Cryopreservation is beset with the challenge of protocol alignment across a wide range of cell types and process variables. By taking a cross-sectional assessment of previously published cryopreservation data (sample means and standard errors) as preliminary meta-data, a decision tree learning analysis (DTLA) was performed to develop an understanding of target survival using optimized pruning methods based on different approaches. Briefly, a clear direction on the decision process for selection of methods was developed with key choices being the cooling rate, plunge temperature on the one hand and biomaterial choice, use of composites (sugars and proteins as additional constituents), loading procedure and cell location in 3D scaffolding on the other. Secondly, using machine learning and generalized approaches via the Naïve Bayes Classification (NBC) method, these metadata were used to develop posterior probabilities for combinatorial approaches that were implicitly recorded in the metadata. These latter results showed that newer protocol choices developed using probability elicitation techniques can unearth improved protocols consistent with multiple unidimensionally-optimized physical protocols. In conclusion, this article proposes the use of DTLA models and subsequently NBC for the improvement of modern cryopreservation techniques through an integrative approach.

Cryopreservation of cells often results in cell survivals that are lower because of suboptimal process variables. When cryopreservation is performed in biological constructs (including encapsulated cells), the results are often worse due to the differentials in cryoprotectant (CPA) concentration, CPA exposure times and cooling rates. These differences are exaggerated for cells that are farthest from the surface which is typical for large specimens (

In using a decision-tree learning analysis (DTLA) approach, it is necessary to leverage existing principles in cryopreservation. The entrapment of CPAs within the capsule during cell resuspension in encapsulating material is an alternative strategy to the modulation of cell location. However, intracellular CPAs are often toxic and encapsulation is not lossless. Hence, when a potentially cytotoxic CPA such as DMSO is added to the encapsulating material, cell survival is often diminished (

Besides using proteins and intracellular CPAs, synthetic non-penetrating polymers (SNPP) can also provide cryoprotection within the scaffold, thereby bypassing the limitations of diffusion in higher-dimensional cryopreservation. A subclass of these SNPPs are the vitrifying polymers which have been used to encourage extracellular vitrification of the cryopreservative during cooling thereby limiting ice crystal growth (

Shifting the focus from solutes to encapsulates, changing the encapsulation material (the matrix) properties by using polymer composites can be avoided if one entraps lower molecular weight encapsulates. One alternative would be to use low molecular weight polymers. Another would be to use sugars with cryoprotective properties. The mechanism for cryoprotection conferred by sugars is three-fold: complex sugars can inhibit the formation of ice (

Each of the techniques mentioned can be represented as random decision variables (

Once the requirement for broader applicability of a learned model is defined, a more general approach to making predictions on related but distinct data sets is required. In this latter case, the Naïve Bayes Classifier (NBC) presents a more efficient and direct approach to prediction. The assumption of

This paper seeks to demonstrate the promising strategies for successful cryopreservation of cells in 3D scaffolds by using a DTLA approach to develop a heuristic for approaching cryopreservation across many subjects. Given this cryopreservation challenge specifically concerns the opportunities in 3D cryopreservation; success is measured by a cell survival percentage that is either equal to or better than suspension cryopreservation.

Data was collected and categorized into the main decision factors namely: dimensionality, cell location, use of a biomaterial, lyoprotection, CPA loading, use of integrins, CPA type, containment, cell line, cooling rate and plunge temperature (11 features) against 153 instances. Where original data was not present, the mean and standard error were used to redraw virtual samples from the original population described by the sample parameters. The predicted property is the survival (as a percent for DTLA with regression or as a category for classification with NBC i.e., long-surviving or short-surviving)

While there are many studies that could be incorporated, the key requirement was the explicit description of decision factors that were continuous from study to study; additionally, the studies were chosen to be different enough to incorporate diverse decision factors but of sufficient relational value as to allow a successful DTLA and/or NBC analysis without algorithmic or model instability—in this regard, many failures were met when studies failed to have the same number of sufficient match critical factors (though of overall good cryopreservation results) to allow acceptable predictions and classifications.

Analysis was performed using

In brief, the collected data (

The DTLA process involves the development of a loss function, computation of a residual over which the learner model is fit. To minimize the loss function, a multiplier is chosen such that through the reapplication of the learner on the training set, the loss function successively diminishes until the tree is fully constructed (

The

From

A recursive partitioning in detail showing the hot-spots at “Integrins,” “Sucrose” and “controlled seeding.” The validation scores were 77% (match) and 23% (failed) for the DTL model.

Given the differentials in cell survival for 3D capsules, the provision of optimized cryoprotection throughout the scaffold has been shown to improve overall cell survival and to minimize differentials along the construct radius (

From

From

A line plot of the R-squared for each branch added at each step in the generation of the decision tree learning model. The prediction is the cell survival (a continuous variable) after cryopreservation.

Further analysis with augmented data (

(A) A metadata analysis of cryopreservation data showing that the right-side analysis is conserved across methods—Temperatures are in °C and Cooling rates in °C/min; (B) plot showing coefficient of determination during model validation; the corresponding classification scores for test data are at 84% correct match and 16% misclassification.

Before a generalization can be developed, an examination of patterns to follow in the construction of the generalizable classifier is required—

A scatter plot matrix capturing the summary statistics for the meta-data collected from previous analyses used to develop a heuristic for predicting the posterior survival probabilities for cells for a given set of process decisions (

(A) A change in survival against the plunge temperature set point against which the prediction changes the ‘leaf’ value. (B) A 2D plot of the survival rate against plunge temperature was drawn from a DTL analysis. The cooling rate is used to lower the temperature from CPA loading temperature (temperature when cells are exposed to CPA for equilibration) to the plunge temperature—this rate is a separate decision factor (see methods section).

Prediction of survival using the Naïve Bayes Classifier on the following factors: dimensionality, location, biomaterial, sugars, step-loading & integrins. The training set has a 79% accuracy while the smaller test set has an 89% accuracy showing that the Naïve Bayes Classifier is a demonstrably accurate predictor even when reduced to a smaller test set where the samples are all cryopreserved in 3D natural RGD-containing biomaterials using controlled slow-cooling with sucrose for lyoprotection, in a two-step loading process. (Similar to the optimal leaves from the recursive partitioning trees developed earlier.) Cross-validations are 10-fold (i.e.,

A synthesis of the previous analyses shows that the use integrin ligands improve cell survival sharply—this result has been verified in more recent publications along with 4 major decision variables mentioned in the methods section (

In conclusion, DTL and NBC were employed on cryopreservation meta-data with NBC demonstrating greater generalizability. These results indicate that the handles for improving cryopreservation outcomes are: integrin-mediated cryopreservation, the modification (by entrapment of benign CPAs or other means) of the scaffolding material and the modification of cell location in scaffolds. The DTL and NBC models were demonstrated to be robust against tougher validation data from different cell types thereby confirming that cryopreservation/bio-preservation technology can be improved upon using these approaches.

The author declares there is no competing interests.