Yoganandan Acceleration Curves Analysis

Introduction

Goals and process

Explore the pertinence of the DRI and SIC criteria based on the Yoganandan study.
Call the data to check by peer-review.

Method

Extract the data from the research paper:

Extract the acceleration curves
Extract the pulse characteristics (duration, peak force, injury risk)

Compute the DRI and SIC values for each acceleration curve.
Compare the DRI and SIC values with the pulse characteristics (force, injury risk).
Explore the influence of the SIC exponent on the results.
Plot the results in the Eiband space.

Source

Yoganandan N, Khandelwal P, Porwal V, Humm J, Banerjee A. Human Thoracolumbar Spine Tolerance to Injury and Mechanisms From Caudo-Cephalad Loading: A Parametric Modeling Study. J Eng Sci Med Diagn Ther. 2021 Feb 1;4(1):011007. doi: 10.1115/1.4049523. PMID: 35832262; PMCID: PMC8597559.

Computation details

g₀ = 9.80665
Mass = 50 kg

DRI parameters

Applied on the full curve, unfiltered
omega_n (ω)_n = 52.9
zeta (ζ) = 0.224

SIC parameters

Applied on the full curve, unfiltered
Time window: 1-200 ms
Exponent p = 2.0 (then explore 1.8, 2.2, 2.5)

Analysis

Main acceleration/velocity overview

Figure 1 - Drop Test Analysis (click to open interactive chart).

General metrics

Data extracted from the research paper

	pulse_ms	Spine compression force_kN	injury_risk
yellow	50	7.64	0.625
red	75	6.20	0.233
darkblue	100	5.28	0.063
blue	150	4.22	0.004
green	200	3.30	0.000

Data computed from the curves

	yellow	red	darkblue	blue	green
drop name	50ms/yellow	75ms/red	100ms/dark-blue	150ms/blue	200ms/green
max acceleration (g)	43.65	29.26	22.0	14.93	11.15
SIC	39.78	26.61	20.07	13.79	10.27
DRI	42.1	34.68	28.18	19.9	14.66
first peak DRI xmax (mm)	147.549	121.525	98.758	69.732	51.381
EN theoritical drop momentum (kg·m/s)	280.0	280.0	280.0	280.0	280.0
measured momentum (kg·m/s)	628.63	625.85	627.59	638.04	637.48
extra momentum (%)	124.51	123.52	124.14	127.87	127.67
first peak max travel (mm)	294.938	447.482	594.195	876.278	1170.737
EN theoritical drop energy (J)	812.25	812.25	812.25	812.25	812.25
measured absorbed energy (J)	3870.68	3905.7	3906.83	3907.9	3907.83
extra energy (%)	-0.91	-0.01	0.01	0.04	0.04
duration above 38 g (ms)	12.18343	0.0	0.0	0.0	0.0
duration above 20 g (ms)	33.373993	38.296454	19.902169	0.0	0.0
pulse duration (ms)	50	75	100	150	200
Spine compression force (kN)	7.64	6.2	5.28	4.22	3.3
injury risk	0.625	0.233	0.063	0.004	0.0

Notes on results

The measured momentum is significantly higher (~620 kg·m/s) than the usual EN drop test (~270 kg·m/s). Assuming a falling mass of 50 kg, this corresponds to an impact velocity of ~12.4 m/s instead of ~5.7 m/s for EN tests.
The SIC results are computed with exponent p = 2.0 over the 1-200 ms window.

Correlation with spine compression force

Figure 2 - SIC (1-200 ms) and DRI vs Force by pulse duration (click for interactive).

Correlation with injury risk

Figure 3 - SIC and DRI vs Injury risk by pulse duration (click for interactive).

SIC exponent influence

Figure 4 - SIC vs spine compression force by HIC exponent (1-200 ms window). Click to open interactive chart.

Eiband space

The idea is to plot these pulses inside the Eiband space.

Figure 5 - Eiband Space - Yoganandan Drops (click for interactive).