Frank
Sauer
*a,
Linda
Oswald
a,
Angela
Ariza de Schellenberger
b,
Heiko
Tzschätzsch
b,
Felix
Schrank
b,
Tony
Fischer
c,
Jürgen
Braun
d,
Claudia Tanja
Mierke
c,
Rustem
Valiullin
e,
Ingolf
Sack
b and
Josef Alfons
Käs
a
aSoft Matter Physics Division, Peter Debye Institute for Soft Matter Physics, Linnestr. 5, Leipzig, Germany. E-mail: sauer@phyisk.uni-leipzig.de
bDepartment of Radiology, Charité-Universitätsmedizin, Charitéplatz 1, Berlin, Germany
cBiological Physics Division, Peter Debye Institute for Soft Matter Physics, Linnestr. 5, Leipzig, Germany
dInstitute of Medical Informatics, Charité-Universitätsmedizin, Hindenburgdamm 30, Berlin, Germany
eApplied Magnetic Resonance Division, Felix Bloch Institute for Solid State Physics, Linnestr. 5, Leipzig, Germany
First published on 20th March 2019
Collagen accounts for the major extracellular matrix (ECM) component in many tissues and provides mechanical support for cells. Magnetic Resonance (MR) Imaging, MR based diffusion measurements and MR Elastography (MRE) are considered sensitive to the microstructure of tissues including collagen networks of the ECM. However, little is known whether water diffusion interacts with viscoelastic properties of tissues. This study combines highfield MR based diffusion measurements, novel compact tabletop MRE and confocal microscopy in collagen networks of different cross-linking states (untreated collagen gels versus additional treatment with glutaraldehyde). The consistency of bulk rheology and MRE within a wide dynamic range is demonstrated in heparin gels, a viscoelastic standard for MRE. Additional crosslinking of collagen led to an 8-fold increased storage modulus, a 4-fold increased loss modulus and a significantly decreased power law exponent, describing multi-relaxational behavior, corresponding to a pronounced transition from viscous-soft to elastic-rigid properties. Collagen network changes were not detectable by MR based diffusion measurements and microscopy which are sensitive to the micrometer scale. The MRE-measured shear modulus is sensitive to collagen fiber interactions which take place on the intrafiber level such as fiber stiffness. The insensitivity of MR based diffusion measurements to collagen hydrogels of different cross-linking states alludes that congeneric collagen structures in connective tissues do not hinder extracellular diffusive water transport. Furthermore, the glutaraldehyde induced rigorous changes in viscoelastic properties indicate that intrafibrillar dissipation is the dominant mode of viscous dissipation in collagen-dominated connective tissue.
MR based diffusion measurements, such as diffusion weighted imaging (DWI), and magnetic resonance elastography (MRE) are known to be sensitive to the microstructure of biological tissues by measurement of water transport and viscoelastic behaviour, respectively. Water diffusion quantified by MR based diffusion measurements has many clinical applications including the detection of ischemic lesions, nerve fiber tracking or tumor characterization7–10 and has also been reported to be to some extent sensitive to the microstructure of collagen gels.11 In contrast to other techniques used to characterize the diffusive properties of ECM-like networks, such as fluorescence recovery after photobleaching (FRAP) or fluorescence correlation spectroscopy (FCS), MR based diffusion measurements are not dependent on small fluorescent molecules and optically accessible sample geometry.
Shear modulus, i.e. ‘stiffness’, quantification by MRE can precisely detect hepatic fibrosis better than tissue-morphology based imaging markers, fat fraction quantification or DWI.12–15 The sensitivity of MRE to hepatic fibrosis originates from the progressive infiltration and replacement of liver tissue with collagen-rich connective tissue in the course of the disease.16 This process yields a tremendous increase of the amount of ECM from less than 1% in healthy liver to more than 30% in cirrhosis.17 Previous work by MRE in liver samples indicates that the shear modulus predominately increases due to the growing number of bridges and crosslinks established in the collagen network during fibrosis progression18 or tissue fixation.19 In fact, cross-linking of very sparse networks (less than 1% volume fraction) can turn liquid tissues into solid materials with rigid body properties.20
The effect hydrodynamic drag has on water diffusion in sparse fibrous networks found in tissues remains unclear. Densely packed structures that contain predominantly cells such as neuronal21 or muscle tissues22 clearly demonstrate restricted water diffusion. Nevertheless, DWI has recently been proposed as a surrogate marker of tissue stiffness in the fibrotic liver.23,24Vice versa, MRE has been paired with diffusion tensor imaging (DTI) for the measurement of anisotropic stiffness along fiber pathways.25
This study addresses MR based collagen network characterization by MRE and MR based diffusion measurements. In biophysics collagen-based hydrogels have been established as scaffolds for investigating 3D cell–matrix interactions,26 due to their physiologic relevance as well as tunability and adaptability. Their unique mechanical properties arising from intrinsic crosslinks prominent to a certain extent in native gels.27 In more detail, intermolecular as well as intra- and intermicrofibrillar crosslinks are formed by aldehyde groups created by the conversion of specific lysine and hydroxylysine residues to peptide bound aldehydes by lysyloxydase.28
In this study, we are using a well-established ECM model system29–31 consisting of collagen gels produced from a mixture of type 1 bovine skin and type 1 rat tail collagen in order to simulate the ECM of human connective tissue.32 To mimic fibrosis induced tissue stiffening additional collagen crosslinking is induced by glutaraldehyde (GA) treatment.33 The idea dates back to the 60ies where it has been shown that GA shows the best efficiency regarding chemical and thermal stability.34 GA reacts primarily with amino groups of proteins. Since the gap between these amine groups on adjacent fiber or fiber bundle surfaces is too large to be bridged by GA crosslinks the additional crosslinks are mostly introduced within fibers rather than in between fibers,35 indicating that the crosslinking of directly touching fibers such as knots or decussating fibers might be possible. The current techniques to characterize the viscoelastic behaviour of collagen networks have some disadvantages. The gold standard plate rheology requires relatively large samples, can be hampered by surface artefacts and is very difficult to use for combination studies with live cells.36 AFM-based microrheology can only probe the surface of the network.37 For microrheological approaches it still remains unclear how the shear modulus can be quantitatively extracted.38,39 MRE is ideally suited to precisely measure the shear modulus deep in the bulk of a collagen network. We will use a compact table-top MRE device which has advantages concerning ease of cost and use and allows stiffness measurements which can be related to results reported for in vivo tissue. Since our MRE console operates above the frequency range of conventional oscillatory rheology we are using heparin gel phantoms to demonstrate the consistency of both methods. In contrast to traditional phantoms such as ultrasound gels, heparin gel as a pharmaceutical is superior regarding reproducibility and international comparability and has thus already been used as viscoelastic phantom material in MRE for hardware calibration and model fitting.40,41 Its properties are characterized by a viscoelastic power law behavior characteristic for multi-relaxational materials and can thus better simulate biological tissue properties than pure rubber-like materials.42,43
We have conducted small-sample MRE tests for the viscoelastic characterization of prototypical differently strong crosslinked collagen networks, combined with MR based diffusion measurements and confocal microscopy as well as pore size analysis of the networks. Our aim is to quantify parameter changes in MRE and MR based diffusion measurements under well-controlled conditions and to identify the length scale of structural changes in model collagen networks to which both modalities are sensitive.
Additional network crosslinking was carried out according to Lang et al. 201533 by adding 0.2% glutaraldehyde solution (diluted in PBS, stock 25%, Serva, Heidelberg, Germany) to the polymerized gels for 1 hour, followed by 12 consecutive washing steps with PBS over the next 24 hours.
Driving frequencies ranged from 200–800 Hz for untreated and from 200–2000 Hz for GA treated collagen samples. The range of frequencies was adapted for each sample to meet the resolution requirements of the shear wave. The upper frequency limit related to the image resolution. Given a spatial resolution of 0.15 mm over 8.0 mm diameter of the sample provided 53 pixels of support for a full wave profile. This resolution supported the shortest wavelengths of at least 0.6 mm, assuming that four voxels were necessary to accurately fit a complex sine function to a discrete waveform. This limit is still several magnitudes over the characteristic length scale of collagen gels, e.g. persistence length48 and pore size (see results), ensuring the measurement of bulk properties. In the low frequency range, the largest wavelength to be properly resolved was on the order of the sample diameter (i.e., 8.0 mm). For each sample the viscoelastic dispersion function was acquired with at least seven frequencies.
Imaging sequence, acquisition parameters and post processing were identical to the method explained in greater detail in a previous publication.19 In brief, data acquisition was carried out twice at each frequency and averaged, resulting in a total acquisition time for a single frequency of 22.6 min. The samples were imaged using the following acquisition parameters: repetition time = 2000 ms, echo time = 42 ms, slice thickness = 3 mm, matrix size = 64 × 64, field of view = (9.6 × 9.6) mm2, voxel size = (0.15 × 0.15 × 3) mm3. The acquired phase data were unwrapped and Fourier-transformed in time to extract complex-valued wave images at driving frequency f (Fig. 3d and e). All data points of the z-deflection (parallel to the cylinder axis) were mapped onto cylindrical coordinates and averaged over the azimuthal angle, yielding a single profile along the radial coordinate (Fig. 3f and g). The resulting profiles were fitted by the analytical solution of shear waves in a z-infinite cylinder49,50 as described previously,19 where the Bessel function of first kind yields the desired result of the fit, the complex wave number k* = k′ + ik′′.
As described by Tzschätzsch et al.,51 we translated k* into two real-valued quantities related to elastic stiffness (shear wave speed c) and inverse attenuation (shear wave penetration rate a), both in the dimension of m s−1:
(1) |
As described in a previous study,19 we directly fitted c and a by a viscoelastic model to derive shear modulus-related parameters instead of first calculating a complex shear modulus G* from k* and then fitting G*. We chose this approach because c and a are the primary results of the Bessel fit instead of G*, which is normally obtained from direct inversion-based MRE. Our model of choice was the fractional element (FE), which predicts a monotonic increase in storage and loss modulus over the full frequency range based on only two parameters: μ (shear modulus in the dimension kPa) and α (dimensionless power law exponent). Based on a fractal ladder and introduced by Helmut Schiessel and Alexander Blumen in 199652 it has among others shown applicability to describe the frequency dependent rheological behavior of eukaryotic cells.42 In this model the complex shear modulus G* = G′ + iG′′ is described as:13
(2) |
(3) |
(4) |
Fig. 1 Overall gel structure and pore size determination in LSM stacks of untreated (a) and GA treated (b) TAMRA stained collagen gels. Depicted are maximum intensity projections of 200 slices covering 75 μm in z-direction. Scale bars represent 10 μm. The gel structure looks identical. (c) Illustration of a reconstructed untreated collagen gel (red) and the corresponding detected pores (blue). Scale bar: 20 μm. The surface plot is created with Fiji/ImageJ69,70 and rendered in blender.71 (d) Pore size results: depicted are the mean values of >22.000 detected pores from 5 different positions for each gel. Box sizes 25% and 75%. Whiskers: 5–95%. |
Fig. 2b displays the signal intensities obtained for different b values at the diffusion times td indicated in the inset for a typical normalized spin-echo attenuation. The linearity of the plots in Fig. 2b and the independence from the diffusion time reveals that normal diffusion occurs, meaning the mean-squared-displacements growing linearly with diffusion time. ADCs obtained for all samples are shown in Table 1 and reveal that ADCs of water in untreated and GA treated collagen gels have no significant difference. Three different samples were measured for each type, where the untreated collagen gels have an ADC of (2.133 ± 0.062) × 10−3 mm2 s−1, and the glutaraldehyde treated samples have an ADC of (2.173 ± 0.094) × 10−3 mm2 s−1. Since the concentration of collagen responsible for the creation of the open pored network only accounts for approx. 0.3% of the sample volume it is not unexpected that the measured ADCs were very close to the unhindered diffusion in pure samples of water (2.5 ± 0.1) × 10−3 mm2 s−1, PBS (2.4 ± 0.1) × 10−3 mm2 s−1 or the 200 mM buffer solution that was used during the preparation of the collagen gels (2.3 ± 0.1) × 10−3 mm2 s−1. The obtained diffusion lengths ld were in the range from 4.6 μm to 18.6 μm and thus larger than the average pore size of the gels. Together with measured ADCs close to bulk properties this alludes to unhindered water diffusion in our samples.
Fig. 2 Water diffusion in collagen gels: (a) 13-interval NMR pulse sequence with bipolar gradients used for the diffusion measurements presented in this study.55 (b) Normalized spin-echo diffusion attenuation functions for a sample of GA treated collagen measured with different diffusion times td indicated in the figure inset. The solid line shows a slope equal to the ADC. The collapse of all spin-echo attenuation functions to one master curve is an indication of normal, i.e. unhindered, diffusion of water in collagen networks. |
ADC in 10−3 mm2 s−1 | |
---|---|
Untreated collagen | 2.133 ± 0.062 (N = 3) |
GA treated collagen | 2.173 ± 0.094 (N =3) |
dH2O at 25 °C | 2.5 ± 0.1 (N = 1) |
PBS | 2.4 ± 0.1 (N = 1) |
Collagen buffer (200 mM) | 2.3 ± 0.1 (N = 1) |
Fig. 3c demonstrates the consistency of MRE and oscillatory plate rheology in heparin gels as a multi-relaxational viscoelastic reference material with a rheological behavior very similar to biological cells.42,56 As expected for a power law rheological behavior the plate rheometer measured viscoelastic dispersion within 0.5 to 80 Hz can readily be extrapolated into the frequency range of MRE (G′ and G′′ derived from eqn (3)) from 120 to 2000 Hz and afterwards showed a relatively good congruency with a single FE fit according to eqn (2) with the model parameters of μ = (513 ± 28) Pa and α = 0.28 ± 0.01 over the entire frequency range.
Fig. 3 Overview over the tabletop MRE system (a) with 0.5 T permanent magnet MRI scanner, piezoelectric actuator with mounted sample tube, four channel gradient amplifier and console with signal preamplifier (not shown) and link to computer control system (not shown). Detailled view of MRE sample (b): glass tube with collagen gel sealed from the bottom with plastic plug with rubber ring. A small layer of closed cell PVC foam is added as a shock absorber. The vibration polarisation is indicated by the double-headed arrow. Comparison of the rheological data (c) obtained by standard oscillatory plate and MRE rheology on the example of a heparin hydrogel. G′ and G′′ extending over frequency range for both measurement types and afterwards fitted by the FE model according to eqn (2) accounting for all data points. MRE wavefields for selected frequencies for untreated (d) and GA treated (e) collagen samples illustrate the altered material behavior by the change of wavelengths. Slice thickness 3 mm. Sample diameter 8 mm. Signal averaged over azimuthal angle and corresponding Bessel-fits (dashed lines) for selected frequencies (f and g, respectively). |
An overview of wave images of untreated and GA treated collagen gels obtained with the table top MRE device at multiple frequencies is shown in Fig. 3d and e. The frequency range accessible to the measurements is dependent on the material properties of the samples that determine the wave length of the recorded wave. This can be clearly seen by comparing the wave images at 400 Hz for the untreated and the GA treated collagen gel. The untreated collagen gel has a wavelength of approx. 1.1 mm, whereas the treated gel has a wavelength of approx. 2.7 mm. The wave speed c and the penetration rate a were obtained from the Bessel fits at individual frequencies for untreated (Fig. 4a) and GA treated collagen gels (Fig. 4b). The dashed lines in Fig. 4a and b represent the FE fits for c(f) and a(f) according to eqn (4). Glutaraldehyde treatment fixes a sample, i.e. it drastically strengthens intrafilament connections and crosslinks. Consequentially, this freezes out relaxation through internal dynamics. The multi-relaxational FE model does not fit as well to rubber-elastic permanently crosslinked polymer gels which also explains the deviations between FE-model (dashed line) and data in Fig. 4b and why the frequency dependent behavior of these samples is better fitted by a Kelvin–Voigt model57 (solid line), for which the complex shear modulus is derived as:
G* = μ + iηω | (5) |
Fig. 4 Shear wave speed c and shear wave penetration rate a plotted over frequency for an untreated (a) and a GA treated (b) collagen gel. Presented data is each from one single measurement and representative FE fits (dashed lines) and an additional fit based on the Kelvin–Voigt model (KV fit, solid line) for GA treated collagen demonstrate the GA induced changes. Model independent storage (G′) and loss modulus (G′′) obtained from eqn (3)vs. frequency for the collagen samples before (c) and after (d) additional glutaraldehyde treatment show the transition from a softer liquid power law behavior to a solid elastic rubber plateau. The fits are from the same nature as in (a) and (b). The displayed data shows the mean + SD (shaded regions) for N = 7 individual samples for each condition. |
Untreated collagen | GA treated collagen | ||
---|---|---|---|
Pore size | (4.58 ± 1.50) μm | (4.44 ± 1.46) μm | |
FE-model parameters | μ | (35.2 ± 4.9) Pa | (1032 ± 84) Pa |
α | 0.380 ± 0.021 | 0.123 ± 0.018 | |
KV-model parameters | μ | — | (1.33 ± 0.18) kPa |
η | — | (0.068 ± 0.016) Pa s | |
Model independent averaged storage and loss modulus | G′ | (155 ± 22) Pa | (1327 ± 75) Pa |
G′′ | (113 ± 24) Pa | (447 ± 210) Pa |
The results obtained by different state-of-the-art techniques can differ by several orders of magnitude.58,59 MRE can be readily performed in vivo and the observed rheological behavior can be cross checked by plate rheology using suitable MRE phantoms.
In polymer physics the viscous part of viscoelastic behavior is greatly attributed to intrafibrillar dissipation and hydrodynamic drag with even minimal amounts of untangled polymers significantly changing viscoelastic properties.60 Assuming sufficient polymer concentration and coupling with the solvent, the latter can be reflected in altered diffusive behavior of the solvent molecules.
Thus, a combination of MR based diffusion measurements and MRE is an ideal research tool to investigate to what extent hydrodynamics contributes to viscous dissipation in soft matter. Our tabletop device technologically permits to combine simultaneous MR based diffusion and MRE measurements.
In dilute solutions of conventional flexible polymers, the increase in viscosity with respect to the pure solvent is attributed to dissipation of the polymer's Brownian motion through hydrodynamic drag. This means that there is a frictional coupling between solvent and collagen filaments. According to free volume models61 increasing polymer concentration will eventually hinder free solvent diffusion. Our results for collagen networks clearly show that water diffusion remains unhindered by the presence of collagen fibers. This is not surprising considering the large pore size and the low volume fraction that collagen fibers take up and is in accordance with the dilute regime from aforementioned free volume models.
While other techniques such as FRAP and FCS were able to detect hindered diffusion in dense collagen-based structures in dependency of the probe size,62,63 the reliance of these techniques on optically accessible slices for the fluorescent probes and the different corresponding ADC regimes renders them to be hardly comparable to MR based diffusion measurements in bulk materials. However, a possible extension of our current experiments would be to use our combination to measure denser ECM substitutes (i.e. centrifuged or artificially aligned collagen samples) with an increased amount of biological or trapped water to identify multiple different diffusion timescales as has been demonstrated before on Amyloid Fibrils.64
From a biological perspective, a regulated extracellular diffusive transport is essential for morphogen gradients to facilitate correct embryonal development, while under hindered nutrient flow solid tumors develop necrotic cores. The semiflexible nature of collagen networks, i.e. filament stiffness, assures that connective tissue can be mechanically stable and strong as well as simultaneously provide a large pore size that does not hinder diffusive transport.
In accordance to a previous microrheological study,65 our data show that collagen networks exhibit a viscoelastic power law behavior in a frequency range not accessible by classical shear rheology and, moreover, that this power law behavior is almost completely reduced by additional treatment with GA. It is essential for connective tissue to protect from mechanical trauma by viscous dissipation. This dampening cannot be caused by the hydrodynamic drag of the polymer strands through the surrounding solvent. It can only be caused by internal dynamics of the collagen fibers themselves. In our experiments the GA treatment fixes the filaments and thus freezes intrafibrillar motions in the filaments66–68 which ultimately leads to a loss of power law behavior in these collagen gels and favors the interpretation that intrafibrillar friction within the filaments is the dominant effect that causes multi-relaxation dissipation.
Our findings convincingly demonstrate that the combination of MR based diffusion measurements and MRE can be a powerful tool in polymer and biophysics. We have shown that MRE is sensitive to viscoelastic alterations in low-volume fraction hydrogel networks while MR based diffusion measurements are known to be sensitive to restricted diffusion in cellular systems. Therefore, our experimental approach permits combined studies on how the water diffusion in ECM-like networks is influenced by interspersed objects that hinder or restrict water diffusion (e.g. cells, spheroids, beads) while simultaneously measuring the effects on the viscoelastic properties of the samples via MRE. Furthermore, the experimental roadmap presented in this study can be easily transferred to other hydrogel systems of interest in polymer physics, such as F-actin and other cytoskeletal filaments. Finally, the combination of the presented techniques seems to be suitable for the in vivo characterization of both viscoelastic and diffusion related properties of tumors and their surrounding microenvironment.
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