Fig 1.
Diagram of the artificial neural network (ANN) used to predict the efficacy of 2400 combinations of orthobiologic factors.
The feedforward network has two layers of hidden units. The first hidden layer receives the input not directly but only after it has been processed by a layer of autoencoder units. The 17 input units project to a layer of 50 autoencoder units, which project to the first layer of 100 hidden units, which in turn project to the second layer of 100 hidden units, which finally project to the set of 26 output units. The connectivity between layers is complete in that each unit in a previous layer projects to every unit in a subsequent layer. The weights from the input layer to the autoencoder layer are trained separately, and then held fixed while the other weights in the network are trained.
Fig 2.
Desired and actual outputs of the best-generalizing ANN after training.
The values of the 26 output units for each of the 225 input/desired-output patterns in the training dataset are shown as images, separately for the desired (left) and actual (right) outputs. The unscaled values of the outputs range from 2 (deep blue) to 277 (bright yellow). Close inspection reveals that the match between the desired and actual outputs is good but not perfect. This is expected due to ambiguity in the training dataset, which is derived directly from the experimental data of multiple labs that often reported different outputs for the same inputs. The pattern of agreement in general, with disagreement in detail, indicates that the neural network has learned to generalize from the data in the training dataset. The ability to generalize is central to the ability of an ANN to predict the outputs for combinations of inputs on which it has not been trained.
Fig 3.
The efficacies of 2400 combinations of orthobiologic factors as predicted by the best-generalizing ANN.
The scores are sorted from least to most effective. Effective combinations were defined as those that were high in 12 / 26 outputs (DR, BF3, BF6, MV/TV, PLF-FR, ODI, FR, FH, OW, RO, HO, and IS), and low in 5 / 26 outputs (TWC/CH, TRU, RBG, NH, and DY). The remaining 9 / 26 outputs were not included in the efficacy measure (see text). For the purposes of ranking, the outputs that should be low were flipped, all outputs were scaled in the range [0, 1], and the output values were averaged. By this measure, which is relative to the maximal and minimal output values, the highest possible efficacy of 1 would be obtained if all of the outputs that should be high / low were at their maximal / minimal levels for that output, and vice-versa for the lowest possible efficacy of 0. The predicted efficacies for the 2400 combinations in the screen varied widely over the [0, 1] range and nearly plateaued for the most effective several hundred.
Fig 4.
The combinations of orthobiologic input factors ordered by predicted efficacy.
The combinations are presented in descending order, so the combinations are most / least effective at the top / bottom of either plot. The plot on the left shows all 2400 combinations while the plot on the right shows the top 200 combinations. The factors ES, BMAC, and PRP are either present or absent; EBG is always present. The factor BMP7 takes 2 levels; BMP2, OG, and PU each take 4 levels; and PDGF takes 5 levels. Input factor levels varied over a broad range but were normalized into [0, 1] for purposes of illustration. In the images, yellow and deep blue correspond to 1 and 0, respectively.
Table 1.
Statistically significant pairwise correlations among the factors in the top 200 orthobiologics combinations as determined from the neural network.
BMP2 and BMP7 are positively correlated, while OG and PDGF are negatively correlated. PDGF is negatively or positively correlated with BMAC or PRP, respectively. PU and ES are negatively correlated, and BMAC and PRP are also negatively correlated. The very low (but still > 0) p values associated with those last two negative correlations is attributed mainly to constraints in the design of the combination screen by which PU and ES could not be nonzero together, and BMAC and PRP likewise could not be nonzero together. All values including p values are reported to four significant places.
Table 2.
The 10 best and 10 worst combinations of orthobiologic factors, as determined from the best-generalizing ANN (Fig 1).
Combinations are ranked, best to worst, out of the total of 2400 combinations in the computational screen. BMP2 and BMP7 are at their highest levels in the 10 best combinations, while they are 0 in the 10 worst combinations. OG tends to be at its highest or lowest levels in the 10 best or worst, respectively, while PDGF tends in the opposite direction. The 10 best and worst combinations seem indifferent to the level of PU. ES or BMAC is present in some of the 10 best but in none of the 10 worst. PRP is absent from all 10 best and worst combinations. EGB is present in them all but it is present in all 2400 combinations by design and is included only for completeness. Units: BMP2 and BMP7 are in milligrams, OG and PDGF are in micrograms, and PU is in total treatment days; the other inputs are either present or absent. The levels (dosages, intensities, amounts, etc) of all inputs are in the ranges as reported in published studies (see S1 Text and S1 Dataset).