T1: Stiffness of two PAAm hydrogels¶
In this tutorial, you will quantify the stiffness of two polyacrylamide (PAAm) hydrogels. The gels were produced according to the protocol in [RLY+17] with an expected Young’s modulus of 0.8 to 1.2 kPa (compliant gel) and 25 to 28 kPa (stiff gel).
To make data analysis easier, we first divide the dataset by copying the files of the compliant gel (PAAm_Compliant_*.jpk-force) and the stiff gel (PAAm_Stiff_*.jpk-force) into two separate folders “compliant” and “stiff”.
In PyJibe, we load each of the folders using File | Open bulk data. We now have two subwindows called Force-Distance #1 and Force-Distance #2 (screenshot below).
We change the analysis pipeline in each of the subwindows as follows:
In the Fit tab, set model to spherical indenter (Sneddon, approximative). The measurements were performed using a spherical indenter. The approximative description indicates, that this model is an analytical representation of the Sneddon model (as used by the JPK analysis software). See
nanite.model.model_sneddon_spherical_approximationfor more information.
In the Fit tab, set the right range to 2 µm. This primarily helps with the visualization of the data.
In the Fit tab, uncheck the Suppress residuals near contact point check box. This feature is not necessary for PAAm gels.
In the Fit tab, set the initial parameter Tip Radius to 5 µm.
Now, click the button Apply Model and Fit All. The results should look like this, for the compliant gel…
…and for the stiff gel:
There are several things to note here:
The fit of the compliant gel looks much better than the fit of the stiff gel: There seems to be a systematic (sine-like) deviation from the fit. One could only speculate about the reason for this deviation. However, compared to the maximal indentation force (setpoint at 32 nN, see Info tab), the deviation is comparatively small.
Furthermore, the stiff gel measurements exhibit a “ringing”, which is clearly visible in the approach part. This is a result of the force-modulation feedback mode. The gel is not probed in contact mode, but in a mixture between contact mode and intermittend mode (See the NanoWizard User Manual v. 4.2, sec. 5.7.). Maybe this ringing is not visible for the compliant gel, because of the setpoint at 6n N (The setpoint likely defines the amplitude of the force-modulation feedback mode and for the compliant gels, this amplitude might be below the noise level).
The stiff gel gets a better rating than the compliant gel with the zef18 + Extra Trees rating scheme (please see the nanite rating workflow and [MAM+19] for how rating works). Of course, this observation is misleading - it nicely illustrates a limit of machine learning. The zef18 training set was created using zebrafish spinal cord section measurements. In the context of hydrogels, it does not make much sense, although it appears to be consistent and gives both, compliant and stiff gels, a “good” rating.
You might have realized that PyJibe creates the file pyjibe_fit_results_leaf.tsv in each of the measurement folders (if the Autosave fit results as .tsv check box is checked). These files contain (amongst other things) the fit results of each curve. With a simple Python script, we can visualize the Young’s modulus of the two gels:
import matplotlib.pylab as plt import searborn as sns data_compl = pandas.read_table("./compliant/pyjibe_fit_results_leaf.tsv") data_stiff = pandas.read_table("./stiff/pyjibe_fit_results_leaf.tsv") sns.set_style("darkgrid") plt.subplot(121, title="compliant hydrogel") sns.boxplot("Young\'s Modulus [Pa]", data=data_compl, fliersize=0, color="#d6ff7d") sns.swarmplot("Young\'s Modulus [Pa]", data=data_compl, size=5, color=".3", linewidth=0) plt.subplot(122, title="stiff hydrogel") sns.boxplot("Young\'s Modulus [Pa]", data=data_stiff, fliersize=0, color="#98ff80") sns.swarmplot("Young\'s Modulus [Pa]", data=data_stiff, size=5, color=".3", linewidth=0) plt.show()
The compliant hydrogel has a Young’s modulus of 1090 ± 12 Pa (mean ± SD) and the stiff hydrogel has a Young’s modulus of 27676 ± 270 Pa. These values agree well with the values we expected initially.