# A METHOD TO ESTIMATE INJURY MEDICAL COST OF OCCUPANTS IN A CRASH TEST

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3 i : is the level of injury, defined by AIS scores ( to 5) j : is a particular AIS body region injured ( to 0). S j : is the probability of each body region j injured in a specific crash type, such as frontal crash. P : is the probability of a particular AIS score i to a specific body region j. C : is the medical cost of each body region j injured with AIS score i. Logistic regression is used to develop the probability equations of S j from real crash data in Taiwan. A mathematical relationship between the dichotomous dependent variable ( injury and no injury ) and independent variable (crash type) is estimated. Wald statistics Z 2 (coefficient β dividing its approximating standard error) and -2log-Likelihood Ration are used to examine the significant of the coefficient and the goodness of fit of this logistic regression model respectively. Linear and non-linear regressions are used to calculate C from Taiwan s real crash data. The AIS score is the independent variable, and medical cost is the continuous dependent variable. R 2 is used to examine the explanation ability of fitted C equations. The P are calculated directly from the injury risk functions proposed by Kleinberger et al. (998), Kuppa (2004), and Kuppa et al. (200). Finite Element Simulation Software LS-DYNA3D is used to simulate the dynamic responses of Hybrid III 50th percentile male dummy (regulations of FMVSS 49CFR PART 572E) restrained with a seatbelt (regulation of FMVSS 208) in a frontal impact sled test. The simulation model is validated according to Prasad s (990) experiment results. In the present study, the test speed is 30mph (FMVSS 208 requirement). The impact on the head, neck, thorax, and knee of the simulation dummy is compared to the result of Khali s (994) study. Injury criteria based on FMVSS 208 (HIC36 to head and N to neck), NHTSA suggestion (CTI to thorax), and Kuppa et al. (200) result (force to femur) are calculated from simulation outputs. Crash Injury Medical Cost Prediction The injury criteria calculated in the above section are converted to the probabilities of various AIS scores by using the equations (2)~(5) which are the injury risk functions of mid-sized adult male based on biomechanical tests from the other studies. Except the seatbelt and the seat, there is no other interior equipment in the sled simulation model. Therefore, the femur and the thorax of the simulated dummy cannot response reasonably in the simulation model. The associated injury criteria of femur and thorax are not calculated. In the future, this shortage can be overcome when the simulation model is upgraded from sled model to full vehicle model. Head: (Kuppa, 2004) ln( HIC36 ) µ P( AIS 3 ) = φ( ) σ µ = , σ = (2). φ : accumulative normal distribution Neck: (Kleinberger et al., 998) p( AIS 3 ) = N + e (3). Thorax: (Kleinberger et al., 998) p( AIS 3 ) = CTI + e (4). Amax Dmax CTI = + Aint Dint Femur: (Kuppa et al., 200) p( AIS 3 ) = F + e (5). The outputs of equations (2)~(3) are substituted into the P in the equation (), together with the associated S j and C stated in the above, to estimate the probable medical cost resulted from passenger car driver in the frontal impact. RESULTS Real Crash Data Analysis There are 330 thousands crash victims reported by police in Taiwan from year 999 to of them are found in the death records, 874 survived victims are successfully linked to hospital data. Among 874 survivals, 577 are passenger car drivers. 7 of these 577 drivers are assigned AIS = 6 by ICDMAP 90, 782 drivers are in unknown injury state, and 7988 drivers are survived in AIS ~ 5. Among 7988 survival drivers, 737 drivers (2.7%) are involved in the frontal crashes. It can be seen in Table that 87 (50.%) of these 737 drivers are head injured, 242 drivers (3.9%) are thorax injured, and 290 drivers (6.7%) are lower extremity injured. Very few neck injured survivals are recorded in Taiwan s data and there are not enough to build up the C equation of the neck. Among the survived drivers in the frontal crash, most of them are AIS < 4 injuries. Lai 3

4 Table. Number of survived passenger car driver by principle injured body region and AIS score in frontal crash AIS score Total body region counts % Head and face Neck Thorax Lower extremity Others Total The original medical cost distribution and transformed natural logarithm function data are a marked positive skewness (See Figure ) and an approximating normal distribution (See Figure 2), respectively. This attribute of medical cost distribution is same trend in each body region. Therefore, natural logarithm of medical cost is used during the regression Medical Cost (NT Dollars) Figure. Original medical cost distribution of survived passenger car driver in frontal crash. ( US dollar = 33 NT dollar) Std. Dev = Mean = 263 N = S j and C Models Development Equations (6)~(8) and (9)~() are the fitted regression functions for S j and C, respectively. From equations (6)~(8), the probability to head, thorax, and lower extremity injured in the frontal crash are in the sequence of 0.56, 0., and 0.. The fitted regression functions (9)~() to head, thorax, and lower extremity could explain 20%, 30%, and 50% of the variation in the associated medical cost. All the coefficients in equations (6)~() are statistical significant. Owing to the few records number of neck injury, the associated equations cannot be obtained in the present study. α + e S j + e x = for βx = α + βx frontal crash,0 for other crashes j = Head and face α = β = (6). j = Neck, associated data were too few to fit equation. j = Thorax α =.8209 β = (7). j = Lower extremity α =.6074 β = (8). i = AIS scores, and j = Head and face C = e AIS (9). j = Neck, associated data were too few to fit equation. j = Thorax AIS C = e (0). j = Lower extremity AIS 0.75AIS C = e () Natural Logarithm of Medical Cost Std. Dev =.50 Mean = 8.70 N = Figure 2. Natural logarithm of medical cost distribution of survived passenger car driver in frontal crash. Validation of the Finite Element Simulation Model The validation of the finite element simulation model is done by comparing the simulation output in the present study to the test results of Prasad s (990) study. The acceleration curve used by Prasad is illustrated in Figure 3, 2ms time history and peaking at 23.7G. The same conditions are substituted into the simulation model to drive the sled. The resulted acceleration outputs are shown in table 2. In general, there is acceptable agreement in these results between the present simulation model and Prasad s study. Lai 4

7 [4] Delia Hendrie, Greg Lyle, Diana Rosman, G. Anthony Ryan, Brian Fildes, and Magda Les. The Cost of Road Trauma: Single and Multiple Injury Cases. Measuring The Burden Of Injury - The 3rd International Conference, DOT HS , April 200. [5] Diana Rosman, and Delia Hendrie. Estimating the Cost of Injury Using the Western Australian Data Linkage System and Injury Cost Database. In proceedings from Symposium On Health Data Linkage, pp , [6] Hosmer DW and Lemeshow S. Applied Logistic Regression. John Wiley and Sons, New York, 989. [7] James A. Newman, Suzanne Tylko, and Ted Miller. Toward A Comprehensive Biomechanical Injury Cost Model. Accident Analysis and Prevention., Vol. 26, No. 3 pp , 994. [4] Rolf Eppinger, Emily Sun, Shashi Kuppa, and Roger Saul. Supplement: Development of Improved Injury Criteria for the Assessment of Advanced Automotive Restraint Systems II. NHTSA March, 998. [5] Shashi Kuppa, Jing wang, Mark Haffner, and Rolf Eppinger. Lower Extremity Injuries and Associated Injury Criteria. In proceeding from ESV conference, Paper no. 457., 200. [6] Shashi Kuppa. Injury Criteria for Side Impact Dummies. National Transportation Biomechanics Research Center, NHTSA. May, [7] The Johns Hopkins University & Tri-Analytics, Inc. ICDMAP-90 User s Guide. [8] John Langley, and Shaun Stephenson. Comparison of Methods of Coding Severity of Injury Using New Zealand Hospital Data. Measuring The Burden Of Injury - The 3rd International Conference, DOT HS , April 200. [9] Khalil T.B., Lin T.C., Simulation of the Hybrid Response to Impact by Nonlinear Finite Element Analysis. SAE Paper No , 994. [0] M. J. Jeng, J. L. Doong, S. L. Tsai and W. S. Huang. Prototype System Of Integrated Road Traffic Accident Data (I) - Basic Environment Implement. Institute Of Transportation, January, (in Chinese) [] Michael Kleinberger, Emily Sun, Rolf Eppinger, Shashi Kuppa, and Roger Saul. Development of Improved Injury Criteria for the Assessment of Advanced Automotive Restraint Systems. NHTSA September, 998. [2] Morgan R. M., Eppinger R. H. and Haffner M. P., Thoracic Trauma Assessment Formulations for Restrained Driver in Simulated Frontal Impact. SAE Technical Paper No , 994. [3] Prasad P. Comparative Evaluation of the Dynamic Responses of the Hybrid and the Hybrid Dummies. SAE Paper No.90238, 990. Lai 7

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