Generalized in vitro-in vivo relationship (IVIVR) model based on artificial neural networks

Figures & data

Figure 1 Schematic calculation of descriptors set encoding hypromellose.

Figure 2 Chemoinformatic description of the excipients included into the native input vector.

Figure 3 General structure of artificial neural network models.

Table 1 General description of the native input vector

Input number	Information encoded
1	Modified release: yes (1), no (0)
2	Dosage form: tablets (0), capsules (1)
3	Amount of polymers (%); for IR formulations (0)
4	Amount of nonpolymeric excipients (%); for IR formulations (0)
5	Amount of API (%); for IR formulations (100%)
6	Dose of API in formulation (mg)
7	ph value of medium in dissolution test
8	Volume of dissolution medium (mL)
9	Presence of SLS in dissolution medium: yes (1), no (0)
10	Rotation speed (rpm) in paddle or basket method of dissolution test
11	Fasting conditions in bioavailability study: yes (0), no (1)
12–107	Set of molecular descriptors of API calculated by chemoinformatic software
108–189	Set of averaged molecular descriptors of polymers; for IR formulations (0)
190–271	Set of averaged molecular descriptors of nonpolymeric excipients; for IR formulations (0)
272–289	Dissolution profile – percent of API released into medium in each sampling time
290–306	Sampling times of dissolution test (h) corresponding with % of API released
307	A sampling time of in vivo study tin vivo (h)
OUT	natural logarithm of API plasma concentration [ng/mL] at tin vivo

Abbreviations: API, active pharmaceutical ingredient; IR, immediate-release; SLS, sodium lauryl sulfate.

Figure 4 Results of sensitivity analysis for the most important 28 inputs, with relative importance computed in the context of the native dataset.

Table 2 Input vector reduced to 28 governing variables

Original input numbera	Information encoded
	Type of dosage form
2	Dosage form: tablets (0), capsules (1)
	Quantitative composition
3	Amount of polymers (%); for IR formulations (0)
4	Amount of nonpolymeric excipients (%); for IR formulations (0)
5	Amount of API (%); for IR formulations (100%)
6	Dose of API in formulation (mg)
	In vitro test conditions
8	Volume of dissolution medium (mL)
	In vivo assay conditions
11	Fasting conditions in bioavailability study (0/1)
	Molecular descriptors of API
14	Aromatic atom count
22	Hetero ring count
23	Heteroaliphatic ring count
30	Largest ring size
40	Balaban index
44	Dreiding energy
48	Maximal projection radius
57	Atom count
58	logD at ph 1
75	Acceptor count
104	Hydrogen bond donor count at ph 12
105	Hydrogen bond donor count at ph 13
106	Hydrogen bond donor count at ph 14
	Molecular descriptors of polymer
130	Maximal projection area
131	Maximal projection radius
151	logD at ph 10
	Dissolution profile
272	Dissolution profile: percent of API released in sampling time t1
288	Dissolution profile: percent of API released in sampling time t17
290	Sampling time of dissolution test [h] in t1
306	Sampling time of dissolution test [h] in t17
	In vivo assay
307	One sampling time of in vivo study tin vivo [h]
OUT	Natural logarithm of API plasma concentration [ng/mL] at tin vivo

Note: ^anumbers refer to the original input vector presented in Table 1.

Abbreviation: API, active pharmaceutical ingredient.

Table 3 Architecture of ANNs selected for expert committee and their generalization errors

ANN number	Nodes in hidden layers 1–7 (n)						Activation function	Scaling range	RMSE
	h1	h2	h3	h4	h6	h7
1	60	40	20	10	8	4	fsr	0.2; 0.8	1.21
2	7	5	–	–	–	–	fsr	0.2; 0.8	1.28
3	60	20	10	8	4	–	tanh	0.2; 0.8	1.30
4	7	5	3	2	–	–	tanh	−0.8; 0.8	1.38
RMSE for the whole ensemble									1.05

Abbreviations: ANN, artificial neural networks; h, hidden layer; RMSE, root mean squared error.

Figure 5 Examples of in vivo profile predictions.

Abbreviations: API, active pharmaceutical ingredient; IR, immediate release formulation; MR, modified release formulation; NRMSE, normalized root mean squared error; OBS, observed profile; PRED, profile predicted by the neural model.

Figure 6 Example of in vivo profile prediction for the new test dataset introduced after the model development phase.

Abbreviations: API, active pharmaceutical ingredient; IR, immediate release formulation; NRMSE, normalized root mean squared error; OBS, observed profile; PRED, profile predicted by the neural model.