https://doi.org/10.5061/dryad.866t1g21x

Description of the data and file structure

Data is stored as CSV files (PVA_25G.csv, NC_25G.csv, NC_22G.csv, NC_20G.csv) and code stored as MATLAB Code (.m) (where its Optimisation, Statistics and Machine Learning, and Bioinformatics Toolboxes are used). Users should ensure all files (data and code) are in the same folder upon use.

File naming

Each CSV file contains print diameter measurements for one material and one nozzle geometry.

The materials include:

• A poly(vinyl alcohol)-based (PVA) hydrogel, or
• Nivea Crème (NC)

The nozzle geometries include:

• 25G (0.00025 m)
• 22G (0.00041 m), or
• 20G (0.00058 m)

There are four data sets, PVA with a 25G conical nozzle and NC with either a 25G, 22G, or a 20G conical nozzle, where a particular range of air pressures have been used in each case. Each CSV contains the air pressures used (in kPa) across the top row and the print diameter measurements (in mm) for each air pressure in its corresponding column. For each set-up and material considered, nine lines of hydrogel were continuously printed onto the build platform via extrusion-based bioprinting, with each line measured at three points (start, middle, end) providing 27 data points. For the Nivea Crème experiments, this was repeated three times for each air pressure, providing 81 data points in total.

During the study, a power-law fitting is compared with a Newtonian fitting (when n = 1). As such, two MATLAB scripts are provided, one for an arbitrary n and one for when n = 1.

The CSV files are named according to: MATERIAL_NOZZLEGEOMETRY.csv. For example, NC_20G.csv indicates the file containing the print diameter measurements for Nivea Crème with a 20G conical nozzle. There are two MATLAB scripts, Model_Fitting_Optimisation.m and Model_Fitting_Optimisation_N.m for a power-law and Newtonian fitting, respectively. 

File content

By uncommenting out the section of code corresponding to the required material/nozzle geometry combination, the air pressures (in kPa) are called in from the corresponding CSV file and stored in P and the diameter measurements (in mm) stored in data. For air pressure (1, x) of P, its corresponding diameter measurements are stored in (1:27, x) and (1:81, x) of data for PVA and Nivea Crème, respectively. P and data are then converted to SI units, to produce DeltaP (Pa) and data2 (m), respectively.

Other variables:

• D_i: nozzle inner diameter, taken to be 0.00402 (m) across all nozzle geometries
• D_o: nozzle outer diameter, taken to be 0.00025, 0.00041, and 0.00058 (m) for 25G, 22G, and 20G nozzles
• U: nozzle travel speed, taken to 0.005 (m/s), and
• L_c: nozzle length, taken to be 0.032 (m) across all nozzle geometries

An average diameter (and the standard deviation, stdev) for each pressure is calculated, and stored in means. Taking parameters, n and K, the flow behaviour and consistency indices, respectively, the fitting of the mathematical model (d) to the data (means) is optimised via objective (the minimum sum of squared residuals) and initialGuess (an appropriate initial guess for parameters [n, K] for either PVA or NC) by implementation of fminsearch.

Once convergence is achieved, the optimised parameters, n and K, are stored in bestParams, and the corresponding fitted values in fitted_model. The coefficient of pressure drop (deltaP), determined from the model, is provided in a. Statistics such as R-squared, are calculated and printed and the experimental data and model fitting plotted.

A Student's t-test is conducted and a false discovery rate (FDR) correction made in order to detect any statistical significance between the model prediction and the experimental data for each element of deltaP.

The only difference in the Newtonian script is that the flow behaviour index, n, is defined as 1, and the initialGuess (and correspondingly bestParams) comprises of only one component, a suitable initial guess for the consistency index, K (the viscosity in a Newtonian regime). It is noted that this script can be used to set n to any value (such as the average optimal n values produced across material/nozzle geometry combinations from the power-law script), but the initialGuess will need to be changed accordingly. 

Note

• The initial guess for Nivea Crème was taken from Paxton et al. [Biofabrication, 9:044107, 2017]
• With a lack of documentation on the rheology of the PVA hydrogel composition used and a Newtonian behaviour being assumed for non-Newtonian materials (in the Newtonian script case), initialGuess was chosen such that convergence was obtained