612.8 1757.2 1641.6 1355.4
0.140 0.168 0.196 0.224 0.234 0.236
0.986 0.991 0.998 0.999 0.999 0.998
Parametersa”andn”werecomputedfrom a linear least-squaresanalysisof the data in Figures 7a and b applied to Equation 2: G” = a”&‘. r is the correlation coefficient from the linear least-squares analysis. The units of G” are dyne/cm’, and the units of f+ are radls.
DISCUSSION Collagen fibre formation kinetics’ 6xl4 decrease with increasing I since collagen intermolecular attractive forces also decrease with increasing I. Decreases in
tv
0
10
20
a Figure 8 described
30 Strain
(%I
40
intermolecular attractive forces would also be expected to decrease the molecular ordering in fibres. This is clearly demonstrated by the photomicrographs in Figures 2-5. There is a distinct decrease in the degree of phase separation at 1 = 0.20relative to 1 = 0.10as can be seen from the decrease in birefringence in Figure 3 as well as from the (volume) expansion and Ioss of texture in the fibres in Figure 5, Mechanically, this decrease in molecular organization would be expected to translate into enhanced fibre flexibility.
Relationship between rheological spectra and collagen fibre rigidity A mechanistic and quantitative interpretation of the dependence on the slope of the relaxation time spectrum on fibre rigidity may be obtained by considering the model of Kamphuis and Jongschaap”) ‘* for concentrated dispersions. Their model describes the mechanical properties of a network of interconnected .webs (or chains) with solvent trapped between the web junctions (points where chains intersect). For collagen fibre dispersions, each fibre would corrrespond to one chain. As derived in Ref. 20, the rheology is described by a statistical mechanics transient network model where the chains are idealized as linear springs. The model allows for non-affine deformation of chains by assuming that chains deform and chain junctions rupture so as to distribute forces equally throughout the network. Chain junction formation and rupture is described by a structure kinetics equation and the anisotropic contribution to the stress tensor is computed by averaging the dyad of the vectors of chain length and chain force over the distribution of chain lengths and orientations. Kamphuis et al. give the following expressions for the
50
b
Strain
(%I
Traces of measured G’ versus strain (at 1 radls) for dispersions of varying ionic strength. Measurement conditions are in the text. a: Cl, f = 0.057: @, I = 0.10; A, I = 0.14. b: +, I = 0.20; 0, / = 0.25; 8, f = 0.30.
Biomaterials
1992, Vol. 13 No. 12
Rheological -
properties
of injectable
collagen
lo21----0
20
10
30
Strain
Figure 9
described
J. Rosenblatt et al.
biomaterials:
40
50
(%)
Traces of measured G” versus strain (at 1 rad/s) for dispersions of varying ionic strength. Measurement in the text. a: 0, I = 0.057; 0, I = 0.10; A, I = 0.14. b: +, I = 0.20; 0, I = 0.25; n , I = 0.30.
Ionic strength dependence of linear viscoelastic time spectrum coefficients K’ and K” as defined in the text
Table 3
Ionic strength 0.057
0.10 0.14 0.20
0.25 0.30
K’
K”
883.3 712.8
754.3 783.0
973.1 1112.6 1001.4 811.8
919.3 981.2 910.3 749.3
G’(w) = j {H(t)oi2fF/(l
relaxation time (ti) and modulus (Gi) for the ith relaxation mode in a system of similar type chains: ti = l/(&J
(71
G, = nflq,/15{3f0 + (1 + f,lc)[cl(l ndo/15{(1+ f,/c)[c/(l i>l
+ A)]}
i = 1
+ Ac)][hz/(l + AC)]‘- ‘1 (81
where h, is the rate constant for chain rupture, no is the initial chain number density, qO is the initial average chain length vector, fO is the average initial force per chain, c is the chain spring constant and A is a parameter which describes the degree to which the deformation is non-affine. The rigidity of the fibres is reflected in c, the fibre elasticity constant. For non-affine flow, which most likely occurs in the highly concentrated dispersions studied here, the long time relaxation modes [smaller i from Equation i’] proportionately weight network configuration (no, qO) as well as chain elasticity (c). Shorter time modes (larger i) display an increasing importance of the chain elasticity (on Gi) as the [AC/(1 + dc)] term in
conditions are
Equation 8 (i > 1) is raised to the i - 1 power. This is particularly important for very short time modes. In contrast, the effect of network configuration (no, qO)on Gi is linear for all relaxation time modes. The relationship between Gi andH(t) can be seen from a comparison of the dependence of G’ (w) on both termslg: G’(w) = Zi{Gi~;t;/(l
The coefficients K’ and K” are defined in the textand have unitsof dyne/cm2. The exponents n’ and n” corresponding to H(f) in Equations 5 and 6 are tabulated in Jab/es 1 and 2 respectively.
’
883
+ wi”ti”)} + w,2t,2)}dlnt
@a) (gb)
Equations 9a and 9b show that both Gi and H(t) reflect the magnitude of specific time-dependent relaxation modes and that they differ only in that H(t) is a continuous representation of this functional dependence and Gi is a discrete representation. For a rigid solid (G’(w) constant) the only non-zero Gi occurs when ti becomes infinite [Equation 9a). The rigid solid corresponds to the case (from Equation I) where n’ goes to zero. Consequently, for the dispersions with smaller values of n’ only the long ti relaxation mechanisms are significant whereas for dispersions with larger values of n’ shorter ti relaxation mechanisms gain increasing significance. Rigid fibres correspond to c (in Equation 8) becoming very large. In this limit, the i = 1 [longest time mode] value Of Gi will be much greater than values of Gi for i > 1 (shorter time modes). Therefore rigid fibre dispersions correspond to the rheological spectra where n’ is small since both limits (n’ small, c large] require the longest time relaxation modes to dominate. Conversely, flexible fibre dispersions correspond to spectra with larger values of n’. In a dispersion, shorter time relaxation modes correspond to fast intrafibre relaxation (elastic fibre contractions) and longer time relaxation modes correspond to slower interfibre relaxation (fibres in unfavourable entanglement configurations rearrange to more favourable configurBiomaterials
1992. Vol. 13 No. 12
884
RheoloQical _
properties
ations]. This interpretation is based on the fact that shorter time relaxation modes are much more strongly weighted by chain elasticity (in Equation 8) whereas longer time modes more proportionately weight chain configuration. The effect of decreasing I in collagen fibre dispersions is a progressive rigidification of the fibres as can be seen from the data (measured values of n’) in Table 1.
Relationship between collagen packing of collagen molecules
fibre rigidity and in fibres
The effect of molecular packing on the rigidity of collagen fibres can be described by treating the collagen fibre as a liquid-crystalline phase of ordered rigid rod collagen molecules3. The relationship between collagen fibre rigidity and molecular packing in the fibres can be established by considering theories describing the rheology of rigid rod polymer liquid-crystalline phases (LCPs). Matheson” has developed a theory for the viscosity [Q)of monodisperse rigid rod polymers in a LCP where q is related to an order parameter (~1, the rod volume fraction in the LCP (41, and the maximum possible rod volume fraction at tight packing (@,,,] as: 17- YW0
- @~4&J
(10)
The order parameter, y is a function of the degree of rod alignment in the LCP. The theory predicts that at small rod volume fractions [@< 0.3) increased rod alignment in the LCP reduces the LCP viscosity; however, at 4 > 0.3, n begins to increase dramatically with increasing @. The effect of rod volume fraction becomes especially pronounced as 4 approaches &,,,. Collagen fibres become more rigid as n increases. The rigidification of collagen fibres is expected to correspond to collagen molecule packing conditions where 4 approaches Q,,,. The Matheson theory predicts that in concentrated LCPs [such as collagen fibres) the rigidity will be dominated by the volume fraction of solvent (water) remaining in the fibre. One complexity not considered in the Matheson theory is that the collagen fibres studied here contain a polydisperse rod (molecule) size distributior?. Aharoniz4 has developed a theory for q in LCPs composed of polydisperse rigid rods. The Aharoni theory predicts behaviour similar to the Matheson theory where at @ > 0.4, n increases precipitously with increasing @ due to close packing effects. Thus it is clear that the measured changes in collagen fibre rigidity as I increases must be accompanied by an increase in the water volume fraction in the fibres. This probably explains the observed changes in fibre structure between Figures 2 and 3 (as well as between Figures 4 and 5).
Relationship between ionic strength and molecular packing of collagen fibres Insight into the mechanism by which ionic strength alters the volume fraction of water in collagen fibres can be obtained by considering thermodynamic theories which describe the equilibrium compositions of LCPs created by the phase separation of rod molecules. The extended Flory-Matheson theoryI describes the effect of electrostatic contributions to the phase equilibrium compositions of collagen fibres. This theory applies the more general Biomaterials
1992, Vol. 13 No. 12
of injectable
collagen
biomaterials:
J. Rosenblatt
et a/.
Flory theoryz5 describing the equilibrium of phaseseparated rigid-rod polymers to collagen, The Flory theory predicts the volume fraction of solvent and rod polymer in the separated LCP as well as in the nonseparated solvent phase. The phase equilibrium predictions depend on the magnitude of the Flory x parameter which describes the interaction energies between solvent molecules and rod polymer molecules. The extended Flory-Matheson theory splits the contributions tax in a collagen-water system into electrostatic and hydrophobic components: x = -(Af,,
+ AfJRT
(11)
where Af,, and Af,i are the free energies of hydrophobic and electrostatic bonding per collagen polymer segment during fibril formation. Afh is shown16 to be sensitive to temperature but is very weakly dependent on I. Af,, is the sum of a smeared charge repulsion between neighbouring rods and discrete nearest neighbour point charge attractions and repulsions. At pH 7, collagen is nearly isoelectric so the smeared charge contribution is negligible. The discrete charge interactions (AFeldiscrete) are given by: AFeldiscrete = [e2/ZDR] {e-KR}Czizj
(12)
where D is the effective dielectric constant in the neighbourhood of the charges, R is the distance between nearest neighbour charges, e is the electronic charge (in units of esu), zi and zj are the charges of each nearest neighbour and K is the Debye-Huckel parameter. AF,, is equal to Af,, when AF,, is divided by the number of polymer segments (approximately 200) in a collagen molecule. In Equation 12, ZZiZjimplies summing over all nearest neighbour point charges. As is discussed in Ref. 16, this detailed accounting of charges was replaced by a net effective discrete charge made up of a small number of charge pairs which approximate the actual charge distribution. AFeldiscrete is dependent on I and T, since: K = {(8ne2N,1)l(1000 kD,T)}“’
(13)
where D, is the dielectric constant for the bulk electrolytic medium, iV, is Avogadro’s number, k is Boltzman’s constant and T is temperature. Since temperature was held constant in the experimental measurements conducted here, hfh is expected to be the same for all the dispersions. Equation 13 gives the following Af,, scaling with I: WI
- exp{-Z”‘]
(141
Thus, electrostatic attractive forces between collagen molecules in fibres are very sensitive to I, with small increases in Z expected to significantly diminish Af,,. Calculations of the volume fraction of water present in collagen fibres as a function of Z were performed for comparison with the measured rheological properties of the fibre dispersions. Since the collagen used in these experiments was pepsin digested, a variation of the Flory equilibrium theory was used” which could account for the presence of the residual portion of the C-terminal telopeptide of collagen which is not cleaved during enzyme digestion. Details of the phase equilibria calculations have been described elsewherez7. Computations of the solvent and rod volume fractions in collagen fibres corresponding to the range of conditions studied experi-
Rheolonical _
properties
of injectable
collaaen
biomaterials:
mentally are presented in Table 4. The results show that, based on thermodynamic principles, the variation in solvent volume fraction in the collagen fibres is minimal; however, since collagen volume fractions are nearly @max, the changes in Table 4 correspond (in Equation 10) to a range where 17[hence rigidity) of the fibres changes precipitously. These theories give a rational framework explaining how electrostatic forces alter the physical properties of collagen fibre dispersions. In these experiments electrostatic forces between collagen molecules in fibres were systematically altered by changing the prevailing ionic strength. Changes in electrostatic attractive forces alter the volume fraction of water present in the phaseseparated fibre phase. These changes in the water content of fibres then alter fibre rigidities which govern the physical properties of the dispersions. There are several practical complications in this system that might make the actual water volume fractions in collagen fibres different from those calculated in Table 4. The theoretical calculations were premised on a system composition of monodisperse rods which are linear. The collagen used in these studies is known to have significant polydispersitti3, containing rods which are double or triple the length of a collagen monomer (oligomers) as well as rod fragments which are shorter than a collagen monomer”. In addition, it is possible for higher-order oligomers to be branchedz3. In polydisperse rod systems, LCPs are known to grow by incorporating the rods of the largest length firstz4, “, Thus, with fibre-nuclei containing a high concentration of collagen oligomers it is unlikely that collagen fibres could grow with packings as dense as the theoretical predictions would suggest. This effect is further exacerbated by the presence of branched oligomers. Furthermore, there is dramatic evidence3’ that even small defects in collagen molecules significantly affect the structure of fibres which grow. In these studies, point mutations of amino acids in collagen monomers yielded fibres substantially less robust than fibres grown from non-defective monomers. An additional practical factor which can affect the actual volume fraction of water in collagen fibres is the storage history of the fibres following precipitation.
Table4 Phase equilibrium calculations of collagen volume fractions in both fibre and solvent phases in collagen fibre dispersions
0.02 0.04 0.08 0.12 0.16 0.20 0.28 0.30
-12.55 -10.92 -8.96 -7.70 -6.77 -6.05 -4.98 -4.76
-67.92 -67.92 -67.92 -67.92 -67.92 -67.92 -67.92 -67.92
1.58 2.67 4.99 7.46 9.98 1.26 1.75 1.87
x x x x x X x x
10m5 10m5 10-5 1O-5 lo-’ 1O-4 10-4 1O-4
0.930 0.928 0.926 0.925 0.924 0.923 0.922 0.922
Calculations are based on an initial dispersion of monodisperse pepsindigested collagen monomers. Collagen fibre dispersions are at pH 7.2 and 293 K. I is the ionic strength of the dispersion. Afe, and Af,, are the free energies (in calories) per mole of polymer segment used in computing the Flory X-factor in the phase equilibria calculations (there are 201 polymer segments in a pepsin-digested collagen monomer). Calculation of these terms is described in detail in Refs 16 and 27. @ is the volume fraction of soluble collagen in the solvent (water) phase and @’ is the volume fraction of collagen in the (phase-separated) fibre phase.
J. Rosenblatt
et al.
885
Here, experiments were performed on fibres which were disassembled by increasing the ionic strength of the solvent they were resuspended in, whereas the model predictions were based on soluble collagen molecules phase-separating into fibres. The process is not completely reversible because collagen molecules can undergo when in the fibrillar state. Partial crosscross-linking3’ linking would have a similar effect to oligomers in altering the equilibrium rod volume fractions which would be attained in collagen fibres. Storage of the fibres at 277 K is possibly too cold to permit equilibrium fibre in response to the ionic structural rearrangement3 strength of the buffer the fibres are resuspended in following precipitation. Decreasing the temperature has an effect analogous to increasing the I of the dispersions, in that colder temperatures significantly diminish Af,, (Ref. 3). Reassembly of fibres [at 293 K) in such a highly concentrated system could proceed very slowly from dispersions that were thermally disassembled at 277 K. It is possible that measurements here were performed on dispersions which were not at equilibrium, yet were kinetically trapped in a non-equilibrium state. Precipitating the fibres at specific ionic strengths and incubating the dispersions at 293 K might yield different results.
Non-linear
viscoelastic
bebaviour
Figures 8 and 9 show significant differences in the strainthinning behaviour of collagen dispersions as a function of ionic strength [measured at 1 rad/s). Dispersions composed of fibres of high ionic strength (more flexible] display less strain thinning than low ionic strength [more rigid] fibres. Thus the dispersion appears to undergo a transition from emulsion-like to suspension-like behaviour 33. The data in Refs 32 and as ionic strength decreases 32X 33 show that the frequency of 1 rad/s used in the experiments here is within a small frequency range which is sensitive to these different flow behaviours. This behaviour is consistent with the results of the polarized microscopy and linear viscoelastic measurements where high prevailing ionic strengths result in weaker intermolecular attractive forces (due to screening of the discrete charges interactions), a higher water content in the fibres, more flexible fibres, and a more emulsion-like dispersion. Dispersions at low ionic strengths, in contrast, are subject to greater intermolecular attractive forces which give more rigid fibres and result in a more suspension-like dispersion. The jump in the low strain value of G’ at ionic strengths of less than 0.25 is probably a result of the formation of a gel (three-dimensional network of fibres) due to the presence of sufficient fibre rigidity and sufficiently strong interfibre attractive forces to form a continuous soft solid. Similar gel-like behaviour has been reported for other rigid rod polymers which phase separate into LCPS~~.
CONCLUSIONS Electrostatic forces in collagen fibre dispersions mediate the dispersion rheological behaviour through changes in fibre rigidities. Fibre rigidities appear to be altered by changes in the water volume fraction of the fibres. Polydispersity, other defects in the collagen monomers, Biomaterials
1992, Vol. 13 No. 12
Rheological
886
properties
and non-equilibrium conditions can significantly affect the fibre structure and consequently the range of ionic strengths over which fibre rigidities change. From a practical standpoint, fibre rigidity and inte~ibre attractive forces define whether the dispersion flows like a suspension or an emulsion. The degree of emulsion- and suspension-like character in injectable collagen is crucial to its efficacy in clinical applications where it is injected intradermally through very fine gauge needles (25-30 gauge). A dispersion which is too emulsion-like does not thin sufficiently during flow and requires excessive injection pressure. Conversely, a dispersion which is too suspension-like is subject to occlusion of the mouth of the needle due to excessive fibre entanglement.
16
17
18
19 20
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11 12
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15
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