# Aging with Autism Departs Greatly from Typical Aging

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Demographics and Boot Strapping Technique to Form Age Groups of Equal Size

#### Bootstrapping Method

#### 2.2. Data Processing

#### 2.2.1. Motion Extraction

#### 2.2.2. Statistical Analyses

#### 2.2.3. Micro-Movement Spikes Data Type

#### 2.3. Distance in Probability Space: The Earth Mover’s Distance

_{r}and P

_{θ}

_{,}each with m possible states x or y, respectively; the EMD computes how much mass needs to be moved how far, to turn one distribution into the other. Figure 2D shows two sample distributions derived from the linear speed that we obtained from head involuntary motions of two participants, one TD and one ASD, while Figure 3A shows the matrix of pairwise EMD quantities across all 500 TD participants in the 5–10-year-old group.

^{2}log(n)) vs. a more recent version in O(n) [38]. Briefly, if one considers these histograms as two piles of earth, there are infinite ways to move the earth from one pile to the other. The goal is to find the optimal one (a unique value despite non-unique ways to do it). These are known as transport problems, with transport plan γ(x,y), to distribute the amount of earth from one place x over the domain of y (or vice versa.)

_{r}and P

_{θ}respectively. To obtain the EMD, every value of the matrix $\gamma $ is multiplied with the Euclidean distance between x and y:

#### 2.4. Stochastic Analyses

#### 2.5. Network Connectivity Analyses

## 3. Results

#### 3.1. High Heterogeneity of ASD is Automatically Captured by the Earth Movers’ Distance

#### 3.2. Differences in the Scatters Representing Each Age Group

#### 3.3. Aging with ASD Is Fundamentally Different from Typically Aging

#### 3.4. Network Connectivity Metrics Derived from the Autistic Cohort Reveal Fundamental Departures from Normative Data

## 4. Discussion

#### Limitations

## 5. Conclusions

## 6. Patents

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Proposed taxonomy of neuromotor control with phylogenetic order of maturation to stratify autism spectrum disorders (figure reproduced from Chapter 1 in [29], with permission from Elsevier). (

**A**) Current wearable biosensors enable non-invasive co-registration of multiple biorhythms streamed from different levels of somatic-sensory-motor control, from the face and body. (

**B**) Fluctuations in these biorhythms from the different levels of the taxonomy are modeled as standardized unitless micro-movement spikes MMS. It is proposed that these continuous spikes serve as a form of kinesthetic reafference, mapping the sensory consequences of actions according to different levels of neuromotor control (e.g., autonomic sensory consequences vs. voluntary sensory consequences). These in turn, map differently for trigeminal and dorsal-root ganglia systems defining socio-motor axes that could be used to stratify autism’s social differences (e.g., eye control, auditory, communication, taste, smell and swallowing issues in the face, vs. pointing, balance, gait, coordination, vestibular issues of the body -as possible scenario whereby data is readily available using non-invasive, off-the-shelf means to categorize autism.

**Figure 2.**Methods: (

**A**) Raw data in the form of linear speed (mm/s) extracted from images of ABIDE using traditional methods to clean the motor artifacts generated by involuntary motions of the head, as the participant attempts to remain still upon instruction during resting state fMRI. Peaks denoting fluctuations in amplitude are highlighted in red dots. Insets show histograms of the raw peaks. (

**B**) The micro-movement spikes (MMS see methods explanation) are extracted from the moment by moment fluctuations in peak amplitude (see methods for normalization). They are unitless spike trains and the normalized peaks are gathered in frequency histograms (see insets in A) (

**C**) Full micro-movement spikes from all original frames are used to ascertain statistical differences using the same number of frames in the original raw data. (

**D**) The frequency histograms of the peaks are compared using the earth mover’s distance (EMD see methods explanation) quantifying the cost to transform one histogram into the other. (

**E**) Comparison of stochastic signatures on the Gamma parameter plane spanned by the shape of the empirically estimated distribution and the scale (noise to signal ratio) indicating the dispersion of the PDFs in (

**F**). (

**G**) Gamma moments are used to build a scatter of points on a parameter space where the first three moments (mean, variance and skewness) are represented as x, y, z axes and the fourth moment, the kurtosis is reflected in the size of the marker. A fifth dimension is used to represent the color of the marker using e.g., the range of EMD values determined in (

**D**).

**Figure 3.**Methods: (

**A**) Sample adjacency matrix built using the pairwise EMD across all 500 participants of the 5–10-year-old group. (

**B**) Multi-modal frequency histogram of EMD values across the matrix entries. (

**C**) Curve of the bin count order represented in the jagged dashed curve smoothed using loess method to localize the local minima and maxima. (

**D**) Another sample multi-modal histogram and multi-peaked curve derived from it to explain the process of clustering. Each local minima and maxima are automatically detected along the histogram bin count order spanning the red curve and mapped back to the original histogram of EMD values. As such, given a participant i vs. all other participants, we can localize its maximal distance across the entire age group as the blue circle in (

**E**). (

**F**) These values are then mapped to a normalized scale and used to color the individual points in the scatter according to their values. For example, here the blue dot representing the local maxima from the first bump is localized along the color bar representing the full range spanned by all age groups in the TD and ASD cohorts.

**Figure 4.**Normative stochastic signatures of cross-section of neurotypical population vs. Autism Spectrum Disorders (ASD) signatures from age-matched groups, empirically estimated from the involuntary head displacements (micro-movement spikes reflecting fluctuations in linear speed). Scatters show high heterogeneity in ASD according to the ranges of pairwise Earth Mover’s Distance (EMD) values (color coded normalized while considering the full range of values from both cohorts.).

**Figure 5.**Smooth stochastic shifts of Gamma moment parameters characterize typical aging, with broader spread in the scatter for younger years tending to decrease the spread with aging. Pairwise ranges of EMD values are high, denoting unambiguous maximal separation from each member of the age group to every other member. The normalized color map uses the full range of neurotypical controls and ASD values across all age groups in both cohorts.

**Figure 6.**Stratification of ASD by EMD capturing the pairwise differences in probability distributions empirically estimated from the MMS representing the involuntary fluctuations in the linear displacements of the head. Notice that each scatter is different in spread and range of EMD. Earlier years up to 20 are more heterogeneous than later years in that they have a broader spread in the Gamma moment parameter space that is accompanied by heterogeneous distances in probability space. This trend changes with aging. After 20 years of age, the scatter spread decreases and the EMD maximally separating each individual within the group from the rest of the age group becomes more homogeneous. Each person’s signature is close in probability space. Their fluctuations in involuntary motions become statistically closer. Then, by 40 years of age they are maximally close in probability space and their scatter’s spread tends to shrink. After 40 years of age, there is a fundamental departure of the ASD signatures from the rest of the cohort. Compare these scatters to those in Figure 2 representing the normative data, to best appreciate that aging with ASD is different from typical aging. The trajectory evolution of the stochastic signatures in the probability landscape serves as a natural classifier of autism’s involuntary motions.

**Figure 7.**Characterization of the scatters’ spread using the patterns of variability of the area of the triangles making up the Delaunay triangulation in each age group. Color map represents the average EMD of the triangle area PDFs of each cluster taken as a normalized scale across the full range of values in both TD and ASD scatter spreads. Each three-dimensional scatter in Figure 5 and Figure 6 representing the stochastic signatures of the involuntary MMS from the linear speed was characterized by a different Delaunay triangulation and the triangles’ areas spanned probability distribution capturing the variability of the scatter. Each age group spanned a statistically separable scatter when comparing normative data vs. ASD, empirically fitted by different probability distribution (dashed PDFs are from the ASD scatters). In the last right most panel, the evolution of the stochastic signatures of involuntary movements’ variability over the 5–65 years of age period can be appreciated as a trajectory on the log-log Gamma plane parameter space.

**Figure 8.**Aging trajectories captured cross-sectionally in each cohort (

**A**) Dots denote the location of the mean values of the empirically estimated Gamma moments of each age-group and group type. These show different trajectories with non-uniform changes in ASD during the early years and large departure from normative data from age-match neurotypically developing controls (TD) throughout aging, particularly after 41 years of age. Notice that the rates of change of the shifts in the points are different in ASD. They do not change as regularly as the controls during the first 15 years. (

**B**) The acceleration of the trajectory shows the differences in the rates of change of the shifts in the averaged Gamma moments for each cohort, with inflection points around 26–30 years of age that take the systems into different directions. (

**C**) The position plus each increment (trajectory velocity) is also accumulated to examine the trajectory over time. This reveals differences that become more pronounced after 20 years of age and decrease by 40, right before the largest departure from normative data that separates the oldest ASD cohort form the age-matched TD. (

**D**) The pointwise difference between the two trajectories reveals a large change after 20 and an inflection point by 40, right before the accelerated change of the 41–65 ASD group. (

**E**) The trajectories are embedded in the scatter to give a sense of the differences in relation to the full TD cloud. (

**F**) The cloud of ASD with the embedded trajectories highlights the large departure of the 41–65 group from the normative trajectory.

**Figure 9.**Network connectivity metrics used to separate the two cohorts by age groups and automatically detect significant statistical differences across age groups and between each control and ASD same-age group. (

**A**) Values of network’s clustering coefficient for each node (representing a participant) in neurotypical controls distinguish each age group. (

**B**) Likewise, the clustering coefficient distinguishes each age group, with higher values in ASD relative to controls. Nodes are more connected in earlier years (up to 20 years of age) in ASD according to the similarity metric of EMD computed pairwise and determining the weighted connected graph of each cohort. (

**C**) Non-parametric ANOVA, Kruskal-Wallis test captures the within and between group differences. (

**D**) The characteristic pathlength computing the average shortest distance path from all nodes to each node also captures differences within each group and between the two cohorts of typical controls and ASD. Minimum and maximum characteristic pathlength values are shown with corresponding adjacency matrices (

**E**) and network distance matrices (

**F**) for each cohort.

AGE GROUP | ASD | TD |
---|---|---|

5 TO 10 YEARS OLD | 228 | 265 |

11 TO 15 YEARS OLD | 374 | 417 |

16 TO 20 YEARS OLD | 200 | 178 |

21 TO 25 YEARS OLD | 103 | 116 |

26 TO 30 YEARS OLD | 43 | 76 |

31 TO 40 YEARS OLD | 39 | 43 |

41 TO 65 YEARS OLD | 30 | 32 |

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**MDPI and ACS Style**

Torres, E.B.; Caballero, C.; Mistry, S.
Aging with Autism Departs Greatly from Typical Aging. *Sensors* **2020**, *20*, 572.
https://doi.org/10.3390/s20020572

**AMA Style**

Torres EB, Caballero C, Mistry S.
Aging with Autism Departs Greatly from Typical Aging. *Sensors*. 2020; 20(2):572.
https://doi.org/10.3390/s20020572

**Chicago/Turabian Style**

Torres, Elizabeth B., Carla Caballero, and Sejal Mistry.
2020. "Aging with Autism Departs Greatly from Typical Aging" *Sensors* 20, no. 2: 572.
https://doi.org/10.3390/s20020572