Designing Anatomical Organ Replicas

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Anatomically realistic organ replicas provide more consistent results than the use of a living subject or cadaver. In the case of a kidney replica, the related work did neither deal with its design, nor its development using silicone as the only material. The major challenge and objective of silicone-based organ replicas is the mimicry of their mechanical properties. 
To reach certain organ-specific mechanical properties, we first investigated the response of silicone mixtures to compression. As reported in a recent study, compression tests were conducted with kidneys derived from human beings (1). Our work not only replicates the entire study with several compositions of two commercially available silicones, but also provides a two step experimental pipeline to conduct Uniaxial Compression (UC) testing and validate the measurements using Cauchy stress modeling. 

First, to prepare for UC testing, the silicones were mixed with their respective thinners in several proportions. The resulting silicone mixtures were molded, then cured in a vacuum chamber until full polymerization was reached. To prepare for the measurements using UC testing, cylindrical samples were cut out using a biopsy punch. Measurements were conducted with repeated testing of multiple charges in order to reduce bias as a result of manually preparing the different silicone mixtures. The compression tests were carried out by compressing the cylinders uniformly through two plates. Ten replicates per batch were tested with at least two batches per silicone mixture. Force and distance were obtained from the measurements which were recalculated into stress and strain. Stress and strain were then used for data modeling as well as the calculation of the elastic moduli.

Second, Cauchy stress modeling relied on two different regression approaches: non-linear and segmented. On one hand, the non-linear regression model describing the stress-strain relationship as a Blatz function was fitted to the data. We reflected the population structure by accounting for both the nested experiment design and the repeated measurements. Indeed, one of the coefficients of the Blatz function was considered to be random. On the other hand, the segmented linear regression was used to estimate three important values: the low (E1) and high-strain (E2) elastic moduli, and the maximum reachable stress (Emax). 
The initial approximation for the change points between the segments has been set at the nominal stress of 30%, 40% and 60%, which are the values between which the stress-strain relationship becomes almost linear. The statistical analysis was carried out using the R packages lmerTest and segmented.

Although the pipeline revealed that none of the available manufacturer silicone brands are suitable for the task of creating a realistic kidney, we were able to present a reference for future work concerned by the task of designing mechanically realistic organ replicas. Besides providing all measurements and curated data from the UC testing as well as the source code for the Cauchy stress modeling and technical validation, we found that: 

  1. the silicones advertised as corresponding to the target ranges of elastic properties of a human kidney do not fall within the required target compression moduli,
  2. the data we’ve shared showcases less variability and uncertainty (inc. low (E1) and high (E2) strain moduli), 
  3. the (Emax) occurs at a much later stage,
  4. the maximal reachable stress of the tested silicone mixtures is larger than literature-based reports, and
  5. the parameters characterizing the nonlinear elastic model of the silicone mixtures are made available for the purpose of nonlinear finite element simulation of an entire kidney.

For more information, please refer to the full paper at Scientific Reports and the corresponding scripts and data at the Materials Cloud Archive.

(1) Snedeker, J. G., Barbezat, M., Niederer, P., Schmidlin, F. R., & Farshad, M. (2005). Strain energy density as a rupture criterion for the kidney: impact tests on porcine organs, finite element simulation, and a baseline comparison between human and porcine tissues. Journal of Biomechanics, 38(5), 993-1001.

Georges Hattab

Junior group leader, Dept. of Mathematics and Computer Science, Philipps-University Marburg, Germany

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