Open Access Article

This Open Access Article is licensed under a Creative Commons Attribution-Non Commercial 3.0 Unported Licence

Eline E.
van Haaften
^{ab},
Mark C.
van Turnhout
^{a} and
Nicholas A.
Kurniawan†
*^{ab}
^{a}Department of Biomedical Engineering, Eindhoven University of Technology, The Netherlands
^{b}Institute for Complex Molecular Systems, Eindhoven University of Technology, The Netherlands

Received
16th November 2018
, Accepted 15th March 2019

First published on 25th March 2019

Uniaxial ring test is a widely used mechanical characterization method for a variety of materials, from industrial elastomers to biological materials. Here we show that the combination of local material compression, bending, and stretching during uniaxial ring test results in a geometry-dependent deformation profile that can introduce systematic errors in the extraction of mechanical parameters. We identify the stress and strain regimes under which stretching dominates and develop a simple image-based analysis approach that eliminates these systematic errors. We rigorously test this approach computationally and experimentally, and demonstrate that we can accurately estimate the sample mechanical properties for a wide range of ring geometries. As a proof of concept for its application, we use the approach to analyze explanted rat vascular tissues and find a clear temporal change in the mechanical properties of these explants after graft implantation. The image-based approach can therefore offer a straightforward, versatile, and accurate method for mechanically characterizing new classes of soft and biological materials.

More recently, uniaxial ring test has also found a large application area in the mechanical characterization of biological tissues and biomaterials. In particular, uniaxial ring test has been increasingly shown to be the method of choice for the assessment of mechanical properties of blood vessels and blood vessel substitutes, due to its ability to mimic the physiological loading in the circumferential direction.^{5–7} Moreover, uniaxial ring test allows mechanical characterization of small and delicate vascular specimens, for which other testing methods such as uniaxial tensile test of cut-out sample strips and biaxial test of planar samples are unfeasible or can introduce undesired measurement artifacts.^{8–11} As such, biomedical researchers have started to explore the usefulness of uniaxial ring test for the mechanical measurement of small blood vessels,^{12} vascular grafts,^{12,13} tissue-engineered vascular constructs,^{14,15} and even arterial tissues.^{7} Such mechanical assessments are important not only for improving the design of vascular constructs and developing mathematical models,^{16,17} but also for understanding and diagnosing various vascular diseases.^{18,19}

One key challenge that commonly arises in the uniaxial ring test is the extraction of useful material parameters from the raw measurement data. A typical approach is by fitting the force vs. arm distance (or pin displacement) data to a linear function, from which the Young's modulus of the material is inferred. However, in a uniaxial ring test, the initial force response recorded on the pins contains a mixed contribution from bending and stretching forces, as the ring is deformed to a straight shape. Furthermore, as we shall show in this article, during this initial bending stage, pin displacements are not a suitable measurement metric for material stretches. These effects make accurate and reliable material parameters estimation from force–displacement curves a challenge.

We propose that there exists a stretch regime under which the bending and stretching contributions can be sufficiently separated, so that the material properties can be accurately estimated from a uniaxial ring test without using inverse analysis. This knowledge will greatly expand the use of the uniaxial ring test method for the characterizations of new classes of materials, especially when the material behavior is not a priori known, for example in the context of soft hydrogels and biological materials.

In this work, we demonstrate that deformation above a certain critical stretch in uniaxial ring tests is effectively dominated by stretching, thereby allowing accurate estimation of material mechanical stiffness. We further propose a simple image-based approach that both exploits this idea and circumvents the current problem with stretch estimation from pin displacement. We validate our approach computationally and experimentally through a direct comparison with uniaxial tensile testing measurements, and quantify how various parameters such as ring geometry can affect the analysis and outcomes. Finally, we show a proof of concept where we apply the method to characterize the temporal change in the mechanical properties as a result of tissue formation and scaffold degradation in explants from aortic interposition grafts in rats.

2.1.1 Finite element model.
The samples are modeled as rings with an initial inner radius R, thickness t, and height h, whereas the pin is modeled as a cylindrical rigid surface with a radius r (Fig. 1A). Frictionless contact is prescribed between the pin and the inside of the ring, and the ring is stretched in 100 increments by displacement of the ring in the positive x-direction for a total displacement of R. Thanks to symmetry, only one eighth of the ring is necessary to be simulated: half the height of a quadrant of the complete ring (Fig. 1A). Symmetrical boundary conditions are prescribed for the ring for the cross section in the yz-plane, the cross section in the xz-plane (at the pin), and the xy-plane at the bottom of the mesh (i.e., symmetry over the height).

with μ_{0} the shear modulus, the deviatoric principal stretches, J the determinant of the deformation gradient tensor F, and κ_{0} the compression modulus. The shear modulus μ_{0} and compression modulus κ_{0} are derived from the Young's modulus E and Poisson's ratio ν as:

The following read-outs are recorded: the reaction force in x-direction on the pin, the initial coordinates and displacements of the nodes on the outer perimeter of the ring in the xy-symmetry plane (i.e., bottom of the mesh) and of the highest node in the yz-symmetry plane of the ring, and the strains in x-direction for the nodes in the yz-symmetry plane of the ring. These read-outs are post-processed with Matlab (R2015a, the Mathworks, Matick, MA, USA).

All finite element (FE) simulations were performed with Simulia Abaqus 6.14-1 (Dassault Systèmes Simulia Corp., Providence, RI, USA). The ring is meshed with 20-node quadratic brick elements (C3D20RH) that are kept approximately equal in size (determined with initial mesh convergence tests) for all simulations. We use an isotropic compressible Neo-Hookean material model for the ring with strain energy potential function:

(1) |

(2) |

(3) |

We calculate the stress σ_{ring} for the ring in each displacement increment using σ_{ring} = F/A, where F is the reaction force on the pin. A is the cross-sectional area of the ring in the yz-symmetry plane, as obtained from the coordinates and displacements of the highest node on the outer perimeter and those of the opposite node in the inner perimeter of the ring.

Because of sample bending during the uniaxial ring test, pin displacement is not suitable for the assessment of ring stretches. Instead, we use the stretch of the outer perimeter of the ring λ_{OP}, calculated for each increment in the simulation, as a measurement metric of ring stretch. We further propose that at sufficiently large pin displacements, sample deformation is dominated by stretching. Therefore, we anticipate that: (1) λ_{OP} becomes linear in pin displacements; and (2) stresses in the ring become linear in λ_{OP} (in the symmetry plane between the pins). Following these premises, we estimate the Young's modulus of the ring that is being tested, E_{ring}, as:

(4) |

In practice, the initial bending also results in compressive strains in the yz-symmetry plane of the ring. We use the strains in x-direction over this plane to find the point of maximum compression: λ_{±}. For λ_{OP} > λ_{±}, all the strains over this cross section monotonically increase in the simulations (Fig. 1C, dashed line). We then estimate E_{ring} with Δλ_{OP} = 2.5%, starting at λ_{±} + 2.5%:

(5) |

2.1.2 Sensitivity analysis.
Experimental parameters, such as the ring geometry, Poisson's ratio, as well as the pin radius, can affect the bending modes and therefore the accuracy of the extraction of material parameters in a uniaxial ring test. To investigate this effect, we performed a sensitivity analysis by running 100 simulations of ring deformations. For each simulation, we pulled random variables from a uniform distribution of the parameter space, with the geometry of the ring and the pin, and the mechanical properties of the ring as experimental variables (Table 1). Specifically, we explored the effects of the inner radius of the ring R, the height of the ring h, the thickness of the ring t, the pin radius r, the ring's stiffness E and the ring's Poisson's ratio ν. From these 100 simulations, we calculate λ_{±} and E_{ring} (eqn (5)).

giving us the following regression model:

with y = λ_{±} or y = π_{1}. We report the coefficients, their 95% confidence intervals, the fraction of the variation that is explained by the parameter (the associated sum of squares divided by the total sum of squares), and the associated p-values.

Symbol | Property | Unit | Parameter space |
---|---|---|---|

R | Inner ring radius | mm | [0.5–2.5] |

h/R | Ring height to radius | — | [0.2–4.0] |

t/R | Ring thickness to radius | — | [0–1] |

r/R | Pin radius to radius | — | [0.1–0.9] |

E | Young's modulus | MPa | [0.1–5.1] |

ν | Poisson's ratio | — | [0–0.475] |

We investigate the effects of the explored parameters on λ_{±} and E_{ring} with a multiple linear regression model. Buckingham π theorem was used to define a nondimensional equation by constructing the following dimensionless groups out of the dimensioned variables:

(6) |

y = a_{1} + a_{2}π_{2} + a_{3}π_{3} + a_{4}π_{4} + a_{5}ν + error | (7) |

2.2.1 Mechanical tests.
Uniaxial ring tests were performed in a modified biaxial tensile tester setup (CellScale Biomaterial Testing, Waterloo, Canada), equipped with a 5000 mN load cell. To test for the validity of the proposed approach, ring shaped samples with various geometries were punched from a rubber flap (thickness ≈ 700 μm) and subjected to the tensile test. Prior to mounting, the height h, radius R, and thickness t of the rings were measured at multiple locations with a digital microscope (Keyence VHX-500FE, Table 2). The rings were mounted onto the tensile tester using two stainless steel pins (∅ ≈250 μm) that were fixed in the testing device with magnets (Fig. 4A). The rings were deformed at 10 mm min^{−1} crosshead speed until failure, and the associated forces and displacements were recorded at a frequency of 5 Hz. The stretch λ_{OP} was defined as the outer perimeter length normalized to initial outer perimeter length, calculated via image analysis (see Section 2.2.2). Assuming isotropic material properties, the estimated ring stress was derived from the force and displacement measurements:

with the transverse stretch, λ_{tr}, calculated via:

The Poisson's ratio was calculated from the uniaxial tensile testing data, and set at ν = 0.41. With σ_{ring} and λ_{OP}, we use eqn (5) to estimate E_{ring}.

(8) |

λ_{tr} = 1 − ν(λ_{OP} − 1) | (9) |

Group | h (mm) | R (mm) | t (mm) | t/R (−) |
---|---|---|---|---|

1 | 0.69 ± 0.00 | 0.92 ± 0.01 | 0.48 ± 0.02 | 0.52 ± 0.02 |

2 | 0.68 ± 0.00 | 0.97 ± 0.01 | 0.29 ± 0.03 | 0.30 ± 0.03 |

3 | 0.67 ± 0.01 | 1.43 ± 0.01 | 0.27 ± 0.03 | 0.19 ± 0.02 |

To compare the uniaxial ring test results against traditional uniaxial tensile data, dogbone shaped samples (n = 4) from the same material were uniaxially stretched in the biaxial tensile tester at the same crosshead speed of 10 mm min^{−1}. Before mounting the sample, graphite particles were applied onto the surface facilitating optical strain analysis by digital image correlation (using LabJoy software, Fig. 4B). Assuming isotropic material properties, the Poisson's ratio was derived from the slopes of the longitudinal and transverse stretch, up to a longitudinal stretch of 1.2 (eqn (9)). Similar to the ring tests, we calculate the ratio between σ and λ over a 2.5% stretch range, starting at λ = 2.5%:

(10) |

2.2.2 Displacement tracking.
To obtain the ring stretch in a robust manner, we developed an image-based tracking algorithm that computes the outer perimeter length of the ring (in pixels), allowing the user to calculate the outer perimeter stretch λ_{OP}. To minimize analysis artifacts arising from sample and image irregularities, the outer perimeter length is obtained based on the circumference of a super ellipse that is fitted through a set of 20 points on this outer perimeter.

where a and b denote the major and minor axes. For n = 2, the curve reduces to an ordinary ellipse.

In short, the image is converted into a binary image with sample coordinates (X, Y). For the image of the undeformed samples, this set of coordinates is fitted with an ellipse to calculate the center of mass (i.e. x_{0}, y_{0}), the major and minor axes a and b, and the orientation ϕ. However, at larger stretches, an ellipse cannot accurately describe the outline of the sample. Therefore, a shape parameter n is introduced, which transforms the ellipse into a super ellipse. We use the fit of the ordinary ellipse as an initial guess for this super ellipse. The parameters x_{0}, y_{0} and ϕ are fixed, and with those we fit the parametric form of the super ellipse:

(11) |

We select a number of points on the outer perimeter of (X,Y) and compare their distance to the center of mass with the distance of the estimated super ellipse to the center of mass. With the fminsearch function in Matlab, we minimize the root-mean-square (RMS) of the differences in distances between the sample points and the corresponding super ellipse points. Using this approach, any number of data points can be generated and used to calculate the RMS. Here, t is discretized into 20 points between 0 and 2π, resulting in excellent shape-fitting results (Fig. 2B).

This algorithm, schematically depicted in Fig. 2A, is implemented in Matlab and is made freely accessible viahttps://gitlab.tue.nl/stem/orlab.

We next asked whether the point of maximum compression is influenced by the geometry of the ring samples and the pin, as well as the Poisson's ratio of the sample. To rigorously test this, we run a large number of simulations with varying experimental parameters and statistically analyzed the results using a multiple linear regression model to find the key parameters that sensitively affect the deformation mode. For the point of maximum compression in the simulations we find:

(12) |

λ
_{±} = |
1.005 | +0.048t/R | +0.000h/R | −0.011r/R | +0.013ν | + error |
---|---|---|---|---|---|---|

95% CI | 0.999 1.011 | 0.043 0.053 | −0.002 0.003 | −0.017 −0.005 | 0.002 0.025 | |

SS/SS_{tot} |
0.751 | 0.002 | 0.026 | 0.011 | 0.212 | |

p | 0.000 | 0.000 | 0.769 | 0.001 | 0.027 | |

n = 100 |
R
_{
a
}
^{2} = 0.773 |

These results suggest that for r/R ≪ 1 the variation in λ_{±} can be largely attributed to variation in the thickness of the ring t/R. When we apply a post hoc linear regression analysis, we find that:

(13) |

Not all simulations converged up to stretches of λ_{±} + 5%, which is necessary for our analysis of E_{ring} (eqn (5)). Therefore we could only use 85 out of the 100 simulations that we ran, but this did not introduce a noteworthy bias in the uniform distribution of the tested parameter space (Fig. 3C). From these 85 simulations, we find for the relationship between the actual Young's modulus E and the estimated Young's modulus E_{ring}:

E = 0.950E_{ring} + 0.169 | (14) |

As can be seen from eqn (14), E_{ring} overestimates the actual E by 5% on average. For the remaining, small variation on this overestimation, we find (Table 4):

(15) |

E/E_{ring} = |
1.387 | −0.445t/R | +0.020h/R | +0.042r/R | −0.706ν | + error |
---|---|---|---|---|---|---|

95% CI | 1.338 1.437 | −0.492 −0.340 | 0.001 0.040 | −0.019 0.103 | −0.807 −0.604 | |

SS/SS_{tot} |
0.557 | 0.007 | 0.003 | 0.306 | 0.128 | |

p | 0.000 | 0.000 | 0.038 | 0.170 | 0.000 | |

n = 85 |
R
_{
a
}
^{2} = 0.856 |

These results indicate that the remaining variation can be best explained by t/R and ν: for larger t/R and ν, E_{ring} tends to become larger with respect to the actual E (Fig. 3E).

To directly compare the uniaxial ring test results against the ‘conventional’ uniaxial tensile test of the same material, we plot the average stress–stretch relations measured using the two techniques (Fig. 4D). It can be qualitatively observed that the curves are close to each other and that the computed stresses measured in the ring tests are slightly but consistently larger compared to those in the tensile tests. To make a quantitative comparison, we take into account the point of maximum compression λ_{±}, which is estimated viaeqn (13) and highlighted in the inset of Fig. 4C. Using eqn (4), E_{ring} is estimated and compared against the average stiffness of the tensile test (Fig. 4E). We find that the stiffness estimated from the ring test (1.46 ± 0.15 MPa) agrees closely with the actual stiffness (1.17 ± 0.02 MPa), with only a minor discrepancy as predicted by our simulation results.

In the present study, we offer a straightforward and accurate approach to estimate material stiffness from uniaxial ring test measurements. The simplicity of the approach is based on the notion that the contributions of sample bending and stretching in the force response can be well delineated from geometry alone, and thereby the outer perimeter stretch of the ring, λ_{OP}, can be used as a valid deformation metric (i.e., instead of using the pin-to-pin distance). We develop a robust and freely-accessible algorithm for quantifying λ_{OP} from the measurement images and rigorously validate the approach computationally and experimentally.

The numerical simulations confirmed (1) that for large deformations, outer perimeter stretch λ_{OP} becomes linear with pin displacement; and (2) that for large deformations, the estimated ring stress from pin reaction forces and cross sectional area σ_{ring} becomes linear in λ_{OP} (Fig. 1B and 3A, B). Similarly, this linear behavior for large deformations was also confirmed in our experiments (Fig. 4A). The numerical simulations further showed that quantification of E_{ring} based on λ_{OP} is in very good agreement with the actual stiffness E (eqn (4)). Extensive survey over a large parameter space shows that the actual stiffness is typically 5% lower than estimated by E_{ring} (eqn (14)), with outliers of up to ≈30% (Fig. 3E).

In the calculation of E_{ring}, we take into account that in the initial phase of the ring test the deformation is dominated by bending. With regard to this, our simulations revealed a simple empirical relation between the point of maximum compression (i.e., monotonic extension over the entire cross section of the ring) and ring geometry (i.e., t/R), independent of the intrinsic material properties (eqn (13)). Although ν (as a measure of incompressibility) and r/R (which affects the extent of ring bending) also contribute to this relation, their effects are negligible compared to t/R (<2.5% vs. 75%, Table 3), particularly when we consider that these effects are also limited by the possible range of the parameters: in general 0 < ν < 0.5, and by definition 0 < r/R < 1. Using this relation, the stretch-dominating region in the ring test data can be identified and used to calculate a valid first-order, linear stiffness of the material (i.e., E) without time-consuming and complex inverse analysis methods.

We emphasize that our proposed image-based analysis is optimally suited for the accurate extraction of this linear stiffness, which is particularly valuable in the field of vascular tissue engineering and biology. Extension of the approach to estimate other, non-linear parameters of soft tissues (for instance by a Fung material model) is possible, but inevitably requires an inverse analysis of some kind, because these parameters cannot be directly calculated from the slope of the σ–λ_{±}-curve.

The results from the simulations thus allow us to proceed with the experimental validation, where we tested ring-shaped and dog-bone-shaped samples from the same material. Taking into account the point of maximum compression for the calculation of E_{ring}, we found that the actual stiffness, as determined from the uniaxial tensile test, is typically 20% lower than E_{ring}, as determined from ring test data (Fig. 4E). This overestimation of E is larger than the 5% overestimation found by the simulations (eqn (14)) and can likely be attributed to experimental noise, which is common to all mechanical tests (e.g., noise on force and displacement transducers, pixel discretization of the images, sample irregularities). In fact, due to the geometry and symmetry of uniaxial ring tests, the signal-to-noise ratio of ring tests is expected to be higher than that of conventional tensile tests.

It can be observed that previous studies that use the ring test approach to estimate burst pressures have also consistently shown to overestimate the actual burst pressure by between 25% and >400%.^{25} Although these values cannot be directly compared to our results, it supports the idea that the ring-test method has a tendency to overestimate material properties. In fact, our simulations and experiments reveal that the degree of overestimation by E_{ring} is related to the geometry of the ring, t/R, and to the compressibility of the ring, ν (Fig. 3E and 4C): the larger these ratios, the larger the tendency to overestimate the stiffness. However, since Poisson's ratios of biological tissues typically fall in the narrow range of 0.3 < ν < 0.5, t/R remains the most relevant variable to account for. Based on this, we conclude that the accuracy of the method becomes better for relatively thin-walled ring samples, and that for a given t/R, the method is very sensitive to detect differences in stiffness. Therefore, it is recommended to always take into account this geometrical effect when comparing data from rings with different geometrical properties.

Finally, we applied the method, as an exemplary proof of concept, to measure the mechanical properties of ring-shaped vascular explants from rat aortic grafts. Given the agreement between the experimental and computational analysis, it is expected that the actual stiffness of the explants is slightly lower than the values reported in Fig. 5. Despite this, the temporal changes in mechanical properties, as a result of tissue formation and scaffold degradation, remain evident, illustrating the merit of this approach.

- J. H. Wu, P. F. Li, C. L. Dong, H. T. Jiang, B. Xue, X. Gao, M. Qin, W. Wang, B. Chen and Y. Cao, Nat. Commun., 2018, 9, 620 CrossRef PubMed.
- H. Jung and W. B. Yoon, J. Food Sci., 2017, 82, 2894–2900 CrossRef CAS PubMed.
- A. International, Annual Book of ASTM Standards; Section 9: RUBBER, ASTM International, Conshohocken, USA, 2008, vol. 09.02 Rubber Products, Industrial Specifications and Related Test Methods; Gaskets; Tires Search PubMed.
- J. R. Davis, Tensile Testing, ASM International, Materials Park, OH, 2nd edn, 2004 Search PubMed.
- M. J. Mulvany and W. Halpern, Nature, 1976, 260, 617–619 CrossRef CAS PubMed.
- D. Seliktar, R. A. Black, R. P. Vito and R. M. Nerem, Ann. Biomed. Eng., 2000, 28, 351–362 CrossRef CAS PubMed.
- R. A. Macrae, K. Miller and B. J. Doyle, Strain, 2016, 52, 380–399 CrossRef.
- T. H. Petersen, E. A. Calle, M. B. Colehour and L. E. Niklason, Cells Tissues Organs, 2012, 195, 222–231 CrossRef CAS PubMed.
- E. Claes, J. M. Atienza, G. V. Guinea, F. J. Rojo, J. M. Bernal, J. M. Revuelta and M. Elices, Conf. Proc. IEEE Eng. Med. Biol. Soc., 2010, 2010, 3792–3795 CAS.
- A. V. Kamenskiy, Y. A. Dzenis, S. A. J. Kazmi, M. A. Pemberton, I. I. Pipinos, N. Y. Phillips, K. Herber, T. Woodford, R. E. Bowen, C. S. Lomneth and J. N. MacTaggart, Biomech. Model. Mechanobiol., 2014, 13, 1341–1359 CrossRef PubMed.
- J. T. Keyes, D. G. Haskett, U. Utzinger, M. Azhar and J. P. Vande Geest, J. Biomech. Eng., 2011, 133, 075001 CrossRef PubMed.
- M. Stoiber, B. Messner, C. Grasl, V. Gschlad, H. Bergmeister, D. Bernhard and H. Schima, Exp. Mech., 2015, 55, 1591–1595 CrossRef.
- C. Grasl, H. Bergmeister, M. Stoiber, H. Schima and G. Weigel, J. Biomed. Mater. Res., Part A, 2010, 93, 716–723 Search PubMed.
- T. Shazly, A. Rachev, S. Lessner, W. S. Argraves, J. Ferdous, B. Zhou, A. M. Moreira and M. Sutton, Exp. Mech., 2015, 55, 41–51 CrossRef CAS.
- J. J. Stankus, L. Soletti, K. Fujimoto, Y. Hong, D. A. Vorp and W. R. Wagner, Biomaterials, 2007, 28, 2738–2746 CrossRef CAS PubMed.
- E. E. van Haaften, C. V. C. Bouten and N. A. Kurniawan, Cells, 2017, 6, 19 CrossRef PubMed.
- G. A. Holzapfel, J. Theor. Biol., 2006, 238, 290–302 CrossRef PubMed.
- G. S. Kassab, J. R. Soc., Interface, 2006, 3, 719–740 CrossRef PubMed.
- F. Safshekan, M. Tafazzoli-Shadpour, M. Abdouss and M. B. Shadmehr, Materials, 2016, 9, 456 CrossRef PubMed.
- V. Bonito, A. I. Smits, O. J. Goor, B. D. Ippel, A. Driessen-Mol, T. J. Münker, A. W. Bosman, T. Mes, P. Y. Dankers and C. V. Bouten, Acta Biomater., 2018, 71, 247–260 CrossRef CAS PubMed.
- V. Bonito, PhD thesis, Eindhoven University of Technology, 2018.
- L. Soffer, X. Wang, X. Zhang, J. Kluge, L. Dorfmann, D. L. Kaplan and G. Leisk, J. Biomater. Sci., Polym. Ed., 2008, 19, 653–664 CrossRef CAS PubMed.
- B. C. Isenberg and R. T. Tranquillo, Ann. Biomed. Eng., 2003, 31, 937–949 CrossRef PubMed.
- H. Ahn, Y. M. Ju, H. Takahashi, D. F. Williams, J. J. Yoo, S. J. Lee, T. Okano and A. Atala, Acta Biomater., 2015, 16, 14–22 CrossRef CAS PubMed.
- G. Konig, T. N. McAllister, N. Dusserre, S. A. Garrido, C. Iyican, A. Marini, A. Fiorillo, H. Avila, W. Wystrychowski, K. Zagalski, M. Maruszewski, A. Linthurst, L. Cierpka, L. M. De and N. L'Heureux, Biomaterials, 2009, 30, 1542–1550 CrossRef CAS PubMed.
- R. Gauvin, M. Guillemette, T. Galbraith, J.-M. Bourget, D. Larouche, H. Marcoux, D. Aubé, C. Hayward, F. A. Auger and L. Germain, Tissue Eng., Part A, 2011, 17, 2049–2059 CrossRef PubMed.
- J. Johnson, D. Ohst, T. Groehl, S. Hetterscheidt and M. Jones, J. Tissue Sci. Eng., 2015, 6, 1000151 Search PubMed.

## Footnote |

† Department of Biomedical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands. E-mail: kurniawan@tue.nl |

This journal is © The Royal Society of Chemistry 2019 |