Development and application of a lumped parameter model for predicting blast wave effects on middle ear dynamics

doi:10.1007/s10483-026-3366-8

Abstract

Abstract:

The human ear is one of the most vulnerable organs to blast damage in modern warfare. The accurate prediction of blast wave effects on the ear has become a key challenge in auditory trauma research. A lumped parameter (LP) model, with parameters optimized using a genetic algorithm, is developed to efficiently predict the middle ear’s dynamic response to blast waves. The model accurately predicts tympanic membrane (TM) and stapes responses, particularly the first peak. Frequency-domain displacement and sensitivity analyses show that the middle ear responses are concentrated in a low-frequency range, with the blast wave amplitude significantly influencing the overall responses. TM responses are more sensitive to decay time at higher frequencies, while stapes responses are more sensitive at lower frequencies. This method achieves competitive accuracy and high computational efficiency. Based on this model, a risk index based on stapes displacements is proposed to optimize and evaluate hearing protection systems.

Key words: blast wave, lumped parameter (LP) model, genetic algorithm, middle ear response, hearing protection

2010 MSC Number:

O325

Hongge HAN, Liang WANG, Zhanli LIU, Yongtao SUN, Anshuai WANG, Yueting ZHU, Jie WANG, Haoqiang GAO, Qian DING. Development and application of a lumped parameter model for predicting blast wave effects on middle ear dynamics. Applied Mathematics and Mechanics (English Edition), 2026, 47(4): 695-718.

TrendMD

Figures/Tables 20

Fig. 1

Fig. 2

Table 1

Material properties of the components in the FE model"

Structure	Component	Young’s modulus/Pa	Density/ $(kg ⋅ m − 3)$
TM	Pars tensa	$3.20 × 107$	$1.20 × 103$
TM	Pars flaccida	$1.00 × 107$	$1.20 × 103$
Ossicles
Malleus	Head	$1.41 × 1010$	$2.55 × 103$
	Neck		$4.53 × 103$
	Handle		$3.70 × 103$
Incus	Body	$1.41 × 1010$	$2.36 × 103$
	Short process		$2.26 × 103$
	Long process		$5.08 × 103$
Stapes		$1.41 × 1010$	$2.20 × 103$
Joints	Incudomalleolar joint	$1.41 × 1010$	$3.20 × 103$
Joints	Incudostapedial joint	$6.00 × 105$	$1.20 × 103$
Manubrium fold		$4.70 × 109$	$1.00 × 103$
Ligaments and tendons	Superior mallear ligament	$4.90 × 106$	$1.20 × 103$
	Lateral mallear ligament	$6.70 × 106$
	Anterior mallear ligament	$2.10 × 107$
	Posterior incudal ligament	$6.50 × 106$
	Stapedial tendon	$5.20 × 107$
	Tympanic annulus ligament	$6.00 × 105$
	Superior incudal ligament	$4.90 × 106$
	Tensor tympani tendon	$4.90 × 106$
	Stapedial annular ligament	$4.10 × 105$
Skin		$4.20 × 105$	$1.05 × 103$
Relevant data sources: Gan et al.^[42], Gan et al.^[43], and Liu et al.^[44]

Table 1

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Table 2

Optimal values for the LP model to predict the TM response"

LP model parameter	m/kg	c/ $(N ⋅ s ⋅ m − 1)$	k/ $(N ⋅ m − 1)$
Optimal value	$1.338 × 10 − 5$	0.030	$6.022 × 103$

Table 2

Fig. 7

Table 3

Detailed parameters and numbers of the twelve blast waves"

Condition	Peak pressure/dB	A/kPa	t₀/ms	$t d$ /ms
1	183.5	30	0	1
2	183.5	30	0.5	1
3	183.5	30	1	1
4	183.5	30	0	0.5
5	183.5	30	0	1
6	183.5	30	0	2
7	180	20	0	0.5
8	180	20	0	1
9	180	20	0	2
10	174	10	0	0.5
11	174	10	0	1
12	174	10	0	2

Table 3

Fig. 8

Fig. 9

Table 4

Optimal values for the LP model to predict the stapes response"

LP model parameter	m/kg	c/ $(N ⋅ s ⋅ m − 1)$	k/ $(N ⋅ m − 1)$
Optimal value	$7.965 6 × 10 − 6$	0.048	$3.605 × 105$

Table 4

Fig. 10

Fig. 11

Fig. 12

Fig. 13

Fig. 14

Fig. 15

Fig. 16

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