Comparison of Flexion–Extension Responses between Male and Female sub-Axial Cervical Spine Segments

Pranav Duraisamy, Davidson Jebaseelan, Jobin D. John

Hi, Im pranav, recently completed my bachelors in mech. This study is an outcome of my bachelor’s pjt thesis. It mainly focused on sex differences in subaxial c spine segments.

Introduction

• Cervical spine segment - Two vertebra, Soft tissues
• Female have more risk of neck injury than male in traffic accidents

• Recent dummies and HBMs also focus on average female
• Sex-specific calibration and validation are either limited or non-existent

I can see many ppl in this hall who were majorly working on spine biomech. To give a brief intro on C spine segments. It consists of 2 vertebra, and some ligaments in between like CL, ligamentum flavum, articular processes and so on.. then there is also IVD which have Annulus fibers and nucleus. Spinal injuries esp neck injuries in women are more than men specifically in traffic accidents. To study the injury in female, We use female HBM. However female HBMs are morphed versions of male HBMs and sex specific validation is not done on those models.

Objective

Quantify the differences between the male and female cervical spine segments in flexion and extension

That leads to the objective of this study, thats to quantify the differences between the male and female cervical spine segments in flexion and extension

A Bit of Background…

Let’s take a look at some avl data that is related to this study. In some experiments, there were both male & female specimens but in the analysis everything was clubbed together. So we dunno the diff bw male & female. For example, this study by Wheeldon et al. Then we have this study by winkelstein et al but all the specimens in this study were male.

A Bit of Background…

Experimental setup used by Nightingale et al.

Finally we have these studies by nightingale, where the data for male & female were reported separately & its available openly in NHTSA database. the exp setup was same for both the nightingale studies. so it can be made as a comparable study which was not done by the original author. c spine segments were cut from unembalmed pmhs and tested in flexibility & failure tests

Methods

Exploratory Data Analysis

This slide shows no of specimens tested. just for the moment, consider c3c4 there are 11 specimens for female but there is only 1 specimen for its very adjacent c4c5 . this is because of the segmentation of fsus. same trend follows for male too but different segments.

Exploratory Data Analysis

This plot shows the distribution of rotation angle at 3nm. you could see that even in this eda that the extension is similar in male & female but thats not the case for flexion. females rot angle is higher than male.

Concept behind Linear Regression

This is the linear reg as we know it, there will be a set of points, we fit the line & the residuals would be normally distributed. behind the screen you would use MLE or least squares or smthng similar to minimise these residuals.

Classical vs Bayesian Regression

MLE Approach

\[\begin{align} Y &= \alpha + \beta X ± \sigma\\ \\ \alpha &= \text{Constant (Intercept)}\\ \beta &= \text{Constant (Slope)}\\ \sigma &\sim \text{Normally distributed} \end{align}\]

Probabilistic Approach

\[\begin{align} Y &\sim \operatorname{N}(\mu,~\sigma)\\ \mu &= \alpha + \beta X\\ \alpha &\sim \text{A distribution}\\ \beta &\sim \text{Another distribution}\\ \sigma &\sim \text{Some other distribution}\\ \end{align}\]

From the line of best fit, you could find the parameters a & b as consts. another approach is to do bayesian linear reg. where these parameters are estimated as probability distributions

Bayesian Analysis - In a nutshell

Bayesian Linear Regression Model

As you can see here bayesian is other way around than a classical regression. all the relations are probabilistic than deterministic. every parameter whether it can be slope, intercept or even output variable is a probability distribution than singular values.

Adapted from Bayesian Analysis with Python by Oswaldo Martin

Bayesian Model Building

\[\begin{align} L_i &= \text{Coeff. for loading mode}\\ l_{ij} &= \text{Coeff. for loading mode specific to sex}\\ E &= \text{Residual random error}\\ \end{align}\]

R = Segmental rotation angle at 3Nm

Coming back to this study, we know that when 3nm moment is applied, the rotation would be more than 0 deg and from previous studies we know that it wont be more than 20 deg. we use that prior information as a starting point for fitting. we used a hierarchical model in which sex was treated as level. so that each flex & ext have diff parameters for male & female

Results & Discussion

Prior to Posterior Predictive

If you compare the x-axis of both the plots, you could find that plausible range for rotation angle at 3Nm got shrinked after fitting the nightingale data to the model. Also the mean of all the samples (blue lines) are closely aligned with the observed data.

Posterior Distributions

Coeff. for loading mode

Coeff. for loading mode specific to sex

we can see the dist of coeff for loading are similar in ext & flex. they are literally on top of each other. but if you look at this, the coeff for multilevel loading given sex in Ext, male & female are similar. but in flexion, we can see a clear difference between male & female.

Comparison: Flexion & Extension

You could see a more fancier version of previous plot in this slide. In male, the top left plot, the dist of segmental rot at 3nm. the dist of flex & ext, they overlap, they are not different. Then if you look at the left bottom plot, for female, the ext is similar to male & the flex is higher & they dont overlap. And we can quantify that using contrast plots. the contrast dist is a diff of 2 dist. And in this case its the difference of flex & ext. if yu look for male in top right , its distributed around 0 which means there is no diff between flex & ext. But when we come to the female, we see the contrast dist is not abt 0, rather its about 4 deg showing that there is significant diff b/w flex & ext in female.

Comparison: Female & Male

Now we can see the data in a different way also. you could see the differnece in male & female in extension which is in top row.. and flexion is in bottom row. Anyways we see similar differences.

Conclusion

• Male and female segments in extension tends to be similar
• But in flexion, the female rotation was 4.5° more than male in average
• Female cervical spine segmental kinematics cannot be considered as size-scaled versions of male

key take aways from this study are:

Acknowledgement

• Travel Grant for IRCOBI 2025 by Toyota
• ANRF-SERB-CRG (CRG/2023/004727) in India
• SPARC (SP23241582EDSPAR008343) in India
• Swedish Transport Administration/Trafikverket grant (TRV2024/107142)

Finally, i would like to acknowledge all the grants recieved for this study

Comparison of Flexion–Extension Responses between Male and Female sub-Axial Cervical Spine Segments

Pranav Duraisamy, Davidson Jebaseelan, Jobin D. John

✨ Bonus Slides ✨

Data Extraction

• Extracted reports and ASCII data from NHTSA database using API
• Consists of spine segments from 16 female and 16 male PMHS
• After filtering and processing, there were 48 female and 29 male FSUs
• Out of which 36 are tested for flexion while 41 are tested for extension

Inclusion Criteria

• Flexibility Tests
• Rotation angle interpolated at 3Nm
• Sub-Axial Cervical segments (C3 to C7)

meow meow

Bayesian Model Building

\[\begin{align} L_i &= \text{Coeff. for loading mode}\\ l_{ij} &= \text{Coeff. for loading mode specific to sex}\\ E &= \text{Residual random error}\\ R &=\text{Segmental Rotation angle at 3Nm}\\ \end{align}\]

Common Effect

\[ L_{i} \sim \operatorname{Normal}(\mu_{i},~\sigma_{i}) \]

\[ \mu_{i} = \left\{ \begin{array}{ll} 5.3 & \textrm{for Extension} \\ 5.8 & \textrm{for Flexion} \end{array} \right. \]

\[ \sigma_{i} = \left\{ \begin{array}{ll} 2.3 & \textrm{for Extension} \\ 2.9 & \textrm{for Flexion} \end{array} \right. \]

Group-level Effect

\[ l_{ij} \sim \operatorname{Normal}(0,~\sigma_{l_{i}}) \]

Hyperprior

\[ \sigma_{l_{i}} \sim \operatorname{HalfNormal}(\tau_{i}) \]

\[ \tau_{i} = \left\{ \begin{array}{ll} 2.3 & \textrm{for Extension} \\ 2.9 & \textrm{for Flexion} \end{array} \right. \]

Residual Error

\[ E \sim \operatorname{Normal}(0,~\sigma_{E}) \]

\[ \sigma_{E} \sim \operatorname{HalfStudentT}(\nu,~\sigma) \]

\[ \nu = 4, \sigma = 3.4 \]

Likelihood & Posterior

\[ R = L_{i} + l_{ij} + E \]

Bayesian Linear Regression Model

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Bayesian Model Building

• Bambi v0.14.0 (python package) was used for building the Bayesian models
• Used weakly informative priors from other studies ¹
• Sampled using MCMC NUTS sampler in 4 chains, each with 1500 draws
• Posterior predictive distributions were used for comparing the responses

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1. Winkelstein et al., (2000)

Posterior Distributions

What is posterior?

• Probability distribution for the parameters in the model after sampling
• Reflects all we know about the problem

Residual Error

Common Effect

Hyperprior

Group-level Effect

    Forest Plot

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Future Study