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Design of a Passive Flow Regulator Using a Genetic Algorithm
Available online at www.sciencedirect.com
ScienceDirect Procedia Engineering 168 (2016) 1016 – 1019
30th Eurosensors Conference, EUROSENSORS 2016
Design of a passive flow regulator using a genetic algorithm D. Dumont-Fillona*, M. Hannebelleb, H. Van Lintelb, E. Chappela a
b
Debiotech SA, 28 avenue Sévelin, Lausanne 1004, Switzerland
LMIS4, Swiss Federal Institute of Technology, Lausanne 1015, Switzerland
Abstract Passive flow regulators are usually intended to deliver or drain a fluid at a constant rate independently from pressure variations. Microfluidic devices made of a stack of two plates are considered here: the first plate comprises a flexible silicon membrane having through holes while the second plate is a rigid substrate with a cavity, an outlet hole and pillars aligned with the through holes of the membrane. The liquid flows through the holes etched in the membrane and through the small gap between the bottom of the membrane and the pillars: each hole can therefore be considered as a valve which progressively closes as the pressure increases, thus leading to a non-linear fluidic behaviour. FEM simulations have been performed to ensure a constant flow rate in the specified range of pressure. To make the design reliable, the device characteristics have been optimized using an evolutionary algorithm. The fitness function notably takes into account machining and alignment tolerances. Typical designs dedicated to drug delivery and hydrocephalus treatment are discussed. © 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license © 2016 The Authors. Published by Elsevier Ltd. (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of the 30th Eurosensors Conference. Peer-review under responsibility of the organizing committee of the 30th Eurosensors Conference Keywords: Valve ; flow regulator ; optimization ; genetic algorithm ; hydrocephalus ; drug delivery
1. Introduction We present here a passive flow regulator that can be used for many applications from hydrocephalus treatment to drug infusion. In order to address the complexity of design optimization while accounting for micromachining tolerances, we propose to use an original method based on random mutations using a genetic algorithm.
* Corresponding author. Tel.: +41-216-236-022; fax: +41-216-236-001. E-mail address: [email protected]
1877-7058 © 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of the 30th Eurosensors Conference
doi:10.1016/j.proeng.2016.11.329
1017
D. Dumont-Fillon et al. / Procedia Engineering 168 (2016) 1016 – 1019
(a)
(b)
Top wafer
Membrane
Gap
Fitness (a.u.)
Inlet holes
Mean fitness per generation Max fitness per generation
Bottom wafer
Pillars 0 Outlet hole
100 200 Number of generations
300
Fig. 1. (a) Schematic cross-section of the valve (not to scale); (b) Evolution of the fitness over 350 generations.
1.1. ChronoFlow device ChronoFlow is a passive flow regulator for biomedical applications which can deliver a constant flow rate independently from pressure variations. The device is made of a stack of two patterned wafers (see Fig. 1). The one on top is etched to create a membrane having through holes facing pillars etched in the bottom one. A gap separates the bottom of the holes from the top of the pillars when no pressure is applied on the device. The bottom wafer also comprises a large outlet hole. The inlet of the device is in direct communication with the top surface of the flexible membrane. When the pressure of the fluid at the inlet increases, the membrane deflects, closing progressively the membrane holes with the facing pillars thus reducing the flow. A typical low pressure (P < 200 mbar) application is the derivation of cerebrospinal fluid from the brain ventricles toward the peritoneum. A high pressure application is for instance intravenous protein infusion for immunotherapy. The adjustment of the device dimensions is made step by step to finally get the expected flow regulation profile [1]. This iterative process starts with the positioning of a first valve located on the outer edge of the membrane. This valve is intended to determine the high pressure fluidic characteristics of the device. Additional valves located near the centre of the membrane are then introduced to gradually describe the expected flow rate profile at lower pressures. Because there is potentially a large number of valve configurations meeting the requirements for the targeted flow rate profile, there is a need to define design rules in order to make a selection and to find an optimum configuration. Instead of mimicking the manual iterative design phase described above, we have considered a genetic algorithm since it is well adapted to solve complex problems with a large number of variables. 1.2. Dealing with fabrication tolerances The key parameters to achieve delivery accuracy within the range +/-10% are: the membrane thickness, the gap depth, the hole diameters and the alignment between the holes and the pillars. The two first parameters can easily be controlled using SOI wafers. The impact of the other machining or alignment tolerances on delivery accuracy are reduced as much as possible by design. Fig. 2a provides the fluidic simulations of a device for which the difference of radius between one of the two holes and its facing pillar is only 13.5 µm. A misalignment of 12 µm induces here an increase of about 50% of the flow rate at low pressure. This kind of large misalignment can be observed, for example, when the wafers are bonded together using an intermediate layer made of a thermoplastic material such as parylene. Instead of trying to reduce further the tolerances, we chose to improve the valve design in order to make it more tolerant to process variabilities. But, given the complexity of this optimization problem, manual design with a trial and error process was no longer possible. A specific program that accounts for fabrication tolerances and flow regulation requirements has therefore been developed in order to design a safe, effective and reliable valve.
1018
D. Dumont-Fillon et al. / Procedia Engineering 168 (2016) 1016 – 1019
(b) 8
8
7
7
6
6
5
Flow rate (mL/h)
Flow rate (mL/h)
(a)
Max at 3 sigma Nominal Target
4 3 2 1
5
Max at 3 sigma Nominal Target
4 3 2 1
0
0
0
200
400
Pressure (mbar)
600
800
0
200
400
600
800
Pressure (mbar)
Fig. 2. Simulation of the flow profile for a valve design delivering a constant flow rate of 5 mL/h in the range 100 to 300 mbar, (a) before optimisation considering the tolerances of the different fabrication process steps; (b) after 350 generations of optimisation.
2. Genetic algorithm 2.1. Principle Conventional optimization algorithms, such as gradient-descent, becomes very complex for multivariable and nonlinear systems. On the other side, some bio-inspired algorithms are being increasingly used for automatic solving of complex problems [2]. Based on Darwinian principles, an evolutionary algorithm relies on random mutations, selection and reproduction of the best individuals (being valves in our case) over the generations. 2.2. Creating a population of valves In the algorithm, each individual (device) is described by its genotype (set of parameters) : number of holes and pillars, hole position and diameter, pillar diameter… These parameters vary from one valve to the other and may change during mutations. Other characteristics suh as global geometry of the device or membrane thickness are kept constant since the large mechanical deformation profile of the membrane is obtained through non-linear FEM simulations and not using an analytical formula. These parameters are initially defined by simple consideration on the regulation pressure range, burst pressure and fluidic interconnection issues. 2.3. Simulation of a valve performance Two models have been developed: a finite element model to compute the membrane deflection as a function of pressure, and an analytical fluidic model, to derive the flow based on membrane deflection and pressure. By combining these two models, it is possible to determine the flow going through a valve for a given pressure applied on the membrane. There is an excellent match between the output of these models and experimental measurements [1]. We give here a brief overview of the fluidic pathway through the device and basic considerations for the fluidic modeling. The pressure of the reservoir is active on the top surface of the membrane. This pressure deflects the membrane towards the substrate, thus progressively obturating the holes and pushes the fluid through the hole and the annular valve seat made of the membrane bottom side and the pillar top side. Using the deformation profile of the membrane for different pressure conditions, we have built an approximated analytical mathematical model of the fluid flow rate for each valve. This model is based on the expression of the fluid flow rate as a function of the pressure difference between inlet and outlet as well as the fluidic resistance. The singular losses are established from geometrical considerations regarding the fluid flow behavior in the valve as a function of its position. This model includes potential misalignments between the two wafers. 3D FEM simulations of an individual valve has been made to refine the
D. Dumont-Fillon et al. / Procedia Engineering 168 (2016) 1016 – 1019
1019
analytical model, in particular the numerical constants used for singular head losses. These losses are proportional to the square of the flow rate and therefore we should consider them at high flow rate. It is important to note that the reversibility of the flow is no longer valid. We should therefore build a model for each direction of the flow. 2.4. Selection, reproduction and mutation The fitness function (see Fig. 1b) is a measure of the valve performance, like a grade. It is used to determine which individuals are the best to be selected and duplicated for the next generation. The simulation program eliminates all others. Even though mutations are random in the current version of the program, all parameters are set to vary in a given range of values. Additionally to valve dimensional variations (hole/pillar diameter and radial position), the program can also randomly add or delete a new valve to the design. In the same way, a pillar can also randomly get removed from a valve, leaving only a hole that would remain unobstructed even at high pressure. This sort of particularity can be desired for applications such as hydrocephalus care when one wants to rapidly evacuate a large intracranial overpressure. Mutation probability and amplitude are also tuneable. Moreover, a minimal diameter difference between pillar and hole has to be chosen in order to minimize the effects of wafer misalignment on the device operation. It is also possible to adjust the importance, in the fitness evaluation, of the maximum fabrication induced error at 3σ, leading to more reliable designs with respect to standard variability in production. This additional curve (see Fig. 2) simulates the output flow rate of the design not with perfect dimensions but altered ones, taking into account the worst combination of tolerances at 3σ that would increase this flow rate. The fitness function is set to measure two main parameters: x valve flow control = its flow curve must be as close as possible to a target value in a given range of pressure x valve sensitivity to fabrication tolerances = if the differences between the valve with no fabrication tolerances, and the one in the worst case is too high, the fitness is decreased 3. Results 3.1. Evolution over the generations Fig. 2 shows the importance of design optimization with respect to micromachining tolerances. Fig. 2a displays a design having a good nominal fitness, with respect to the targeted flow rate, but a very poor tolerance to process variations at 3σ during fabrication. This kind of design can pass as viable on paper but when confronted with production reality, it can show a high rejetion ratio. On the other hand, the design of Fig. 2b demonstrates a good reliability even at 3σ. About 100 generations have been necessary to significantly improve the design (see Fig. 1b). After that, we see minor improvements until generation 175 and then a plateau until generation 250. At that point, mutation amplitude has been reduced to allow some more finer optimization. It is noticeable when looking at the mean fitness per generation. A large difference between mean and max implies that variation amplitude is too large with respect to the remaining design improvement margin. Hence a low probability of effectively improving the design. 4. Conclusion The designs of passive flow regulators for applications such as drug delivery or hydrocephalus treatment have been optimized using an evolutionary algorithm. Machining and alignment tolerances for estimating the fitness function have been taken into account. In mass production, we show that Chronoflow device can achieve, at fixed temperature, a flow rate accuracy in the range of +/-10% at 3σ. References [1] E. Chappel, D. Dumont-Fillon, S. Mefti, Passive flow regulators for drug delivery and hydrocephalus treatment, Proc. SPIE 8976, Microfluidics, BioMEMS, and Medical Microsystems XII, 89760S, March 6, 2014. [2] D. Floreano, C. Mattiussi, Bio-inspired artificial intelligence: theories, methods and technologies, MIT Press, Aug. 2008.
ScienceDirect Procedia Engineering 168 (2016) 1016 – 1019
30th Eurosensors Conference, EUROSENSORS 2016
Design of a passive flow regulator using a genetic algorithm D. Dumont-Fillona*, M. Hannebelleb, H. Van Lintelb, E. Chappela a
b
Debiotech SA, 28 avenue Sévelin, Lausanne 1004, Switzerland
LMIS4, Swiss Federal Institute of Technology, Lausanne 1015, Switzerland
Abstract Passive flow regulators are usually intended to deliver or drain a fluid at a constant rate independently from pressure variations. Microfluidic devices made of a stack of two plates are considered here: the first plate comprises a flexible silicon membrane having through holes while the second plate is a rigid substrate with a cavity, an outlet hole and pillars aligned with the through holes of the membrane. The liquid flows through the holes etched in the membrane and through the small gap between the bottom of the membrane and the pillars: each hole can therefore be considered as a valve which progressively closes as the pressure increases, thus leading to a non-linear fluidic behaviour. FEM simulations have been performed to ensure a constant flow rate in the specified range of pressure. To make the design reliable, the device characteristics have been optimized using an evolutionary algorithm. The fitness function notably takes into account machining and alignment tolerances. Typical designs dedicated to drug delivery and hydrocephalus treatment are discussed. © 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license © 2016 The Authors. Published by Elsevier Ltd. (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of the 30th Eurosensors Conference. Peer-review under responsibility of the organizing committee of the 30th Eurosensors Conference Keywords: Valve ; flow regulator ; optimization ; genetic algorithm ; hydrocephalus ; drug delivery
1. Introduction We present here a passive flow regulator that can be used for many applications from hydrocephalus treatment to drug infusion. In order to address the complexity of design optimization while accounting for micromachining tolerances, we propose to use an original method based on random mutations using a genetic algorithm.
* Corresponding author. Tel.: +41-216-236-022; fax: +41-216-236-001. E-mail address: [email protected]
1877-7058 © 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of the 30th Eurosensors Conference
doi:10.1016/j.proeng.2016.11.329
1017
D. Dumont-Fillon et al. / Procedia Engineering 168 (2016) 1016 – 1019
(a)
(b)
Top wafer
Membrane
Gap
Fitness (a.u.)
Inlet holes
Mean fitness per generation Max fitness per generation
Bottom wafer
Pillars 0 Outlet hole
100 200 Number of generations
300
Fig. 1. (a) Schematic cross-section of the valve (not to scale); (b) Evolution of the fitness over 350 generations.
1.1. ChronoFlow device ChronoFlow is a passive flow regulator for biomedical applications which can deliver a constant flow rate independently from pressure variations. The device is made of a stack of two patterned wafers (see Fig. 1). The one on top is etched to create a membrane having through holes facing pillars etched in the bottom one. A gap separates the bottom of the holes from the top of the pillars when no pressure is applied on the device. The bottom wafer also comprises a large outlet hole. The inlet of the device is in direct communication with the top surface of the flexible membrane. When the pressure of the fluid at the inlet increases, the membrane deflects, closing progressively the membrane holes with the facing pillars thus reducing the flow. A typical low pressure (P < 200 mbar) application is the derivation of cerebrospinal fluid from the brain ventricles toward the peritoneum. A high pressure application is for instance intravenous protein infusion for immunotherapy. The adjustment of the device dimensions is made step by step to finally get the expected flow regulation profile [1]. This iterative process starts with the positioning of a first valve located on the outer edge of the membrane. This valve is intended to determine the high pressure fluidic characteristics of the device. Additional valves located near the centre of the membrane are then introduced to gradually describe the expected flow rate profile at lower pressures. Because there is potentially a large number of valve configurations meeting the requirements for the targeted flow rate profile, there is a need to define design rules in order to make a selection and to find an optimum configuration. Instead of mimicking the manual iterative design phase described above, we have considered a genetic algorithm since it is well adapted to solve complex problems with a large number of variables. 1.2. Dealing with fabrication tolerances The key parameters to achieve delivery accuracy within the range +/-10% are: the membrane thickness, the gap depth, the hole diameters and the alignment between the holes and the pillars. The two first parameters can easily be controlled using SOI wafers. The impact of the other machining or alignment tolerances on delivery accuracy are reduced as much as possible by design. Fig. 2a provides the fluidic simulations of a device for which the difference of radius between one of the two holes and its facing pillar is only 13.5 µm. A misalignment of 12 µm induces here an increase of about 50% of the flow rate at low pressure. This kind of large misalignment can be observed, for example, when the wafers are bonded together using an intermediate layer made of a thermoplastic material such as parylene. Instead of trying to reduce further the tolerances, we chose to improve the valve design in order to make it more tolerant to process variabilities. But, given the complexity of this optimization problem, manual design with a trial and error process was no longer possible. A specific program that accounts for fabrication tolerances and flow regulation requirements has therefore been developed in order to design a safe, effective and reliable valve.
1018
D. Dumont-Fillon et al. / Procedia Engineering 168 (2016) 1016 – 1019
(b) 8
8
7
7
6
6
5
Flow rate (mL/h)
Flow rate (mL/h)
(a)
Max at 3 sigma Nominal Target
4 3 2 1
5
Max at 3 sigma Nominal Target
4 3 2 1
0
0
0
200
400
Pressure (mbar)
600
800
0
200
400
600
800
Pressure (mbar)
Fig. 2. Simulation of the flow profile for a valve design delivering a constant flow rate of 5 mL/h in the range 100 to 300 mbar, (a) before optimisation considering the tolerances of the different fabrication process steps; (b) after 350 generations of optimisation.
2. Genetic algorithm 2.1. Principle Conventional optimization algorithms, such as gradient-descent, becomes very complex for multivariable and nonlinear systems. On the other side, some bio-inspired algorithms are being increasingly used for automatic solving of complex problems [2]. Based on Darwinian principles, an evolutionary algorithm relies on random mutations, selection and reproduction of the best individuals (being valves in our case) over the generations. 2.2. Creating a population of valves In the algorithm, each individual (device) is described by its genotype (set of parameters) : number of holes and pillars, hole position and diameter, pillar diameter… These parameters vary from one valve to the other and may change during mutations. Other characteristics suh as global geometry of the device or membrane thickness are kept constant since the large mechanical deformation profile of the membrane is obtained through non-linear FEM simulations and not using an analytical formula. These parameters are initially defined by simple consideration on the regulation pressure range, burst pressure and fluidic interconnection issues. 2.3. Simulation of a valve performance Two models have been developed: a finite element model to compute the membrane deflection as a function of pressure, and an analytical fluidic model, to derive the flow based on membrane deflection and pressure. By combining these two models, it is possible to determine the flow going through a valve for a given pressure applied on the membrane. There is an excellent match between the output of these models and experimental measurements [1]. We give here a brief overview of the fluidic pathway through the device and basic considerations for the fluidic modeling. The pressure of the reservoir is active on the top surface of the membrane. This pressure deflects the membrane towards the substrate, thus progressively obturating the holes and pushes the fluid through the hole and the annular valve seat made of the membrane bottom side and the pillar top side. Using the deformation profile of the membrane for different pressure conditions, we have built an approximated analytical mathematical model of the fluid flow rate for each valve. This model is based on the expression of the fluid flow rate as a function of the pressure difference between inlet and outlet as well as the fluidic resistance. The singular losses are established from geometrical considerations regarding the fluid flow behavior in the valve as a function of its position. This model includes potential misalignments between the two wafers. 3D FEM simulations of an individual valve has been made to refine the
D. Dumont-Fillon et al. / Procedia Engineering 168 (2016) 1016 – 1019
1019
analytical model, in particular the numerical constants used for singular head losses. These losses are proportional to the square of the flow rate and therefore we should consider them at high flow rate. It is important to note that the reversibility of the flow is no longer valid. We should therefore build a model for each direction of the flow. 2.4. Selection, reproduction and mutation The fitness function (see Fig. 1b) is a measure of the valve performance, like a grade. It is used to determine which individuals are the best to be selected and duplicated for the next generation. The simulation program eliminates all others. Even though mutations are random in the current version of the program, all parameters are set to vary in a given range of values. Additionally to valve dimensional variations (hole/pillar diameter and radial position), the program can also randomly add or delete a new valve to the design. In the same way, a pillar can also randomly get removed from a valve, leaving only a hole that would remain unobstructed even at high pressure. This sort of particularity can be desired for applications such as hydrocephalus care when one wants to rapidly evacuate a large intracranial overpressure. Mutation probability and amplitude are also tuneable. Moreover, a minimal diameter difference between pillar and hole has to be chosen in order to minimize the effects of wafer misalignment on the device operation. It is also possible to adjust the importance, in the fitness evaluation, of the maximum fabrication induced error at 3σ, leading to more reliable designs with respect to standard variability in production. This additional curve (see Fig. 2) simulates the output flow rate of the design not with perfect dimensions but altered ones, taking into account the worst combination of tolerances at 3σ that would increase this flow rate. The fitness function is set to measure two main parameters: x valve flow control = its flow curve must be as close as possible to a target value in a given range of pressure x valve sensitivity to fabrication tolerances = if the differences between the valve with no fabrication tolerances, and the one in the worst case is too high, the fitness is decreased 3. Results 3.1. Evolution over the generations Fig. 2 shows the importance of design optimization with respect to micromachining tolerances. Fig. 2a displays a design having a good nominal fitness, with respect to the targeted flow rate, but a very poor tolerance to process variations at 3σ during fabrication. This kind of design can pass as viable on paper but when confronted with production reality, it can show a high rejetion ratio. On the other hand, the design of Fig. 2b demonstrates a good reliability even at 3σ. About 100 generations have been necessary to significantly improve the design (see Fig. 1b). After that, we see minor improvements until generation 175 and then a plateau until generation 250. At that point, mutation amplitude has been reduced to allow some more finer optimization. It is noticeable when looking at the mean fitness per generation. A large difference between mean and max implies that variation amplitude is too large with respect to the remaining design improvement margin. Hence a low probability of effectively improving the design. 4. Conclusion The designs of passive flow regulators for applications such as drug delivery or hydrocephalus treatment have been optimized using an evolutionary algorithm. Machining and alignment tolerances for estimating the fitness function have been taken into account. In mass production, we show that Chronoflow device can achieve, at fixed temperature, a flow rate accuracy in the range of +/-10% at 3σ. References [1] E. Chappel, D. Dumont-Fillon, S. Mefti, Passive flow regulators for drug delivery and hydrocephalus treatment, Proc. SPIE 8976, Microfluidics, BioMEMS, and Medical Microsystems XII, 89760S, March 6, 2014. [2] D. Floreano, C. Mattiussi, Bio-inspired artificial intelligence: theories, methods and technologies, MIT Press, Aug. 2008.