# US 11,443,085 B2 · Model for fluid and mass transport in a recirculating microfluidic system

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- Number: US 11,443,085 B2
- Document ID: US11443085B2
- Status: Granted
- Kind: B2
- Application number: 16/381,660
- Filed: 2019-04-11
- Published: 2019-10-17
- Granted: 2022-09-13
- Earliest claimed: 2018-04-11
- Assignees: University of Central Florida Research Foundation, Inc.
- Applicants: University of Central Florida Research Foundation, Inc.
- Inventors: James Hickman; Kazi Tasneem; Christopher Long
- Web page: https://patentgrep.com/patent/US11443085B2

## CPC

- G01N 33/52: Use of compounds or compositions for colorimetric, spectrophotometric or fluorometric investigation, e.g. use of reagent paper {and including single- and multilayer analytical elements (immunological elements G01N33/54386; involving labelled immunochemicals G01N33/58; for haemoglobin or occult blood G01N33/72)}
- G06F 30/23: using finite element methods [FEM] or finite difference methods [FDM]
- B01L 3/5023: {with a sample being transported to, and subsequently stored in an absorbent for analysis}
- B01L 3/5027: {by integrated microfluidic structures, i.e. dimensions of channels and chambers are such that surface tension forces are important, e.g. lab-on-a-chip}
- G01N 33/53: Immunoassay; Biospecific binding assay; Materials therefor
- C12Q 2565/629: being a microfluidic device
- G06F 2111/20: Configuration CAD, e.g. designing by assembling or positioning modules selected from libraries of predesigned modules
- G01N: INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES (measuring or testing apparatus or processes other than immunoassay, involving enzymes or microorganisms C12M, C12Q)
- G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N)
- B01L: CHEMICAL OR PHYSICAL LABORATORY APPARATUS FOR GENERAL USE
- C12Q: MEASURING OR TESTING PROCESSES INVOLVING ENZYMES, NUCLEIC ACIDS OR MICROORGANISMS (immunoassay G01N33/53); COMPOSITIONS OR TEST PAPERS THEREFOR; PROCESSES OF PREPARING SUCH COMPOSITIONS; CONDITION-RESPONSIVE CONTROL IN MICROBIOLOGICAL OR ENZYMOLOGICAL PROCESSES

## Abstract

Disclosed herein are microfluidic systems with recirculation of fluid and computer-implemented methods of calculating conditions within the microfluidic systems. The microfluidic systems include a computing device and a microfluidic device having first and second reservoirs, at least one chamber, and a fluid path connecting the first reservoir, the chamber, and the second reservoir. The methods for calculating conditions include receiving a first reservoir fluid volume, a second reservoir fluid volume, a first concentration, and a second concentration. The methods further include receiving a time-dependent imposed pressure difference between the first reservoir and the second reservoir, then determining a hydraulic pressure difference and an effective pressure difference. The effective pressure difference is used to account for reactions occurring within the microfluidic device and to determine the value of the condition within the microfluidic device. Methods of performing an experiment using a microfluidic device with recirculation are also disclosed herein.

## Claims

### Claim 1

A computer-implemented method of calculating a condition within a microfluidic device with recirculation, the method comprising:
receiving a first reservoir fluid volume,
receiving a second reservoir fluid volume,
receiving a first concentration, the first concentration being the concentration of a component in a first reservoir,
receiving a second concentration, the second concentration being the concentration of the same component in a second reservoir,
receiving a time-dependent imposed pressure difference between the first reservoir and the second reservoir,
determining a hydraulic pressure difference, wherein the hydraulic pressure difference is based on a first volumetric height of fluid in the first reservoir and a second volumetric height of fluid in the second reservoir,
determining an effective pressure difference between the first and second reservoirs, wherein the effective pressure difference is based on the imposed pressure difference and the hydraulic pressure difference,
using the effective pressure difference, accounting for reactions occurring within the microfluidic device that deplete or increase the first and second concentrations of the component,
determining a value of the condition within the microfluidic device, and
controlling an experiment using the microfluidic device with recirculation based on the value of the condition within the microfluidic device.

### Claim 2 (depends on 1)

The computer-implemented method of claim 1, wherein the condition is the concentration of the component at a specific spatial location, a concentration profile over a specified spatial region, an effective flow rate of the fluid between the first and second reservoirs, a mass transport property of the component, a shear stress on a unit of the microfluidic device, a shear stress on an object positioned within a unit of the microfluidic device, a shear stress at a material interface, a shear rate within the microfluidic device, a flow rate between two chambers of the microfluidic device, or the average molecular velocity of the component.

### Claim 3 (depends on 1)

The computer-implemented method of claim 1, wherein the imposed pressure difference changes over at least one time step.

### Claim 4 (depends on 3)

The computer-implemented method of claim 3, further comprising receiving the imposed pressure difference, the first reservoir fluid volume, the second reservoir fluid volume, the first concentration, and the second concentration before the at least one time step.

### Claim 5 (depends on 3)

The computer-implemented method of claim 3, wherein the value of the condition is determined before and after the at least one time step.

### Claim 6 (depends on 1)

The computer-implemented method of claim 1, wherein accounting for reactions comprises accounting for at least one surface or volume reaction.

### Claim 7 (depends on 6)

The computer-implemented method of claim 6, wherein the at least one surface or volume reaction results in the generation or depletion of a biological molecule.

### Claim 8 (depends on 6)

The computer-implemented method of claim 6, wherein the at least one surface or volume reaction is a reaction of the component with a surface component that is attached to a surface within the microfluidic device.

### Claim 9 (depends on 8)

The computer-implemented method of claim 8, wherein the surface component is selected from a group consisting of an enzyme and a cell.

### Claim 10 (depends on 6)

The computer-implemented method of claim 6, wherein the at least one surface or volume reaction is affected by one or more of the following variables: the dimensions of the surface, the spatial location of the surface within the microfluidic device, the concentration of the component at the specific spatial location of the surface, a concentration profile over a specified spatial region around the surface, an effective flow rate of the fluid between the first and second reservoirs, a time dependent mass transport rate, a time dependent shear rate, a time dependent shear stress, a time dependent flow rate of fluid among the microfluidic chambers, and the average molecular velocity of the component.

### Claim 11 (depends on 1)

The computer-implemented method of claim 1, wherein accounting for reactions comprises accounting for at least one bulk reaction.

### Claim 12 (depends on 11)

The computer-implemented method of claim 11, wherein the at least one bulk reaction is affected by one or more of the following variables: the concentration of the component at the specific spatial location within the fluid, a concentration profile over a specified spatial region within the fluid, an effective flow rate of the fluid between the first and second reservoirs, time dependent mass transport rates, time dependent shear rates, time dependent shear stresses, time dependent flow rates of fluid among the microfluidic chambers, and the average molecular velocity of the component.

### Claim 13 (depends on 1)

The computer-implemented method of claim 1, further comprising accounting for convection or diffusion of the component.

### Claim 14 (depends on 13)

The computer-implemented method of claim 13, wherein convection or diffusion is affected by one or more of the following variables: the spatial location within the fluid, the concentration of the component at the specific spatial location within the microfluidic device, a concentration profile over a specified spatial region within the fluid, an effective flow rate of the fluid between the first and second reservoirs, time dependent mass transport rates, time dependent shear rates, time dependent shear stresses, time dependent flow rates of fluid among the microfluidic chambers, the average molecular velocity of the component, and bulk or surface or volume reactions taking place within the microfluidic device.

### Claim 15 (depends on 13)

The computer-implemented method of claim 13, wherein the imposed pressure difference changes over at least one time step, and accounting for convection or diffusion occurs before and after the at least one time step.

### Claim 16 (depends on 1)

The computer-implemented method of claim 1, wherein the method further comprises using a finite element method with boundary conditions.

### Claim 17 (depends on 16)

The computer-implemented method of claim 16, wherein the boundary conditions are set for an opening between at least one of the first or second reservoir, and wherein the boundary conditions are selected from a group consisting of the imposed pressure difference; the first reservoir fluid volume, the second reservoir fluid volume, or both; the value of a condition determined in a previous time step; and the first concentration, the second concentration, or both.

### Claim 18 (depends on 1)

The computer-implemented method of claim 1, wherein the method further comprises determining the value of the condition using analytical methods.

### Claim 19 (depends on 18)

The computer-implemented method of claim 18, further comprising at least one chamber in fluid communication with the first reservoir and the second reservoir, and wherein the at least one chamber is modeled as a fluid resistor in the analytical methods.

### Claim 20 (depends on 19)

The computer-implemented method of claim 19, wherein the first and second reservoirs are modeled as capacitors in the analytical methods.