Vascular cavity simulation platform
By designing a vascular lumen simulation platform, the problem of difficulty in real-time acquisition of cell potential signals in the existing technology under real blood flow conditions is solved, and rapid and accurate signal acquisition and flow field stress regulation are achieved to meet the needs of different environmental simulations.
Patent Information
- Application Number
- CN202411636507.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-11-15
- Publication Date
- 2025-02-28
- Estimated Expiration
- 2044-11-15
AI Technical Summary
The prior art is difficult to collect cellular potential signals in real time under the simulated real blood flow conditions, and lacks a device that can change the magnitude of the flow field stress, which cannot meet the sampling needs of different environmental simulations.
A vascular lumen simulation platform is designed, including a fluid mechanics flow cavity base, a conductive membrane positioning substrate, a cell-bearing conductive membrane, an upper cover and a signal-derived electrode. Blood flow is simulated through the fluid mechanics flow chamber base, the conductive film positioning substrate and the cell-carrying conductive film are used to collect potential signals in real time, and the flow rate and shear stress are adjusted through the control unit and flow rate sensor to meet the needs of different environmental simulations.
It realizes real-time collection of cell potential signals under simulated real blood flow conditions, quickly and accurately reflects the endothelial state of blood flow, providing the possibility for visualization of routine cell status monitoring in physiological states.
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Figure CN119534589A_ABST
Abstract
Description
Technical Field
[0001] The invention relates to the technical field of cell electrochemistry, and in particular to a vascular cavity simulation platform. Background Art
[0002] In traditional research, cell potential can only be cultured in a static state, and then sampled in different time periods. The existing blood flow chambers are based on simulating real blood flow conditions and blood supply problems, and the evaluation results are obtained through three-dimensional calculations. They are only limited to modeling and calculation. That is, in the existing technology, there is a lack of a device that can truly simulate the blood flow in the human body and collect potential signals in real time. Summary of the invention
[0003] In view of the shortcomings of the prior art mentioned above, the purpose of the present invention is to provide a vascular cavity simulation platform to break through the traditional experimental methods, and can simulate the blood flow in the human body to collect potential signals in real time, so that the collected data is closer to the real scene, and at the same time, the flow field stress size can be changed to meet the sampling needs of different environmental simulations.
[0004] In order to achieve the above object, the present invention adopts the following technical scheme:
[0005] The present invention provides a vascular cavity simulation platform, comprising:
[0006] A fluid mechanics flow chamber base, wherein a flow chamber with an upper opening is arranged in the fluid mechanics flow chamber base, and two ends of the flow chamber are respectively connected to a first channel and a second channel;
[0007] A conductive film positioning substrate, wherein the conductive film positioning substrate is disposed in the flow chamber;
[0008] A cell-carrying conductive film, wherein the cell-carrying conductive film is fixed to the conductive film positioning substrate;
[0009] An upper cover, the upper cover is connected to the upper end of the fluid mechanics flow chamber base through a sealing ring to cover the flow chamber;
[0010] A signal derivation electrode, one end of which is connected to the cell-bearing conductive membrane, and the other end of which is sealed and passes through the upper cover through a signal derivation through hole provided on the upper cover.
[0011] Preferably, in the above-mentioned vascular cavity simulation platform, at least one laminar flow groove and at least one turbulent flow groove are arranged on the conductive membrane positioning substrate, and the cell-carrying conductive membrane is arranged in at least two, at least one of the cell-carrying conductive membranes is arranged in the laminar flow groove, and at least one of the cell-carrying conductive membranes is arranged in the turbulent flow groove.
[0012] Preferably, in the above-mentioned vascular cavity simulation platform, the length of the laminar flow groove is 8 to 12 mm, and the width is 4 to 6 mm; the semi-arc of the turbulent flow groove is 4 to 6 mm, and the length is 8 to 12 mm.
[0013] Preferably, in the above-mentioned vascular cavity simulation platform, at least two laminar grooves and at least two turbulent grooves are arranged on the conductive membrane positioning substrate, and the laminar grooves and turbulent grooves are arranged on the conductive membrane positioning substrate in a uniformly spaced manner, and each laminar groove and each turbulent groove is provided with a cell-carrying conductive membrane.
[0014] Preferably, the above-mentioned vascular cavity simulation platform also includes a liquid inlet power unit, a control unit and a flow rate sensor; wherein the liquid inlet power unit is connected to the first channel or the second channel to provide power for injecting liquid into the flow cavity, the signal output end of the control unit is connected to the signal input end of the liquid inlet power unit, the flow rate sensor is used to collect the flow rate signal at the cell-bearing conductive membrane, the signal output end of the flow rate sensor is connected to the signal input end of the control unit to feed the flow rate signal at the cell-bearing conductive membrane to the control unit, the control unit is used to calculate the shear stress at the cell-bearing conductive membrane based on the flow rate signal at the cell-bearing conductive membrane, and based on the set shear stress threshold, control the liquid inlet power unit to operate so that the shear stress at the cell-bearing conductive membrane is within the set shear stress threshold range.
[0015] Preferably, in the above-mentioned vascular cavity simulation platform, when the cell-carrying conductive membrane is arranged in the laminar flow groove, the shear stress at the cell-carrying conductive membrane is calculated as the laminar shear stress based on the flow velocity signal at the cell-carrying conductive membrane, and the control unit calculates the laminar shear stress by the following formula:
[0016]
[0017] In the formula, F1 represents the laminar shear stress, μ represents the liquid viscosity coefficient, and u x1 represents the relative movement speed of the liquid plane in the laminar flow groove, and y1 represents the liquid surface thickness in the laminar flow groove.
[0018] Preferably, in the above-mentioned vascular cavity simulation platform, when the cell-carrying conductive membrane is arranged in the turbulent groove, the shear stress at the cell-carrying conductive membrane is calculated as the turbulent shear stress based on the flow velocity signal at the cell-carrying conductive membrane, and the control unit calculates the turbulent shear stress by the following formula:
[0019]
[0020] Where μ is the viscosity coefficient of the liquid, u xrepresents the relative motion speed of the liquid plane in the turbulent groove, y represents the liquid surface thickness of the turbulent groove, ρ is the liquid density, and l is the motion path of the turbulent molecules in the vertical direction.
[0021] Preferably, in the above-mentioned vascular cavity simulation platform, the same number of first mounting holes and second mounting holes are respectively arranged on the fluid dynamics flow cavity base and the upper cover, and also include fastening bolts with the same number as the first mounting holes and the second mounting holes, and the fastening bolts tightly assemble the fluid dynamics flow cavity base and the upper cover through the first mounting holes and the second mounting holes.
[0022] Compared with the prior art, the present invention has the following beneficial effects:
[0023] The present invention provides a platform for combining and transforming real blood flow mechanical signals with electrochemical signals, converting invisible mechanical sensing into electrical information for real-time monitoring, quickly and accurately reflecting the state of blood flow endothelium, and providing the possibility for visualization of conventional cell state monitoring under physiological conditions. BRIEF DESCRIPTION OF THE DRAWINGS
[0024] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the structures shown in these drawings without paying creative work.
[0025] Figure 1 It is a schematic structural diagram of a vascular cavity simulation platform according to an embodiment of the invention.
[0026] Figure 2 The figure is a schematic diagram of the connection of electronic components of a water sampling unit of a vascular cavity simulation platform according to an embodiment of the present invention.
[0027] Reference numerals:
[0028] 1. Fluid mechanics flow chamber base; 101. Flow chamber; 102. First channel; 103. Second channel; 104. 2. Conductive membrane positioning substrate; 201. Laminar flow groove; 202. Turbulent flow groove; 3. Cell-bearing conductive membrane; 4. Upper cover; 401. 402. 5. Signal derivation electrode; 6. Sealing ring; 7. Liquid inlet power unit; 8. Control unit; 9. Flow rate sensor; 10. Fastening bolts. DETAILED DESCRIPTION
[0029] The following describes the embodiments of the present invention by specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the following embodiments and features in the embodiments can be combined with each other without conflict.
[0030] In the description of the present invention, unless otherwise specified, "plurality" means two or more than two; the orientations or positional relationships indicated by the terms "upper", "lower", "left", "right", "inner", "outer", "front end", "rear end", "head", "tail", etc. are based on the orientations or positional relationships shown in the drawings, and are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operate in a specific orientation, and therefore cannot be understood as limiting the present invention. In addition, the terms "first", "second", "third", etc. are only used for descriptive purposes and cannot be understood as indicating or implying relative importance.
[0031] In the description of the present invention, it should be noted that, unless otherwise clearly specified and limited, the terms "connected" and "connection" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection or an indirect connection through an intermediate medium. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.
[0032] The present invention will now be further described with reference to the accompanying drawings.
[0033] The embodiment of the present invention provides a vascular cavity simulation platform, such as Figure 1 As shown, the vascular cavity simulation platform includes a fluid dynamics flow cavity base 1, a conductive membrane positioning substrate 2, a cell-carrying conductive membrane 3, an upper cover 4, and a signal exporting electrode 5. A flow cavity 101 with an upper end opening is arranged in the fluid dynamics flow cavity base 1, and the two ends of the flow cavity 101 are respectively connected to a first channel 102 and a second channel 103; the conductive membrane positioning substrate 2 is arranged in the flow cavity 101; the cell-carrying conductive membrane 3 is fixed to the conductive membrane positioning substrate 2; the upper cover 4 is connected to the upper end of the fluid dynamics flow cavity base 1 through a sealing ring 6 to cover the flow cavity 101; one end of the signal exporting electrode 5 is connected to the cell-carrying conductive membrane 3, and the other end is sealed and passes through the upper cover 4 through a signal exporting through hole 401 arranged on the upper cover 4.
[0034] In this embodiment, the vascular cavity simulation platform can simulate the potential signal of cells under real blood flow conditions. Specifically, the cell-carrying conductive membrane 3 is used to carry a set number of cells, and a liquid at a constant speed can be passed into the flow cavity 101. The flow of the liquid in the flow cavity 101 is used to simulate the flow of blood. The liquid can be, for example, a liquid with similar physical properties to blood, wherein similar physical properties refer to the selected liquid having the same flow characteristics as normal blood, and common ones are TL2, TL3, TL4, artificial plasma, etc. By adjusting the liquid flow rate in the flow cavity 101, the cell potential signal under different liquid flow rates can be obtained. Among them, the cell potential signal refers to the electrical signal derived by the signal derivation electrode 5 in the case of liquid flow, and the electrical signal can be detected by a corresponding electronic detection device, and the electronic detection device here includes but is not limited to a potentiometer.
[0035] The overall structural design of the vascular cavity simulation platform is reasonable. The conductive membrane positioning substrate 2 is fixed in the flow cavity 101 to provide an installation environment for the cell-carrying conductive membrane 3 used to carry cells. The upper cover 4 cooperates with the sealing ring 6 to seal the flow cavity 101 with an upper opening to ensure that the liquid can move in the flow cavity 101. The cell-carrying conductive membrane 3 can transmit the potential signal of the cell in real time through the signal extraction electrode 5, and is connected to the electronic detection equipment arranged outside the platform, so as to collect the potential signal of the cell under simulated blood flow conditions.
[0036] In some embodiments, Figure 1 As shown, at least one laminar groove 201 and at least one turbulent groove 202 are arranged on the conductive film positioning substrate 2, and at least two cell-carrying conductive films 3 are arranged, at least one cell-carrying conductive film 3 is arranged in the laminar groove 201, and at least one cell-carrying conductive film 3 is arranged in the turbulent groove 202.
[0037] In this embodiment, in order to more realistically simulate the blood flow conditions, two grooves of different shapes are set on the conductive film positioning substrate 2, namely the laminar flow groove 201 and the turbulent flow groove 202. The cell-carrying conductive film 3 is set in multiple forms and can be fixed in the laminar flow groove 201 and the turbulent flow groove 202 by adhesion. When the liquid flows through these two grooves, different shear stresses will be generated, thereby simulating the potential signals of the cells in two different positions.
[0038] In some embodiments, the laminar groove 201 has a length of 8 to 12 mm and a width of 4 to 6 mm; the turbulent groove 202 has a semi-arc of 4 to 6 mm and a length of 8 to 12 mm.
[0039] Exemplarily, the length of the laminar groove 201 can be 10 mm and the width can be 5 mm; the semi-arc of the turbulent groove 202 is 5 mm and the length can be 10 mm. It is understandable that the above-mentioned specific size restrictions on the laminar groove 201 and the turbulent groove 202 are merely examples and are not limitations of the present invention. In some embodiments, the length of the laminar groove 201 can be any value within the range of 8 to 12 mm, and the width can be any value within the range of 4 to 6 mm; the width of the turbulent groove 202 can be any value within the range of 4 to 6 mm, and the length can be any value within the range of 8 to 12 mm.
[0040] In some embodiments, Figure 1 As shown, at least two laminar grooves 201 and at least two turbulent grooves 202 are arranged on the conductive film positioning substrate 2. The laminar grooves 201 and the turbulent grooves 202 are arranged on the conductive film positioning substrate 2 in a uniformly spaced manner, and a cell-bearing conductive film 3 is arranged in each laminar groove 201 and each turbulent groove 202.
[0041] In this embodiment, the laminar grooves 201 and the turbulent grooves 202 are arranged on the conductive film positioning substrate 2 in the form of evenly spaced arrangements, which refers to an arrangement in the manner of ABAB...AB, wherein A refers to the laminar groove 201, and B refers to the turbulent groove 202. The spacing between each laminar groove 201 and the adjacent turbulent groove 202 is equal, so that multiple laminar positions and multiple turbulent positions can be simulated simultaneously.
[0042] For example, Figure 1 As shown, the laminar flow groove 201 and the turbulent flow groove 202 are both set to four, and the cell-carrying conductive membrane 3 and the signal exporting electrode 5 are correspondingly set to eight, and each cell-carrying conductive membrane 3 is respectively connected to a signal exporting electrode 5 to export the cell potential signal of the corresponding detection position. The effect of simulating the blood flow dynamics at different positions can be achieved by regulating the flow velocity of the blood flow cavity.
[0043] In some embodiments, in order to enable the real blood flow simulation to achieve the set blood flow dynamic effect, such as Figure 2As shown, the vascular cavity simulation platform includes a fluid inlet power unit 7, a control unit 8 and a flow rate sensor 9; the flow rate signal at the corresponding position is collected by the flow rate sensor 9, and the control unit 8 converts the corresponding flow rate signal into shear stress to control the power output of the fluid inlet power unit 7 according to the shear stress, so that the blood flow dynamic effect at the detection position can achieve the set effect, that is, this embodiment uses shear stress as a parameter to characterize the working condition of cells under blood flow conditions, and different shear stresses represent the working conditions of cells under different blood flow dynamics. By adjusting the fluid inlet power unit 7, the cells can be placed in the set working condition, thereby realizing the cell potential signal collection under various set working conditions to meet various experimental needs.
[0044] Specifically, the liquid inlet power unit 7 is connected to the first channel 102 or the second channel 103, and is used to provide power for injecting liquid into the flow chamber. The signal output end of the control unit 8 is connected to the signal input end of the liquid inlet power unit 7. The flow rate sensor 9 is used to collect the flow rate signal at the cell-bearing conductive membrane 3. The signal output end of the flow rate sensor 9 is connected to the signal input end of the control unit 8 to feed the flow rate signal at the cell-bearing conductive membrane 3 to the control unit. The control unit 8 is used to calculate the shear stress at the cell-bearing conductive membrane 3 based on the flow rate signal at the cell-bearing conductive membrane 3, and based on the set shear stress threshold, control the liquid inlet power unit 7 to operate so that the shear stress at the cell-bearing conductive membrane is within the set shear stress threshold range.
[0045] In this embodiment, the control unit 8 can be a general-purpose processor, including a central processing unit (CPU), a network processor (NP), etc.; it can also be a digital signal processor (DSP), an application-specific integrated circuit ASIC, a field programmable gate array FPGA or other programmable logic devices, discrete gates or transistor logic devices, and discrete hardware components. The liquid inlet power unit 7 can be a pump component, such as an electrochemical pump, which can be connected to the first channel 102 or the second channel 103 through a pipeline to introduce the liquid into the flow chamber 101 at a certain flow rate, wherein the liquid can be stored in a storage container outside the platform. In some embodiments, the liquid inlet power unit 7 can be set to two, respectively connected to the first channel 102 and the second channel 103, and the two liquid inlet power units 7 can be respectively connected to a storage container for storing liquid, so that the first channel 102 or the second channel 103 can be used as a liquid inlet port, and the second channel 103 or the first channel 102 can be used as a liquid outlet port. The flow rate sensor 9 may be a differential pressure sensor, which is respectively arranged at the corresponding detection positions, that is, one is arranged at each position of the cell-bearing conductive membrane 3 (laminar flow groove 201 or turbulent flow groove 202) to detect the corresponding liquid flow rate signal.
[0046] Taking the shear stress control at a cell-bearing conductive membrane 3 as an example, the shear stress threshold is set as a range value, such as (F a , F b ), if the current shear stress F at the cell-bearing conductive membrane 3 is less than F a The control unit 8 controls the liquid inlet power unit 7 to increase the working power to increase the shear stress F until it is within the range value (F a , F b ). If the shear stress F at the current cell-bearing conductive membrane 3 is greater than F a The control unit 8 controls the liquid inlet power unit 7 to reduce the working power to reduce the shear stress F until it is within the range value (F a , F b ). If the shear stress F at the current cell-bearing conductive membrane 3 is within the range (F a , F b ), the control unit 8 controls the liquid inlet power unit 7 to maintain the current working parameters and operate until the end of the experiment.
[0047] In some embodiments, when the cell-carrying conductive membrane 3 is disposed in the laminar flow groove 201, the shear stress at the cell-carrying conductive membrane 3 is calculated as the laminar shear stress based on the flow velocity signal at the cell-carrying conductive membrane 3, and the control unit 8 calculates the laminar shear stress by the following formula:
[0048]
[0049] In the formula, F1 represents the laminar shear stress, μ represents the liquid viscosity coefficient, and u x1 represents the relative movement speed of the liquid plane in the laminar flow groove, and y1 represents the liquid surface thickness in the laminar flow groove.
[0050] In some embodiments, when the cell-carrying conductive membrane 3 is disposed in the turbulent groove 202, the shear stress at the cell-carrying conductive membrane 3 is calculated based on the flow velocity signal at the cell-carrying conductive membrane 3 as the turbulent shear stress, and the control unit 8 calculates the turbulent shear stress by the following formula:
[0051]
[0052] Where μ is the viscosity coefficient of the liquid, u x represents the relative motion speed of the liquid plane in the turbulent groove, y represents the liquid surface thickness of the turbulent groove, ρ is the liquid density, and l is the motion path of the turbulent molecules in the vertical direction.
[0053] In some embodiments, Figure 1As shown, the same number of first mounting holes 104 and second mounting holes 402 are respectively arranged on the fluid dynamics flow chamber base 1 and the upper cover 4, and also include the same number of fastening bolts 10 as the first mounting holes 104 and the second mounting holes 402. The fastening bolts 10 tightly assemble the fluid dynamics flow chamber base 1 and the upper cover 4 through the first mounting holes 104 and the second mounting holes 402.
[0054] It is understandable that the connection method between the fluid dynamics flow chamber base 1 and the upper cover 4 described above is only an example and is not a limitation of the present invention. In some embodiments, the connection method between the fluid dynamics flow chamber base 1 and the upper cover 4 can also use snap-fit, integrated cover sealing and other methods to replace the above-mentioned assembly method using bolts.
[0055] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that the technical solutions described in the above embodiments may still be modified, or some or all of the technical features may be replaced by equivalents. Such modifications or replacements do not deviate the essence of the corresponding technical solutions from the scope of the technical solutions of the embodiments of the present invention, and should all be included in the scope of the claims and specification of the present invention.
Claims
1. A vascular cavity simulation platform, characterized in that: include: A fluid mechanics flow chamber base, wherein a flow chamber with an upper opening is arranged in the fluid mechanics flow chamber base, and two ends of the flow chamber are respectively connected to a first channel and a second channel; A conductive film positioning substrate, wherein the conductive film positioning substrate is disposed in the flow chamber; A cell-carrying conductive film, wherein the cell-carrying conductive film is fixed to the conductive film positioning substrate; An upper cover, the upper cover is connected to the upper end of the fluid mechanics flow chamber base through a sealing ring to cover the flow chamber; A signal derivation electrode, one end of which is connected to the cell-bearing conductive membrane, and the other end of which is sealed and passes through the upper cover through a signal derivation through hole provided on the upper cover.
2. The vascular cavity simulation platform according to claim 1, characterized in that: At least one laminar groove and at least one turbulent groove are arranged on the conductive film positioning substrate, and at least two cell-carrying conductive films are arranged, at least one of which is arranged in the laminar groove and at least one of which is arranged in the turbulent groove.
3. The vascular cavity simulation platform according to claim 2, characterized in that: The laminar flow groove has a length of 8 to 12 mm and a width of 4 to 6 mm; the turbulent flow groove has a semi-arc of 4 to 6 mm and a length of 8 to 12 mm.
4. The vascular cavity simulation platform according to claim 2, characterized in that: At least two laminar grooves and at least two turbulent grooves are arranged on the conductive film positioning substrate. The laminar grooves and turbulent grooves are arranged on the conductive film positioning substrate in a uniformly spaced manner. A cell-bearing conductive film is arranged in each laminar groove and each turbulent groove.
5. The vascular cavity simulation platform according to claim 2, characterized in that: It also includes a liquid inlet power unit, a control unit and a flow rate sensor; wherein the liquid inlet power unit is connected to the first channel or the second channel to provide power for injecting liquid into the flow chamber, the signal output end of the control unit is connected to the signal input end of the liquid inlet power unit, the flow rate sensor is used to collect the flow rate signal at the cell-bearing conductive membrane, the signal output end of the flow rate sensor is connected to the signal input end of the control unit to feed the flow rate signal at the cell-bearing conductive membrane to the control unit, the control unit is used to calculate the shear stress at the cell-bearing conductive membrane based on the flow rate signal at the cell-bearing conductive membrane, and based on the set shear stress threshold, control the liquid inlet power unit to work so that the shear stress at the cell-bearing conductive membrane is within the set shear stress threshold range.
6. The vascular cavity simulation platform according to claim 5, characterized in that: When the cell-carrying conductive membrane is disposed in the laminar flow groove, the shear stress at the cell-carrying conductive membrane is calculated as the laminar shear stress based on the flow velocity signal at the cell-carrying conductive membrane, and the control unit calculates the laminar shear stress by the following formula: In the formula, F1 represents the laminar shear stress, μ represents the liquid viscosity coefficient, and u x1 represents the relative movement speed of the liquid plane in the laminar flow groove, and y1 represents the liquid surface thickness in the laminar flow groove.
7. The vascular cavity simulation platform according to claim 5, characterized in that: When the cell-carrying conductive membrane is disposed in the turbulent groove, the shear stress at the cell-carrying conductive membrane is calculated as the turbulent shear stress based on the flow velocity signal at the cell-carrying conductive membrane, and the control unit calculates the turbulent shear stress by the following formula: Where μ is the viscosity coefficient of the liquid, u x represents the relative motion speed of the liquid plane in the turbulent groove, y represents the liquid surface thickness of the turbulent groove, ρ is the liquid density, and l is the motion path of the turbulent molecules in the vertical direction.
8. The vascular cavity simulation platform according to claim 1, characterized in that: The fluid dynamics flow chamber base and the upper cover are respectively provided with the same number of first mounting holes and second mounting holes, and also include fastening bolts with the same number as the first mounting holes and the second mounting holes. The fastening bolts tightly assemble the fluid dynamics flow chamber base and the upper cover through the first mounting holes and the second mounting holes.
Citation Information
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