With Shape-Out, it is possible to translate the measured area and deformation to the Young’s modulus based on numerical simulation for fully elastic spheres according to Mokbel et al. [MMM+17].
The theoretical background, including the computation of the viscosity for the MC-PBS media used in RT-DC, is discussed in more detail in the dclab docs.
For reservoir data, the Young’s modulus cannot be computed. The corresponding options are hidden.
The parameters for computing the Young’s modulus can be set in the Dataset tab of the Analysis View. The Young’s modulus is computed using a precomputed look-up table and additionally depends on channel width, flow rate, pixel size (pixelation correction), and viscosity. For known media, such as CellCarrier, the viscosity can be derived from channel width, flow rate, and temperature. In some RT-DC setups, the chip temperature is recorded during the measurement. For instance, in Fig. 15, the average chip temperature of 22.5°C from the [setup] metadata section is used. The value of the resulting viscosity is shown below. If the chip temperature is recorded for each event, then the user may select the From feature option (Fig. 16). In this case, the Young’s modulus is computed from the individual viscosities for each event.
If the temperature is not given as a feature or as metadata, then you may select the temperature manually. This case is visualized in Fig. 17. Here, the temperature is purposely set outside of the known range defined in [BBN+23], which is highlighted by coloring the viscosity red.
You may also set the viscosity manually by selecting other as a medium (Fig. 18). In this case, the values for temperature are irrelevant. Please only use this option if you know what you are doing (e.g. you have considered shear-thinning and temperature-dependence [BBN+23, Her17]).
Click Apply for any changes to take effect. The Young’s modulus is then available for the selected dataset.
In order to prevent users from doing a wrong analysis, Shape-Out does not allow users to change the buffer in the Dataset tab if CellCarrier, CellCarrier B or water/PBS were selected in Shape-In. Therefore, the analysis of the Young’s modulus cannot be re-done for a different buffer.
The Bulk action menu has an entry for Young’s modulus computation. In the associated dialog you can set the corresponding parameters for all datasets of the current session. Note that the options in this dialog do not necessarily reflect the options available for the individual datasets. Only valid options are adopted. For instance, you will not be able to change the medium for a dataset if a medium is already given in its metadata. To verify the options set, you can always check the current setting via the Analysis View (see above).
The computation of the Young’s modulus is valid only for objects that initially have a spherical shape. In addition, the deformation and size values must be in a “valid region”. Events outside this region will have a nan-valued (not a number) Young’s modulus. Note that as a result, these events will be excluded from all plots when remove invalid events is checked in the Filter configuration tab.
The invalid regions (white in the figure above) include objects that are very small or objects with very low deformation values. The reason for that is a very steep increase of the Young’s modulus with little decrease in deformation that could potentially result in very large simulation errors. In addition, regions with high deformation are invalid as well, because the simulations do not converge (objects simulated with lower Young’s moduli become more and more elongated until they rupture). In practice, this means that the channel size has to be selected carefully to match the object sizes. Larger object sizes require wider channels if meaningful values for the Young’s modulus are to be computed.
In the following, additional visualizations for other commonly used channel sizes and flow rates are shown:
As described above, the Young’s modulus can be derived in multiple ways, for known media and global or event-based temperature values. The underlying implementation is described in the dclab docs.