CN109117497B - Time optimization method for computer aided design layout of digital microfluidic biochip - Google Patents
Time optimization method for computer aided design layout of digital microfluidic biochip Download PDFInfo
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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
Technical Field
The invention relates to the field of computer-aided design of digital microfluidic biochips, in particular to a time optimization method for computer-aided design layout of a digital microfluidic biochip.
Background
First, the physical design of the microfluidic biochip is described. As shown in fig. 1, the microfluidic biochip is mainly composed of electrode plates, droplets are driven by electrowetting electrodes to move, mix, react, store and the like, relevant reagent samples required by biochemical experiments are stored in the droplets, and all the droplets are sandwiched between two layers of indium tin oxide electrode plates. There are two non-reconfigurable resources, an optical detector to detect whether each operation is performed properly, as a special resource whose position is fixed at the manufacturing stage and cannot be moved throughout the physical design, and an optical dispense port to generate a droplet.
With the scientific progress, biochemical experiments are increasingly complex, the traditional microfluidic biochip design can not meet the requirements, but the problem is solved by the aid of computer-aided design, and the microfluidic biochip has the advantages of low cost, high precision and high efficiency. The computer aided design of the microfluidic biochip mainly comprises three parts, namely task planning, layout and wiring, and comprises two optimization targets of time and size, the computer aided design simulates a series of experimental processes of the microfluidic biochip by establishing a 3D model, as shown in FIG. 2, the physical plane of the biochip is taken as an x-y plane, time t is a z axis, each module contains liquid drops, the liquid drops perform relevant operations in the module, such as moving, mixing, reacting, storing and the like, the length and the width of the module represent the size of space required by the operation, and the height represents the time required by the operation. The micro-fluidic biochip is used for biochemical reaction under certain experimental constraint conditions, and how to control the micro-fluidic biochip to quickly complete all biochemical reactions is a research direction in the micro-fluidic biochip, and then the technical problem is not well solved at present.
Disclosure of Invention
The technical problem to be solved by the invention is to provide a time optimization method for computer-aided design layout of a digital microfluidic biochip, aiming at the technical defect that how to quickly complete all biochemical reactions in the microfluidic biochip with computer-aided design layout in the prior art is not effectively solved.
The technical scheme adopted by the invention for solving the technical problems is as follows: a time optimization method for constructing a computer aided design layout of a digital microfluidic biochip comprises the following steps:
s1, establishing a model of the following four constraint conditions:
1) Preferential constraint conditions are as follows: the order of precedence of the chemical reactions defines the order of execution for the different operations during the design of the digital microfluidic biochip;
2) Resource constraint conditions are as follows: ensuring that each type of chemical agent is used in the whole series of biochemical reactions and does not exceed the upper limit of the resource limit;
3) Overlap constraint conditions: the series of biochemical reactions are ensured not to be executed at the same position at the same time point;
4) Fluid constraint conditions: defining a minimum spacing between droplets of the digital microfluidic biochip;
s2, establishing a target model of the total time of the chain biochemical reaction on the digital microfluidic biochip:
wherein, { o 1 ,o 2 ,…,o n Represents all the run set of experiments, n.gtoreq. 2,t (o) i ) Represents each operation o i The execution time of (c);
s3, solving the optimal solution of the target model of the completion time according to the models of the four constraint conditions based on Markov decision;
and S4, controlling the implementation process of biochemical reaction on the digital microfluidic biochip according to the optimal solution.
Preferably, in the method for optimizing the layout of the digital microfluidic biochip based on computer aided design according to the present invention, the modeling of the preferential constraint specifically includes:
aiming at a series of chain biochemical reactions, according to the interdependence relation between reactants, establishing a directed graph to define the constraint relation between the biochemical reactions, and marking as G = { O, P }, wherein two parameters of O and O in the graph G 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 a preferential constraint between two chemical reactions, m.gtoreq.n.
Preferably, in the method for time optimization of computer-aided design layout of digital microfluidic biochips according to the present invention, the modeling of the resource constraint specifically includes:
define the dosage of the chemical agent a in the chemical reaction as m a The total amount of the medicament a is M a The resource constraint model is:
preferably, in the method for time optimization of computer-aided design layout of digital microfluidic biochips according to the present invention, the modeling of the overlap constraint specifically comprises:
define a C x,y E {0,1}: indicates whether a chemical agent may be present at point (x, y) if C x,y =1, which means that the spot can be placed with chemical reagent, and is regarded as a free cell; if C x,y =0, meaning that the spot is already occupied and no more chemical reagents than currently exist;
the model of the overlap constraint is:
∑ x,y C x,y (L)≤1,
all reagents L.
Preferably, in the method for time optimization of computer-aided design layout of digital microfluidic biochip of the present invention, the modeling of fluid constraints specifically includes:
the digital microfluidic biochip is unitized, namely the digital microfluidic biochip is divided into a plurality of unit cells according to a set industrial size standard, the lower left corner of each unit cell is the starting point of the unit cell, the coordinate of each unit cell is calculated according to the relative position of the unit cell and the starting point unit cell and is marked as (x, y), and chemical agents move, remain and react on the digital microfluidic biochip by taking the unit cell as a unit so as to ensure that a fluid constraint condition is met.
Preferably, in the method for time optimization of computer-aided design layout of digital microfluidic biochip of the present invention, the minimum distance in the fluid constraint condition in step S1 is one cell on the chip.
Preferably, in the method for time optimization of computer-aided design layout of digital microfluidic biochips according to the present invention, step S3 specifically includes:
establishing a topological relation graph G = { O, P }; the topological relation graph generates directed edges according to the dependency relationship of chemical reactions, and each node in the graph is a chemical reaction;
searching from the topological relation graph G according to the priority of the directed graph, and judging whether chemical reactions which are not carried out and are finished exist or not; if yes, selecting preset nodes from the G to carry out Markov decision, updating the G according to a decision result, and then judging whether the unused nodes exist in the G again until the unused nodes do not exist in the G;
and obtaining the final G as the optimal solution.
The time optimization method of the digital microfluidic biochip computer-aided design layout can minimize the biochemical reaction time in the digital microfluidic biochip, and has the advantages of low cost, high precision and high efficiency.
Drawings
The invention will be further described with reference to the following drawings and examples, in which:
FIG. 1 is a physical design of a digital microfluidic biochip;
FIG. 2 is a 3D model of computer-aided design of a digital microfluidic biochip;
FIG. 3 is a flow chart of a method for time optimization of a computer-aided design layout of a digital microfluidic biochip;
FIG. 4 is an example of a topological relationship diagram of an operation;
FIG. 5 is a resource constraint example;
FIG. 6 is a simple example of a Markov decision algorithm;
FIG. 7 is a Markov decision algorithm iteration process;
FIG. 8 is a flow diagram for solving an optimal solution based on Markov decisions.
Detailed Description
For a more clear understanding of the technical features, objects and effects of the present invention, embodiments of the present invention will now be described in detail with reference to the accompanying drawings.
Referring to fig. 3, it is a flow chart of a time optimization method for a digital microfluidic biochip computer aided design layout, the method specifically includes:
s1, establishing models of preferential constraint, resource constraint, non-overlapping constraint and fluid constraint conditions:
each standard simulation experiment of the microfluidic biochip has its own parameter setting, and the upper size limit and the upper time limit of the experiment are given in the input file, for example, the parameter setting Fixed:10 360, which means that the upper size limit of the experiment is 10 × 10, the upper time limit is 360, each reagent or operation also gives the occupied size, and in the course of performing a series of reactions of the experiment, all operations cannot exceed the boundary of the size, and the total reaction time cannot exceed the upper time limit.
In the computer aided design, the following four constraints are also considered:
(1) And (6) preferentially constraining. The order of preference of chemical reactions defines the order of execution for different operations during the design of a digital microfluidic biochip. During the computer aided design of a chip, the precedence constraints define the execution sequence of all operations. Aiming at a series of chain biochemical reactions, according to the interdependence relation between reactants, establishing a directed graph to define the constraint relation between the biochemical reactions, and marking as G = { O, P }, wherein two parameters of O and P in the graph G 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 a preferential constraint between two chemical reactions, m.gtoreq.n.
As shown in FIG. 4, the execution sequence of operations may be represented by a time-based topology, with each node representing a buffer or an operation, and the t-axis representing when each node executes. DsB represents buffering, buffering needs to be carried out after preparation time before being used and entering the next operation, dsR represents reaction reagents, mix represents mixing operation, dlt represents diluting operation, most nodes need to be executed after own predecessors are executed, and meanwhile, a part of nodes have no predecessors and have preparation time. In fig. 3, only the Mix products of Mix2 and Mix3 are obtained, the dilution operation of Dlt2, the mixed product of DsB1 and DsB2 with DsR, and the dilution operation of the mixed product of DsB3 and DsB4 with the mixed product of DsB4 and DsB5 are performed to obtain the final product Opt.
(2) And (4) resource constraint. Ensuring that each type of chemical agent is used in the whole series of biochemical reactions, and the resource limit of the chemical agent is not exceeded. The resources are divided into non-reconfigurable resources and reconfigurable resources, the non-reconfigurable resources including optical detectors and optical distribution ports. Reconfigurable resources include all buffers, reagents and operation artifacts, and resource constraints define that all reconfigurable resources cannot exceed the upper bound on the amount of ownership of the resource when used by multiple operations at the same time. The modeling of the resource constraint specifically includes:
defining the dosage of the chemical agent a in the chemical reaction as m a The total amount of the agent a is M a The resource constraint model is:
as shown in fig. 5, a simple 2D diagram is used to explain that there are only two resources i at time t, but in this case, operation 1, operation 2, and operation 3 all need to use resource i, and only two of them can be completed.
(3) No overlapping constraints. Non-overlapping constraints ensure that no two or more operations are performed at the same time and at the same location. The modeling of the overlap constraint specifically includes:
define a C x,y E {0,1}: indicates whether a chemical agent may be present at point (x, y) if C x,y =1, meaning that the spot can be placed with a chemical reagent, which is considered as a free cell; if C x,y =0, indicating that the spot is already occupied and that no more chemicals different from the current one can be present;
the model of the overlap constraint is:
∑ x,y C x,y (L)≤1,
all reagents L.
(4) And (4) fluid restriction. The fluid confinement defines the minimum spacing between two non-reactive droplets in the same module, which is one cell on the chip. The modeling of the fluid constraints specifically includes:
the digital microfluidic biochip is unitized, namely the digital microfluidic biochip is divided into a plurality of unit cells according to a set industrial size standard, the lower left corner of each unit cell is the starting point of the unit cell, the coordinate of each unit cell is calculated according to the relative position of the unit cell and the starting point unit cell and is marked as (x, y), and chemical agents move, remain and react on the digital microfluidic biochip by taking the unit cell as a unit so as to ensure that a fluid constraint condition is met.
All operations must comply with the above constraints.
S2, establishing a target model of the total time of the chain biochemical reaction on the digital microfluidic biochip:
wherein, { o 1 ,o 2 ,…,o n Represents all the run set of the experiment, n ≧ 2,t (o) i ) Represents each operation o i The execution time of (c);
s3, solving the optimal solution of the target model of the completion time according to the models of the four constraint conditions based on Markov decision;
in probability theory and statistics, the Markov Decision process (abbreviated as MDPs) provides a mathematical architecture model for how decisions are made in the face of partially random, partially Decision-maker controlled, states. The Markov decision process is a five-tuple { S, A, P } a (s,s′),R a (s, s'), δ ∈ (0,1) }, wherein
(1)S＝{s 0 ,s 1 ,…,s n Is a set of states;
(2) A is a movementMaking an album, A s Indicating acceptable action at state s;
(3)R a (s, s ') represents the probability that state s is transformed into state s' by action a;
(4)R a (s, s ') represents the value of the reward for which state s is transformed into state s' by action a, the value being calculated by the reward function R;
(5) δ is a discount factor that is used to represent the effect of future state transitions on the present reward.
A markov decision process has the feature that every two states are conditionally independent of each other, and the next state s' depends on the current state s. The core problem of the markov decision process is to find the scheme with the largest accumulated reward value, where pi(s) is used to store the state s and the action.
FIG. 6 shows an example of a Markov decision process with 4 states, 5 actions and corresponding probabilities and reward values en route, assuming s 0 Is to start upState, it has only one action a available 0 ，s 0 Can be implemented by action a 0 Is converted into a state s 1 And state s 2 Is converted into a state s 1 Has a reward value of 0.6 x2, which is converted into a state s 2 Has a prize value of 0.4 x 3. Their prize values are 1.2, but the former has a small probability with a large return and the latter has a small probability with a large return. The Markov decision process then proceeds to the next iteration from state s 1 Or state s 2 And starting. It can be seen that there are four schemes in the figure that can reach the final state s 3 And calculating and comparing the four schemes to obtain the best scheme(s) 0 ,a 0 ,s 2 ,a 2 ,s 3 ) As shown in fig. 7.
Referring to FIG. 8, a flow diagram for solving an optimal solution based on Markov decisions.
Firstly, importing data, wherein the imported data comprises constraint conditions, reactants and products of chemical reactions to be generated, reaction time, chip space required by the reaction to be completed, the total amount of each chemical and the total size of a chip;
then establishing a topological relation graph G = { O, P }; generating directed edges by the topological relation graph according to the dependency of chemical reactions, wherein each node in the graph is a chemical reaction;
searching from the topological relation graph G according to the priority of the directed graph, and judging whether the chemical reactions which are not carried out and are finished exist or not; if yes, selecting preset nodes from the G to carry out Markov decision, updating the G according to a decision result, and judging whether the unused nodes exist in the G again until the unused nodes do not exist in the G;
and obtaining the final G as the optimal solution.
And S4, controlling the implementation process of biochemical reaction on the digital microfluidic biochip according to the optimal solution.
The invention provides a time optimization algorithm of a computer-aided design layout of a digital microfluidic biochip based on a Markov decision process. We represent the input to the layout problem as the graph G = { O, P }, G contains all protocols of the experiment,O＝{o 1 ,o 2 ,…,o n represents the operating set of the experiment, P = { P ≧ 2) 1 ,p 2 ,…,p m The } n.gtoreq.2 represents a preferential constraint between all operations, the following is an objective function of the total reaction time:
s.t.
wherein n represents the total number of operations, t (o) i ) Represents each operation o i The execution time of the chemical reaction is m, the dosage of the chemical reaction agent a is m a The total amount of the medicament a is M a ，C x,y E {0,1} indicates whether a chemical agent can exist at point (x, y), each operation is treated as a module, the projection of the module onto the x-y plane becomes a rectangle, and the position of each rectangle is determined by four coordinates.
While the present invention has been described with reference to the embodiments shown in the drawings, the present invention is not limited to the embodiments, which are illustrative and not restrictive, and it will be apparent to those skilled in the art that various changes and modifications can be made therein without departing from the spirit and scope of the invention as defined in the appended claims.
Claims (3)
1. A time optimization method for computer aided design layout of a digital microfluidic biochip is characterized by comprising the following steps:
s1, establishing a model of the following four constraint conditions:
1) Preferential constraint conditions are as follows: the order of precedence of chemical reactions defines the order of execution for different operations during the design of the digital microfluidic biochip; the modeling of the precedence constraint specifically includes:
aiming at a series of chain biochemical reactions, according to the interdependence relation between reactants, establishing a directed graph to define the constraint relation between the biochemical reactions, and marking as G = { O, P }, wherein two parameters of O and P in the graph G are defined as follows:
O＝{o 1 ,o 2 ,…,o n }: represents a series of biochemical reactions;
P＝{p 1 ,p 2 ,…,p m }: representing a preferential constraint condition between two chemical reactions, wherein m is more than or equal to n;
2) Resource constraint conditions are as follows: ensuring that each type of chemical agent is used in the whole series of biochemical reactions and does not exceed the upper limit of the resource limit; the modeling of the resource constraint specifically includes:
defining the dosage of the chemical agent a in the chemical reaction as m a The total amount of the medicament a is M a The resource constraint model is:
3) Overlap constraint conditions: the series of biochemical reactions are ensured not to be executed at the same position at the same time point; the modeling of the overlap constraint specifically includes:
define a C x,y E {0,1}: indicates whether a chemical agent may be present at point (x, y) if C x,y =1, meaning that the spot can be placed with a chemical reagent, which is considered as a free cell; if C x,y =0, meaning that the spot is already occupied and no more chemical reagents than currently exist;
the model of the overlap constraint is:
∑ x,y C x,y (L)≤1,
all reagents L;
4) Fluid constraint conditions: defining a minimum spacing between droplets of the digital microfluidic biochip; the digital microfluidic biochip is unitized, namely the digital microfluidic biochip is divided into a plurality of cells according to a set industrial size standard, the lower left corner of each cell is the starting point of the cell, the coordinate of each cell is calculated by the relative position of the cell and the starting point cell and is marked as (x, y), and chemical agents move, remain and react on the digital microfluidic biochip by taking the cell as a unit so as to ensure that a fluid constraint condition is met;
s2, establishing a target model of the total time of the chain biochemical reaction on the digital microfluidic biochip:
wherein, { o 1 ,o 2 ,…,o n Represents all the run set of the experiment, n ≧ 2,t (o) i ) Represents each operation o i The execution time of (c);
s3, solving the optimal solution of the target model of the completion time according to the models of the four constraint conditions based on Markov decision;
and S4, controlling the implementation process of biochemical reaction on the digital microfluidic biochip according to the optimal solution.
2. The method for time optimization of computer-aided design layout of digital microfluidic biochips according to claim 1, wherein step S3 specifically comprises:
establishing a topological relation graph G = { O, P };
the topological relation graph generates directed edges according to the dependency relation of chemical reactions, and each node in the graph is a chemical reaction;
searching from the topological relation graph G according to the priority of the directed graph, and judging whether chemical reactions which are not carried out and are finished exist or not; if yes, selecting preset nodes from the G to carry out Markov decision, updating the G according to a decision result, and then judging whether the unused nodes exist in the G again until the unused nodes do not exist in the G;
and obtaining the final G as the optimal solution.
3. The method for time optimization of computer-aided design layout of digital microfluidic biochip according to claim 1, wherein the minimum distance in the fluid constraints in step S1 is one cell on the chip.
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