Test configuration
Disk (Nucleus Pulposus)
The nucleus pulposus is the central part of an intervertebral disc.
About this material
The nucleus pulposus is the central part of an intervertebral disc. It is composed of a proteoglycan-water gel embedded in a randomly oriented network of fine collagen fiber and non-collagenous proteins. One of the primary changes in disc degeneration is decreasing proteoglycans and water content within the nucleus pulpus. Knowledge on the mechanical properties of healthy nucleus pulposus will aid in the development of suitable replacement materials and successful disc degeneration treatments.
Test configurations (13)
Test configuration
Unconfined Compression
Test configuration
Indentation (Stiffness)
Test configuration
3D Thickness Mapping
Test configuration
Torsion
Test configuration
Shear
Test configuration
Temperature Control
Test configuration
Mechanical Stimulation (Shear)
Test configuration
Mechanical Stimulation (Compressive)
Test configuration
External Analog Sensors
Test configuration
Camera Feed
Test configuration
Positioning (Manual)
Test configuration
Positioning (X Auto)
Case studies (1)
Related resources (5)
FAQ
How does the "Elastic Model in Indentation" works?
This tool allows for the computing and visualizing of the shear modulus (MPa) and the Young’s modulus (MPa) from an indentation test performed using a spherical indenter (Figure 1). This model is well adapted for the mechanical characterization of samples (with critical diameter (width) at least 5 times the indenter diameter) bonded on a flat rigid support (at least 10 times stiffer than the sample), for example: any sheet of material lying on a rigid chamber base (limited sliding at the interface can be assumed) or a cartilage layer attached to a thick sub-chondral bone. A user license is required to obtain the results of the elastic model in indentation (Software Add-On, contact Biomomentum to obtain your license).
Results analysis is performed considering the indentation mechanics of an infinitely wide elastic layer bonded to a rigid half-space which has been developed as a model for the layered geometry of cartilage and subchondral bone (Hayes et al., 1972). (Figure 2) shows a schematic representing the modeled situation.
Many parameters need to be specified in order to calculate the different material properties.
1. Indenter Shape is:
- Spherical
- Plane-Ended Cylindrical
2. Indenter radius in mm.
3. Poisson ratio can be selected from a drop-down list (Figure 3)
4. Position @ contact is – defines the position of the left cursor:
- to be curvefit – will automatically find the position contact which will give the smallest mean squared error (mse)
- the value at t0 – will automatically take the position contact at the start of the curve
- the following value (mm) – the user need to specify the value in the corresponding field next to the drop-down list
- cursor position – the user can drag the left cursor to the wanted position contact
5. Sample thickness is the:
- position @ contact – will automatically find the position at contact (position of the left cursor)
- following value (mm) – the user need to specify the value in the corresponding field next to the drop-down list
6. Curvefit is up to – defines the position of the right cursor:
- peak load – will automatically take the position of the peak load
- delta load (unit) – the user need to specify the value of the desired delta load in the corresponding field next to the drop-down list
- delta position (mm) – the user need to specify the value of the desired delta position in the corresponding field next to the drop-down list
The error on the estimation of the best curve representing the stress relaxation curve is calculated using the root of the mean squares (RMS) method and is displayed under “RMSE”. For example, (Figure 4) shows parameters used for the “Normal Indentation” (Mach-1 Motion) function in an indentation testing protocol on ovine articular surfaces. Corresponding results are shown in (Figure 1).
Spherical Indentation Guide – Mach-1 Mechanical Tester – Biomomentum
Mach-1 Analysis – Elastic Model in Indentation – Parameters
Mach-1 Analysis – Elastic Model in Indentation – Poisson ratio choices
Mach-1 Analysis – Elastic Model in Indentation – Cartilage & Subchondral bone
How does the "Poroelastic Model in Confined Compression" feature works?
This tool allows for the computing and visualizing of the aggregate modulus (MPa), the permeability (mm2/MPa·s) and the mean square error (RMSE) of the fit calculated from a “Stress Relaxation” curve (load or force vs. time) in confined compression (Figure 1) on a disk sample. The curve is fitted to the linear biphasic model (Mow et al., 1980 or Bursać et al., 1999) in order to obtain the mechanical properties of the disk. Sample radius, strain and sample thickness need to be specified.
This model is well adapted for the mechanical characterization of samples containing a liquid fraction and a solid matrix, for example: cartilage or gel samples. A user license is required in order to obtain the results of the poroelastic model in confined compression (Software Add-On, contact Biomomentum to obtain your license).
Mechanical properties can be obtained from the stress relaxation curves obtained under confined compression such as the aggregate modulus (HA) and the hydraulic permeability (k). The aggregate modulus is a measure of stiffness of the sample at equilibrium while the hydraulic permeability is the ability of the fluid to flow through the cartilage matrix.
For example, (Figure 2) shows parameters used for the “Stress Relaxation” function in a confined compression testing protocol on human cartilage disks. Corresponding results are shown in (Figure 1).
This model is well adapted for the mechanical characterization of samples containing a liquid fraction and a solid matrix, for example: cartilage or gel samples. A user license is required in order to obtain the results of the poroelastic model in confined compression (Software Add-On, contact Biomomentum to obtain your license).
Mechanical properties can be obtained from the stress relaxation curves obtained under confined compression such as the aggregate modulus (HA) and the hydraulic permeability (k). The aggregate modulus is a measure of stiffness of the sample at equilibrium while the hydraulic permeability is the ability of the fluid to flow through the cartilage matrix.
For example, (Figure 2) shows parameters used for the “Stress Relaxation” function in a confined compression testing protocol on human cartilage disks. Corresponding results are shown in (Figure 1).
Mach-1 Analysis – Poroelastic Model in Confined Compression – Parameters
Mach-1 Analysis – Poroelastic Model in Confined Compression – Example
How does the "Poroelastic Model in Unconfined Compression" feature works?
This tool allows for the computing and visualizing of the fibril network modulus (MPa), the equilibrium modulus (MPa), the permeability (mm2/MPa·s), and the mean square error (RMSE) of the fit calculated from a “Stress Relaxation” curve (load or force vs. time) in unconfined compression (Figure 1) on a disk or osteochondral core sample. The curve is fitted to the linear fibril-network-reinforced biphasic model (Soulhat et al. 1999) in order to obtain the mechanical properties of the disk. Sample radius, strain, and Poisson’s ratio need to be specified. This model is well adapted for the mechanical description of samples containing a liquid fraction and a fibril network, for example: cartilage or gel samples. A user license is required in order to obtain the results of the poroelastic model in unconfined compression (Software Add-On, contact Biomomentum to obtain your license).
The nonhomogeneous composite model (i.e. linear fibril-network-reinforced biphasic model) is an extension of the previously developed isotropic homogeneous biphasic model, and was achieved by reinforcing the latter with a network of nonlinear fibrils distributed homogeneously in the r, θ, z directions and which resist extension only (Figure 2). The isotropic matrix is described by the drained elastic constants Em (Young’s modulus), vm (Poisson’s ratio) and a hydraulic permeability k. The fibril network is described by the Young’s modulus of individual fibrils ef which, combined with a fibril volume fraction χ (fibrils volume/ total-volume), results in an equivalent tensile modulus of the fibril network, Ef = 1/3 χ ef (since 1/3 of the fibrils are oriented in each of three mutually orthogonal directions).
For example, (Figure 3) shows parameters used for the “Stress Relaxation” function in an unconfined compression testing protocol on ovine cartilage disks. Corresponding results are shown in (Figure 1).
The nonhomogeneous composite model (i.e. linear fibril-network-reinforced biphasic model) is an extension of the previously developed isotropic homogeneous biphasic model, and was achieved by reinforcing the latter with a network of nonlinear fibrils distributed homogeneously in the r, θ, z directions and which resist extension only (Figure 2). The isotropic matrix is described by the drained elastic constants Em (Young’s modulus), vm (Poisson’s ratio) and a hydraulic permeability k. The fibril network is described by the Young’s modulus of individual fibrils ef which, combined with a fibril volume fraction χ (fibrils volume/ total-volume), results in an equivalent tensile modulus of the fibril network, Ef = 1/3 χ ef (since 1/3 of the fibrils are oriented in each of three mutually orthogonal directions).
For example, (Figure 3) shows parameters used for the “Stress Relaxation” function in an unconfined compression testing protocol on ovine cartilage disks. Corresponding results are shown in (Figure 1).
Mach-1 Analysis – Poroelastic Model in Unconfined Compression – Parameters
Mach-1 Analysis – Poroelastic Model in Unconfined Compression – Cartilage
Mach-1 Analysis – Poroelastic Model in Unconfined Compression – Example
How does the "Sinusoid" model works?
This feature is used to obtain the Frequency, Amplitude and Offset of a sinusoidal signal. A blue line displays the theoretical sinusoid with the Frequency, Amplitude and Offset obtained (Figure 1). The values of the Frequency, Amplitude and Offset are indicated in the "Results" field. The units vary according to the graph’s axes.
This feature can also be used for sinusoidal stimulus-response analysis. Sinusoidal stimulus shall be selected on the x-axis and the sinusoidal response on the y-axis. The Modulus is the ratio of the response Amplitude over the stimulus Amplitude. The Phase is the phase difference between the response and the stimulus. The Modulus’ is computed as the Modulus*Cos(Phase) and the Modulus” is computed as the Modulus*Sin(Phase). A blue line displays the theoretical sinusoidal stimulus-response with the Frequency, Modulus and Phase obtained (Figure 2). The values of the Modulus and Phase are indicated in the “Results” field. The units vary according to the graph’s axes.
One use for this feature would be to compute material properties by multiplying the Modulus obtained by the appropriate geometric factors. For example, the Young’s Modulus can be obtained during uniaxial compression or tension on cylindrical sample with t/pi*r2 as the geometric factor, t is the thickness and r is the radius of the sample.
Mach-1 Analysis – Sinusoid – Example for stimulus-response analysis
What is an aggregate modulus?
The aggregate modulus (Ha) corresponds to the stiffness of the material at equilibrium when fluid has ceased flowing through it in a confined compression test configuration. The aggregate modulus can be calculated from Young's modulus (E) and the Poisson ratio (v) using the formula Ha=E(1-v)/[(1+v)(1-2v)].
How does the creep function works?
The Creep function moves a stage until a predefined load variation (Load Target (relative to initial load)) is reached and maintains this loading through real-time closed-loop PID adjustment of the stage position. This function can be used, for example, to study the deformation of a sample under constant loading. Note that tuning a PID requires a reasonable amount of closed-loop system understanding. A set of PID parameters optimized for a particular experimental configuration will probably be inappropriate for a different configuration and could even create system instabilities (oscillations) that can result in damage to the system.
Parameters:
STAGE AXIS - On multi-axis systems, the user must specify which axis will perform the “Creep”.
DIRECTION - Specify if the stage has to start moving in the positive or negative direction. With a positive displacement, a vertical stage will move down (compression), a horizontal stage will move right, and a rotation stage will move clockwise. Enter a negative value for stage displacements in opposite directions.
STAGE VELOCITY, MM/S - Specify the speed at which the stage will move. Refer to the specifications of your Mach-1™ model to learn about the velocity range allowed. In Mach-1 Motion, the speed is always specified in absolute value terms.
RELATIVE LOAD TARGET, GF OR N - Specify the relative amount of load to be applied and maintained on the sample. When a value is entered, the stage will initiate its movement until a change in load of that magnitude is reached. The value for Relative Load Target is specified in absolute value terms.
CREEP TIME, SEC - This is the time period during which the relative loading will be maintained. Note that after this period, the final stage position will be maintained.
P GAIN - This is the Proportional gain of the PID control loop. This is the main parameter that drives the feedback loop. Our experiments revealed that a good starting point for the optimization of this parameter is given by P = 0.001 (and I = 0), then raising P in logarithmic increments (0.01, 0.1, 1) until a satisfactory amplitude in reached. The higher the P value, the faster the error will be corrected, however if the P is made too large, the error can go negative (actual load > desired load) which may start a process where the stage starts to oscillate between speeding up and slowing down. This oscillation can result in the motor control system going unstable. A simple way to eliminate this instability would be to decrease P until the oscillation stops.
I GAIN - This is the Integral gain of the PID control loop. Integral control sums the error from each position update then multiplies the sum by the Integral gain, I. Our experiments revealed that for most creep tests, best results are achieved with I = 0. If a residual error exists while holding a load, the I value can also be incrementally increased until the error disappears.
What is viscoelasticity?
Property of a material to exhibit both viscous and elastic characteristics when undergoing deformation. Such material will show time-dependent mechanical behavior.
LAB MODULE – Torsion of Disk-Shaped Samples – Student Version
What is the elasticity?
Property of a material to deform under load or strain and to return to its original shape when the stress is released.
LAB MODULE – Unconfined Compression of Hydrogel Disks – Student Version