CN109117497B - Time optimization method for computer aided design layout of digital microfluidic biochip - Google Patents

Abstract

The invention discloses a time optimization method for computer-aided design layout of a digital microfluidic biochip, which comprises the following steps: establishing models of four constraint conditions including priority constraint, resource constraint, overlapping constraint and fluid constraint; establishing a target model of the total completion time of the chain biochemical reaction on the digital microfluidic biochip; solving an optimal solution of the target model of the completion time according to the models of the four constraint conditions based on a Markov decision; and controlling the implementation process of the biochemical reaction on the digital microfluidic biochip according to the optimal solution. The invention can minimize the time of biochemical reaction in the digital microfluidic biochip, and has the advantages of low cost, high precision and high efficiency.

Description

Time-optimized method for computer-aided design layout of digital microfluidic biochip

technical field

The invention relates to the field of computer-aided design of digital microfluidic biochips, and more specifically relates to a time optimization method for computer-aided design layout of digital microfluidic biochips.

Background technique

First, the physical design of the microfluidic biochip is introduced. As shown in Figure 1, the microfluidic biochip is mainly composed of electrode plates, and the droplets are driven by electrowetting electrodes to move, mix, react, and store. The droplets store relevant reagent samples required for biochemical experiments. , all droplets are sandwiched between two layers of indium tin oxide electrode plates. There are two non-reconfigurable resources here, optical detector and optical distribution port. The optical detector is used to detect whether each operation is running normally. As a special resource, its position is fixed during the manufacturing stage and in the There is no movement throughout the physical design, and an optical distribution port is used to generate the droplets.

With the advancement of science, biochemical experiments are becoming more and more complex. The traditional microfluidic biochip design can no longer meet the needs. However, with the help of computer-aided design, not only has this problem been solved, but it also has low cost, high precision and high efficiency. The advantages. The computer-aided design of microfluidic biochip is mainly composed of three parts: task planning, layout and wiring, including two optimization goals of time and size. Computer-aided design simulates a series of experiments of microfluidic biochip by establishing a 3D model. The process, as shown in Figure 2, takes the physical plane of the biochip as the x-y plane, and the time t as the z-axis. Each module contains droplets, and the droplets perform related operations in the modules, such as moving, mixing, reacting and For storage, etc., the length and width of the module represent the space required for the operation, and the height represents the time required for the operation. Microfluidic biochips perform biochemical reactions under certain experimental constraints. How to control microfluidic biochips to quickly complete all biochemical reactions is a research direction in microfluidic biochips. However, this technical problem has not yet been resolved. Get well resolved.

Contents of the invention

The technical problem to be solved by the present invention is to provide a digital microfluidic biochip for the technical defect of how to quickly complete all biochemical reactions in the microfluidic biochip of the prior art that has not been effectively solved. A Time-Optimized Method for Computer-Aided Design Layout of Fluidic Biochips.

The technical solution adopted by the present invention to solve the technical problem is: to construct a time optimization method for computer-aided design layout of a digital microfluidic biochip, including the following steps:

S1. Establish a model with the following four constraints:

1) Priority constraints: The priority order of chemical reactions defines the execution order of different operations during digital microfluidic biochip design;

2) Resource constraints: ensure that the use of each type of chemical agent in the entire series of biochemical reactions does not exceed the upper limit of its resource constraints;

3) Overlap constraints: ensure that a series of biochemical reactions will not be performed at the same location at the same time point;

4) Fluid constraints: define the minimum distance between droplets of digital microfluidic biochip;

S2. Establish the target model of the total time for chain biochemical reactions to complete on the digital microfluidic biochip:

Among them, {o ₁ ,o ₂ ,…,o _n } represent all the operation sets of the experiment, n≥2, t(o _i ) represents the execution time of each operation o _i ;

S3. Based on the Markov decision, solve the optimal solution of the target model of the completion time according to the model of the four constraint conditions;

S4. According to the optimal solution, control the implementation process of the biochemical reaction on the digital microfluidic biochip.

Preferably, in the digital microfluidic biochip computer-aided design layout time optimization method of the present invention, the modeling of the priority constraints specifically includes:

For a series of chain biochemical reactions, according to the interdependence between reactants, a directed graph is established to define the constraint relationship between biochemical reactions, which is recorded as G={O,P}, and O,O in graph G The two parameters are defined as follows:

O={o ₁ ,o ₂ ,…,o _n }: represents a series of biochemical reactions;

P={p ₁ ,p ₂ ,…,p _m }: represents the priority constraints between two chemical reactions, m≥n.

Preferably, in the time optimization method of digital microfluidic biochip computer-aided design layout of the present invention, the modeling of resource constraints specifically includes:

The amount of agent a used to define the chemical reaction is ma , the total amount of agent a is M _a , and the model of _resource constraints is:

Preferably, in the digital microfluidic biochip computer-aided design layout time optimization method of the present invention, the modeling of overlapping constraints specifically includes:

Define a C _x,y ∈ {0,1}: indicates whether chemical reagents can exist at point (x,y), if C _x,y = 1, it means that chemical reagents can be placed at this point, and it is regarded as a free unit grid; if C _{x, y} = 0, it means that this point has been occupied, and there can no longer exist chemical reagents different from the current one;

The model for overlapping constraints is:

所有的试剂L。∑ _x,y C _x,y (L)≤1,

All reagents L.

Preferably, in the time optimization method of digital microfluidic biochip computer-aided design layout of the present invention, the modeling of fluid constraints specifically includes:

The digital microfluidic biochip is unitized, that is, the digital microfluidic biochip is divided into several cells according to the established industrial size standard, the lower left corner of each cell is the starting point of the cell, and the coordinates of each cell Calculated by their relative position with the starting cell, denoted as (x, y), on the digital microfluidic biochip, the chemical agent moves, retains, and reacts in units of cells to ensure that the fluid constraints are met.

Preferably, in the time optimization method for computer-aided design layout of digital microfluidic biochips of the present invention, the minimum spacing in the fluid constraints in step S1 is one cell on the chip.

Preferably, in the method for time optimization of digital microfluidic biochip computer-aided design layout of the present invention, step S3 specifically includes:

Establish a topological relationship graph G={O, P}; wherein, the topological relationship graph generates directed edges according to the dependencies of chemical reactions, and each node in the graph is a chemical reaction;

Then search from the topological relationship graph G according to the priority order of the directed graph to determine whether there are chemical reactions that have not yet been carried out and completed; if so, select a preset node from it to make a Markov decision, and update it according to the decision result G, and then re-judge whether there are unused nodes in G until there are no unused nodes in G;

Get the final G as the optimal solution.

Implementing the time optimization method for computer-aided design layout of digital microfluidic biochips of the present invention can minimize the time of biochemical reactions in digital microfluidic biochips, and also has the advantages of low cost, high precision and high efficiency .

Description of drawings

The present invention will be further described below in conjunction with accompanying drawing and embodiment, in the accompanying drawing:

Figure 1 is the physical design of the digital microfluidic biochip;

Fig. 2 is the 3D model of digital microfluidic biochip computer-aided design;

Fig. 3 is a flow chart of a time optimization method for computer-aided design layout of a digital microfluidic biochip;

Fig. 4 is the example of the topological relationship diagram of operation;

Figure 5 is an example of resource constraints;

Fig. 6 is a simple example about the Markov decision algorithm;

Fig. 7 is the iterative process of the Markov decision algorithm;

Fig. 8 is a flow chart of finding an optimal solution based on Markov decision.

Detailed ways

In order to have a clearer understanding of the technical features, purposes and effects of the present invention, the specific implementation manners of the present invention will now be described in detail with reference to the accompanying drawings.

With reference to Fig. 3, it is the flow chart of the time optimization method of digital microfluidic biochip computer-aided design layout of the present invention, and this method specifically comprises:

S1. Establish a model of priority constraints, resource constraints, non-overlapping constraints, and fluid constraints:

Each standard simulation experiment of a microfluidic biochip has its own parameter settings. The upper limit of the size and time of the experiment is given in the input file. For example, the parameter setting Fixed: 10 10 360 indicates the size of the experiment The upper limit is 10*10, and the upper limit of time is 360. Each reagent or operation is also given a size occupied. During a series of reactions in this experiment, all operations cannot exceed the boundary of this size. The reaction time cannot exceed the time limit.

When doing computer-aided design, the following four constraints need to be considered:

(1) Priority constraints. The prioritization of chemical reactions defines the execution order for different operations during digital microfluidic biochip design. During the computer-aided design of the chip, priority constraints define the execution sequence of all operations. For a series of chain biochemical reactions, according to the interdependence relationship between reactants, a directed graph is established to define the constraint relationship between biochemical reactions, which is recorded as G={O,P}, and O,P in graph G The two parameters are defined as follows:

O={o ₁ ,o ₂ ,…,o _n }: represents a series of biochemical reactions;

P={p ₁ ,p ₂ ,…,p _m }: represents the priority constraints between two chemical reactions, m≥n.

As shown in Figure 4, the execution sequence of operations can be represented by a time-based topology graph, each node represents a buffer or an operation, and the t-axis represents when each node is executed. DsB stands for buffering, buffering must pass the preparation time before it can be put into use and enter the next step of operation, DsR stands for reaction reagent, Mix stands for mixing operation, Dlt stands for dilution operation, most nodes can only be executed after their precursors are executed, and at the same time There are some nodes that have no predecessors but have preparation time. In Figure 3, Dlt2 can be performed only when Mix2 and Mix3 products are obtained. The product mixed with DsB1 and DsB2 can be diluted with DsR, and the product mixed with DsB3 and DsB4 can be diluted with the product mixed with DsB4 and DsB5 to obtain the final product. Product Opt.

(2) Resource constraints. Ensure that the entire series of biochemical reactions uses each type of chemical agent within its resource limit. Resources are divided into non-reconfigurable resources and reconfigurable resources, and non-reconfigurable resources include optical detectors and optical distribution ports. Reconfigurable resources include all buffers, reagents, and operation products. Resource constraints limit that when all reconfigurable resources are used by multiple operations at the same time, they cannot exceed the upper limit of the resources. The modeling of resource constraints specifically includes:

The amount of agent a used to define the chemical reaction is ma , the total amount of agent a is M _a , and the model of _resource constraints is:

As shown in Figure 5, a simple 2D diagram is used to explain here. There are only two copies of resource i at time t, but at this time operation 1, operation 2 and operation 3 all need to use resource i, so there are only two of them. able to complete.

(3) Non-overlapping constraints. Non-overlapping constraints ensure that no two or more operations are performed at the same location at the same time. The modeling of overlapping constraints specifically includes:

Define a C _x,y ∈ {0,1}: indicates whether chemical reagents can exist at point (x,y), if C _x,y = 1, it means that chemical reagents can be placed at this point, and it is regarded as a free unit grid; if C _{x, y} = 0, it means that this point has been occupied, and there can no longer exist chemical reagents different from the current one;

The model for overlapping constraints is:

所有的试剂L。∑ _x,y C _x,y (L)≤1,

All reagents L.

(4) Fluid constraints. Fluidic constraints define the minimum distance, one cell on the chip, between two non-reactive droplets in the same module. The modeling of fluid constraints specifically includes:

The digital microfluidic biochip is unitized, that is, the digital microfluidic biochip is divided into several cells according to the established industrial size standard, the lower left corner of each cell is the starting point of the cell, and the coordinates of each cell Calculated by their relative position with the starting cell, denoted as (x, y), on the digital microfluidic biochip, the chemical agent moves, retains, and reacts in units of cells to ensure that the fluid constraints are met.

All operations must comply with the above constraints.

S2. Establish the target model of the total time for chain biochemical reactions to complete on the digital microfluidic biochip:

Among them, {o ₁ ,o ₂ ,…,o _n } represent all the operation sets of the experiment, n≥2, t(o _i ) represents the execution time of each operation o _i ;

S3. Based on the Markov decision, solve the optimal solution of the target model of the completion time according to the model of the four constraint conditions;

In probability theory and statistics, Markov decision processes (English: Markov Decision Processes, abbreviated as MDPs) provide a mathematical framework model for how to make decisions in a state that is partly random and partly controllable by the decision maker . A Markov decision process is a five-tuple {S,A,P _a (s,s′),R _a (s,s′),δ∈(0,1)}, where

(1) S={s ₀ ,s ₁ ,…,s _n } is a state set;

(2) A is an action set, and A _s represents acceptable actions in state s;

(3) R _a (s, s′) represents the probability that state s is transformed into state s′ through action a;

(4) R _a (s, s′) represents the reward value of state s transformed into state s′ through action a, which is calculated by reward function R;

(5) δ is a discount factor, which is used to represent the impact of future state transitions on current rewards.

A feature of the Markov decision process is that each of its two states is conditionally independent of each other, and the next state s' depends on the current state s. Each state transition will have a reward value calculated by the reward function R. The core problem of the Markov decision process is to find the plan with the largest cumulative reward value. π(s) is used to store the state s and actions in the plan.

Equation 1 shows the workflow of the Markov decision process, π(s) represents the plan with the largest cumulative reward value starting from state s, v(s) is the cumulative reward value, and the selected action and state are determined by π(s) to decide. The Markov decision process obtains the scheme π(s) through iteration. During each iteration, when the state is in s, the decision maker can choose all available actions, and the state s will be randomly transformed after a certain action reaction. To the next state s′, the Markov decision process will calculate the reward value of all state transitions. At the same time, each transition of the state will have its own probability. During the iterative process, the reward value will continue to decay, and finally the accumulated reward value will be returned. When all calculation results are returned, the Markov decision process will choose the solution with the largest cumulative reward value. Here are the definitions of π(s) and v(s):

Figure 6 shows an example of a Markov decision process. There are 4 states, 5 actions and corresponding probabilities and reward values on the way. Assuming s ₀ is the initial state, it has only one available action a ₀ , s ₀ can Through action a ₀ is transformed into state s ₁ and state s ₂ , the reward value of transforming into state s ₁ is 0.6*2, and the reward value of transforming into state s ₂ is 0.4*3. Their reward values are both 1.2, but the former has a large probability and a small reward, while the latter has a small probability and a large reward. Then the Markov decision process enters the next iteration, starting from state _s1 or state _s2 . It is not difficult to see that there are four schemes in the figure that can reach the final state s ₃ , and the calculation and comparison of the four schemes shows that the best scheme is (s ₀ , a ₀ , s ₂ , a ₂ , s ₃ ), as shown in Figure 7 .

Referring to FIG. 8 , it is a flow chart of finding an optimal solution based on Markov decision.

First import the data, the imported data includes the constraints, the reactants and products of the chemical reactions that need to occur, the reaction time and the chip space required to complete the reaction, the total amount of each chemical, and the total size of the chip;

Then set up the topological relationship graph G={O, P}; the topological relationship graph generates directed edges according to the dependence of the chemical reactions, and each node in the graph is a chemical reaction;

Then search from the topological relationship graph G according to the priority order of the directed graph to determine whether there are chemical reactions that have not yet been carried out and completed; if so, select a preset node from it to make a Markov decision, and update it according to the decision result G, and then re-judge whether there are unused nodes in G until there are no unused nodes in G;

Get the final G as the optimal solution.

S4. According to the optimal solution, control the implementation process of the biochemical reaction on the digital microfluidic biochip.

Based on the Markov decision-making process, the invention proposes a time optimization algorithm for computer-aided design layout of digital microfluidic biochips. We represent the input of the layout problem as a graph G={O,P}, G contains all the protocols of the experiment, O={o ₁ ,o ₂ ,…,o _n }(n≥2) represents the operation set of the experiment , P={p ₁ ,p ₂ ,…,p _m }(n≥2) represents the priority constraints among all operations, and the following is the objective function of the total reaction time:

s.t.

Among them, n represents the total number of operations, t(o _i ) represents the execution time of each operation o _i , the amount of agent a in the chemical reaction is m _a , the total amount of agent a is M _a , and C _x,y ∈ {0,1} represents Whether the chemical reagent can exist at the point (x, y), each operation is regarded as a module, and the module becomes a rectangle when projected onto the xy plane, and the position of each rectangle is determined by four coordinates.

Embodiments of the present invention have been described above in conjunction with the accompanying drawings, but the present invention is not limited to the above-mentioned specific implementations, and the above-mentioned specific implementations are only illustrative, rather than restrictive, and those of ordinary skill in the art will Under the enlightenment of the present invention, many forms can also be made without departing from the gist of the present invention and the protection scope of the claims, and these all belong to the protection of the present invention.

Claims (3)

1. A time optimization method for digital microfluidic biochip computer-aided design layout, characterized in that, comprising the steps: S1. Establish a model with the following four constraints: 1) Priority constraints: The priority order of chemical reactions defines the execution order of different operations during the design of digital microfluidic biochips; the modeling of the priority constraints specifically includes: For a series of chain biochemical reactions, according to the interdependence relationship between reactants, a directed graph is established to define the constraint relationship between biochemical reactions, which is recorded as G={O,P}, and O,P in graph G The two parameters are defined as follows: O={o ₁ ,o ₂ ,…,o _n }: represents a series of biochemical reactions; P={p ₁ ,p ₂ ,…,p _m }: Indicates the priority constraints between two chemical reactions, m≥n; 2) Resource constraints: ensure that the use of each type of chemical agent in the entire series of biochemical reactions does not exceed the upper limit of its resource constraints; the modeling of resource constraints specifically includes: The amount of agent a used to define the chemical reaction is ma , the total amount of agent a is M _a , and the model of _resource constraints is:

3) Overlapping constraints: It ensures that a series of biochemical reactions will not be performed at the same location at the same time point; the modeling of overlapping constraints specifically includes: Define a C _x,y ∈ {0,1}: indicates whether chemical reagents can exist at point (x,y), if C _x,y = 1, it means that chemical reagents can be placed at this point, and it is regarded as a free unit grid; if C _{x, y} = 0, it means that this point has been occupied, and there can no longer exist chemical reagents different from the current one; The model for overlapping constraints is: ∑ _x,y C _x,y (L)≤1,

All reagents L; 4) Fluid constraints: define the minimum spacing between droplets of digital microfluidic biochips; unitize digital microfluidic biochips, that is, divide digital microfluidic biochips into several parts according to established industrial size standards The cell, the lower left corner of each cell is the starting point of the cell, and the coordinates of each cell are calculated by its relative position with the starting cell, recorded as (x, y), on the digital microfluidic biochip , the chemical agent moves, retains, and reacts in units of cells to ensure that the fluid constraints are met; S2. Establish the target model of the total time for chain biochemical reactions to complete on the digital microfluidic biochip:

Among them, {o ₁ ,o ₂ ,…,o _n } represent all the operation sets of the experiment, n≥2, t(o _i ) represents the execution time of each operation o _i ; S3. Based on the Markov decision, solve the optimal solution of the target model of the completion time according to the model of the four constraint conditions; S4. According to the optimal solution, control the implementation process of the biochemical reaction on the digital microfluidic biochip. 2. The time optimization method of digital microfluidic biochip computer aided design layout according to claim 1, is characterized in that, step S3 specifically comprises: Establish a topological relationship graph G={O, P}; Among them, the topological relationship graph generates directed edges according to the dependency relationship of chemical reactions, and each node in the graph is a chemical reaction; Then search from the topological relationship graph G according to the priority order of the directed graph to determine whether there are chemical reactions that have not yet been carried out and completed; if so, select a preset node from it to make a Markov decision, and update it according to the decision result G, and then re-judge whether there are unused nodes in G until there are no unused nodes in G; Get the final G as the optimal solution. 3. The method for time optimization of digital microfluidic biochip computer-aided design layout according to claim 1, characterized in that the minimum spacing in the fluid constraints in step S1 is one cell on the chip.

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