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Posttraumatic stress disorder (PTSD) is a prevalent psychiatric condition that is associated with symptoms such as hyperarousal and overreactions. Treatments for PTSD are limited to medications and insession therapies. Assessing the way the heart responds to PTSD has shown promise in detecting and understanding the onset of symptoms.
This study aimed to extract statistical and mathematical approaches that researchers can use to analyze heart rate (HR) data to understand PTSD.
A scoping literature review was conducted to extract HR models. A total of 5 databases including Medical Literature Analysis and Retrieval System Online (Medline) OVID, Medline EBSCO, Cumulative Index to Nursing and Allied Health Literature (CINAHL) EBSCO, Excerpta Medica Database (Embase) Ovid, and Google Scholar were searched. Non–English language studies, as well as studies that did not analyze human data, were excluded. A total of 54 studies that met the inclusion criteria were included in this review.
We identified 4 categories of models: descriptive timeindependent output, descriptive and timedependent output, predictive and timeindependent output, and predictive and timedependent output. Descriptive and timeindependent output models include analysis of variance and firstorder exponential; the descriptive timedependent output model includes a classical time series analysis and mixed regression. Predictive timeindependent output models include machine learning methods and analysis of the HRbased fluctuationdissipation method. Finally, predictive timedependent output models include the timevariant method and nonlinear dynamic modeling.
All of the identified modeling categories have relevance in PTSD, although the modeling selection is dependent on the specific goals of the study. Descriptive models are wellfounded for the inference of PTSD. However, there is a need for additional studies in this area that explore a broader set of predictive models and other factors (eg, activity level) that have not been analyzed with descriptive models.
Posttraumatic stress disorder (PTSD) is a psychiatric condition that develops as a result of experiencing injury, severe psychological shock, and other trauma [
Although an alarming number of individuals are afflicted with PTSD, there are significant barriers to care delivery [
Despite recent work, the extent of knowledge on the physiological reactions to PTSD and, in particular, HR is limited, and research is needed to better understand the changes in HR associated with PTSD. Few models (eg, analysis of variance [ANOVA], regression analysis) have been developed to relate changes in heart activity to disorder states. In particular, given the opportunity to collect HR data nonintrusively, it is important to use appropriate mathematical and statistical methods to ensure the accumulation of convergent knowledge in this field and to characterize and understand HR in terms of PTSD. In this paper, we document the findings from a review of the current literature on measures and models used in various domains to analyze HR data. In addition to summarizing and synthesizing the HR analysis methods, we provide an evaluation of methods for applications relevant to PTSD detection and diagnosis.
A scoping review was conducted using the strategies outlined in the preferred reporting items for systematic reviews and metaanalyses (PRISMA) methodology [
Abstracts were reviewed for relevance, and articles that did not discuss HRrelated measures in detail and did not provide or use quantitative methods for analysis were excluded. Other exclusion criteria were non–English language articles and articles that assessed non–heartbased physiological measures such as skin conductance and blood pressure. Furthermore, studies that did not analyze human physiology were excluded. The inclusion criteria were all articles that discussed human HR analysis. Our initial search yielded 1905 results. After removing duplicate articles and checking for eligibility using Rayyan QCRI (a web app for assisting literature reviews), 270 articles were further reviewed. Out of the 270, 138 were exclusively about non–heartbased measures reactions, 67 did not focus on human physiology, and 11 had duplicated content. Of these, 54 articles from the search were included in this review based on their relevance to the topic.
Furthermore, the bibliography of references in each research paper was investigated thoroughly (backward search) to identify pertinent articles, and then Google Scholar searches (forward search) were conducted to find the full text.
Preferred reporting items for systematic reviews and metaanalyses flow chart for the literature review.
We listed the articles identified by the search process into 2 categories based on our synthesis: studies of the effects of PTSD on heart physiology and quantitative modeling techniques for heart data. We further partitioned studies of PTSD effects into 2 types: (1) studies that investigate the effect of PTSD on heart rate variability (HRV) and (2) studies that explore the effect of PTSD on HR. The literature on models can be further classified by the model’s focus on describing versus predicting data and the model output. These categories and subdivisions are discussed in the following sections.
HRV measures variations in heartbeats and is related to the electrical activity of the heart [
The reviewed articles found that PTSD causes sustained changes in the autonomic nervous system (ANS; the part of the nervous system that is responsible for regulating automated functions in the body, such as heart activity) [
RMSSD and SDNN are timedomain measures of HRV. SDNN is an index of SNS activity [
Although an HRV analysis is common among studies of anxiety [
HR is the number of heartbeats per 60 seconds. Normal HR differs among individuals based on age and gender, health level, and respiratory activity [
PTSD can affect HR in 2 modalities: resting and fluctuation tone [
Another HR measure that has been investigated in terms of PTSD is HR fluctuations (changes in HR levels) in the presence of stimuli [
On the basis of our synthesis of the existing literature, we categorized mathematical models of HR into descriptive and predictive models, both of which could provide insight relevant to understanding the psychophysiological responses to PTSD. Descriptive methods can be used to describe and make inferences about a data set, whereas predictive methods can be applied to forecast trends and patterns in the data. Predictive and descriptive models can be further characterized by their type of output—time independent or time dependent (
Taxonomy of heart rate analysis methods. ANOVA: analysis of variance.
Linear regression, and in particular ANOVA, is a statistical model used for the analysis of HR in several articles (
A firstorder exponential model provides a function with a sustained growth or decay rate [
BartelsFerreira et al [
Results of studies that used descriptive models with timeindependent output.
Method and authors  Domain  Independent variables  Dependent variables  



Shalev et al [ 
PTSD^{b}  Gender, age, HR^{c}, trauma history, event security  HR 

Strath et al [ 
Physical activity  HR, oxygen intake, age, fitness  HR 

RomeroUgalde et al [ 
Physical activity  Accelerometer, energy expenditure, HR  HR 

Khoueiry et al [ 
Medical  HR, hospitalization duration, age  HR 

Tonhajzerova et al [ 
Physiology  Resting HR, major depressive disorder  HR 



Bartels et al [ 
Physical activity  HR peak, resting HR, HRR^{d}  HR variation 
^{a}ANOVA: analysis of variance.
^{b}PTSD: posttraumatic stress disorder.
^{c}HR: heart rate.
^{d}HRR: heart rate recovery.
Classical time series analysis is a common statistical method that can analyze timedependent data trends by looking into linear relationships. Classical time series analysis is also a promising method for analyzing HR and HR fluctuations as these measures are timebased [
Peng et al [
Beyond the analogous use case, the classical time series has several benefits compared with ANOVA. As the model explicitly considers autocorrelation, it does not require the assumption of independence of observations [
Mixed regression analysis has been used in the literature to evaluate physiological responses to energy expenditure [
The ability of mixed regression models to account for individual differences makes them an advantageous choice for modeling PTSD. Several studies have identified significant individual differences in people with PTSD [
This type of modeling might produce similar results to ANOVA in many cases. However, in comparison with ANOVA, mixed regression models are more effective for data sets with missing values and multiple random effects [
Results from studies that used descriptive models with timedependent output.
Method and authors  Domain  Independent variables  Dependent variable  



Chen et al [ 
Health care (patient data)  HR^{a}, resting HR  Heartbeat  

Kazmi et al [ 
Physiology  HR, HRV^{b}, time  HR  

Zakeri et al [ 
Physical activity  HR, energy expenditure, accelerometer, age  Energy expenditure  

Peng et al [ 
Medical  HR, heartbeat, time  HR  



Gee et al [ 
Biomedical  HR, heartbeat, respiration, time  HR  

Bonomi et al [ 
Physical activity  HR, energy expenditure, photoplethysmography, accelerometer  HR  

Xu et al [ 
Physical activity  HR, energy expenditure, different training paradigms, age, height, weight  Energy expenditure 
^{a}HR: heart rate.
^{b}HRV: heart rate variability.
Machine learning methods refer to a set of training and predictive algorithms that use data to learn complex trends associated with labels (eg, symptom presence) in a data set. Machine learning analysis is a multiplestep process consisting of dividing a data set into training and testing data (or leveraging resampling techniques such as crossvalidation), developing a model from the training data, and evaluating the model on the testing data. This approach is advantageous relative to approaches that use all of the data for training a model (eg, ANOVA) and approximate metrics to evaluate generalizability (eg, adjusted
The success of applying machine learning methods depends on the data used to train and evaluate the algorithm. Machine learning algorithms typically require large training sets—several thousand observations—and they implicitly assume that the data and associated labels are of equal quality. In cases where the data are noisy, or labels are unreliable, machine learning training algorithms may fail to converge to a generalizable solution. Furthermore, if the training data examples are biased (eg, nonrepresentative population samples), the machine learning algorithms trained on the data may also be similarly biased. It is often difficult to identify these issues through standard training and testing processes of machine learning algorithms; thus, machine learning analyses should be accompanied by descriptive analyses to obtain a better understanding of the data and potential errors or bias [
Most of the reviewed studies used HRV, along with machine learning algorithms to predict stress levels in individuals [
The fluctuationdissipation theory (FDT) is a common approach in thermodynamics that is used to predict system behavior by breaking the system responses into small forces [
Chen et al [
In terms of mathematical concepts, this type of modeling has a powerful predictive capability by grouping individuals and therefore minimizing the error rate [
Results from example studies that used predictive models with timeindependent output.
Method and authors  Domain  Independent variables  Dependent variable  



Kolus et al [ 
Biomedical (energy expenditure)  HR^{a}, oxygen consumption, work rate  Work rate  

McDonald et al [ 
PTSD^{b}  HR, subjective stress moments  Stress moment  

Healey et al [ 
Driving  HR, HRV^{c}, skin conductance, muscle activity, muscle tension, breathing rate  To detect stress  

Kolus et al [ 
Physical activity  HR, maximum HR, oxygen consumption, body type, work rate  Work rate  

Zhang et al [ 
Physical activity  HR, body attitude information, body movement  HR  



Chen et al [ 
Health care  HR recovery, blood pressure, instantaneous HR  HR 
^{a}HR: heart rate.
^{b}PTSD: posttraumatic stress disorder.
^{c}HRV: heart rate variability.
Timevariant modeling is a mathematical approach used to analyze timedependent data sets and provide a timedependent output. Timevariant models of HR can generate HRR measures in real time. Some studies suggest that measuring HRR in real time can especially help assess arousals and arousability in different individuals in response to mental stressors [
Although timevariant modeling has been replicated in the literature and has shown promise in analyzing HR data [
Nonlinear dynamic modeling of HR consists of depicting HR as the output of a nonlinear dynamic system [
Nonlinear dynamic modeling of HR can be a promising method to assess arousal patterns by measuring SNS activity [
This model accounts for the natural nonlinearity and timedependent features of HR data. In addition, the learnability and predictability of this method can help detect the onset of symptoms in patients with PTSD. A limitation of this method for characterizing PTSD aspects is the assumption of invertibility [
Results from studies that used predictive models with timedependent output.
Method and authors  Domain  Independent variables  Dependent variable  



Lefever et al [ 
Sports science—biomedical  HR^{a}, participants’ input power, road gradient,  HRV^{b}  

Olufsen et al [ 
Biology, health care  HR, resting HR, blood pressure  HR regulations  



Chen et al [ 
Health care (patient data)  Resting HR, arterial blood pressure, HR, HRV  Heart beat  

Kazmi et al [ 
Biophysics  Human normal sinus rhythm, human congestive heart rate failure  HRV (they look at the correlation) 
^{a}HR: heart rate.
^{b}HRV: heart rate variability.
We categorized the methods used to analyze HR data into 2 categories: descriptive and predictive. In the context of PTSD, descriptive models may be used to characterize PTSD triggers and the factors that affect their occurrence, whereas predictive models may be useful to predict PTSD onset to facilitate timely intervention. The extracted models provide methods for evaluating, describing, comparing, interpreting, and understanding patterns in the HR data. However, interpreting the data in a meaningful way depends on the specific objectives of the study. The data at hand can be analyzed with one or many of the reviewed models based on the goal of the study and the assumptions of the models. Each model corresponds to a distinct type of output and different interpretations of the data with different assumptions. On the basis of the process of data collection, the number of observations, and variables in the data, researchers might choose one or a combination of models provided.
Descriptive framework for heart rate–related analysis methods extracted from the literature.
Model  Assumptions  Features  Limitations  Cases  



ANOVA^{a} 
Normal distribution of residuals Constant variance of populations Independence and identically distributed observations 
Capable of comparing groups and looking at trends Computationally simple 
Restrictive assumptions Type 1 error Just applicable to linear analysis 
[ 

A firstorder exponential model 
Continuous observations Observations should be identical (eg, no age, gender difference) Environmental effects are constant 
Easy to apply and learn Gives higher weights to recent observations 
Not repeated in studies Higher error rates than classical time series and mixed regression Does not show trends Not accurate for very small and very large windows of time 
[ 



Classical time series analysis 
Stationary observations (constant mean values of series) 
Advantageous for analyzing timebased trends Does not require independence of data points Used in the literature to analyze cardiovascular disease Includes linear and nonlinear analysis 
Requires stationary data sets 
[ 

Mixed regression model 
Normality of residuals distribution 
Accounts for differences between individuals (eg, age, gender) Can be used for analyzing repeated measures Can be applied to nonnormal data 
Cannot be used for nonlinear models 
[ 



Machine learning methods 
Limited dependencies of the observations (each machine learning algorithm has its assumptions that need to be checked) 
Proactive algorithm (can be used for actionreaction type of data sets) Powerful predictive method Rapid analysis prediction, and processing Simplifies timeintensive computations 
Can over fit or under fit data Cannot be applied to data sets with highly dependent variables The process has little rational explanation 
[ 

Fluctuationdissipation theory 
Equilibrium system (the system and observations are not changing) 
Powerful predictive capability Does not have restrictive assumptions such as normality of residuals Significantly less data needed compared with a general data fitting approach 
Computationally intense Time consuming 
[ 



Timevariant modeling 
Requires big data sets with highfrequency data points (more than 60 Hz) 
Can be used to describe data as well as forecasting the future 
Computationally intense Slow process 
[ 

Nonlinear dynamic modeling 
Invertible matrices 
Very accurate Replicated multiple times in studies 
Computationally intense Slow process Requires invertible matrices that is not always feasible in naturalistic settings 
[ 
^{a}ANOVA: analysis of variance.
Fit assessment can be conducted to examine the efficiency of each method in modeling a specific dataset. Fit assessment is especially promising for comparing different methods if they are applied to the same data set. However, considering the wide range of applicable fit indices, researchers might struggle to compare them. In the category of descriptive models,
In the statistical analysis of data in the PTSD domain, fit assessments have been used to show the efficiency of the results. For instance, McDonald et al [
Examples of fit assessment for different methods used in studies.
Study  Method  Variables  Fit measure 
Strath et al [ 
ANOVA^{a}  HR^{b}, oxygen intake, age, fitness  
Zakeri et al [ 
Classical time series  HR, energy expenditure, accelerometer, age  
McDonald et al [ 
Machine learning  HR, subjective stress moments  Area under receiver operating characteristics curve=0.67 
Healey et al [ 
Machine learning  HR, HRV^{c}, skin conductance, muscle activity, muscle tension, breathing rate  Accuracy=97% 
Chen et al [ 
Fluctuationdissipation theory  HR recovery, blood pressure, instantaneous HR  Error rate=25% 
Chen et al [ 
Nonlinear dynamic  Resting HR, arterial blood pressure, HR, HRV  Sensitivity=0.941; predictability=0.988 
^{a}ANOVA: analysis of variance.
^{b}HR: heart rate.
^{c}HRV: heart rate variability.
The models identified in this review represent several promising directions for future exploration, but they also illustrate a hidden complexity in the use of HR data as model input. HR is impacted by individual characteristics including age, sex, health, resting HR, respiration, and lifestyle [
Beyond these general characteristics, it is important to consider the type of physical activity in the analysis. Physical activity significantly affects HR [
HR data have been widely investigated in the domains of physical activity and energy expenditure. Although there are some differences between the effects of mental stress on HR and the effects of physical activity on HR, there are many similarities that make these domains connected. Physical activity affects SNS performance in the short term and PNS performance in the long term [
Similarly, in terms of mental stress, whereas acute stress or immediate response to stressors activates SNS, chronic stress increases vagal and parasympathetic activity [
This scoping review attempted to include all articles that analyzed HR; however, it is still likely that some were overlooked. Furthermore, the authors categorized the HR models based on their own synthesis of the literature and relevance to PTSD. These models can be listed and categorized in a variety of ways, such as deterministic versus stochastic.
Another limitation of this review is that although the identified models have been applied across various domains (eg, energy expenditure and general stress prediction), to our knowledge, only 2 papers [
Beyond the specific application of these models to PTSD, there are several more general challenges. The reviewed research often proceeded independently, with few links between the various studies. This diversity makes comparisons across studies difficult. Studies have used different data sets with different variables based on individual goals. Furthermore, the reviewed work often focused on testing 1 specific model rather than a broad comparison. Often critical details, such as the model and parameter selection process, were not reported in the articles. Another critical detail often not addressed in the reviewed studies was the mismatch between the model requirements and the sampling rates, which may result in conditions such as overfitting [
Collectively, these limitations suggest a need for substantial additional work in modeling the relationship between HR and PTSD. Future studies should consider comparisons between several models, analyze or explicitly discuss decisions made throughout the modeling process, and comprehensively document their HR data collection. As future studies are conducted that enact these criteria, the utility of the modeling approaches identified here will become clearer, and the path to more effective PTSD treatments will become more attainable.
The goals of this review were to identify and characterize quantitative HR models for relevant applications in PTSD. One of the gaps in this area is the absence of a framework that researchers can use before, during, and after their data collection to choose a method to analyze HR data. In this regard, we developed a descriptive framework that can be used to determine the method to apply to HR data to achieve more efficient results. We identified 4 broad categories of methods: descriptive timeindependent output, descriptive timedependent output, predictive timeindependent output, and predictive timedependent output. Descriptive timeindependent output models include ANOVA and firstorder exponential, whereas descriptive timedependent output models include classical time series analysis and mixed regression. Predictive timeindependent output models include machine learning methods and analysis of HRbased FDT. Finally, predictive timeindependent output models include the timevariant method and nonlinear dynamic modeling.
All of the identified modeling categories have relevance in PTSD, although modeling selection is highly dependent on the specific goals of the modeler. For instance, one might use ANOVA to examine the differences in resting HR in individuals with PTSD versus without PTSD [
adaptive neurofuzzy inference system
analysis of variance
autonomic nervous system
area under the receiver operating characteristics curve
coherence score
fluctuationdissipation theory
high frequency power
heart rate
heart rate response
heart rate variability
low frequency power
mobile health
parasympathetic nervous system
preferred reporting items for systematic reviews and metaanalyses
posttraumatic stress disorder
root mean square of successive differences between normal heart beats
SD of the interbeat interval of normal sinus beats
sympathetic nervous system
The authors would like to acknowledge Ms Margaret Foster, a systematic review expert librarian at the Texas A&M University system, who helped to develop the search strategy.
None declared.