# Development and Evaluation of a Flexible PVDF-Based Balloon Sensor for Detecting Mechanical Forces at Key Esophageal Nodes in Esophageal Motility Disorders

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Stress Detection System Design and Fabrication

#### 2.2. Stress Reconstruction at Key Esophageal Nodes

#### 2.2.1. Balloon Membrane Surface Stress Calculation

**F**of the balloon was employed as an input parameter, from which the surface stress of the balloon was derived as follows:

_{b}_{r}is the radial stress along the radius of the balloon, h is the thickness of the balloon film, σ

_{θ}is the tangential stress along the perimeter of the balloon, and r is the radius of the balloon.

**ε**is the radial strain along the radius of the balloon,

_{r}**ε**is the tangential strain along the perimeter of the balloon, and u is the displacement in the radius of the balloon. Its physical equation is shown in Equation (4):

_{θ}#### 2.2.2. Catheter Bending Stress Calculation

_{r}. As the catheter remains unexposed to the esophageal wall during balloon inflation, we simplify the analysis by considering only the bending stress arising from the balloon membrane’s traction on the catheter. Adhering to the Euler–Bernoulli beam theory [38,39], the bending stress σ

_{bend}in the catheter can be expressed as Equation 5):

_{i}represents the inner radius of the catheter, and π symbolizes the mathematical constant pi.

#### 2.2.3. Intra-Balloon Fluid Shear Stress

_{r}and ε

_{θ}) and bulk modulus K (where K = 2.2 × 10

^{9}Pa for distilled water), as shown in Equation (6):

^{−3}Pa·s for distilled water), and the fluid velocity field (u), as depicted in Equation (7):

#### 2.2.4. PVDF Force-Electric Conversion Calculation

_{bend}), pressure surface stress (σ

_{surface}), and the fluid’s shear stress (τ) in the capsule.

_{bend}and τ is perpendicular to these stress vectors, with the output charge (Q

_{out}) of PVDF computed as outlined in Equation (12):

_{out}is converted to output voltage (V

_{out}), as shown in Equation (13):

_{31}is the voltage constant (200 mV/N). This theoretical deduction of the balloon surface load is pivotal in actual esophageal mechanical testing.

#### 2.2.5. Model of Balloon Input–Output Inverse Problem

^{−1}) calculates the static stress of key esophageal nodes, represented in Equation (15):

#### 2.3. Sensor Static Output Characteristic Test

^{2}, 4.91 cm

^{2}, and 4.91 cm

^{2}, respectively. As direct detection of the load from the esophageal wall onto the balloon film surface is not viable in simulations, we devised an esophageal pressure detection test. This test requires the balloon to be suspended and fixed vertically to minimize gravity-induced errors, while a 2 cm diameter circle serves as the load input. By electronically adjusting the manometer’s load input position and value, we evaluate the sensor’s static characteristics at different fill degrees, providing a basis for assessing the feasibility of our balloon design.

_{S}-V

_{S}curve, the static calibration curve, is derived via a predetermined load spectrum of [0, 4.5] N ([20, 150] mmHg) at a gradient of 0.045 N (1.3 mmHg). The computation of crucial parameters such as sensor linearity, sensitivity, and zero-input response in the concluding phase consolidates the understanding of the sensor’s static performance features.

_{S}-V

_{S}curve, yields the linear parameter calculation formula as illustrated in Equation (16):

_{out}, K

_{s}, F

_{b}, and PVDF

_{0}embody sensor output, linear fitting sensitivity, balloon load input, and zero input response, respectively. The conjunction of these empirical results with theoretical sensor output unveils the linearity degree, delineated in Equation (17).

_{out}is the actual sensor output, PVDF

_{tov}represents the ideal sensor output, and PVDF

_{fso}indicates the full-scale sensor output. Notably, PVDF

_{fso}is the PVDF

_{out}value when F = 4.5 N (150 mmHg), from Equation (17), while PVDF

_{tov}is the output of the balloon node stress analytical algorithm.

_{out}indicating the minimum input load variation, and ∆F

_{b}representing the minimum input gradient difference of balloon load (0.045 N).

#### 2.4. Experimental Methods for Simulating Esophageal Peristalsis

#### 2.4.1. Stress Reconstruction at Key Esophageal Nodes

_{dss}(t) represents the time-sequenced load value, in units of N. T

_{d}denotes the load fluctuation period, and P

_{d}(t) is the load application position. The values 1, 2, 3, and 4 correspond to the critical nodes on the balloon’s outer wall from position1 to position4, respectively. P

_{0}equals 1, indicating the initial position, and $\lfloor \frac{t}{{T}_{d}}\rfloor $ is the integer quotient of the time over the load fluctuation period.

#### 2.4.2. Dynamic Output Test under Esophageal Peristalsis during Simulated Swallowing

_{c}(t) is the time-sequenced load value, given in N. T

_{c}represents the load fluctuation period, set at 2.5 S, with the total number of fluctuation periods being 8. P

_{c}(t) indicates the load application position, where values 1, 2, 3, and 4 correspond to the critical nodes on the balloon’s outer wall from position1 to position4, respectively. A

_{n}is the load amplitude varying with position. When P

_{c}(t) = [1, 2, 3, 4], the corresponding values are [2.75, 3.00, 3.25, 3.50, 3.75, 4.00, 4.25, 4.50], respectively, after conversion to mmHg, the corresponding values would be [99.44, 106.67, 113.89, 121.11, 128.33, 135.56, 142.78, 150.00].

## 3. Results and Discussion

#### 3.1. Theoretical Value of Analytical Model of Joint Stress

#### 3.2. Static Performance Curve and Analysis Results of PVDF Array

_{n}, which encompasses P

_{1}, P

_{2}, P

_{3}, and P

_{4}, represents the pressure loading positions on the outer wall of the balloon, that is, the key nodes Position1 to Position4. The value m denotes the sensor number, and both P

_{n}and m take the values of 1, 2, 3, and 4. The variable k represents the degree of inflation, which can be 0%, 25%, 50%, 75%, or 100%. Figure 7 depicts the static test outputs of the sensor array when loads are applied at different positions under the five types of inflation states of the balloon.

#### 3.3. Esophageal Creep Simulation Test

#### 3.3.1. Dynamic Performance Curve and Analysis

_{in}. The average peak was 94.97334 mmHg, and a standard amplitude error of 20.85556% was noted between P

_{in}and P_PVDF. This thorough investigation substantiates the sensor’s proficiency in accurately tracking physiological esophageal behavior.

#### 3.3.2. Dynamic Analysis under Simulated Esophageal Peristalsis

#### 3.4. Robustness and Reproducibility

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Flexible balloon structure at key points of esophagus based on PVDF: (

**a**) schematic diagram of the balloon structure; (

**b**) working schematic of the sensor system; and (

**c**) PVDF piezoelectric film sensor on the catheter.

**Figure 2.**Circuit architecture of esophagus dynamic detection system based on piezoelectric sensor: (

**a**) test circuit system architecture and (

**b**) sensing device architecture.

**Figure 3.**Sensor performance test platform: (

**a**) overall structure of the experimental platform and (

**b**) static characteristic test procedure of the sensor balloon.

**Figure 4.**Schematic of dynamic pressure measurement of key nodes: (

**a**) key node dynamic pressure measurement process and (

**b**) single position sinusoidal load curve.

**Figure 8.**Balloon state under different filling degrees (k, %, the amount of fluid filled into the vacuum anhydrous balloon as a percentage of the balloon volume when filled with liquid): (

**a**) k = 0; (

**b**) k = 25; (

**c**) k = 50; (

**d**) k = 75; and (

**e**) k = 100.

**Figure 15.**Output curve of sensor array under peristaltic waves simulating the swallowing process (k = 75).

Parameter\Filling Degree | 0% | 25% | 50% | 75% | 100% |
---|---|---|---|---|---|

1. Elasticity modulus (E, MPa) | 20 | 20 | 20 | 20 | 20 |

2. Calculated diameter of balloon (R, mm) | 0.5 | 5.6 | 11.2 | 16.8 | 22.2 |

3. Balloon thickness (h, mm) | 0.2 | 0.2 | 0.2 | 0.2 | 0.2 |

4. Poisson’s Ratio (v, \) | 0.35 | 0.35 | 0.35 | 0.35 | 0.35 |

5. Diameter of load surface (d_{n}, mm) | 15 | 15 | 15 | 15 | 15 |

6. Inner tube radius (R_{i}, mm) | 3.3 | 3.3 | 3.3 | 3.3 | 3.3 |

7. Outer tube radius(R_{o}, mm) | 5.0 | 5.0 | 5.0 | 5.0 | 5.0 |

8. Distance to the central axis of the balloon membrane in the filled state (d, mm) | 45 | 45 | 45 | 45 | 45 |

9. Tube cross-sectional area (A, mm^{2}) | 11.07 | 11.07 | 11.07 | 11.07 | 11.07 |

10. Volume modulus (K, MPa) | 2200 | 2200 | 2200 | 2200 | 2200 |

11. Fluid dynamic viscosity (μ, cP) | 1.5 | 1.5 | 1.5 | 1.5 | 1.5 |

12. Piezoelectric coefficient (g_{31}, mV/N) | 0.2 | 0.2 | 0.2 | 0.2 | 0.2 |

13. PVDF surface area(s, cm^{2}) | 1 | 1 | 1 | 1 | 1 |

14. PVDF Zero Input Response (PVDF_{0}, V) | 1.33 | 1.33 | 1.33 | 1.33 | 1.33 |

Steady-State Performance\Filling Degree | 0% | 25% | 50% | 75% | 100% |
---|---|---|---|---|---|

1. Linearity_PVDF1(LD_P1, %) | 29.59382 | 36.4666 | 46.11891 | 44.44342 | 1.38517 |

Sensitivity_PVDF1(S_{C}_P1, V/N) | 0.18967 | 0.18496 | 0.13494 | 0.10848 | 0.02607 |

Zero-input_PVDF1(PVDF_{0}_P1, V) | 1.33055 | 1.33015 | 1.33096 | 1.33015 | 1.33015 |

2. Linearity_PVDF2(LD_P2, %) | 27.63658 | 21.69366 | 46.32882 | 43.31854 | 4.02154 |

Sensitivity_PVDF2(S_{C}_P2, V/N)) | 0.19472 | 0.27715 | 0.13105 | 0.10608 | 0.01425 |

Zero-input_PVDF2(PVDF_{0}_P2, V) | 1.33203 | 1.33337 | 1.33305 | 1.34124 | 1.33015 |

3. Linearity_PVDF3(LD_P3, %) | 28.31165 | 15.49573 | 20.0427 | 25.09424 | 2.12105 |

Sensitivity_PVDF3(S_{C}_P3, V/N)) | 0.19786 | 0.29016 | 0.26229 | 0.18705 | 0.02494 |

Zero-input_PVDF3(PVDF_{0}_P3, V) | 1.33337 | 1.3374 | 1.33096 | 1.33096 | 1.33015 |

4. Linearity_PVDF4(LD_P4, %) | 30.09618 | 16.30085 | 23.40208 | 30.11328 | 4.45227 |

Sensitivity_PVDF4(S_{C}_P4, V/N)) | 0.19206 | 0.29136 | 0.28059 | 0.16042 | 0.01287 |

Zero-input_PVDF4(PVDF_{0}_P4, V) | 1.33176 | 1.3374 | 1.33176 | 1.33257 | 1.33096 |

Loading Condition\Filling Degree | 0% | 25% | 50% | 75% | 100% |
---|---|---|---|---|---|

1. Pressure_2 times (%) | 0.81545 | 0.94521 | 1.10525 | 1.21594 | \ |

Pressure_3 times (%) | 0.99452 | 1.08452 | 1.18752 | 1.28751 | \ |

Pressure_4 times (%) | 1.23015 | 1.43541 | 1.59627 | 1.65873 | \ |

Pressure_5 times (%) | 1.69854 | 1.85463 | 1.93309 | 2.10548 | \ |

2. Tensile_2 times (%) | 1.56248 | 1.86326 | 1.96247 | 2.05478 | \ |

Tensile_3 times (%) | 1.76236 | 1.89631 | 1.99632 | 2.18236 | \ |

Tensile_4 times (%) | 1.89544 | 1.93325 | 2.16548 | 2.36514 | \ |

Tensile_5 times (%) | 1.95421 | 2.15659 | 2.35623 | 2.59874 | \ |

3. Torsion_2 times (%) | 1.71219 | 1.89654 | 1.96587 | 2.16594 | \ |

Torsion_3 times (%) | 1.90548 | 1.95631 | 2.14856 | 2.23658 | \ |

Torsion_4 times (%) | 2.10585 | 2.15698 | 2.19658 | 2.37892 | \ |

Torsion_5 times (%) | 2.43289 | 2.56612 | 2.69878 | 2.72364 | \ |

Temperature\Filling Degree | 0% | 25% | 50% | 75% | 100% |
---|---|---|---|---|---|

1. Temperature _10 °C (%) | 2.41202 | 1.93325 | 2.16548 | 2.36514 | \ |

2. Temperature _12 °C (%) | 2.25456 | 1.89631 | 1.99632 | 2.18236 | \ |

3. Temperature _14 °C (%) | 2.19455 | 1.86326 | 1.96247 | 2.05478 | \ |

4. Temperature _16 °C (%) | 2.11483 | 2.19878 | 2.30154 | 2.41254 | \ |

5. Temperature _18 °C (%) | 1.98457 | 2.15664 | 2.18965 | 2.32549 | \ |

6. Temperature _20 °C (%) | 1.82365 | 1.92345 | 1.98544 | 2.08934 | \ |

7. Temperature _22 °C (%) | 1.65452 | 1.78953 | 1.85412 | 1.92302 | \ |

8. Temperature _24 °C (%) | 0.659514 | 0.79862 | 0.84512 | 0.98754 | \ |

9. Temperature _26 °C (%) | 1.14854 | 1.23144 | 1.25478 | 1.28656 | \ |

10. Temperature _28 °C (%) | 1.28563 | 1.37894 | 1.48951 | 1.56334 | \ |

11. Temperature _30 °C (%) | 1.36578 | 1.54872 | 1.66891 | 1.89541 | \ |

12. Temperature _32 °C (%) | 1.64214 | 1.89651 | 1.99842 | 2.14523 | \ |

13. Temperature _34 °C (%) | 1.85415 | 2.05998 | 2.25486 | 2.32786 | \ |

14. Temperature _36 °C (%) | 2.08654 | 2.30154 | 2.48965 | 2.55483 | \ |

15. Temperature _38 °C (%) | 2.28124 | 2.51243 | 2.64877 | 2.89654 | \ |

16. Temperature _40 °C (%) | 2.68872 | 2.87541 | 2.98545 | 3.15568 | \ |

Times of Repetition\Filling Degree | 0% | 25% | 50% | 75% | 100% |
---|---|---|---|---|---|

1. 1 time (%) | 4.23124 | 4.92346 | 5.25442 | 5.85621 | \ |

2. 2 times (%) | 3.86042 | 4.56211 | 4.98847 | 5.13234 | \ |

3. 4 times (%) | 3.24427 | 3.98551 | 4.26591 | 4.86214 | \ |

4. 8 times (%) | 2.87563 | 3.15478 | 3.45337 | 4.23668 | \ |

5. 16 times (%) | 2.12567 | 2.56448 | 2.89314 | 3.54120 | \ |

6. 32 times (%) | 1.42588 | 1.59846 | 2.04518 | 2.13354 | \ |

7. 64 times (%) | \ | \ | \ | \ | \ |

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**MDPI and ACS Style**

Ran, P.; Li, M.; Zhang, K.; Sun, D.; Lai, Y.; Liu, W.; Zhong, Y.; Li, Z.
Development and Evaluation of a Flexible PVDF-Based Balloon Sensor for Detecting Mechanical Forces at Key Esophageal Nodes in Esophageal Motility Disorders. *Biosensors* **2023**, *13*, 791.
https://doi.org/10.3390/bios13080791

**AMA Style**

Ran P, Li M, Zhang K, Sun D, Lai Y, Liu W, Zhong Y, Li Z.
Development and Evaluation of a Flexible PVDF-Based Balloon Sensor for Detecting Mechanical Forces at Key Esophageal Nodes in Esophageal Motility Disorders. *Biosensors*. 2023; 13(8):791.
https://doi.org/10.3390/bios13080791

**Chicago/Turabian Style**

Ran, Peng, Minchuan Li, Kunlin Zhang, Daming Sun, Yingbing Lai, Wei Liu, Ying Zhong, and Zhangyong Li.
2023. "Development and Evaluation of a Flexible PVDF-Based Balloon Sensor for Detecting Mechanical Forces at Key Esophageal Nodes in Esophageal Motility Disorders" *Biosensors* 13, no. 8: 791.
https://doi.org/10.3390/bios13080791