Estimation of Blood Drug Concentration by LSTM network

Medical treatment cannot avoid the risk like side effects. In general, appropriate dosages and dosing intervals will vary among patients. The most important consideration in administration design is blood drug concentration of the patient, and it is necessary to estimate the concentration beforehand for the administration plan. However, since it is difficult to estimate personal blood drug concentration of patient, it is extremely difficult to precisely decide administration design. In this study, we construct a model to estimate personal blood drug concentration of patients using LSTM network. The proposed method is compared to models constructed in conventional studies and examined with methods. They are a statistical model and Neural Network model proposed in previous studies. As results, our model outperformed those methods.


Introduction
Drug is administered for treatments as antibacterial drug.Nevertheless, to precisely design drug administration plan is difficult.Medical treatment is not able to avoid the risk of side effects and sequelae [1] .In general, appropriate dosages and dosing intervals are different among patients.The most important consideration to decide administration design is blood drug concentration of the patient, and it is necessary to predict the concentration beforehand for the administration plan.However, in the pharmacokinetics models constructed to estimate the concentration, the predicted concentration does not depend on the patient.Population pharmacokinetic analysis and Neural Network model have been proposed to estimation the personal concentration.However, since it is difficult to estimate personal blood drug concentration of patient, it is extremely difficult to precisely decide administration design.In this study, we construct a model to predict patient specific blood drug concentration using LSTM network as well as compare and examine with individualized models for predicting blood drug concentration constructed in the previous studies.

Conventional study 2.1 Population Pharmacokinetics Analysis
Fig. 1 shows an example of changes in blood drug concentration of an administration.The vertical axis represents blood drug concentration and the horizontal axis represents the elapsed time after an administration.Blood drug concentration changes markedly until about first 15 hours after administration.After that, in about 30 hours or later, the blood drug concentration is close to zero.In other words, the drug disappears from inside of the blood.Thus, it is considered that the administration before three times do not affect blood drug concentrations at certain time t when we estimated the blood concentration at time t in repeated administrations.Therefore, the sum of three blood drug concentration before t time is the blood drug concentration at t time.This calculation is the following Also, Figure 2 shows an example of changes in blood drug concentration during repeated administrations.
Equation( 2) is a formula to calculate blood drug concentration.Furthermore, Table1 shows these variable's meanings.Ke can be calculated by the following equation.
CL that is Clearance which is used in the blood drug concentration formula, Equation(2).(5) Therefore, they predicted individual blood drug concentration by this formula [2] .However, to decide Equation(4) take a lot of trouble, and it is more difficult.

Model-Driven Neural Network
In conventional study, Model-Driven Neural Network has been proposed to predict blood drug concentration using Neural Network [3] .In the multilayer perceptron, the structure is represented by determinant.The relation   In that model, there are 2 processes to train.That structure is shown in Fig. 3. Ke in Equation( 2) is regarded as important item to estimate personal blood drug concentration.Thus, a model to predict Ke was constructed.
The model needs to do backpropagation from blood drug concentration since Ke cannot be observed.Equation( 2) was trained at first and set that trained model in before output of whole structure.Finally, a model to output Ke was trained while fixing parameters of equation model.

LSTM
Long short-term memory (LSTM) network is used in this study.LSTM is suitable for handling time series data and improved Recurrent Neural Network (RNN) [4] .Unless LSTM layer is reset, that can hold previous time information alike Fig. 4. Compared to RNN, LSTM can deal with the exploding and vanishing gradient problem at training of RNN [5] .LSTM layer has a cell, an input gate, an output gate and a forget gate.Also, there are some parameters at each gate.When training, these are updated like normal parameters, weight and bias.

Proposed Structure
The used data in this study is time series since that has elapsed time data after administration.Thus, in my study, LSTM network is adopted to predict Blood drug concentration.Figure 5 shows the purposed structure used LSTM.These input items are Dose, Age, TBW and data for evaluation of liver function.Detail of the items is presented in Section 4.1.Also, the output of this network is only blood drug concentration and this network has 2 hidden layers.Regarding to these LSTM layers, the input at one time is data for 14 time series.In the future, that number is needed to reduce possible because that number is tentatively decided.
Figure 6 shows flow of purposed structure when 14 time series data are input.By inputting of first 13 time series data, the value in LSTM layer can be calculated and updated.In the other word, the timing information of 13 time series data can be hold before the data at 14 time is input.Finally, when last 14 time series data are input to the network, blood drug concentration can be output from that whole network using the value updated in LSTM layer.
In general, training of Neural Network is in need of numerous datasets.However, the used data in this study is observed from only 36 patients.That number is 89 and insufficient for general training of Neural Network.Therefore, Transfer Learning is adopted to compensate the few data in my study.Transfer Learning is a method to help purposed training utilizing models trained in other cases.At first, the proposed model is trained using data, which is similar to data in considering case.Those trained parameters are set as the initial value of network of purpose before purposed training.Thus, better results are gotten at training using real data.[13] In this study, based on Transfer Learning, Equation(5) that is constructed by conventional study is utilized to training of advance.First the data for training of advance is generated by Equation(5) and proposed network is trained using that data.Next, the network is trained with real data.In other word, that do finetuning [6] .

Datasets
This section describes the data that is used in training of LSTM network.The data is clinical data which was to use in this study.

Conclusions
The purpose of this study is to exceed the accuracy of the DV estimation model constructed in previous studies.We attempted to construct LSTM network model to estimate blood drug concentration since the type of data is time series.As a result, the trained model in this study is better than Neural Network model and Pharmacokinetics model.Observed data for training is only 89 numbers, 36 patients, though, Transfer Learning was able to compensate the few data.In general, there are few clinical data.Thus, Transfer Learning is efficient to medical field.Furthermore, LSTM is suitable for handling clinical data because almost all the data is time series type and time data is important in medical field.
However, in this study, structure shape was decided tentatively and trained.If that is considered and can be set suitable structure, proposed model can be getting more accuracy.For example, the number of LSTM layer and unit of hidden layer etc. should be considered.
In the future, our proposed model should be improved.Additionally, we will attempt to propose Ladder Network.This method is one of excellent semi-supervised training.LSTM network and Ladder network will be helpful in medical research.
According to Yasuhiro Tsuji et al, they considered that the CL depends on the patient's age and total body weight.First, they decided the individualized estimation formula of CL as follows.

Fig 1 .
Fig 1.An example of changes in blood drug concentration after an administration.

Fig. 2 .
Fig. 2.An example of changes in blood drug concentration by repeated administrations.

Fig. 3 .
Fig. 3. Model-Driven Neural Network model diagram to estimate blood drug concentration.

Fig. 7 .
Fig. 7. Distribution of observed data.touse in this study.Table.2. Data of a certain patient.ID Date Time Dose Age … CCR DV

Table . 2
. Data of a certain patient.ID

Date Time Dose Age … CCR DV
Table 7 shows RMSE of prediction of data for training and test by each model.Proposed network, LSTM network, is better than 2 conventional studies in terms of RMSE of testing.Also, in this study, the number of unit in hidden1-hidden2 layer was tentatively 20-15, 30-25, 40-35.In any cases, test loss was able to be around 20 or under as Table 8.Moreover, compared to training loss, test loss is close in that.It was found that Transfer Learning can make training for purpose efficient.