# Frailty Syndrome as a Transition from Compensation to Decompensation: Application to the Biomechanical Regulation of Gait

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Participants

#### 2.2. Description of Participant Groups

#### 2.3. Materials

#### 2.4. Design and Procedure

#### 2.5. Calculation of Gait Parameters

_{VT}[34] (see Supplementary Materials Figure S2 of Supplementary Information) and the average cadence, or the number of steps per minute, as c = 1/τ. The total number of steps was N = T/τ, and the average step length was l = L/N [50]. As smaller people tend to walk with smaller steps and higher cadence than taller people, we also calculated normalized cadence and normalized step length, adjusting for the average body height of each population, l

_{n}= l. <h>/h and c

_{n}= c.√(h/<h>), where h is the height of the individual and <h> is the average height of the corresponding groups C1, C2, nF, or F [51]. We also calculated the walk ratio (WR), or step length-to-step frequency or step length-to-cadence ratio, l/c, and its normalized variant, l

_{n}/c

_{n}[26].

_{AP}, mediolateral a

_{ML}, and vertical a

_{VT}. For each direction of movement, we calculated the maximum and minimum acceleration per 1 s interval, and our calculated values corresponded well with the peak and min values given by the automatic analysis of the Bioharness 3.0 software. Then, we subtracted these values to estimate the magnitude of movement for every axis, Δa

_{AP}= max(a

_{AP}) − min(a

_{AP}), and similarly for Δa

_{ML}and Δa

_{VT}. The rationale behind this procedure is as follows: it is known that cadence is approximately 1 stride/s or 2 steps/s [26]. Therefore, Δa

_{AP}, Δa

_{ML}, and Δa

_{VT}estimate the magnitude of acceleration of individual steps in different directions. We also calculated the root mean square (RMS) of the acceleration signals a

_{AP}, a

_{ML}, and a

_{VT}, which offers an alternative quantification of the magnitude of acceleration per step [35]. However, while Δa

_{AP}, Δa

_{ML}, and Δa

_{VT}quantify acceleration of individual steps, RMS of the raw accelerometry signal includes whatever movement of the human body. Analogous to the walk ratio l/c, we also calculated acceleration ratios Δa

_{AP}/Δa

_{ML}and Δa

_{VT}/Δa

_{ML}.

#### 2.6. Statistical Analysis

_{AP}/Δa

_{ML}) and Welch’s robustness test with post hoc Games–Howell test for heteroscedastic variables. We used the Statistical Package for the Social Sciences (SPSS) version 22.0 (SPSS Inc., Chicago, IL, USA). A p-value ≤ 0.05 was considered significant.

## 3. Results

## 4. Discussion

_{ML}of the non-frail older adults (group nF) as a reflection of an increased base support to compensate for reduced stability. Frail older adults (group F) have significantly decreased mediolateral acceleration compared to non-frail older adults (group nF). Although the mediolateral acceleration of frail older adults (group F) is similar to that of young adults (group C1), their base support may not be sufficient to ensure adequate stability and may explain the increased risk of falls in frail older adults [63], which we interpret as a phenomenon of decompensation. The effect of compensation by lateral movement is known as a “wide-based gait” or “waddle” and occurs in the face of both internal perturbations, such as in the case of pregnant women [64] or obesity [65], or external perturbations, such as ship passengers [66] or train conductors [62]. Again, a wide-based gait appears to be more characteristic of non-frail older adults (group nF) than frail older adults (group F).

_{ML}with aging and frailty discussed so far, the ratios of gait parameters l/c, Δa

_{AP}/Δa

_{ML}, and Δa

_{VT}/Δa

_{ML}of Table 4 and Figure 4 show a monotonous decreasing trend over all four populations from no compensation (groups C1 and C2) to compensation (group nF) and finally to decompensation (group F). The walk ratio l/c has been interpreted as a measure of the quality of the overall neuromotor gait regulation [29], and the same interpretation may be valid as well for Δa

_{AP}/Δa

_{ML}and Δa

_{VT}/Δa

_{ML}given their very similar behavior. Here, we propose the ratios l/c, Δa

_{AP}/Δa

_{ML}, and Δa

_{VT}/Δa

_{ML}as concrete and practical metrics to quantify compensation and decompensation in gait dynamics. The rationale is the following: each of these ratios evaluates a gait parameter that is being compensated with respect to the gait parameter that is actively performing the compensation; therefore, both an increased compensation and an underperforming regulatory mechanism (decompensation) result in a reduced ratio. We speculate that the underlying reason for a transition from compensation with aging to decompensation with frailty is due to homeostatic effort, i.e., the extra energy needed for compensation and increased load to keep a specific regulatory mechanism working [67]. These additional energy requirements are taken from the physiological reserves, such that there must be a proportionality relation between how much a system compensates and how much of the physiological reserves are in use. Such a reduction in available physiological reserves has been called presbyhomeostenosis [68,69]. When reserves are no longer available, the only possible outcome is decompensation, describing an energetic pathway to mobility loss and slowing down of gait speed [67].

#### Strengths, Limitations, and Implications of This Study

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Diagram of the experimental area with sides S1 = 19 and S2 = 21 m and total distance L = 2 (2S1 + 2S2) = 160 m, (

**b**) the physiological and biomechanical monitoring device Zephyr BioHarness 3.0 consisting of a chest strap and a bioModule containing the internal memory and battery. The anteroposterior (AP), medio-lateral (ML), and vertical (VT) axes of triaxial accelerometry are also indicated. Modified from Zephyr Technology Corporation, Annapolis, MD, USA—a division of Medtronic.

**Figure 2.**Gait parameters along the time axis, (

**a**) velocity v, (

**b**) normalized step length l

_{n}and (

**c**) normalized cadence c

_{n}. The evolution of gait parameters is shown for young adults (group C1), middle-aged adults (group C2), non-frail older adults (group nF), and frail older adults (group F). Indicated are mean ± standard error, pairwise statistically significant differences with p < 0.05 (*), p < 0.005 (**), p < 0.001 (***), and the gait velocity threshold (v = 0.83 m/s) for frailty obtained with ROC analysis (horizontal gridline).

**Figure 3.**Gait parameters along the magnitude axis, (

**a**) vector acceleration Δa, (

**b**) anteroposterior acceleration Δa

_{AP}, and vertical acceleration Δa

_{VT}, and (

**c**) mediolateral acceleration Δa

_{ML}. The evolution of gait parameters is shown for young adults (group C1), middle-aged adults (group C2), non-frail older adults (group nF), and frail older adults (group F). Indicated are mean ± standard error, and pairwise statistically significant differences with p < 0.05 (*), p < 0.005 (**), p < 0.001 (***).

**Figure 4.**Ratios of gait parameters, (

**a**) normalized walk ratio l

_{n}/c

_{n}, (

**b**) acceleration ratio Δa

_{AP}/Δa

_{ML}, and (

**c**) acceleration ratio Δa

_{VT}/Δa

_{ML}. The evolution of gait parameters is shown for young adults (group C1), middle-aged adults (group C2), non-frail older adults (group nF), and frail older adults (group F). Indicated are mean ± standard error, and pairwise statistically significant differences with p < 0.05 (*), p < 0.005 (**), p < 0.001 (***).

**Table 1.**Demographic and anthropometric measures (mean and standard error) are shown for each group. The sample size is represented with n. Results are given for young control adults (group C1), middle-aged control adults (group C2), non-frail older adults (group nF), and frail older adults (group F).

Variable | Group C1 (n = 27) | Group C2 (n = 16) | Group nF (n = 15) | Group F (n = 31) | p-Value between All Groups |
---|---|---|---|---|---|

Age (years) (% female) | 22.3 ± 0.4 (59%) | 48.5 ± 2.2 (62%) | 72.7 ± 2.5 ^{¶,#}(33%) | 78.5 ± 1 ^{¶,#} (71%) | 0.000 |

Weight (kg) | 66.8 ± 2.4 | 70.7 ± 4.4 | 69.3 ± 3.1 | 61.6 ± 2.2 | 0.154 |

Height (m) | 1.7 ± 0.02 | 1.6 ± 0.02 | 1.6 ± 0.02 | 1.5 ± 0.02 ^{¶} | 0.000 |

BMI (kg/m^{2}) | 23.9 ± 0.6 | 27.4 ± 1.5 | 26.8 ± 1.03 | 26.3 ± 0.7 | 0.060 |

^{¶}p < 0.05 compared to C1;

^{#}p < 0.05 compared to C2;

^{§}p < 0.05 compared to nF.

**Table 2.**Gait parameters along the time axis. Shown are gait speed (v), average step length (l), normalized average step length (${\mathrm{l}}_{\mathrm{n}}$), average cadence (c), and normalized average cadence (${\mathrm{c}}_{\mathrm{n}}$). Results are given for young control adults (group C1), middle-aged control adults (group C2), non-frail older adults (group nF), and frail older adults (group F).

Variable | Group C1 (n = 27) | Group C2 (n = 16) | Group nF (n = 15) | Group F (n = 31) | p-Value between All Groups |
---|---|---|---|---|---|

v (m/s) | 1.08 ± 0.03 | 1.09 ± 0.05 | 1.05 ± 0.06 | 0.74 ± 0.05 ^{¶,#,§} | 0.000 |

l (m) | 0.61 ± 0.01 | 0.59 ± 0.04 | 0.55 ± 0.02 | 0.42 ± 0.03 ^{¶,#,§} | 0.000 |

l_{n} (m) | 0.61 ± 0.01 | 0.6 ± 0.02 | 0.55 ± 0.02 | 0.42 ± 0.02 ^{¶,#,§} | 0.000 |

c (1/min) | 105.26 ± 1.72 | 111.25 ± 1.78 | 114.35 ± 3.21 ^{¶} | 103.1 ± 3.1 ^{§} | 0.005 |

c_{n} (1/min) | 105.64 ± 1.7 | 110.62 ± 1.7 | 114.05 ± 2.1 ^{¶} | 103.53 ± 3.2 ^{§} | 0.005 |

^{¶}p < 0.05 compared to C1;

^{#}p < 0.05 compared to C2;

^{§}p < 0.05 compared to nF.

**Table 3.**Gait parameters along the amplitude axis. Shown are amplitudes of the acceleration vector (Δa), anteroposterior acceleration (Δ${\mathrm{a}}_{\mathrm{A}\mathrm{P}}$), vertical acceleration (Δ${\mathrm{a}}_{\mathrm{V}\mathrm{T}}$) and mediolateral acceleration (Δ${\mathrm{a}}_{\mathrm{M}\mathrm{L}}$), root mean square of vector acceleration RMS(a), anteroposterior acceleration RMS(${\mathrm{a}}_{\mathrm{A}\mathrm{P}})$, vertical acceleration RMS(${\mathrm{a}}_{\mathrm{V}\mathrm{T}}$), and mediolateral acceleration RMS(${\mathrm{a}}_{\mathrm{M}\mathrm{L}})$. Results are given for young control adults (group C1), middle-aged control adults (group C2), non-frail older adults (group nF), and frail older adults (group F).

Variable | Group C1 (n = 27) | Group C2 (n = 16) | Group nF (n = 15) | Group F (n = 31) | p-Value between All Groups |
---|---|---|---|---|---|

Δa (g) | 1.04 ± 0.05 | 1.10 ± 0.07 | 1.06 ± 0.06 | 0.80 ± 0.05 ^{¶,#,§} | 0.000 |

Δa_{AP} (g) | 0.57 ± 0.03 | 0.61 ± 0.05 | 0.56 ± 0.04 | 0.39 ± 0.03 ^{¶,#,§} | 0.000 |

Δa_{VT} (g) | 0.81 ± 0.04 | 0.83 ± 0.05 | 0.79 ± 0.05 | 0.58 ± 0.04 ^{¶,#,§} | 0.000 |

Δa_{ML} (g) | 0.31 ± 0.02 | 0.35 ± 0.02 | 0.41 ± 0.02 ^{¶} | 0.32 ± 0.01 ^{§} | 0.002 |

RMS(a) (g) | 0.12 ± 0.007 | 0.13 ± 0.008 | 0.12 ± 0.008 | 0.09 ± 0.006 ^{¶,#,§} | 0.000 |

RMS(${\mathrm{a}}_{\mathrm{A}\mathrm{P}}$) (g) | 0.13 ± 0.007 | 0.14 ± 0.01 | 0.14 ± 0.008 | 0.1 ± 0.006 ^{¶,#,§} | 0.001 |

RMS(${\mathrm{a}}_{\mathrm{V}\mathrm{T}}$) (g) | 0.2 ± 0.01 | 0.22 ± 0.02 | 0.22 ± 0.02 | 0.14 ± 0.01 ^{¶,#,§} | 0.000 |

RMS (${\mathrm{a}}_{\mathrm{M}\mathrm{L}}$) (g) | 0.08 ± 0.003 | 0.09 ± 0.004 | 0.1 ± 0.003 ^{¶} | 0.09 ± 0.003 | 0.002 |

^{¶}p < 0.05 compared to C1;

^{#}p < 0.05 compared to C2;

^{§}p < 0.05 compared to nF.

**Table 4.**Ratios of gait parameters. Shown are the walk ratio l/c, the normalized walk ratio ${\mathrm{l}}_{\mathrm{n}}$/${\mathrm{c}}_{\mathrm{n}}$, and the acceleration ratios Δ${\mathrm{a}}_{\mathrm{A}\mathrm{P}}$ /Δ${\mathrm{a}}_{\mathrm{M}\mathrm{L}}$ and Δ${\mathrm{a}}_{\mathrm{V}\mathrm{T}}$ /Δ${\mathrm{a}}_{\mathrm{M}\mathrm{L}}$. Results are given for young control adults (group C1), middle-aged control adults (group C2), non-frail older adults (group nF), and frail older adults (group F).

Variable. | Group C1 (n = 27) | Group C2 (n = 16) | Group nF (n = 15) | Group F (n = 31) | p-Value between All Groups |
---|---|---|---|---|---|

l/c (m.s) | 0.35 ± 0.006 | 0.32 ± 0.012 | 0.29 ± 0.01 ^{¶} | 0.25 ± 0.01 ^{¶,#} | 0.000 |

l_{n}/c_{n} (m.s) | 0.34 ± 0.006 | 0.32 ± 0.01 | 0.29 ± 0.01 ^{¶} | 0.25 ± 0.01 ^{¶,#} | 0.000 |

Δa_{AP}/Δa_{ML} | 1.9 ± 0.08 | 1.8 ± 0.15 | 1.4 ± 0.1 ^{¶} | 1.2 ± 0.06 ^{¶,#} | 0.000 |

Δa_{VT}/Δa_{ML} | 2.6 ± 0.11 | 2.4 ± 0.16 | 1.9 ± 0.1 ^{¶} | 1.8 ± 0.08 ^{¶,#} | 0.000 |

^{¶}p < 0.05 compared to C1;

^{#}p < 0.05 compared to C2;

^{§}p < 0.05 compared to nF.

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**MDPI and ACS Style**

Álvarez-Millán, L.; Castillo-Castillo, D.; Quispe-Siccha, R.; Pérez-Pacheco, A.; Angelova, M.; Rivera-Sánchez, J.; Fossion, R.
Frailty Syndrome as a Transition from Compensation to Decompensation: Application to the Biomechanical Regulation of Gait. *Int. J. Environ. Res. Public Health* **2023**, *20*, 5995.
https://doi.org/10.3390/ijerph20115995

**AMA Style**

Álvarez-Millán L, Castillo-Castillo D, Quispe-Siccha R, Pérez-Pacheco A, Angelova M, Rivera-Sánchez J, Fossion R.
Frailty Syndrome as a Transition from Compensation to Decompensation: Application to the Biomechanical Regulation of Gait. *International Journal of Environmental Research and Public Health*. 2023; 20(11):5995.
https://doi.org/10.3390/ijerph20115995

**Chicago/Turabian Style**

Álvarez-Millán, Lesli, Daniel Castillo-Castillo, Rosa Quispe-Siccha, Argelia Pérez-Pacheco, Maia Angelova, Jesús Rivera-Sánchez, and Ruben Fossion.
2023. "Frailty Syndrome as a Transition from Compensation to Decompensation: Application to the Biomechanical Regulation of Gait" *International Journal of Environmental Research and Public Health* 20, no. 11: 5995.
https://doi.org/10.3390/ijerph20115995