Interspecies Scaling in Blast Pulmonary Trauma

  • Garrett W. Wood
  • Matthew B. Panzer
  • Courtney A. Cox
  • Cameron R. Bass
Original Paper


The increased frequency of blast exposure from improvised explosive devices in military settings and terrorist bombings in civilian settings has led to extensive investigation of blast trauma. Thousands of tests have been conducted in animal models of blast trauma across a large range of body size. Experimental results are often compared without consideration of interspecies scaling. A dataset of published fatality data from 4193 tests using 5 different large and small blast trauma model species was compiled to assess interspecies scaling and pulmonary fatality risk. Simultaneously, an overpressure duration interspecies scaling based on allometric principles was optimized to create a common fatality risk model scaled for species. A two-variable nonlinear logistic regression model was used to describe fatality risk. Minimization of the loglikelihood was used to optimize the fit. A large portion of existing blast trauma data was excluded due to incomplete reporting of methodology or blast dosage. The most common species used was mice with 1828 tests followed by sheep with 1309. A nonlinear regression model with an optimized duration interspecies scaling model was used to fit the experimental data from all species. Long duration peak pressure tolerance for small and large animals was found to be approximately 90 and 145 kPa, respectively. Using a body mass ratio scaling model for overpressure duration, the duration interspecies scaling exponent was found to be α = 0.351. This study shows the importance and strong effect of interspecies scaling for blast research, especially when extrapolating the human equivalent dose from the small species commonly used.


Animal models Blast Interspecies scaling Pulmonary trauma 


The increased risk of exposure to blast in both military and civilian settings emphasizes the importance of blast trauma research. Use of improvised explosive devices (IEDs) has made blast the most common source of injury for American military personnel in Iraq and Afghanistan [1]. An apparent decrease in the occurrence of blast pulmonary trauma [2] has largely shifted the focus of blast injury research, historically dominated by pulmonary studies, to traumatic brain injury. This shift in injury pattern is thought to be the result of widespread thoracic body armor usage [3] and a previously unappreciated vulnerability to mild blast TBI [4]. However, pulmonary blast trauma is still of interest and is of special importance in unprotected military personnel or civilian exposure to blast from terrorist or occupational explosive events.

Incidence and severity of pulmonary blast trauma is driven by blast physics. A shock is characterized by an approximately discontinuous increase in pressure, temperature, and density. The shock of a free-field blast results in a pressure profile, when measured at a stationary location, with a very short rise time (< 10 μs) to a peak overpressure followed by a decay to a negative pressure phase before returning to ambient conditions. In the absence of reflective surfaces or confinement of the shock, this pressure profile can be described as a Friedlander profile characterized by a peak overpressure, overpressure duration, and pressure impulse. This type of wave is ideal for research as it is a free-field representation of blast exposure and is dependent upon the size/type of charge and standoff distance. Wave complexity can be introduced through reflecting surfaces, and such complex blast waves are difficult to characterize and reproduce for injury research. Complex waves often contain more pressure impulse and are more injurious than simple waves with similar peak pressures [5, 6].

A large source of inconsistency and confusion within blast injury literature is the methodology for measuring pressure and the differences between incident and reflected pressure. A simple overpressure pulse may be measured in an incident orientation, perpendicular to the wave propagation (side-on), or reflected orientation, parallel to the wave propagation (face-on), to receive different magnitudes of pressure [7]. Depending on the shock strength, a reflected measurement will result in values 2 to more than 8 times greater in magnitude than incident measurements in the very near field [8]. For ideal blasts the Rankine-Hugoniot relations may be used to reliably convert reflected to incident magnitudes and vice versa [8]. Therefore, it is vital to distinguish between these two types of measurement when reporting blast injury results.

Overpressure duration is overlooked or not reported in many blast injury studies, despite the importance of this parameter on the severity of blast trauma. Injury tolerance in animal models is dependent on peak pressure and overpressure duration, at least for short duration blast (< 30 ms scaled) [9]. These short duration blasts are typical of the explosive exposures caused by the detonation of IEDs, artillery, and mortar fire [10]. Pulmonary injury from short overpressure duration blast is thought to occur due to an impedance mismatch mechanism between lung tissue and the air contained within, leading to localized trauma from spalling and cavitation [11]. Long overpressure duration blasts (> 30 ms) are less frequent in current conflicts and are produced from very large conventional explosive charges (> 1000 kg), thermobaric, or nuclear weapons [7]. Injury tolerance to long overpressure duration blasts is primarily dependent on peak pressure and is characterized by large momentum transfer to the chest leading to diffuse lung injury [11]. Humans have a high areal density and low loading areas compared to structures, and so quasi-static loading does not produce damage in the same manner cf. [12]. It is important to note that the transition from short to long overpressure duration trauma is not clearly defined and there is not likely a discrete transition between the two [13].

One of the goals of blast injury research is to establish injury thresholds and mechanisms from different types of exposures. To measure these experimental injuries, it is necessary to employ living systems with active physiology and biophysical response; thus, animal models are required. Many species have been used to assess blast injury. Small species, particularly mice and rats, are commonly used due to easy handling and care, as well as established injury biomarkers, gene expression, and immune response [14, 15, 16]. Large species such as pig and sheep are used as models with similar body size to humans but are studied less often, since they have more extensive care requirements, are more expensive, and exhibit more variability between subjects [17, 18].

Interpretation and comparison of injury results across species is complicated by large differences in size and morphology. Variation in physiology between common animal model species may further complicate comparison of injury endpoints. Differences in parameters such as heart rate, life span, and immune response may dictate time course and severity of injury response to blast exposure. Biomechanical and other scaling procedures are often necessary when comparing experimental results across different subjects and across different species. Allometric scaling laws have been developed for many parameters across a very large range of mammalian species, mouse to elephant. Body size, organ size, metabolic rate, respiratory rate, and many other parameters have been measured and scaling models have been empirically derived [19, 20, 21].

In early pulmonary blast injury research, Bowen et al. [22] recognized the need for interspecies scaling when combining different species to derive a human equivalent exposure. Bowen found injury tolerance and fatality risk to require scaling of overpressure duration, while peak pressure scaling based upon animal size was found to be negligible [22]. Bowen’s interspecies scaling is a simple model using the cube root of a body mass ratio producing an effective overpressure duration scaling by characteristic body length [22]. The reference mass is a 70 kg human body mass. In blast literature where interspecies scaling is considered, Bowen’s scaling is commonly used [6, 23]. The validity of Bowen’s scaling, especially outside of pulmonary injury for which it was derived, is unknown, and the biomechanical basis for Bowen’s scaling is unknown. It is possible that interspecies scaling for blast traumatic brain injury or other injury endpoints do not follow this model.

Blast injury risk models have been derived from literature data on pulmonary trauma but have focused primarily on large animal species [9, 13, 24]. Separate nonlinear pulmonary risk models for short [9] and long [13] overpressure duration exposures have been published. Recent work by Panzer [24] derived risk models across a large overpressure duration range by implementing a piecewise log-linear model and considering the effects of multiple blast exposures. These studies assume Bowen’s scaling to account for interspecies differences.

The goal of this study is to develop a fatality risk model due to pulmonary injury from primary blast exposure based on a meta-analysis of a large database of animal model injury data. Additionally, an interspecies scaling model based upon this dataset will be empirically derived to optimize the model fit.

Materials and Methods

A database of blast animal model data was created which includes 14 different species and over 12,000 tests. A literature search was conducted through Google Scholar and Medline databases. Search keywords included “BLAST INJURY,” ‘BLAST TRAUMA,” “BLAST LUNG,” “BLAST PULMONARY,” and “BLAST ANIMAL.” This body of data was filtered for this study through the use of several exclusion criteria. Only studies reporting fatality data due to primary blast exposure from a simple Friedlander type pressure wave were included. Studies with thoracic protection were excluded from this analysis. Cases of multiple blast exposure where excluded, except in cases that resulted in no injury. Studies were excluded which did not provide sufficient methodological detail to recreate the blast dosage, mainly peak overpressure and overpressure duration. In some cases, especially with free-field explosives where only charge size and standoff distance was reported, blast data was calculated through the use of CONWEP to calculate exposure level [10]. Orientation and the presence of a reflecting surface behind the animal were not considered as their effects were previously found to be insignificant in large animals [9, 13]. Only species with sufficient data to fit a single species fatality risk model were included, resulting in a dataset of 4193 total tests with 5 different species, which were used to develop pulmonary fatality risk in this study. A list of studies is presented in Table 1. Injuries reported varied from minor petechiae [16] and hemorrhage [27] to rapid fatality resulting from major lung hemorrhage [25]. The studies used included whole-body and thorax-isolated blast exposures. Fatality data was only included from studies which determined fatality as a result of pulmonary trauma. Only fatality from early, direct consequences of blast were considered in this work.
Table 1

Published blast animal model work used for pulmonary interspecies scaling and injury model derivation


Species used


Species used

Bowen et al. 1968 [25]


Richmond et al. 1961 [26]

Mouse, rabbit, dog, goat

Celander et al. 1955 [27]


Richmond et al. 1962 [28]

Mouse, rabbit

Cernak et al. 2011 [29]


Richmond et al. 1962 [30]

Mouse, rabbit

Clifford et al. 1984 [31]


Richmond et al. 1966 [32]

Mouse, rabbit, dog, goat

Damon et al. 1964 [33]


Richmond et al. 1968 [34]

Dog, goat, sheep

Damon et al. 1966 [35]

Dog, Goat

Richmond et al. 1981 [36]


Damon et al. 1970 [37]

Dog, Sheep

Richmond et al. 1982 [38]


DASA 1965 [39]


Rubovitch et al. 2011 [40]


Dodd et al. 1989 [41]


Woods et al. 2013 [42]


Mundie et al. 2000 [43]


Yang et al. 1996 [44]


Phillips et al. 1988 [45]


Young et al. 1985 [17]


Ambient pressure scaling (Eq. 1 and Eq. 2) was employed for both peak pressure and overpressure duration for body mass scaled durations longer than 30 ms as described by Bowen [25] but was not used for scaled durations less than 30 ms as discussed by Bass [9]. This accounts for the effects of high altitude testing or the modification of ambient pressure during testing, and this scale factor approaches one at normal sea level ambient pressure.
$$ {P}_{P,\mathrm{scaled}}=P\left(\frac{P_{\mathrm{sealevel}}}{P_{\mathrm{ambient}}}\right) $$
$$ \Delta {t}_{P,\mathrm{scaled}}=\Delta t{\left(\frac{P_{\mathrm{ambient}}}{P_{\mathrm{sealevel}}}\right)}^{1/2} $$
A simple overpressure duration scaling model was used to account for interspecies body mass differences (Eq. 3). This scaling uses a ratio of body masses between the test subject and a reference human body mass. This allows the blast dosage to be transformed to an equivalent human biomechanical input. The scale factor, α, was optimized to best fit the experimental data.
$$ \Delta {t}_{\mathrm{scaled}}=\Delta t{\left(\frac{{\mathrm{mass}}_{\mathrm{reference}}}{\mathrm{mass}}\right)}^{\alpha } $$
To describe the fatality risk, a nonlinear logistic regression model was constructed (Eq. 4) that was dependent upon peak incident overpressure and scaled overpressure duration [9, 25].
$$ P={P}^{\ast}\left(1+\alpha \Delta {t}^{-b}\right) $$

P*, a, and b are model parameters to be fit by the data. This form describes the decreasing peak pressure tolerance as overpressure duration increases while at short durations. As durations increase, the peak pressure tolerance approaches a constant, P*.

Fatality risk models were fit to the five individual species to determine the long overpressure duration peak pressure threshold, P*, for each species. Values of P* fell into two distinct groups, large and small species [25]. As human body size and pulmonary system anatomy suggest, it would fall within the large animal group, a mean P* value for the three large species was used as the human P*. To correct for differences in peak pressure tolerance, the pressure values for each test were scaled according to a ratio of the human P* value and that for the species (Eq. 5).
$$ {P}_{P\ast, \mathrm{scaled}}=P\left(\frac{P{\ast}_{\mathrm{human}}}{P^{\ast }}\right) $$
Regression was then performed on the complete set of data from five species to simultaneously determine the fatality risk model and overpressure duration scaling model. Nonlinear regression and statistical analyses were performed in Excel 2010 (Microsoft, Redmond, Washington) and JMP Pro 10 (SAS Institute Inc., Cary, NC) for the logistic regression model in Eqs. 6 and 7. The details of the statistical origins of these models are largely heuristic and based on extensive work performed by the Lovelace Foundation in the 1950s and 1960s [22, 25].
$$ \pi =\frac{e^F}{1+{e}^F} $$
$$ F=f\left\{\ln \left[{P}^{\ast}\left(1+a\Delta {t}^{-b}\right)\right]-\ln (P)\right\} $$
π is the probability of fatality, while f, a, and b are fitted model parameters.
The area under the receiver operating characteristic curve (AUC) was used to assess model goodness-of-fit. AUC (Eq. 8) measures sensitivity versus (1-specificity) of the fit and values greater than 0.8 are considered good model discrimination cf. [46].
$$ \mathrm{AUC}={\int}_0^{100}\mathrm{sensitivity}\ d\left(100-\mathrm{specificity}\right) $$
Unscaled fatality and survival data is shown in Fig. 1. It is important to note that when all of the injury data across different species is plotted against incident overpressure and overpressure duration exposure without incorporating any interspecies scaling the data appears unorganized, and there is no clear delineation between injury and non-injury cases. This is the incident overpressure of the undisturbed blast field. Many injury points fall well below levels of non-injury and likewise, non-injury points appear at high exposure levels for some species relative to others. Without interspecies scaling, model fit statistics in Table 2 show poor model parameter fits with large standard error values; additionally, the AUC value of 0.78 indicates only fair specificity and sensitivity of the unscaled model.
Fig. 1

Unscaled pulmonary fatality models. Unscaled pulmonary injury data across five species lacks separation between injury and non-injury cases

Table 2

Species data with regression models and goodness-of-fit (coefficient ± SE). Unscaled pulmonary data results in poor model parameter fits compared to scaled full model








# of tests







Reported mass (kg ± SD)

0.023 ± 0.004

2.08 ± 0.55

16.36 ± 1.30

24.16 ± 4.17

47.76 ± 8.75


P* (kPa)







Avg. loglike







P *








71.84 ± 74.04

1.49 ± 2.55

0.13 ± 0.13

1.85 ± 0.08




Full model


3.53 ± 0.23

1.06 ± 0.04

4.41 ± 0.20





When each of the five species were fit with individual fatality models to determine long-term pressure tolerance (P*) values, there was a clear grouping of small species (mouse, rabbit) and large species (dog, goat, sheep). Figure 2 shows the small species grouped around a pressure value of 90 kPa and the large species around approximately 145 kPa. Since human pulmonary anatomy most closely resembles that of the large species [47], a mean of those P* values (143.4 kPa) was used as the human reference value. P* is equivalent to the lowest peak pressure capable of 50% fatality from exposure. This means that, independent of overpressure duration, peak pressure values less than P* will always produce less than 50% fatality, regardless of blast duration. As the overpressure duration decreases, the risk will decrease.
Fig. 2

Individual species P* values. Long overpressure duration 50% fatality values, P*, for individual species shows a clear separation between small and large animal model species

From five species, 4193 data points were fit with an interspecies scaling and fatality risk model. This dataset included 2866 survival and 1327 fatality cases. The results of the nonlinear regression are presented in Table 2. The optimized overpressure duration scaling according to Eq. 3 resulted in an α of 0.351. The use of interspecies scaling improved the model fit, supporting the need for interspecies scaling to describe fatality risk. An AUC of 0.88 indicates good specificity and sensitivity of the model. The fatality risk model is shown in Fig. 3 along with the fatality data. Not only does the interspecies scaling organize the injury data to see a clear delineation between fatality and survival levels across all species, model loglikelihood data shows that this holds true individually for large and small species. Values in Table 2 for average loglikelihood show that contribution, per test, to the overall loglikelihood is consistent across species. The model best fits the sheep data as shown by the low average loglikelihood of 0.105. The other four species have similar values indicating that the model does not fit either small or large species better than the other.
Fig. 3

Optimized scaling and pulmonary fatality models. Optimized interspecies scaling results in a regression model for fatality due to pulmonary trauma that describe behavior well over five large and small species (α = 0.351)


This study produced the first statistically based interspecies scaling for fatalities from pulmonary blast based on five model species of disparate sizes. The new scaled pulmonary fatality model (Fig. 4) behaves similarly to previously published fatality risk curves [9, 13, 24, 25]. The model from this study predicts a slightly higher peak pressure tolerance at very short durations, less than 0.5 ms. At 0.1 ms, Panzer’s model [6] predicts 50% fatality at 3994 kPa, while the current model from this study predicts a 50% risk of fatality at approximately 6000 kPa. The models behave similarly beyond 1 ms with the exception of the long and short bounds of the Bass [9] and Rafaels [13] curves, respectively. However, if the model of Bass [9] is considered to transition to Rafaels [13] at approximately 15 ms, they create a single model which agrees well with the other models presented. Bass, Rafaels, and Panzer [9, 13, 24] utilized only large animals in their risk models, and the good agreement with the current model supports the use of pressure scaling to compare small and large animal results.
Fig. 4

Comparison of blast pulmonary fatality risk models. The fifty percent pulmonary injury risk model compares well to existing models [9, 13, 24, 25]

Since the pulmonary risk model derived here is intended to be used across mammalian species, it must fit pulmonary blast fatality data not used to develop the model. Other species can be used as essentially validation cases for this risk model. Four additional species have a substantial set of blast pulmonary fatality data but were not over a wide enough range to develop individual species models. For example, in Bowen’s pulmonary blast risk model, there is a test series of 29 sheep below 1 ms and no other data [25]. Since long-term pressure tolerance values, P*, for each of these species could not be derived, they were assumed to follow either small (rat) or large (cattle, monkey, pig) animal behavior. Average values of 90.6 and 143.4 kPa were used for small and large species, respectively. The peak pressure and overpressure duration scaling described in this study were then applied to the fatality data. Data from cattle, monkeys, pigs, and rats are compared to the pulmonary fatality risk models derived from this study in Fig. 5. The fatality risk model described the behavior of this data well. There was a clear delineation, by the 50% fatality risk, between the survival and fatality cases. The average loglikelihood values for cattle (0.389), monkey (0.567), pig (0.276), and rat (0.761) data were comparable to those species used to fit the model. This suggests that this pulmonary risk model can be used for species beyond the five used to derive the model.
Fig. 5

Comparison of additional species to fatality risk models. Experimental blast pulmonary fatality data from additional animal model species compares well to the pulmonary fatality risk models derived in this study

Large differences in body size, morphology, and anatomy between large and small species have led to the idea that injury tolerance and perhaps scaling laws cannot apply to both groups without some additional compensation. For blast models, species have generally been categorized as large animal models if they exceed 15 kg in body mass or are of high phylogenetic order [25]. The source of the influence of phylogeny is unclear, but the effects are clear. For example, squirrel monkeys (~ 1 kg body mass) have “large animal” blast response while rabbits (~ 3 kg body mass) have “small animal” response [48]. It is thought that small animal species, especially rodents, are more susceptible to lung injury from blast because of lower normalized lung density [48]. Other pulmonary variables, such as average gaseous lung volume have been correlated to differences in long overpressure duration tolerance [25], but an interspecies scaling method has not been developed. This led to Bowen [25] to develop separate fatality risk models for large and small species. Large differences in physiology, especially rate-dependent processes, such as metabolism, may also lead to different injury response in small animal model species.

Developing fatality risk models for small species is complicated by the lack of test data below 10 ms when body mass scaling is used; therefore, the current model is dominated by large animal data at short overpressure duration. The validity of the model in this study is supported by its ability to fit data well over a size range of three orders of magnitude from mouse to sheep. Confidence in the optimized model would be strengthened by further data from small animal species as short-scaled durations.

There are a number of important features of the pulmonary fatality risk models. First, the overall form of the model can inform as to the nature of injury dependence on different aspects of the blast exposure. For short durations, the slope of the model suggests a strong dependence upon overpressure duration on the peak pressure tolerance for injury. Alternatively, at long durations, the curve flattens and implies that injury tolerance is primarily dictated by the peak pressure alone. The transition to flat portion of the curve may approximately indicate a shift in injury mechanism leading to this change in dependence upon overpressure duration. This transition occurs at approximately 30 ms duration, but a precise cutoff between “short” and “long” overpressure duration is not provided by this data.

The results of this study are important in the context of the recent focus on blast neurotrauma. There are some pervasive methodological practices in recent blast animal model testing which complicate interpretation and application of findings. Despite the susceptibility of the pulmonary system to blast injury, many studies focused on traumatic brain injury fail to protect the thorax from blast exposure. The effect of pulmonary injury in these studies is largely unknown, but it would be expected to influence brain injury findings. The threshold for pulmonary injury has been shown to be lower than some neurotrauma endpoints, including blast-induced apnea and moderate brain bleeding [4].

Perhaps more importantly, there is a large body of blast injury literature which ignores the effects of interspecies scaling and the dependence of injury upon overpressure duration. The inclusion of scaling principles when attempting to interpret any findings as they relate to human exposure is essential. The failure to consider interspecies differences has led to experimental exposure levels in animal model tests that directly mimic human exposure. When interspecies scaling is considered, especially in rodent species, it leads to scaled durations well outside the realm of exposures which would reasonably be expected to occur (Fig. 6). The majority of data that falls within the realistic exposure range is that of large animal tests where scaling has a smaller effect. In addition, most of the small animal test conditions within the realistic range are that of rabbits with almost all of the rodent model test conditions having scaled durations much longer than conventional explosives weapon exposure. This realistic exposure range is bounded by a small 0.25 kg charge and a very large 1000 kg charge size, as determined by CONWEP [10]. The test conditions are also compared to the exposure due a 155 mm artillery round at varied standoff, which is representative of a common IED threat of approximately 7.5 kg TNT charge equivalent. Many current studies test blast rodent models at scaled overpressure duration levels only achievable by large thermobaric devices or nuclear weapons. Though some early animal model blast testing studied nuclear blast effects, these effects are qualitatively different than effects of high explosives. This points to the importance of standardization of blast methodology to ensure we maximize the useful information gained from animal model studies.
Fig. 6

Scaled blast exposure levels at the animal compared to a realistic human exposure range. Many scaled pulmonary injury test conditions fall outside realm of realistic exposure, especially for small animals

The scaling methodology of this study is limited by the consideration of only body mass interspecies scaling. While this simple body mass scaling is commonly used and describes injury well, there may be other anatomical parameters, such as lung density and physiological parameters which would improve the predictive capability of the injury risk model and better account for interspecies differences. This study includes the effects of phylogentic order by grouping animals as either large or small animals. While this is limited in the response of large and small animals is largely based on observation, factors beyond phylogeny are unknown for interspecies scaling. A lack of theoretical understanding of this scaling response is a limitation for all pulmonary blast work done to date. This study considers only peak overpressure and overpressure duration for description of the blast exposure. It is possible that other blast characteristics, including overpressure impulse which accounts for pulse shape, may improve the exposure description for the model for more arbitrary and non-ideal blast exposure. The effects of orientation relative to blast direction and the presence of reflecting surfaces were not considered for this analysis. This has been shown to be valid for large animal species but this assumption may currently be considered a limitation for the analysis of small animal data.


In conclusion, this study utilized a large set of published experimental data to optimize interspecies scaling for fatalities from exposure to blast using a overpressure duration scaling model for 5 different animal model species. An interspecies scaling exponent, α, of 0.351 compares well with previously published pulmonary injury scaling by Bowen [22]. This suggests a characteristic length scaling based on cube root of mass is appropriate for pulmonary injury. This study has derived the scaling exponent from a statistical basis, rather than assuming the previous value of 0.333 used by Bowen [22] based on assumption alone. Pulmonary injury risk is largely overpressure duration dependent for short-scaled durations but is peak pressure dictated as overpressure duration increases. The clinical implications of this study are that without thoracic protection the pulmonary system is susceptible to blast injury and should be a focus in a trauma setting. Finally, it is common practice to directly compare animal model results for blast injury to human exposures and outcomes. This study highlights the importance of scaling considerations, and the use of appropriate scaling procedures for injury model data will serve to improve our understanding of blast injury prevention and treatment.



The authors gratefully acknowledge Dr. Bruce Capehart for his clinical expertise and input for this study.

Funding Information

Funding for this study was provided by the US Army MURI program (U Penn prime—W911NF-10-1-0526) partially supporting Cameron Bass (PI) and Garrett Wood.


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Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  • Garrett W. Wood
    • 1
  • Matthew B. Panzer
    • 2
  • Courtney A. Cox
    • 1
  • Cameron R. Bass
    • 1
  1. 1.Department of Biomedical EngineeringDuke UniversityDurhamUSA
  2. 2.Center for Applied BiomechanicsUniversity of VirginiaCharlottesvilleUSA

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