# The Impact of Visual Input and Support Area Manipulation on Postural Control in Subjects after Osteoporotic Vertebral Fracture

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## Abstract

**:**

## 1. Introduction

**Hypothesis**

**1.**

**Hypothesis**

**2.**

## 2. Materials and Methods

#### 2.1. Participants and Procedure

#### 2.2. Data Analysis

#### 2.2.1. Stationarity of CoP data

#### 2.2.2. Sample Entropy (SampEn)

- (1)
- From a vector $X={x}_{1},{x}_{2},\dots ,{x}_{N}$ two sequences of m consecutive points: ${x}_{m}(i)={x}_{1},{x}_{2},\dots ,{x}_{i+m-1}$ and ${x}_{m}(j)={x}_{1},{x}_{2},\dots ,{x}_{j+m-1},$ $i,j\in [1,N-m],i\ne j$ were selected to compute the maximum distance and compared to tolerance r for repeated sequence counting, according to:$$d[{X}_{m}(i),{X}_{m}(j)]=\mathrm{max}[\left|{x}_{i+k},{x}_{j+k}\right|]\le r,\text{}(k\in [0,m-1],\text{}r\ge 0)$$
_{N}[19]. - (2)
- ${B}^{m}(r)$ is the average amount of ${B}_{i}^{m}(r)$ for $i\in [1,N-m]$ and ${B}^{m+1}(r)$ is the average of m + 1 consecutive points. Thus, sample entropy can be computed as follows:$$SampEn(N,m,r)=-\mathrm{ln}\left[\frac{{B}^{m+1}(r)}{{B}^{m}(r)}\right]$$

#### 2.2.3. Fractal Dimension (FD)

- (1)
- For one dimensional time series: $X=x[1],x[2],\dots ,x[N]$, a new k time series can be formed as follows:$${X}_{k}^{m}=x[m],x[m+k],x[m+2k],\dots ,x\left[m+\mathrm{int}\left(\frac{N-m}{k}\right)\xb7k\right],$$
- (2)
- The length of each new time series can be defined as follows:$$L(m,k)=\left({\displaystyle \sum _{i=1}^{\mathrm{int}\left(\frac{N-m}{k}\right)}\left|x\left[m+ik\right]-x\left[m+(i-1)k\right]\right|}\right)\frac{N-1}{\mathrm{int}\left(\frac{N-m}{k}\right){k}^{2}},$$
- (3)
- The length of the curve for the time interval k is defined as the average of the k values L(m, k), for m = 1, 2, …, k:$$L(k)=\frac{1}{k}{\displaystyle \sum _{m=1}^{k}L(m,k).}$$
_{max}, the data should fall on a straight line, with a slope equal to the FD of X. Thus, Higuchi’s FD is defined as the slope of the line that fits the pairs $(\mathrm{ln}[L(k)],\mathrm{ln}\left(\frac{1}{k}\right))$ in a least-squares sense. In order to choose an appropriate value of the parameter k_{max}, Higuchi’s FD values were plotted against a range of k_{max}. The point at which the FD plateaus was considered a saturation point, and that k_{max}value should be selected [29]. A value of k_{max}= 100 was chosen for our study.

#### 2.2.4. ANOVA Skillings–Mack (Missing Data)

## 3. Results

#### 3.1. Increasing Task Difficulty

#### 3.2. Nonlinear Dynamics Indicators

#### 3.2.1. Analysis between Groups

#### 3.2.2. Analysis within Groups

#### 3.3. Fall Risk Test and Summary of Balance Test Results

## 4. Discussion

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Path length values in subsequent trials for people with osteoporosis (OS) and the healthy group (C), where: * marks statistically significant differences between groups, the red line marks statistically significant differences between trials for OS group, and the blue line marks statistically significant differences between trials for the C group (p < 0.05).

**Figure 2.**Coefficient values in subsequent trials for people with osteoporosis (OS) and healthy group (C): (

**a**) sample entropy (SampEn); (

**b**) fractal dimension (FD), where x—medio-lateral direction, y—anterior–posterior direction. * marks statistically significant differences between groups, the red line marks statistically significant differences between trials for the OS group, and the blue line marks statistically significant differences between trials for the C group (p < 0.05).

Task | Symbol | Number of Subjects Who Completed the OS/C Tasks |
---|---|---|

Standing on both legs with eyes open | 2eo | 17/17 |

Standing on both legs with eyes closed | 2ec | 16/17 |

Standing on both legs with eyes closed and with dual-task | 2ec_dt | 15/17 |

Standing on one leg with eyes open | 1eo | 8/17 |

Standing on one leg with eyes closed | 1ec | 1/17 |

Standing on one leg with eyes closed and with dual-task | 1ec_dt | 0/17 |

**Table 2.**Number of individuals from the OS group who completed the (FRT—Fall Risk Test) at a specific level, and data showing which subjects completed the static tasks, where an X means that the task was completed, and a dash (-) means that the task was not completed.

Number of Subjects Who Completed the FRT | Norm Level for the FRT Test | 2eo | 2ec | 2ec_dt | 1eo | 1ec | 1ec_dt |
---|---|---|---|---|---|---|---|

3 | Fall | X | X | X | - | - | - |

1 | Fall | X | X | - | - | - | - |

1 | Fall | X | - | - | - | - | - |

2 | Fall | X | X | X | X | - | - |

3 | Norm | X | X | X | - | - | - |

3 | Norm | X | X | X | X | - | - |

1 | Below | X | X | X | X | X | - |

2 | Below | X | X | X | X | - | - |

1 | Below | X | X | X | - | - | - |

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**MDPI and ACS Style**

Błażkiewicz, M.; Kędziorek, J.; Hadamus, A.
The Impact of Visual Input and Support Area Manipulation on Postural Control in Subjects after Osteoporotic Vertebral Fracture. *Entropy* **2021**, *23*, 375.
https://doi.org/10.3390/e23030375

**AMA Style**

Błażkiewicz M, Kędziorek J, Hadamus A.
The Impact of Visual Input and Support Area Manipulation on Postural Control in Subjects after Osteoporotic Vertebral Fracture. *Entropy*. 2021; 23(3):375.
https://doi.org/10.3390/e23030375

**Chicago/Turabian Style**

Błażkiewicz, Michalina, Justyna Kędziorek, and Anna Hadamus.
2021. "The Impact of Visual Input and Support Area Manipulation on Postural Control in Subjects after Osteoporotic Vertebral Fracture" *Entropy* 23, no. 3: 375.
https://doi.org/10.3390/e23030375