Application of a Thermo-Biomechanical Virtual Manikin Used in Transient Systems Eusébio Z. E. Conceição 1 Faculdade de Ciências e Tecnologia - Universidade do Algarve Campus de Gambelas, 8005-139 Faro, Portugal Mª Inês L. Conceição 2 Instituto Superior Técnico Av. Rovisco Pais, 1049-001 Lisboa, Portugal Mª Manuela J. R. Lúcio 3 Universidade do Algarve Campus de Gambelas, 8005-139 Faro, Portugal João Gomes 4 CINTAL Campus de Gambelas, 8005-139 Faro, Portugal Hazim Awbi 5 University of Reading Reading, RG6 6AW, UK

ABSTRACT This article presents the development and application of a thermo-biomechanical virtual manikin to be used in transient systems. The numerical models used here, under transient conditions, are applied in the evaluation of thermal and vibrations values of the different sections of the human body. The thermal numerical model is based on energy and mass balance integral equations of first order. The biomechanical numerical model is based on Newton equation, whose second order equations system were converted in first order equations system. The Runge-Kutta-Fehlberg method with error control is utilized to obtain the solutions of the numerical models simulation. The thermal numerical model is used to study the influence of periodical and random airflow fluctuations applied to a specific human body section. The biomechanical numerical model is used to study the influence of periodical and random vibrations applied to the feet of a person standing, for example, on a moving public transport. The results show the stimulus signals obtained with the application of a turbulent airflow 1 econcei@ualg.pt 2 ines.conceicao@tecnico.ulisboa.pt 3 maria.manuela.lucio@gmail.com 4 jgomes@ualg.pt 5 h.b.awbi@reading.ac.uk

in the area of the person's neck and with the application of a floor vibration under the feet of a person standing on a moving vehicle. The results show that the biomechanical stimulus signals are dampened from the lower to the upper sections of the human body. After an initial damping, temperatures in the different layers of the skin will also fluctuate similarly with fluctuations in air velocity. Keywords: Thermal response, Vibrations, Virtual Manikin. 1. INTRODUCTION

The human body response, subjected to a turbulent airflow in transient conditions and to floor vibrations also in transient conditions, inside, e.g., a vehicle is evaluated in this work. In transient conditions, the Runge-Kutta-Fehlberg method with error control is used.

A virtual manikin can be used to assess the thermal comfort, indoor air quality, noise, vibrations and other environmental and personal factors. In this work, the virtual thermal-biomechanical manikin is used to evaluate the thermal and vibration levels that an occupant is subjected. Silva [1], e.g., presents the concepts related with the thermal comfort, indoor air quality, noise, vibrations among others.

The Human Thermal Modelling software calculates the temperature distribution in the human body and its clothing. This software is used to calculate the thermal comfort level of each occupant and allows also to assess the level of thermal comfort in each section of the occupant body. As example, the application of this software can be seen in the works of Conceição and Lúcio [2], in which experimental and numerical values were used, Conceição et al. [3], in which a coupling methodology with a Computer Fluid Dynamics application was implemented, and Conceição et al. [4], in which experimental data were used as input data.

To implement a thermal-biomechanical system, that will make it possible to evaluate the vibrations of the human body in the face of a certain external stimulus, it is important to know and to define the human posture (by defining its geometry) and the human thermal system (fundamental to obtain the temperature distribution). Consequently, it was necessary to develop models for human geometry, human and clothing thermal responses and the thermoregulatory system. The human geometry model was developed using empirical equations, which are based on parameters of human body such as weight and height. The human and clothing thermal response models were developed using energy and mass balance integral equations. The thermoregulatory system model was developed using empirical equations.

The joint use of the human thermal response model with other models, as in the study presented here with the human biomechanical response model, was applied in other works. For example, in the work of Conceição et al. [5] was used in a coupling methodology with a Computational Fluids Dynamics application to simultaneously assess the temperature field distribution in the human body and the environmental variables of the indoor space. This coupling methodology takes into account both the human and space geometries, in which the output data of the Computational Fluids Dynamics are used as input data in the human thermal response model and the input data of the Computational Fluids Dynamics are given by the output data of the human thermal response model. Other examples are shown in Conceição et al. [6, 7].

In the evaluation of the human body vibrations, using human geometry, one must consider the different sections into which the human body is divided. In Grieve and Goldman [8], the authors considered the human body divide into the head, upper torsos, arm-shoulders, thorax-abdomen, spinal column, hips and legs. In Bruel and Kjaer [9], the authors considered the human body divided into the head, eyeballs, shoulders girdle, lower arms, arms, hands, chest wall, abdominal mass, spinal column, hips, legs and feet.

The biomechanical response model is used to calculate the acceleration, velocity and displacement verified in the 42 elements into which the body was divided when the body is under the effect of an external stimulus located in a certain area of it. This biomechanical response model was applied in a study in which the human body mechanical vibrations were evaluated under the influence of a stimulus in the feet. The human thermal response, the validation tests and three cases studied were

analyzed. The human geometry and temperature distribution in the human body were evaluated by the human thermal response. The validation tests were done comparing the numerical results obtained for resonance vibration frequencies by the biomechanical response with measurement results available in the specialized literature. The vibration resonance frequencies for each human body section are presented in Bruel and Kjaer [9]. Similar biomechanical response models were used by other authors. Wu et al. (1999) [10, 11] used a human-seat and a human-seat-suspension models to analyses the human body vibrations in a moving vehicle. Biomechanical response models were used to identify the human body under vibration [12], to characterize a human vibration model [13], and to study the consequences in the human body of mechanical vibrations [14].

The main purpose of this study is to evaluate the application of the thermal-biomechanical response model when an area of the human body (neck) is under the effect of an external stimulus (air velocity fluctuation) and when the feet of a standing occupant of a moving public passenger vehicle are subject to two different types of vibration signals. Another objective is also to evaluate the performance of the Runge-Kutta-Fehlberg method with error control implemented to obtain the solution of the system of equations of the thermal-biomechanical response model.

2. MODELS AND MATERIALS

2.1. Numerical model The human thermal response model considers the human body divided into a spherical element and twenty-four cylindrical elements. Each element is divided into four constituents (fat, muscle, core and skin) which are in turn divided into several layers. These elements can also be protected from the surrounding environment by several layers of clothing.

The human thermal response model consists of a set of energy balance integral equations established for the tissues of the human body and for clothing, and a set of mass balance integral equations established for blood and for the perspiration water existing on the skin surface and in the various layers of clothing

The human biomechanical model considers the human body divided into forty-two elements: head, eyeballs, maxillary, spinal column, chest wall, thorax and abdominal mass, shoulders, arms, hands, fingers, hips, thighs, legs and feet. Each element is represented by its equivalent mass, elastic and damping elements.

The biomechanical numerical model is founded on Newton equation applied to each element. The obtained second-order integral equations system, that considers the elastic and damping forces, is converted into a first-order integral equations system. For the different elements, this model calculates the vibration frequencies, the acceleration, the velocity and the displacement [15].

2.2. Numerical methodology This study was divided into two parts, one to analyze the performance of the human thermal response model and another to analyze the performance of the human biomechanical response model, both in transient conditions.

In the first part is simulated the human thermal response to an airflow fluctuation in the area of the neck of an occupant of a moving vehicle. The airflow fluctuation is characterized by a periodic (sinusoidal) signal (Figure 1) of the air velocity with a frequency of 1 Hz, an amplitude of 0.08 m/s and an average value of 0.40 m/s. The numerical simulation was performed for 10 s.

In the second part is simulated the human biomechanical response to two different types of floor vibrations occurred in a moving vehicle given by the following signals:  Signal 1 (Figure 2): sum of two sinusoidal signals, one with a frequency of 100 Hz and an amplitude of 5 mm, and another with a frequency of 400 Hz and an amplitude of 2 mm;  Signal 2 (Figure 3): sum of two signals, one sinusoidal with a frequency of 100 Hz and an amplitude of 5 mm, and another random. In these cases, the numerical simulations were performed for 1 s.

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Figure 1: Air velocity sinusoidal signal used in the human thermal response numerical simulation.

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Figure 2: Floor vibration periodic signal 1 used in the human biomechanical response numerical

simulation one.

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Figure 3: Floor vibration periodic signal 2 used in the human biomechanical response numerical

simulation two. With the human thermal response model, the temperatures verified on the skin surface (Tskin), and on the cold (Tcold) and warm (Twarm) thermoreceptor are obtained.

With the human biomechanical response model, the mechanical vibrations verified in different areas of the body are obtained: foot, leg, thigh, hand, shoulder, arm, abdominal mass and head. 3. RESULTS

In this section, the results obtained in the transient regime are presented, using the simulations defined in the previous point, for the human thermal response and the human biomechanical response.

3.1. Thermal Transient Response

Figure 4 shows the evolution of temperatures verified on the skin surface (Tskin), on the cold (Tcold) thermoreceptor and on the heat (Twarm) thermoreceptor obtained for an airflow fluctuation (see Figure 1) occurred in the neck area of a person.

The results show that the evolution of temperatures presents an initial damping, stabilizing after about 4 s. This means that fluctuations in air velocity impose an initial drop in temperatures until they stabilize again. These temperatures evolve with a fluctuation with a frequency equal to the air velocity. The warm thermoreceptor temperature has the highest mean value, while the skin surface temperature has the lowest mean value. The cold thermoreceptor is more sensitive to temperature variation because it has lower temperature values than the warm thermoreceptor. In steady state, the temperature amplitudes of the skin surface, cold thermoreceptor and warm thermoreceptor are, respectively, 0.021ºC, 0.026ºC and 0.029ºC.

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Figure 4: Evolution of the temperatures of the skin surface (Tskin), cold thermoreceptor (Tcold) and

warm thermoreceptor (Twarm) for an air velocity fluctuation in the occupant’s neck area.

3.2. Biomechanical Transient Response Figure 5 shows the vibration in the thigh, leg and foot. Figure 6 shows the vibration in the shoulder, arm and hand. Figure 7 shows the vibration in the head and abdominal mass. In Figure 5a) to Figure 7a) are presented the vibrations obtained as consequence of the application of the floor vibration periodic signal 1 (see Figure 2). In Figure 5b) to Figure 7b) are presented the vibrations obtained as consequence of the application of the floor vibration periodic signal 2 (see Figure 3).

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a) b) Figure 5: Vibration in the thigh, leg and foot obtained as consequence of the application of the floor

vibration periodic: a) signal 1; b) signal 2.

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a) b) Figure 6: Vibration in the shoulder, arm and hand obtained as consequence of the application of the

floor vibration periodic: a) signal 1; b) signal 2.

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a) b) Figure 7: Vibration in the head and abdominal mass obtained as consequence of the application of

the floor vibration periodic: a) signal 1; b) signal 2. Comparing the results obtained in the different sections of the human body evaluated, it appears that there are no significant differences when the floor vibration periodic signal 1 or the floor vibration periodic signal 2 is applied. However, it verifies that the amplitudes of the vibrations obtained in the sections of the human body with the floor vibration periodic signal 1 are slightly higher than those obtained with the floor vibration periodic signal 2.

For both floor vibration periodic signals, the influence of the vibrations in the human body is found. The amplitudes of vibrations obtained in the lower sections of the human body are greater than in the upper sections of the human body. It is also found that the frequencies of vibrations in the lower sections of the human body are higher than in the upper sections of the human body. As can be seen, the main movement of the human body produces characteristic vibrations which are particularly reflected in the different sections of the human body.

The application of the Runge-Kutta-Fehlberg with error control in the resolution of both numerical models (human thermal response and human biomechanical response) efficiently calculates vibrations both for low frequencies (human thermal response) and for higher frequencies (human biomechanical response), and does not present instability problems during numeric integration.

4. CONCLUSIONS

In this work, the human body response, subjected to a turbulent airflow in transient conditions and to floor vibrations also in transient conditions, inside, e.g., a vehicle, was evaluated. In this sense, the human thermal response and the biomechanical thermal response numerical models were used, in which the Runge-Kutta-Fehlberg method with error control was used to obtain their resolutions in

transient regime. The simulations were carried out considering the airflow fluctuation characterized by a periodic signal of the air velocity, and two different periodic signals for the floor vibrations.

The air velocity fluctuations impose fluctuations in the temperatures in the skin surface, cold thermoreceptor and warm thermoreceptor with the same frequency. It was verified that the temperature of the cold thermoreceptor is lower than that of warm thermoreceptor, so it is more sensitive.

There are no significant differences between the results obtained for vibrations in the human body sections when the floor vibration periodic signal 1 or 2 is used. The influence of the vibrations in the human body was found. Both amplitudes and frequencies of the vibrations obtained in the lower sections of the human body are greater than in the upper sections of the human body.

Runge-Kutta-Fehlberg with error control can be applied in the resolution of both numerical models, human thermal response and human biomechanical response, regardless of the vibration frequency values (either low or high). It also does not present any problem of numerical instability during the integration process. 5. ACKNOWLEDGEMENTS

The authors would like to acknowledge the support of the project (SAICT-ALG/39586/2018) supported by Algarve Regional Operational Program (CRESC Algarve 2020), under the Portugal 2020 partnership agreement, through the European Regional Development Fund (ERDF) and the National Science and Technology Foundation (FCT). 6. REFERENCES

1. Silva, M. Measurements of comfort in vehicles. Measurements in Science and Technology , 13 ,

41-60 (2002). 2. Conceição, E. & Lúcio, M. Numerical and subjective responses of human thermal sensation. Sixth

Portugues Conference on Biomedical Engineering “BioEng’2001”, Faro, Portugal, 2001. 3. Conceição, E., Santiago, C., Lúcio, M. & Awbi, H. Predicting the air quality, thermal comfort

and draught risk for a virtual classroom with desk-type personalized ventilation systems. Buildings, 8(2) , 35 (2018). 4. Conceição, E., Lúcio, M. & Farinho, P. Experimental and numerical study of personalized of

ventilation in classrooms desks. Proceedings of the 10th International Conference in Rooms, RoomVent 2007, pp. 13–15. Helsinki, Finland. 5. Conceição, E., Vicente, V. & Lúcio, M. Airflow inside school building office compartments with

moderate environments. HVAC&R Research , 14(2) , 195-207 (2008). 6. Conceição, E., Silva, M. & Viegas, D. Air quality inside the passenger compartment of a bus.

Journal of Exposure Analysis and Environmental Epidemiology , 7(4) , 521-534 (1997). 7. Conceição, E., Silva, M., André, J. & Viegas, D. Thermal behaviour simulation of the passenger

compartment of vehicles. International Journal of Vehicle Design 24 (4), 372-387 (2000). 8. Grieve, E. & Goldman, D. Effect on Sock and Vibration on Man , 3rd Edition, McGraw-Hill, 1988. 9. Kjaer, B. Human Vibration , Naerum, Denmark, 1989. 10. Wu, X., Rakheja, S. & Boileau. Study of Human-Seat Interactions for Dynamic Seating Comfort

Analysis, in Human Factors in Audio Interior System, Driving and Vehicle Seating. Society of Automotive Engineering, pp. 137-146 (1999). 11. Wu, X., Rakheja, S. & Boileau. Dynamic Performance of Suspension Seats Under Vehicular

Vibration and Shock Excitations, in Human Factors in Audio Interior System, Driving and Vehicle Seating. Society of Automotive Engineering, pp. 147-159 (1999). 12. Tregoubov, V. Problems of mechanical model identification for human body under vibration.

Mechanism and Machine Theory , 35(4), 491-504 (2000). 13. Kubo, M., Terauchi, Aoki, H. & Matsuoka, Y. An investigation into a synthetic vibration model

for humans: An investigation into a mechanical vibration human model constructed according to

the relations between the physical, psychological and physiological reactions of humans exposed to vibration. International Journal of Industrial Ergonomics, 27(4), 219-232 (2001). 14. AlShabi, M., Araydah, W., ElShatarat, H., Othman, M., Younis, M. & Gadsden, S. Effect of

mechanical vibrations on human body. World Journal of Mechanics , 6(9) , 273-304 (2016). 15. Conceição, E. & Lúcio, M. Human body biomechanical and thermal response models.

Proceedings of INTER-NOISE and NOISE-CON 2004 , pp. 3678-3684. Prague, Czech Republic, August 22-25 2004.