Subjects
The study data were collected from 47 Chinese healthy subjects at the Second Affiliated Hospital of Zhejiang University, School of Medicine (Hangzhou, Zhejiang, China) in 2017. We enrolled male and female volunteers aged from 18 to 45 years and with a body mass index between 19 and 26 kg∙m−2 The inclusion criteria were as follows: (1) no clinically relevant abnormalities identified by subjects’ medical history, physical examination, clinical laboratory tests, vital signs, chest radiography, and 12-lead ECG; (2) no tobacco, drug, or alcohol abuse; (3) no breastfeeding, pregnancy or childbearing potential of female subjects during the study. The exclusion criteria were as follows: (1) positive blood screening results for HIV or hepatitis or any positive urine drug screen; (2) any hospital admission or major surgery, any donation of blood or acute loss of blood or any participation in other clinical trials within the previous 3 months; (3)no heavy tea or coffee consumption more than 1 L/day; (4) no history of allergies to the study medicines or related substances.
Study design and safety assessment
A single dose of 20 mg omeprazole tablet (AstraZeneca Pharmaceutical Co. Ltd.) was administered with 240 mL of water after an overnight fast. A highly caloric meal was consumed within 30 min before drug administration and water was forbidden 1 h before and after drug administration. Blood samples (2 mL each) were collected in K2EDTA anticoagulant tubes at predose and at 0.5, 1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5, 6, 7, 8, 10, and 12 h postdose. The blood samples were centrifuged at 3000 g and stored at -80℃ until analysis. A validated liquid chromatography tandem mass spectrometry (LC–MS/MS) method was used to determine the plasma concentrations of omeprazole by Shanghai Xihua Scientific Co., Ltd.
For all studies, safety assessments included vital signs, 12-lead ECG, physical examinations, and clinical tests. Adverse events were evaluated with regard to their seriousness, intensity, time course, outcome, and relationship to the study drug.
Pharmacokinetic statistical analysis
Pharmacokinetic analysis was performed by WinNonlin software (Version 6.4, Pharsight Corporation, Mountain View, California, USA), and a noncompartmental method was used to calculate pharmacokinetic parameters. A total of 47 subjects were divided into the low-age group (≤ 26 years, 24 subjects) and the high-age group (> 26 years, 23 subjects) based on the calculation of the median age. Pharmacokinetic data from the low-age and high-age groups or male and female groups were compared with a Student’s t-test.
Principal component analysis
Demographic characteristics and routine biochemical and hematological parameters were collected from all of the subjects. A total of 12 variables were included and converted into independent or irrelative variables by principal component analysis (PCA). PCA is a mathematical algorithm that reduces the dimensionality of the data while retaining most of the variation in the data set. It accomplishes the reduction by identifying directions, called principal components, along which the variation in the data is maximal [10]. This approach can reduce the data dimension and maintain the most original variable information. The main calculation procedures of PCA were as follows: (1) the data collection from the subjects was conducted on standardized processing; (2) the characteristic value and feature vector of the correlation coefficient matrix R were calculated to define new indicator variables; (3) the principal components were chosen and the information contribution rate and accumulated contribution rate were calculated; (4) when the accumulated contribution was close to 1, we chose the principal components to replace the original variables and thereby obtain the key factors.
Metaheuristic optimization algorithms
To get a better fitting effect of the BPANN model, we used particle swarm optimization algorithm (PSO), whale optimization algorithm (WOA), and genetic algorithm (GA) to optimize the model.
The PSO, presented by Eberhart and Kennedy in 1995, is a heuristic and evolutionary algorithm inspired by the behavior of birds to locate desirable positions in a given area through cooperation and competition [11]. Some entities, called particles, are scattered in the search space in the PSO [12]. The position of each particle represents a possible solution, and each solution is the way that in the search of a position in a space, particles change the flying distance and directions via changing the speed [13, 14]. Each particle remembers its optimal position piD in the searching history in the iteration process [15]. All of the optimal positions of all particles are the global optimal position pgD [16]. The equation and parameter of particle movement are as follows [17]:
$${V}_{iD}^{j+1}=\omega {V}_{iD}^{j}+{c}_{1}{r}_{1}\left({p}_{iD}^{j}-{x}_{iD}^{j}\right)+{c}_{2}{r}_{2}\left({p}_{gD}^{j}-{x}_{iD}^{j}\right)$$
$${x}_{iD}^{j+1}={x}_{iD}^{j}+{V}_{iD}^{j+1}$$
where \(i\), \(j\), \(D\) stand for the particle, the current iteration amount and the particle dimension, respectively. \({x}_{iD}^{j}\) and \({V}_{iD}^{j}\) are the velocity and position in the \(j\) iteration. Non-negative constant \({c}_{1}\) and \({c}_{2}\) are the learning factor, which determines the effects of \({p}_{iD}\) and \({p}_{gD}\) on the new velocity. \({r}_{1}\) and \({r}_{2}\) are the pseudo random amount evenly distributed in the interval [0, 1]. \(\omega\) is the inertia weight, adjusting the searching ability in the solution domain [18, 19].
The WOA has been developed by inspiration from humpback whales that hunt by creating a bubble-net. The WOA takes place at three stages which are encircling, bubble-net attacking and searching for prey [20]. The equation and parameter of encircling are as follows:
$${X}_{k}^{j+1}={X}_{k}^{*}-{A}_{1}\bullet {D}_{k},$$
$${D}_{k}=\left|{C}_{1}\bullet {X}_{k}^{*}-{X}_{k}^{j}\right|,$$
$${C}_{1}=2{r}_{2}; {A}_{1}=2a {r}_{1}-a,$$
where \({X}_{k}^{*}\) stands for the best current location for whales; \({X}_{k}^{j+1}\) stands for the kth component of the spatial coordinate \({X}^{j+1}\); a is the coefficient in the iterative process (decreases linearly from 2 to 0 in the iterative process); \({r}_{1}\) and \({r}_{2}\) are random vectors between 0 and 1.
The equation and parameter of bubble-net attacking are as follows:
$${X}_{k}^{j+1}={X}_{k}^{*}+{D}_{k}\bullet {e}^{bl}\bullet \mathrm{cos}2\pi l,$$
$${D}_{k}=\left|{X}_{k}^{*}-{X}_{k}^{j}\right|,$$
where l is a random number in the interval of [-1, 1], and b is a constant for the formation of the spiral shape.
The final equation of searching for prey is as follows:
$${X}_{k}^{j+1}={X}_{k}^{rand}-{A}_{1}\bullet {D}_{k,}$$
$${D}_{k}=\left|{C}_{1}\bullet {X}_{k}^{rand}-{X}_{k}^{j}\right|,$$
$${C}_{1}=2{r}_{2}; {A}_{1}=2\mathrm{a}\cdot {r}_{1}-a,$$
The GA is a popular approach to achieve this optimization approach. The GA approach is inspired by the Darwin’s theory of natural selection survival of the fittest [21]. The equation of GA has been embedded in the MATLAB2020a.
BPANN modeling
The BPANN is a kind of machine learning technology that minimizes the error between the network outputs and the desired outputs, adjusting the weights and biases by a small amount at a time through a gradient-based procedure [22, 23].The BPANN comprises two procedures: a forward stage where the input signals move forward through the network and a backward stage where the error is propagated backward from the output layer to the input layer. The error is calculated in the output layer and the parameters are updated for the direction in which the performance function most rapidly decreases [24].
Although the BPANN algorithm is widely used, it might become stuck at the local minimum if the initial weights and biases are far from the optimal values that can give the global optimal solutions [25]. Several metaheuristic optimization algorithms, such as the PSO, GA, and harmony search algorithm, have been combined with the BPANN to overcome this shortcoming [25,26,27]. In this study, PSO was chosen to improve the performance of the BPANN owing to its simplicity and wide applicability. The variables selected were used as the input layer, and the plasma concentration of omeprazole was used as the output layer. The node numbers of hidden layer were determined based on the formula of l < n-1, where l was the number of the nodes in the hidden layer, and n was the number of nodes in the input layer, and then followed by the trial and error method to identify the best numbers of the node. Through the global search ability of the PSO algorithm, the initial weights and biases of the BPANN were obtained and the true global optimization and performance improvement were found. The overall calculation process is shown in Fig. 1.
