Summary
This article presents a demonstration and summary of protocols of making gelatin phantoms that mimic soft tissues, and the corresponding viscoelastic characterization using indentation and magnetic resonance elastography.
Abstract
Characterization of biomechanical properties of soft biological tissues is important to understand the tissue mechanics and explore the biomechanics-related mechanisms of disease, injury, and development. The mechanical testing method is the most straightforward way for tissue characterization and is considered as verification for in vivo measurement. Among the many ex vivo mechanical testing techniques, the indentation test provides a reliable way, especially for samples that are small, hard to fix, and viscoelastic such as brain tissue. Magnetic resonance elastography (MRE) is a clinically used method to measure the biomechanical properties of soft tissues. Based on shear wave propagation in soft tissues recorded using MRE, viscoelastic properties of soft tissues can be estimated in vivo based on wave equation. Here, the viscoelastic properties of gelatin phantoms with two different concentrations were measured by MRE and indentation. The protocols of phantom fabrication, testing, and modulus estimation have been presented.
Introduction
Most of the soft biological tissues appear to have viscoelastic properties that are important to understand their injury and development1,2. In addition, viscoelastic properties are important biomarkers in the diagnosis of a variety of diseases such as fibrosis and cancer3,4,5,6. Therefore, the characterization of viscoelastic properties of soft tissues is crucial. Among the many characterization techniques used, ex vivo mechanical testing of tissue samples and in vivo elastography using biomedical imaging are the two widely used methods.
Although various mechanical testing techniques have been used for soft tissue characterization, the requirements for sample size and testing conditions are not easy to be satisfied. For example, shear testing needs to have samples fixed firmly between the shear plates7. Biaxial testing is more suitable for membrane tissue and has specific clamping requirements8,9. A compression test is commonly used for tissue testing, but cannot characterize specific positions within one sample10. The indentation test does not have additional requirements to fix the tissue sample and can be used to measure many biological tissue samples such as the brain and liver. In addition, with a small indenter head, regional properties within a sample could be tested. Therefore, indentation tests have been adopted to test a variety of soft tissues1,3,11.
Characterizing the biomechanical properties of soft tissues in vivo is important for translational studies and clinical applications of biomechanics. Biomedical imaging modalities such as ultrasound (US) and magnetic resonance (MR) imaging are the most used techniques. Although US imaging is relatively cheap and easy to carry out, it suffers from low contrast and is hard to measure organs such as the brain. Capable of imaging deep structures, MR Elastography (MRE) could measure a variety of soft tissues6,12, especially the brain13,14. With applied external vibration, MRE could measure the viscoelastic properties of soft tissues at a specific frequency.
Studies have shown that at 50-60 Hz, the shear modulus of the normal brain is ~1.5-2.5kPa5,6,13,14,15 and ~2-2.5 kPa for normal liver16. Therefore, gelatin phantoms that have similar biomechanical properties have been widely used for mimicking soft tissues for testing and validation17,18,19. In this protocol, gelatin phantoms with two different concentrations were prepared and tested. Viscoelastic properties of the gelatin phantoms were characterized using a custom-built electromagnetic MRE device14 and an indentation device1,3. The testing protocols could be used for testing many soft tissues such as the brain or liver.
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Protocol
1. Gelatin phantom preparation
- Weigh gelatin, glycerol, and water according to Table 1. Mix the gelatin powder with water to obtain the gelatin solution.
NOTE: The concentrations of the individual components for preparing the two phantoms are shown in Table 1. The higher the concentration of gelatin, the stiffer the phantom. - Heat the gelatin solution to 60 °C in a water bath. Add glycerol to the gelatin solution while maintaining the temperature.
NOTE: Glycerol stabilizes gelatin mixtures by increasing their melting temperature and shear modulus17. - Stir the solution and heat it to 60 °C again. Pour the mixed solution into a container that will be used for MRE and indentation tests. Cool the solution to room temperature and wait till the solution is solidified.
2. MRE test
- Put the vibration plate on top of the gelatin phantom. Ensure that the contact between the phantom and the vibration plate is firm (Figure 1A).
NOTE: The vibration plate is made of Polyamide with a dimension of 50 x 50 x 5 mm3. - Place the gelatin phantom into the head coil. Put sponges and sandbags around the gelatin phantom to make sure the phantom is firmly placed. Use a custom-built electromagnetic actuator with a transmission bar14,18. Mount an electromagnetic actuator on the head coil. Connect the transmission bar to the vibration plate (Figure 1B).
- Connect the power lines of the actuator with the amplifier. Connect the control lines with the controller (Figure 1C).
- Actuator and MRI scan parameter settings
- Set the waveform, vibration frequency, and amplitude in the function generator. Set the desired vibration amplitude by adjusting the power amplifier.
NOTE: Here, the waveform is set to sinusoidal in the function generator; the vibration frequency is set to 40 Hz or 50 Hz, and the amplitude is set to 1.5 Vpp. In the power amplifier, the amplification ratio is set to 40%. - Set the function generator to work in the trigger mode. Connect the trigger line to the external trigger port of the MRI machine.
- Set the MRE scanning (actuator) frequency the same as that from the function generator, so that the motion encoding gradient is synchronized with the motion of the vibration plate.
- Set the waveform, vibration frequency, and amplitude in the function generator. Set the desired vibration amplitude by adjusting the power amplifier.
- Data measurement and analysis
- Follow the routine imaging positioning procedures. Use a 2D gradient-echo (GRE) based MRE sequence for imaging of the gelatin phantom20. Set the GRE-MRE imaging parameters as follows: Flip-angle = 30°; TR/TE = 50/31 ms; Field-of-view = 300 mm; Slice thickness = 5 mm; Voxel size = 2.34 x 2.34 mm2.
- Measure the phase images at four temporal points in one sinusoidal cycle. Apply both positive and negative motion encoding gradients at each time point.
- Based on the phase image acquired, remove the background phase by subtracting the positive and negative encoded phase images. Unwrap the phase with a reliability sorting-based algorithm21.
- Extract the principal component of the motion by applying fast Fourier Transform to the unwrapped phase images. Filter the phase image with a digital bandpass filter. Estimate the shear modulus with a 2D direct inversion (DI) algorithm to obtain storage modulus G' and loss modulus G''13,14.
NOTE: The cut-off frequency of the bandpass filter is [0.04 0.08]. The size of the fitting window of the DI algorithm is 11 x 11.
3. Indentation test
- Use a circular punch or surgical blade to trim the gelatin phantom into a cylindrical or cuboid sample, respectively. Make sure that the sample thickness is between 3 and 10 mm and the diameter of the cylindrical sample or the long side of the cuboid is larger than 4 mm. Use a sharp blade to trim the surface of the sample to make it as smooth as possible for indentation.
- Turn on the power of the indentation tester. Perform the following using the indenter control program designed to automate the indenter contact procedure (custom program; see Table of Materials).
- Click on the Back off button in the GUI to initialize the calibration process (Figure 2B). Read the value from the laser sensor and type the value in the BaseLine box.
NOTE: During the calibration process, the distance between the laser sensor and the baffle plate is adjusted to a specific pre-defined value. - Place a glass slide on the baffle plate and record the value shown by the laser sensor. Next, put the sample on the glass slide and place them together on the baffle plate. Read the value from the laser sensor and type this value in the Sample+Slide box.
NOTE: The laser sensor is used to record the displacement of the indentation, but it is also used to measure the sample thickness before the test. - Take the difference between the two values obtained in step 3.2.2 as the sample thickness at the region of interest (ROI).
- Carefully place the sample along with the underlying glass slide right below the indenter, and then click on the Contact button to initiate automatic contact between the indenter and the sample surface.
NOTE: If the automatic contact is not satisfactory, i.e., the indenter presses deep into the sample or does not have a contact, adjust the indenter position by typing a value in the range of 0.05-0.1 mm in the Offset box and repeat steps 1.2.1-1.2.4. - Based on the measured sample thickness (step 3.2.3), estimate the indentation displacement (i.e., total indentation depth) by multiplying the thickness with the indented testing strain (here, it is set to ≤8% to keep the indentation within the small strain assumption).
- Type the displacement values (step 3.2.5) in the Displacement (mm) box. Set the relaxation time to 180 s in the Dwell Time box. Click on the Indentation button. The displacement and reactive force during the ramp-hold procedure will be automatically recorded and saved in a file at the specified File Path.
NOTE: The File Path can be pre-defined as the path for saving testing data.
- Click on the Back off button in the GUI to initialize the calibration process (Figure 2B). Read the value from the laser sensor and type the value in the BaseLine box.
- Export the indentation data to a spreadsheet. Use a two-term Prony series
to fit the force relaxation curve1,3,11:
- Estimate the instantaneous shear modulus (G0) and long-term shear modulus (G∞) based on the fitted parameters:
NOTE: In the above equations, C0, Ci, and τi are model parameters of the Prony series, F is the indentation force, R is the radius of the indenter, X is the compensation factor for the infinite half space assumption, V is the indentation velocity, t is the time variable, and tR is the ramp time.
to fit the force relaxation curve1,3,11:
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Representative Results
Following the MRE protocol, a clear shear wave propagation in the gelatin phantoms at 40 and 50 Hz were observed (Figure 3). The viscoelastic properties measured from MRE, and indentation tests are shown in Figure 4. The estimated G' and G" values at each testing for each phantom are summarized in Table 2. Following the indentation protocol, the viscoelastic properties of each phantom at each test point are summarized in Table 3.
As shown in Figure 4, for measurements using MRE, a comparison of G' and G" values measured at 40 and 50 Hz showed significant differences between the two gelatin phantoms (student's t-test, p < 0.05). In addition, significant differences were observed for both G' and G" values between 40 and 50 Hz measurements (student's t-test, p < 0.05). Similarly, for measurements using indentation test, significant differences between the two phantoms were observed for G0 and G∞ values (student's t-test, p < 0.05). Both MRE and indentation provided consistent results for distinguishing soft and stiff gelatin phantoms.
Figure 1: MRE test. (A) Put the vibration plate on top of the gelatin phantom. (B) Place the gelatin phantom inside the head coil and mount the electromagnetic actuator on top of the head coil. (C) An overview of the electromagnetic MRE system showing the connections between each component. Please click here to view a larger version of this figure.
Figure 2: Indentation test. (A) Put the gelatin phantom right under the indenter head in the tester. (B) Prepare the indentation using the Control Setup panel in the GUI. Input the indentation parameters in the GUI to set up the ramp-relaxation test. Observe the indentation curves in the Data Viewer window. Please click here to view a larger version of this figure.
Figure 3: Wave propagation images for the two gelatin phantoms at 40 and 50 Hz. The four phases correspond to the four temporal points at one sinusoidal cycle. Please click here to view a larger version of this figure.
Figure 4: Viscoelastic properties measured from MRE and indentationexperiments. (A) Typical estimated G' and G'' maps at 40 and 50 Hz for the two gelatin phantoms from MRE. (B) Mean and standard deviation of the G0 and G∞ values for the two phantoms from six repeated indentation tests. (C) Mean and standard deviation of the G' and G'' values at 40 and 50 Hz for the two phantoms from six repeated MRE tests. The asterisk symbol indicates a significant difference (student's t-test; p < 0.05). Please click here to view a larger version of this figure.
| Gelatin | Water | Glycerol | Total | |
| Phantom 1 | 100 (4.35%) | 1200 (52.17%) | 1000 (43.48%) | 2300 (100%) |
| Phantom 2 | 160 (6.96%) | 1140 (49.56%) | 1000 (43.48%) | 2300 (100%) |
Table 1: The mass and mass concentration of the gelatin, glycerol, and water used for preparing the two gelatin phantoms. The mass unit is grams.
| Modulus(Pa) | Test 1 | Test 2 | Test 3 | Test 4 | Test 5 | Test 6 | Mean | Std | ||
| Phantom 1 | 40 Hz | G' | 2978 | 2976 | 2976 | 2974 | 2971 | 2972 | 2975 | 3 |
| G'' | 198 | 197 | 197 | 198 | 199 | 199 | 198 | 1 | ||
| 50 Hz | G' | 2854 | 2852 | 2852 | 2851 | 2850 | 2848 | 2851 | 2 | |
| G'' | 341 | 342 | 342 | 342 | 341 | 341 | 341 | 1 | ||
| Phantom 2 | 40 Hz | G' | 5603 | 5589 | 5596 | 5590 | 5586 | 5588 | 5592 | 7 |
| G'' | 419 | 412 | 419 | 413 | 408 | 408 | 413 | 5 | ||
| 50 Hz | G' | 5343 | 5341 | 5336 | 5336 | 5329 | 5331 | 5336 | 6 | |
| G'' | 317 | 317 | 318 | 324 | 321 | 323 | 320 | 3 | ||
Table 2: Storage modulus (G') and loss modulus (G") of the two gelatin phantoms measured by MRE. Each phantom was tested six times at an actuation frequency of 40 and 50 Hz.
| Test 1 | Test 2 | Test 3 | Test 4 | Test 5 | Test 6 | Mean | Std | ||
| Phantom 1 | C0 | 1.54 | 1.88 | 1.81 | 1.71 | 1.65 | 1.60 | 1.70 | 0.13 |
| C1 | 0.64 | 0.16 | 0.09 | 0.16 | 0.16 | 0.21 | 0.23 | 0.20 | |
| C2 | 0.10 | 0.12 | 0.15 | 0.11 | 0.13 | 0.11 | 0.12 | 0.02 | |
| τ1 (s) | 459.71 | 177.52 | 114.14 | 7.32 | 6.1 | 3.73 | 128.09 | 177.51 | |
| τ2 (s) | 9.83 | 6.38 | 5.83 | 199.28 | 200.2 | 55.78 | 79.55 | 94.98 | |
| R2 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 0.99 | 1.00 | 0.00 | |
| G0 (Pa) | 2273 | 2145 | 2040 | 1991 | 1935 | 1920 | 2051 | 136 | |
| G∞ (Pa) | 1535 | 1875 | 1808 | 1714 | 1650 | 1601 | 1697 | 128 | |
| Phantom 2 | C0 | 5.97 | 6.29 | 6.16 | 6.20 | 6.14 | 6.11 | 6.14 | 0.11 |
| C1 | 0.29 | 0.30 | 0.43 | 0.38 | 0.18 | 0.48 | 0.34 | 0.11 | |
| C2 | 0.64 | 0.24 | 0.24 | 0.17 | 0.39 | 0.18 | 0.31 | 0.18 | |
| τ1 (s) | 5.99 | 3.50 | 2.46 | 2.71 | 69.34 | 2.36 | 14.39 | 26.95 | |
| τ2 (s) | 96.28 | 124.98 | 123.87 | 88.01 | 2.34 | 63.35 | 83.14 | 45.88 | |
| R2 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 0.00 | |
| G0 (Pa) | 6899 | 6827 | 6825 | 6751 | 6710 | 6771 | 6797 | 67 | |
| G∞ (Pa) | 5967 | 6286 | 6160 | 6197 | 6144 | 6113 | 6145 | 105 |
Table 3: Viscoelastic parameters estimated from indentation tests for the two gelatin phantoms. Each phantom was tested six times.
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Discussion
Gelatin phantoms are commonly used as tissue-mimicking materials for testing and validation of algorithms and devices17,19,22,23,24,25,26,27. One of the pioneering studies using the gelatin phantom to compare MRE and dynamic shear testing was presented by Okamoto et al. (2011)17. In their study, the mass concentration of the gelatin was ~2.8%, and the estimated G' and G'' values after correction were in the ranges of 1.06-1.15 kPa and 0.11-0.27 kPa, respectively. Zeng et al. (2020)19 also used gelatin phantom to validate the inversion algorithm for MRE. With a gelatin mass concentration of ~3.5%, the estimated G' value was ~2.5 kPa. Since the shear modulus increases with the concentration of gelatin, these values were all consistent with the estimation in this study.
To make gelatin phantoms, it is noted that a complete and thorough stirring is required when mixing a large amount of gelatin powder with water. This is necessary for full dissolution to make homogenized phantoms. To increase the melting temperature and shear modulus, glycerol was added to the mixture17. The water bath at around 60 °C will help accelerate the mixing and is recommended during the stirring process. Usually, the gelatin will be formed in a container with a specific shape, e.g., cube or cylinder. Therefore, it is important to filter out the bubbles before pouring the mixed solution into the container.
When preparing for the MRE test, a stable transmission of the shear wave is crucial. Therefore, it is necessary to make sure the vibrating plate is firmly pressed on top of the phantom. This is to avoid any possible slipping between the plate and the phantom. However, this will potentially bring a certain level of local pre-stress. Thus, it is important not to over-press the plate on the phantom. When setting up the actuation frequency, it is noted that the damping of the wave propagation increases with the frequency.
It is suggested to place the indentation device on a vibration isolation table. This is because even a small vibration will affect the ramp-hold recording process. In addition, re-calibration of the sensors is needed if the device has not been used for more than 1 month.
To have the best measurement performance of MRE, it is suggested to keep the frequency within 100 Hz. This is because the higher the frequency, the more dissipation of the vibration, thus inducing a lower SNR of the images acquired. The indentation test mainly measures the sample at a frequency range lower than that of MRE. For a discussion of the parameter conversions between the two methods, one can refer to Chen et al. (2020)11. The MRE and indentation can be used to measure many soft biological tissues to investigate the biomechanical properties and explore the potential biomechanics-based biomarkers for disease diagnosis or treatment evaluation.
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Disclosures
Authors declare no conflicts of interest.
Acknowledgments
Funding support from the National Natural Science Foundation of China (grant 31870941), Natural Science Foundation of Shanghai (grant 22ZR1429600), and the Science and Technology Commission of Shanghai Municipality (grant 19441907700) is acknowledged.
Materials
| Name | Company | Catalog Number | Comments |
| 24-channel head & Neck coil | United Imaging Healthcare | 100120 | Equipment |
| 3T MR Scanner | United Imaging Healthcare | uMR 790 | Equipment |
| Acquisition board | Advantech Co | PCI-1706U | Equipment |
| Computer-Windows | HP | 790-07 | Equipment |
| Electromagnetic actuator | Shanghai Jiao Tong University | Equipment | |
| Function generator | RIGOL | DG1022Z | Equipment |
| Gelatin | CARTE D’OR | Reagent | |
| Glycerol | Vance Bioenergy Sdn.Bhd | Reagent | |
| Indenter control program | custom-designed | Software; accessed via: https://github.com/aaronfeng369/FengLab_indentation_code. | |
| Laser sensor | Panasonic | HG-C1050 | Equipment |
| Load cell | Transducer Technique | GSO-10 | Equipment |
| MATLAB | Mathworks | Software | |
| Power amplifier | Yamaha | A-S201 | Equipment |
| Voice coil electric motor | SMAC Corporation | DB2583 | Equipment |
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