Liang Ma
email: liang.ma@irccyn.ec-nantes.fr

Damien Chablat
email: damien.chablat@irccyn.ec-nantes.fr

Fouad Bennis
email: fouad.bennis@irccyn.ec-nantes.fr

Wei Zhang
email: zhangwei@tsinghua.edu.cn

François Guillaume
email: francois.guillaume@eads.net

A new muscle fatigue and recovery model and its ergonomics application in human simulation

Keywords: digital human modelling, human simulation, muscle fatigue and recovery model, physical fatigue evaluation, objective work evaluation, ergonomics analysis

Although automatic techniques have been employed in manufacturing industries to increase productivity and efficiency, there are still lots of manual handling jobs, especially for assembly and maintenance jobs. In these jobs, musculoskeletal disorders (MSDs) are one of the major health problems due to overload and cumulative physical fatigue. With combination of conventional posture analysis techniques, digital human modelling and simulation (DHM) techniques have been developed and commercialized to evaluate the potential physical exposures. However, those ergonomics analysis tools are mainly based on posture analysis techniques, and until now there is still no fatigue index available in the commercial software to evaluate the physical fatigue easily and quickly. In this paper, a new muscle fatigue and recovery model is proposed and extended to evaluate joint fatigue level in manual handling jobs. A special application case is described and analyzed by digital human simulation technique.

Introduction

Automation in industry has been increased in recent years and more and more efforts have been made to achieve efficient and flexible manufacturing. However, manual work is still very important due to increase of customized products and human's capability of learning and adapting [START_REF] Forsman | A method for evaluation of manual work using synchronized video recordings and physiological measurements[END_REF]. Musculoskeletal disorder (MSD) is the injuries and disorders to muscles, nerves, tendons, ligaments, joints, cartilage and spinal discs [START_REF] Maier | Work-related Musculoskeletal Disorders[END_REF]. From the report of Health, Safety and Executive [H1] and the report of Washington State Department of Labor and Industries [S1], over 50% of workers in industry have suffered from musculoskeletal disorders, especially for manual handling jobs. According to the analysis in Occupational Biomechanics Virtual and Physical Prototyping, Vol. 5(3), September 2010, pp. 123 -137 [START_REF] Chaffin | Occupational Biomechanics[END_REF], "Overexertion of muscle force or frequent high muscle load is the main reason for muscle fatigue, and furthermore, it results in acute muscle fatigue, pain in muscles and severe functional disability in muscles and other tissues of the human body". Hence, it is very important for ergonomists to find an efficient method to assess the extent of various physical exposures on muscles and to predict muscle fatigue in the work design stage.

In order to assess physical risks to MSDs, there are several posture based ergonomics tools for posture analysis, such as Posturegram, Ovako Working Posture Analyzing System (OWAS), Posture Targeting and Quick Exposure Check for workrelated musculoskeletal risks (QEC). In spite of these general posture analysis tools, some special tools are designed for specific parts of the human body. Rapid Upper Limb Assessment (RULA) is designed for assessing the severity of postural loading for the upper extremity. The similar systems include HAMA (Hand-Arm-Movement Analysis), PLIBEL (method for the identification of musculoskeletal stress factors that may have injurious effects) [START_REF] Stanton | Handbook of Human Factors and Ergonomics Methods[END_REF]. Similar to these methods for posture analysis, there is one tool available for fatigue analysis and that is muscle fatigue analysis (MFA). This technique was developed to characterize the discomfort described by workers on automobile assembly lines and fabrication tasks [R1]. In this method, each body part is scaled into four effort levels according to its working position, duration of the effort, and frequency. The combination of the three factors' levels can determine a "priority to change" score. The task with a high priority score needs to be analyzed and redesigned to reduce the MSD risks [START_REF] Stanton | Handbook of Human Factors and Ergonomics Methods[END_REF][START_REF] Rodgers | Handbook of Human Factors and Ergonomics Methods[END_REF].

After listing these available methods, physical exposure to MSD can be evaluated with respect to its intensity (or magnitude), repetitiveness, and duration [START_REF] Li | Current techniques for assessing physical exposure to work-related musculoskeletal risks, with emphasis on posture-based methods[END_REF]. However, there are still several limitations with the traditional methods. First, the evaluation techniques lack precision and their reliability of the system is a problem for assessing the physical exposures due to their intermittent recording procedures [B1]. Second, most of the traditional methods have to be carried out on site. Therefore, there is no immediate result from the observation. It is also time consuming for later analysis. Furthermore, subjective variability can influence the evaluation results when using the same observation methods for the same task [START_REF] Hanson | The Influence of virtual human model appearance on visual ergonomics posture evaluation[END_REF].

In order to evaluate the human work condition objectively and quickly, digital human techniques have been developed to facilitate the ergonomic evaluation, such as Jack [START_REF] Badler | Simulating Humans: Computer Graphics Animation and Control[END_REF], ErgoMan [START_REF] Schaub | A computer-aided tool for ergonomic workplace design and preventive health care[END_REF], 3DSSPP [C1], Santos [V1]. These techniques have been used in the fields of automotive, military, and aerospace. These human modelling and simulation tools provide mainly visualization information about body posture; accessibility and field of view [START_REF] Hanson | The Influence of virtual human model appearance on visual ergonomics posture evaluation[END_REF]. Combining Digital Mock-Up (DMU) with digital human models (DHM), the simulated human associated with graphics could supply visualization of the work design, and it could decrease the design time and enhance the number and quality of design options that could be rapidly evaluated by the design analysts [C2]. Traditional posture analysis tools have been integrated into these simulation tools for computerization. For example, in 3DSSPP, in CATIA, and in other simulation tools, RULA, OWAS and some other posture analysis tools have been integrated as a module to evaluate the postures in design stage. In these digital human simulation tools, it is possible to generate the motion for certain task, and the load of each key joint and even each muscle can be determined and simulated. In [START_REF] Jayaram | Introducing quantitative analysis methods into virtual environments for real-time and continuous ergonomic evaluations[END_REF], a method to link virtual environment (Jack) and a quantitative ergonomic analysis tool (RULA) for occupational ergonomics studies was developed. This framework verified the conception of evaluating ergonomics study in real time manner by obtaining human motion from motion capture system. However, even today, there is still no effective method in these digital human modelling and simulation tools to predict human motion with consideration of muscle fatigue, and there is still no fatigue evaluation tool integrated in these human simulation tools. Therefore, it is necessary to develop the muscle fatigue model and then integrate it into the virtual human software to evaluate muscle fatigue and specifically analyse the physical work, and even predict the human motion by minimizing the fatigue. In this paper, we are going to present a new framework to evaluate the manual handling jobs objectively and quickly in a virtual environment. In this framework, a new muscle fatigue and recovery model is integrated to evaluate the fatigue and decide the work-rest schedule. A simplified geometrical and biomechanical model of arm is constructed to calculate the load of each joint using inverse dynamics. A special case in EADS is used to evaluate the fatigue of the manual handling job.

Framework for the fatigue analysis

In order to evaluate manual handling work objectively and effectively, a framework based on virtual reality technique is graphically presented in Figure 1. The framework consists of three main modules: virtual environment module, data collection module, and evaluation module.

The module of virtual environment technique and virtual human technique is

used to provide the virtual working environment and to avoid field-dependent work evaluation. Based on VE, immersive work simulation system is constructed to provide the virtual working environment. Virtual human is modelled and driven by the motion data to generate the manual handling job in the virtual environment. Another component, haptic interface is used to enable the interactions between the worker and virtual environment. Data collection module is responsible for obtaining all the necessary information for further data processing. From the introduction part, necessary information for evaluating dynamic manual handling jobs consists of motion, forces and personal factors. To achieve the motion data, motion capture technique can be applied to achieve the motion information with individuality. Nevertheless, the motion information can also be achieved from some existing human simulation tools.

Personal factors can be obtained from anthropometry database or measurements. The forces can be measured by force measurement devices or known external loads.

The evaluation module takes all the input data to evaluate the manual operation. In this module, evaluation criteria of all the aspects of the manual operation are predefined in the framework, such as posture analysis criteria, fatigue criteria and discomfort criteria. With these criteria, different aspect can be evaluated by processing the input data.

The detailed technical analysis of the framework was presented in the literature [START_REF] Ma | Framework for Dynamic Evaluation of Muscle Fatigue in Manual Handling Work[END_REF], and here we just make a brief introduction to its work flow. In this framework, at first the manual handling operation is carried out in the virtual environment module. Virtual working environment is provided for visualization.

Human's motion in a manual handling operation is either captured from motion capture system or simulated using human simulation software. The motion information combined with the interaction information with the virtual environment is collected and further processed in the objective work evaluation module. In this module, with the predefined criteria, different aspects of the manual operation can be Virtual and Physical Prototyping, Vol. 5(3), September 2010, pp. 123 -137 evaluated. The evaluation results can be used for further improvement of the work design.

Muscle fatigue and recovery model

Muscle fatigue is defined as the point at which the muscle is no longer able to sustain the required force or work output level [V1]. In order to evaluate the muscle fatigue during a manual handling operation, a new muscle fatigue and recovery model was developed based on muscle motor mechanisms pattern, and the details are presented in this section. At first, the parameters in this muscle fatigue and recovery model are listed in Table 1. ()

F d U M V C d t F F  (1) cem cem load dF F kF dt M V C  (2)

Muscle recovery model

cem cem dF R M V C F dt  (3)
Therefore, the F cem can be determined by Eq. (4) 0 ()

t Rt cem cem F M VC F M VC e    
(4) With this recovery model, the recovery time from a certain fatigue level F 0 cem to p percentage of MVC can be determined by Eq. (5).

0 1 ( 1) cem p M V C t R F M V C        (5)

Extension of this model to joint level

The muscles attached around a joint are responsible for generating torque to move the joint or keep it stable for maintaining the external load. There are several muscle engaged in generating a simple movement of the arm. Mathematically, to determine the efforts of each muscle involved in the movement is an underdetermined problem, so it is difficult to determine the actual load of each muscle. Although some optimisation methods have been created to solve force distribution problem in muscle levels, it is not easy to achieve the accurate result for each individual muscle.

However, according to inverse dynamics, it is accurate enough to calculate the torque of each joint. And meanwhile, in ergonomics application, the analysts do often evaluate the physical exposures in joint level. MVC is sometimes defined in the literature [START_REF] Mathiassen | Prediction of shoulder flexion endurance from personal factors[END_REF] In our research project, the application case is junction of two fuselage sections with rivets from the assembly line of a virtual aircraft. One part of the job consists of drilling holes all around the section. The properties of this task can be described in natural language as: drilling holes around the fuselage circumference. The number of the holes could be up to 2000 under real work conditions. The drilling machine has a weight around 5 kg, and even up to 7 kg in the worst condition with consideration of the pipe weight. The drilling force applied to the drilling machine is around 49N. In general, it takes 30 seconds to finish a hole. The drilling operation is graphically shown in Figure 2.

In this application case, there are several ergonomics issues and several physical exposures contribute to the difficulty and penalty of the job. It includes posture, heavy load from the drilling effort, the weight of the drilling machine, and vibration. Muscle fatigue is mainly caused by the load on certain postures, and the vibration might result in damage to some other tissues of arm. To maintain the drilling work for a certain time, the load could cause fatigue in elbow, shoulder, and lower back. In this paper, the analysis is only carried out to evaluate the fatigue of right arm in order to verify the conception of the framework. The vibration is excluded from the Virtual and Physical Prototyping, Vol. 5(3), September 2010, pp. 123 -137 analysis. Further more, the external loads are divided by two in order to simplify the calculation, for two arms are usually engaged in drilling operation.

Geometrical modelling of arm

According to the new fatigue model, it is important to calculate the joint torques of human; therefore, geometrical model of the right arm is developed using the modified Denavit-Hartenberg (DH) notation methods [START_REF] Khalil | A new geometric notation for open and close-loop robots[END_REF] to describe the geometric structure of the right arm. In modified DH notation system, four parameters are used to describe the transformation between two Cartesian coordinates in Figure 3. α j : angle between axes Z j-1 and Z j around the axis X j-1 . d j : distance between axes Z j-1 and Z j along the axis X j-1 . θ j : angle between axes X j-1 and X j around the axis Z j r j : distance between axes X j-1 and X j along the axis Z j .

From anatomic, the shoulder joint allows the movement as a sphere joint in flexion and extension, adduction and abduction, and supination and pronation directions. Elbow joint is able to move in flexion and extension direction and supination and in pronation direction. The shoulder complex is separated into 3 rotational joints and the elbow joint is separated into 2 rotational joints shown in Figure 4. Each joint has its own joint coordinate system defined in DH notation system, and the joint can only rotate around its Z-axis within rotation limits. The anatomical function of each joint is explained in Table 2. The parameters in modified DH notation system are listed in Table 3, and the transformation matrix between current joint coordinate to precedent joint coordinate is Eq. ( 6). The right arm is geometrically represented by a chain of rotational joints, by a general vector q=[q 1 ,q 2 ,q 3 ,q 4 ,q 5 ]. Each element q i represents the rotation angle around the Z-axis in R i . Once the geometrical configuration q is given, the posture of the arm can be fixed. In our case, a digital human weighted as 70 kg and with a height as 1.70m is chosen to calculate those parameters of the right arm.

0 0 0 1 j j j j j j j j j j j j j j j j j j j θ θ d α θ α θ α r α T α θ α θ α r α                    (

4.4-Calculation of internal joint forces and torques

The source of the external load is original from two parts: the gravity of the drilling machine with direction vertical down, and the drilling effort in direction of the hole.

The forces and torques at each joint can be calculated following Newton-Euler inverse dynamic methods mentioned in book [START_REF] Khalil | Modelling, identification and control of robots[END_REF]. At the end, the forces and torques are projected into general joint coordinates to calculate the effort generating the corresponding movement of the joint.

4.5-Fatigue evaluation of the joints

As mentioned in the fatigue model, it is necessary to find out the joint strength in order to evaluate the joint fatigue. The standard strength data of shoulder and elbow can be obtained from the occupational biomechanics [START_REF] Chaffin | Occupational Biomechanics[END_REF]. The flexion strength of shoulder and elbow are mainly depending on gender and flexion angles of the arm. In this case, the q 1 and q 4 are used as variables to calculate the joint strength. The result of the joint strength is the mean value Γ j of the population and its standard deviation σ j . In order to analyze the compatibility of the population, 95% (Γ j ±2σ j ) population is taken into consideration in our analysis. As an example, the elbow flexion strength for the 95% male adult population is graphically shown in Figure 5 The joint strength in a given geometrical configuration can be calculated, and then with the new fatigue model, the reduction of the joint strength can be evaluated.

Figure 5: Flexion elbow joint strength within the joint limits. With the new fatigue model, a continuous work procedure is evaluated under a geometrical configuration of the arm listed in Table 5. the strength and variation of the joint can be determined, and they are also listed in Table 5. Different external load generates different torque in flexion joints.

5-Results and Discussion

Results

Endurance Time for continuous work

The endurance time for the static posture is listed in Table 6. Under the same geometrical configuration, different load influences the endurance time. For shoulder, even the difference of the shoulder load is about 4 Nm, but it could decrease almost one forth of endurance time. The higher external load is, the shorter endurance time for maintaining the job is. It is quite clear that different capacity of the population can do the same task with quite different performance. It varies from 60 s to 450 s for drilling a same hole until exhausted stage. For maintaining the posture, the shoulder and elbow have different endurance time. For the overall work capacity evaluation, the minimum capacity is used to avoid any injury on human body. From the last two rows of Table 6, the number of holes which the worker is able to drill in a continuous working procedure is shown. Using our fatigue index, the fatigue of each joint is also evaluated. For drilling only one hole in 30 seconds, the maximum fatigue index occurs at the negative side of the population in the shoulder joint (0.330). From Figure 6 to Figure 9, the reduction of the joint strength during the operation is graphically presented. In a continuous static posture holding procedure, there is no recovery of the joint strength. The joint strength decreases with time. The fatigue index (stress index) is expressed by the summation of the relative joint load. In paper [START_REF] Yang | Multi-objective optimization for upper body posture prediction[END_REF], a discomfort index is proposed as an objective to predict human motion and it is taken into our framework to evaluate the joint discomfort.

Virtual and Physical Prototyping, Vol. 5(3), September 2010, pp. 123 -137

This discomfort index from Eq. (12) to Eq. ( 15) estimates the comfort of the joint by comparing its current position with its upper limitation, lower limitation and its neutral position. The most comfortable position is in neutral position of the joint.

In our case, right shoulder and the hole are predefined in the same horizontal line in sagittal plane. Therefore, different postures need to be adjusted to adapt to the variation of the distance. Different posture causes different fatigue and different discomfort. Therefore, using the discomfort index and stress index in Eq. ( 11) and Eq (12), an optimal posture can be found to balance the requirement of fatigue and discomfort. The results are shown in Figure 12. Both factors are weighted by weight factor w i . The variation of w i allows us to move the optimal solution along the Pareto surface in Figure 13. In our analysis, both weighting factors are set as 1. These weighting factors can be set according to the preference of less fatigue or less discomfort. In the right lower subfigure, an optimal posture can be found at the distance around 0.53m. The optimal position is graphically shown in Figure 14. The flexion angle of shoulder and elbow are 22° and 98° to maintain the drilling machine. By setting different weighting values, different optimal posture can be achieved.

  2 1 () Δ norm discom fort i i i i fq γ q G Q U G Q L G          (12)
Δ N norm ii i UL ii qq q qq    (13)   100 5 1 sin 1 2 2 U i i i U L i i q q π QU q q                          (14)   100 5 1 sin 1 2 2 L i i i U L i i q q π QL q q                          (15)

Discussion

The main difference between the fatigue analysis in this paper and the conventional methods for posture analysis is: all the physical exposure factors are taken into consideration in this method as well, but in a continuous record method. In this way, much detailed analysis of the operation can be achieved.

With the new fatigue and recovery model, it is possible to evaluate the fatigue of a certain manual handling job. Although until now only a specific application case is analyzed, the feasibility of the overall concept is verified in this paper. The fatigue at each joint, the reduction of the joint strength and the recovery time necessary for preventing the worker from cumulative fatigue can be calculated out with respect to physical and temporal parameters of the job. With the analysis result, it is possible to determine suitable work-rest schedules to minimizing fatigue during a job, and to provide recommended postures to the user. With the analysis the distribution of the population, the fatigue model can also be used to select suitable workers for the jobs.

However, in a manual handling job, there are lots of objective factors influencing the performance of the worker, such as, temperature, vibration, and so on.

In a virtual reality framework, it is impossible to reproduce all these factors. From another view, there are different aspects concerning the difficulty of the job, such as accessibility, visibility, comfort, and fatigue. In real working process, the worker can adjust the operation according to the environment, the requirement of the job and his own capacities. For this reason, the actual operation is the result of multiple-objective optimisation. In the drilling case, multiple-objective optimisation posture can be achieved by weighting fatigue and discomfort as the same. Although this cannot reflect the actual posture in the manual handling work, at least the result can provide us a recommended posture to decrease MSD risks.

Conclusions and Perspectives

In this paper, the application of a new muscle fatigue and recovery model in a virtual environment framework is presented. In the digital human simulation, the joint torque load can be calculated after geometrical and dynamic modelling of human. Thus, according to biomechanical limits of each joint, the fatigue level of the joint can be figured out using the fatigue model. Further more, the fatigue model and recovery model can be used to determine the work-rest schedule for manual handling jobs.

Nevertheless, combining fatigue index and discomfort index of joint, virtual human's motion can be predicted or proposed in digital human simulation tools.

In the future, other manual handling jobs are going to be evaluated under this framework with consideration of fatigue. Full body geometrical and dynamic model of virtual human is going to be constructed to evaluate the joint fatigue for all the key joints of human. Experimental validation of the evaluation results is now under construction. It is possible to apply the new fatigue and recovery model in commercialised simulation software to simplify ergonomics evaluation procedures and enhance the work design efficiency, and make contribution to its final goalreduce MSD risks in manual handling jobs.

  Several muscle fatigue models and fatigue indices have been proposed in the literature. In a series of publications [WD1, DW1, DW2, and DW3], a new muscle fatigue model based on Ca 2+ cross-bridge mechanism was verified by stimulation experiments. This model based on the physiological mechanism seems too complex for ergonomic application due to its large number of variables. Another muscle fatigue model [GM1] based on force-pH relationship was obtained by curve fitting of the pH level with time in the course of stimulation and recovery. Komura et al. [KS1, KS2] have used this model in computer graphics to visualize the muscle capacity. However, in this pH muscle fatigue model, all the influences on fatigue from physical aspects are not considered. Rodriguez proposed a half-joint fatigue index in the literature [RB1, RB2, and RB3] based on mechanical properties of muscle groups. This fatigue model was used to calculate the fatigue at joint level, and the fatigue level is expressed as the actual holding time normalized by maximum holding time of the half-joint. The maximum holding time equation of this model was from static posture analysis and it is mainly suitable for evaluating static postures. Because of these limitations in current existing fatigue models, a new simple model is necessary to evaluate the fatigue. Virtual and Physical Prototyping, Vol. 5(3), September 2010, pp. 123 -137

Figure 1 :

 1 Figure 1: Framework for objective work evaluation system

  This model (Eq.(3)) is developed based on recovery models mentioned in the literature [WF1, CN1]. This model can also be explained by muscle motor mechanism pattern. (MVC-F cem ) represents the fatigued motor units in the muscle. The recovery rate from fatigue muscle motor units is assumed to be constant 2.4 [LB2, WF1], in symbol R.

  Figure 2: Drilling task in EADS field application

Figure 3 :

 3 Figure 3: Modified Denavit-Hartenberg notation system

  Figure 4: Geometrical model of the arm

  . Two geometrical variables, flexion angle of elbow and flexion angle of shoulder, are used to calculate the elbow flexion joint strength. It is obvious that different geometrical configuration Virtual and Physical Prototyping, Vol. 5(3), September 2010, pp. 123 -137 determines different flexion joint strength and that the variation of the strength among the population is quite large.

  Δq 1 means the flexion of the shoulder, and Δq 4 means the flexion of the shoulder. The sign of both variables indicates the rotation direction around its Z-axis. With this geometrical configuration, Virtual and Physical Prototyping, Vol. 5(3), September 2010, pp. 123 -137

Figure 6 :Figure 9 :

 69 Figure 6: Reduction of the elbow strength while holding a drilling machine weighted as 2.5 kg

Figure 10 :

 10 Figure 10: Recovery 30 s after drilling a hole

Figure 12 :

 12 Figure 12: Evaluation of the influence of the working distance

Table 1 :

 1 Parameters in muscle fatigue and recovery model load means more type II motor units are involved to generate the force.As a result, the muscle becomes fatigued more rapidly, as expressed in Eq. (2). F cem represents the non-fatigue motor units of the muscle. In the process of force generation, the amount of non-fatigued type II motor units gets smaller and smaller due to fatigue, while the number of the type I motor units remains almost the same due to their high fatigue resistance, and the decrease of F cem with time becomes slower, as expressed in Eq. (2) by term F cem (t)/MVC. This muscle fatigue model has been mathematically validated by comparing 24 existing static endurance time models

	Parameters	Unit Description
	U	-	Fatigue index
	MVC	N	Maximum voluntary contraction
	F cem	N	Muscle force capacity at time instant t
	F load	N	Muscle load at time instant t
	Γ max	Nm Maximum joint strength
	Γ

cem Nm Joint strength at time instant t Γ Nm Torque at the joint at time instant t k min -1 Fatigue ratio, equals to 1 R min -1 Recovery ratio, equals to 2.4 t min Time 3.1 Muscle fatigue model The muscle fatigue model is based on motor mechanism pattern of muscles. A muscle consists of many motor units. Each motor unit has different force generation capability, and different fatigue and recovery properties. In general, there are three types in the muscle: type I is slow-twitch motor units with small force generation capability and low conduction velocity, but a very high fatigue resistance; type II b is of fast-twitch speed, high force capacity, but fast fatigability; type II a, between type I and type II b, has a moderate force capacity and moderate fatigue resistance. The sequence of recruitment is in the order of: I II a  II b [V1]. For a specified Virtual and Physical Prototyping, Vol. 5(3), September 2010, pp. 123 -137 muscle, larger F listed in [EK1] and 3 dynamic models in [LB2, FT1, DW3] in [MC1]. The validation result proves that this model is capable for muscle fatigue evaluation. load cem cem

Table 2 :

 2 Geometrical parameters for modelling right arm

	Joints	Description
	1	Flexion and extension of shoulder joint
	2	Adduction and abduction of shoulder joint
	3	Supination and pronation of upper arm
	4	Flexion and extension of shoulder joint
	5	Supination and pronation of upper arm

Table 3 :

 3 Geometrical parameters for modelling right arm

	Joint	σ	α	d		r	θ	θ ini
	1	0	-π/2	0		0	θ 1	-π/2
	2	0	-π/2	0		0	θ 2	-π/2
	3	0	-π/2	0		-RL3	θ 3	-π/2
	4	0	-π/2	0		0	θ 4	0
	5	0	π/2	0		0	θ 5	0
		cos		sin	0
	1	cos	sin	cos	cos	sin	cos
		sin	sin	sin	cos	cos	sin

Table 5 :

 5 Initial parameters and joints flexion strength under geometrical configuration α E =90° and α S =90°

	Height	1,70 m	Weight	70 kg
	Δq 1	-30°	Δq 4	-90°
		Mean	Std. Deviation 95% Population
	Γ shoulder [Nm]	75.620	17.476
	Γ elbow [Nm]	75.141	18.470
	Extenral Load	Γ 1 (Nm)	Γ 4 (Nm)
	2.5kg	23.043	7.394
	3.5kg	26.873	9.672

Table 6 :

 6 Endurance time [s] and fatigue index U of shoulder and elbow flexion joints under continuous working condition

	External Load	-2σ	-σ	0	-2σ	+2σ
	2.5 kg, Shoulder [s] 60.155 140.125 233.984 338.456 451.520
	Us of 30 s *	0.283	0.198	0.152	0.124	0.104
	2.5 kg, Elbow [s] 509.083 936.582 1413.831 1928.300 2472.535
	Ue of 30 s *	0.097	0.065	0.049	0.039	0.033
	2.5 kg Holes	2	5	8	11	15
	3.5 kg, Shoulder [s] 37.623 100.198 174.683 258.268 349.221
	Us of 30 s	0.330	0.231	0.178	0.144	0.122
	3.5 kg, Elbow [s] 325.501 621.517 955.564 1318.062 1703.315
	Ue of 30 s	0.127	0.085	0.064	0.052	0.043
	3.5 kg Holes	1	3	6	9	11
	External load	Recovery time for 30 s drilling work [s]
	3.5 kg Shoulder	83.542 75.758 69.815 65.011 60.981
	3.5 kg Shoulder	61.945 52.576 45.774 40.432 36.033
	2.5 kg Elbow	80.243 72.301 66.270 61.412 57.343
	2.5 kg Elbow	55.584 46.101 39.240 33.863 29.439

*Us, Ue: Fatigue index of shoulder and elbow

Table 7 :

 7 Parameters used in VSR discomfort index

	Parameters	Unit	Description
	q i		degree current position of joint i
	q U i	degree upper limit of joint i
	q L	i	degree lower limit of joint i
	q N i	degree neutral position of joint i
	G		-	constant, 10 6
	QU i		-	penalty term of upper limits
	QL i		-	penalty term of lower limits
	γ i			-	weighting value of joint i
	() f q	overall	12 m ax( ) fatigue fatigue ff m ax( discom fort discom fort w w ff 	)	(10)
				() fq	fatigue		1 n 	m ax Γ i  Γ  	2	(11)

Acknowledgements

This research was supported by the EADS and by the Région des Pays de la Loire (France) in the context of collaboration between the Ecole Centrale de Nantes (Nantes, France) and Tsinghua University (Beijing, P.R.China).


Hermann Nabi

Martin J Shipley

Jussi Vahtera

Martica Hall

Jyrki Korkeila

Michael G Marmot

Mika Kivimäki

Archana Singh-Manoux

Mika Kivim

Effects of depressive symptoms and coronary heart disease and their interactive associations on mortality in middle-aged adults: the Whitehall II cohort study

Keywords: Coronary heart disease, depressive symptoms, survival

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

The impact of depression on the development and prognosis of chronic diseases, coronary heart disease (CHD) in particular, has attracted significant research attention in recent years. In healthy populations, long-term prospective studies have found depression to be associated with the development of CHD, independently of other risk factors for CHD. , , Successive meta-analyses show [1 2 3 ] depression to increase the risk for the onset of CHD, with pooled relative risk between 1.6 and 1.8 in subjects with diagnosed depression or those reporting depressive symptoms. , , Several other studies have shown that depression is also associated with increased risk of [1 4 5 ] all-cause and cause-specific mortality in general populations. , , , Furthermore, there is increasing evidence of the importance of [3 6 7 8 ] depression as a prognostic factor as the outcomes of myocardial infarction (MI) have been found to be worse among depressive than non-depressive MI-patients after controlling for cardiac disease severity. , , Findings from two recent systematic reviews have [9 10 11 ] shown that in individuals with established CHD, depression is associated with an approximately 2-fold higher risk of death from all-cause and cardiac mortality.

, [12 13 ] However, these studies typically compared depressed and non depressed participants free of CHD or depressed and non depressed patients with CHD. This approach does not allow comparisons across risk-factor groups based on the cross-classification of depression and CHD status, and it remains uncertain whether the effect of depression on mortality in individuals with CHD is larger than that in healthy individuals. The present investigation was therefore conducted to examine effects of depressive symptoms and coronary heart disease and their interactive associations on mortality in middle-aged adults. We examined whether the association between depression and mortality varied among individuals with both CHD and depressive symptoms compared to those: 1) without both these conditions, 2) with depressive symptoms but not CHD, and 3) with CHD but no depressive symptoms. examination Phases 3 (1991 1993), 5 (1997 1999) and 7 (2002 2004) . Depressive symptoms were assessed by the Center for

MATERIAL & METHODS

Data

[ - - - ]
Epidemiologic Studies Depression Scale (CES-D) for the first time at phase 7 and this phase serves as the baseline for the present study.

The University College London ethics committee approved the study.

Measures

Coronary heart disease (CHD)

CHD status at phase 7 was defined as non-fatal MI or definite angina and was based on clinical examinations at phases 1, 3, 5, and 7

' '

and records obtained from general practitioners and hospitals. Potential non-fatal myocardial infarction was ascertained by questionnaire items on chest pain (the World Health Organisation Rose questionnaire.

) and physician diagnosis of heart attack. Confirmation of [START_REF] Rose | Cardiovascular survey methods[END_REF] myocardial infarction according to MONICA criteria (Multinational Monitoring of Trends and Determinants in Cardiovascular

Depressive symptoms

Depressive symptoms were assessed using the Center for Epidemiologic Studies Depression Scale (CES-D, Cronbach alpha 0.83) at = phase 7 of the Whitehall II study (2002 2004). The CES-D, a widely used and validated instrument, is a 20-item self-report questionnaire designed to measure depressive symptomatology in community studies. A score 16 from a total possible score of 60 has been used

[16 ] ≥ extensively to distinguish depressed from nondepressed subjects .

[16 ]

Vital status

Mortality follow-up was available through the National Health Services Central Registry until 30 April 2009. Death certificates were th coded using the 10 revision of the International Classification of Disease (ICD). All-cause mortality was the main outcome, in subsidiary th analysis we also analysed death from cardiovascular diseases (CVD; ICD-10 codes I20 I25 and I60 I67).

--

Covariates

Sociodemographic measures

Sociodemographic measures included age, sex, ethnicity, and socioeconomic position (SEP) assessed by British civil service grade of employment taken from the phase 7 questionnaire.

Biobehavioural risk factors

Behavioural CVD risk factors were assessed using responses to the phase 7 questionnaire and categorised as follows: smoking status (never, ex, and current), physical activity ( 1.5 or <1.5 hours of moderate or vigorous exercise/week), alcohol consumption in the previous ≥ week was categorized as abstention, moderate (1 14 units for women/1 21 units for men), and high consumption (14 units for women/21

- - +
units for men). The following biological CVD risk factors were measured at phase 7 clinical examination: hypertension (systolic blood + pressure 140 mm/Hg or diastolic blood pressure 90 mm/Hg), high total cholesterol (> 5 mmol/l), body mass index (BMI) (<20, 20 24.9,

≥ ≥ -
Resting heart rate (RHR) was measured at the phase 7 screening clinic via electrocardiogram (ECG) from participants in the supine position following a standard protocol. The following classification was used to categorise RHR: RHR<80, and RHR>80 beats/minute (bpm).

Antidepressant medications

Data on antidepressant medications was drawn from the phase 7 questionnaire where participants were asked whether in the last 14 days they had taken antidepressants drugs prescribed by a doctor (yes/no).

Cardiovacular disease medications

CVD medications at phase 7 were also drawn from questions on whether in the last 14 days the participant had taken CVD drugs, including diuretics, beta blockers, ACE inhibitors, calcium channel blockers, other anti-hypertensive, prescribed by a doctor (yes/no).

Statistical analysis

We divided the study sample into 4 risk-factor groups based on the cross classification of depression (depression (CES-D 16) vs. no ≥ depression (CES-D <16)) and CHD (yes/no) at phase 7. Differences in these risk-factor groups as a function of the sample characteristics were assessed using a chi-square test

The risk of death was examined using Cox regression in 5 serially adjusted models, with participants without depressive symptoms and CHD constituting the reference group. Model 1 included adjustment for sex and age and Model 2 was additionally adjusted for ethnicity and SEP. Model 3 was as model 2 but additionally adjusted for smoking, BMI, alcohol consumption, physical activity, hypertension, total cholesterol, diabetes, and RHR. Model 4 was as model 2 plus adjustment for CVD medications and antidepressant medications. Finally, model 5 was the fully adjusted model with simultaneous adjustment for all covariates. In further analysis we changed the reference group and repeated these analyses in order to estimate the risk of death for participants with both depressive symptoms and CHD in comparison to those with depressive symptoms but without CHD and to those with CHD but without depressive symptoms. The time-dependent interaction terms between each predictor and logarithm of follow-up period were all non-significant confirming that the proportional hazards assumption was justified.

To examine whether the coexistence of depressive symptoms and CHD increased risk of death beyond that associated with each of them alone we tested for an interaction on the additive scale as defined by Rothman for calculating the relative excess risk due to [17 ] interaction (RERI) using the methods outlined by Andersson et al. . In the absence of an interaction between depressive symptoms and [START_REF] Andersson | Calculating measures of biological interaction[END_REF] CHD, the RERI is 0. RERI and the associated 95 CIs were computed by the delta method.

% [19 ]

RESULTS

Of the 10308 participants of the Whitehall II Study, the current analysis where the follow-up starts at Phase 7 of the study is based on a total of 5936 participants. Those not included in the analyses due to missing data were more likely to be: women (39.9 vs. 28.1 , % % p <0.001), non-white (15.5 vs. 7.7 , <0.001), in the 70 74 age group (14.5 vs. 9.2 , <0.001), and from lower SEP (34 vs. 15 , % % p -% % p % % p <0.001). Of those included in the analysis, 170 died during the mean follow-up of 5.6 years (SD 0.7, range 0.03 6.6), of which, 47 from -CVD. The mean age of participants at phase 7 was 61 years (SD 6.0). The prevalence of elevated depressive symptoms (CES-D score 16) ≥ was 14.9 . Participants with a history of CHD were more likely to have depressive symptoms (20 vs. 14 , 0.001) than those without

% % % p = CHD.
shows the baseline characteristics of the study participants. Participants with both depressive symptoms and CHD, as Table 1 compared to those free of both conditions, were older and more likely to be from low socioeconomic position, non-White, antidepressant users, current smokers (along with those depressed participants without CHD), less physically active, obese, diabetic, treated by CVD medication and less likely to have high total blood cholesterol (all 0.009). As expected, results from additional analyses conducted p ≤ separately for depression and CHD (data not shown in table), revealed that they both were associated with all cause mortality, the age-sex-adjusted hazards ratios (HRs) being 2.41 ( <0.001) and 2.02 ( <0.001) respectively. The corresponding HRs for CVD mortality p p were 2.83 ( 0.001) and 2.61 ( 0.004). p = p = presents the HRs for the associations with mortality, from all-causes and from CVD, in the groups resulting from the cross Table 2 classification of CHD and depressive symptoms. Model 1 shows that compared with participants without CHD and depressive symptoms (the reference group) the age-and sex-adjusted hazard ratio for death from all-causes was higher in all three exposed groups: those with depressive participants but not CHD (1.67, 95 confidence interval (CI) 1.05 2.66), those with CHD but not depression (2. participants who were depressed but without CHD no substantial risk reduction was observed (HR 2.37, 95 CI 1.07 5.34).

= % -

presents the risk of mortality, first all cause and then CVD mortality, among participants who were depressed and had CHD Figure 1 compared to those who were depressed but free from CHD. These results show 2.4-fold (p<0.006) and 2.7-fold higher (p 0.08) risk for all = cause and CVD mortality respectively when adjustments were made for sex and age. Serial multivariable adjustment substantially attenuated these associations leading to non-significant associations for all-cause mortality (HR 1.66, 0.13), and for CVD mortality For results presented in , the reference category is set to the group of individuals with CHD but no depressive symptoms. In Figure 2 model 1 (age and sex adjusted) the HRs associated with co-existing depression and CHD were 2.99 ( 0.001) and 2.92 ( 0.06) for all p = p = cause and CVD mortality, respectively. Serial multivariable adjustment showed no substantial attenuation for these associations.

The RERI between depressive symptoms and CHD for all-cause mortality was 3.58 (95 CI, 0.09 7.26), providing some evidence

% - -
for the presence of an additive interaction. The corresponding RERI for CVD mortality was 4.61 (95 CI, 4.04 13.26).

% --

DISCUSSION

In this prospective study we sought to evaluate the differential effects of depressive symptoms on all-cause and CVD mortality in a large sample of middle-aged participants, with and without established CHD. We created 4 risk-factor groups based on the cross classification of depressive symptoms (yes/no) and CHD status (yes/no) at baseline. Our results show that compared to participants without depressive symptoms and CHD, the fully adjusted risks of mortality from all-cause and CVD were 2.9-fold and 3.9-fold higher for participants with both CHD and depressive symptoms, respectively. Further comparisons also indicated that the risks of death from all-causes and CVD were higher, but to a lesser extent, for these participants when specifically compared to those with depressive symptoms only or CHD only. There is some evidence of an additive interaction between depressive symptoms and CHD for mortality.

Findings in context of the literature

Several studies have examined the effect of depression on all-cause and CVD mortality in community and patients populations. Our ' results are in line with the findings reported in those studies. , , , , , However, an important contribution of the present [3 6 9 10 11 20 ] study to the current literature is that it is one of the first prospective cohort studies to compare the effects of depressive symptoms for mortality in individuals as a function of their CHD status. Our findings are based on a large well-characterized cohort with depressive symptoms assessed using a validated scale and biological risk factors assessed during a clinical examination. CHD events were ascertained using medical records and electrocardiograms data from clinical examinations. We were able to compare, within the same study, participants with both depressive symptoms and CHD to those free of one or both these conditions. We found fairly similar pattern of associations for both mortality outcomes examined, reinforcing therefore our confidence in the internal validity of our findings.

In the present study, the co-occurrence of depressive symptoms and CHD is associated with an increased risk of all-cause and CVD mortality beyond that due to depressive symptoms and CHD alone. The estimates for the additive interactions largely exceeded the value 0 (absence of interaction), even if the 95 confidence intervals for the RERIs were wide, particularly for CVD mortality. Indeed, we found % that the RERI between depressive symptoms and CHD for all-cause mortality was 3.58 (4.61 for CVD death), suggesting that the relative risk of death from all-cause in depressive participants with CHD is 3.58 (4.61 for CVD death) more than if there were no interaction.

In order to test the robustness of our findings we repeated the main analysis by only considering participants with confirmed MI as CHD cases (see ). Similar pattern of associations were observed as those presented in the main analysis in which CHD online appendix cases were participants with both confirmed MI and definite angina. This suggests that the combined effect of depressive symptoms and CHD on mortality outcomes is not sensitive to the definition of CHD events.

Further comparisons across risk-factor groups revealed ( and ) that participants with both depressive symptoms and CHD figures 1 2 were 2.4-fold (2.7-fold) and 3-fold (2.9-fold) higher age-sex-adjusted risk of all-cause (CVD) death when compared to those with only depression and only CHD, respectively. In combination, these observations illustrate the importance of the choice of the comparison group when estimating the effect size of depressive symptoms on health outcomes. The choice of the reference group seems also to be of great importance when testing the mediating role of third variables in the association between depression, morbidity and mortality. For instance the percentage of reduction in the age-sex adjusted hazards of death outcomes after multivariable adjustments for depressive participants with CHD varied from 49 to 51 , 53 to 62 , and 0 to 16 when compared to those without either depressive symptoms or CHD (

% % % % % %
), those with only depressive symptoms ( ) and those with only CHD ( ), respectively. table 2 figure 1 figure 2 Adjustment for sociodemographic characteristics, biobehavioural risk factors, antidepressant and CVD medications attenuated the increased risk of death in participants with only CHD towards the null, suggesting that this association was attributable to differences in baseline characteristics between the groups. However, this was not the case in those participants with only depressive symptoms and in those with both depressive symptoms and CHD, suggesting that the mechanisms through which depressive symptoms increase the risk of all-cause and CVD death remain to be understood. Further studies should explore other possible mechanisms that have not been addressed

in the present study, including for example inflammatory processes , platelet activation , endothelial dysfunction , [START_REF] Frasure-Smith | Depression, C-reactive protein and two-year major adverse cardiac events in men after acute coronary syndromes[END_REF] [22 ] [START_REF] Sherwood | Impaired endothelial function in coronary heart disease patients with depressive symptomatology[END_REF] polyunsaturated fatty acids and plasma lipoproteins metabolism , and the role of non adherence to medical regimens , .

[ 24 25 ] [26 27 ] Moreover, depressive symptoms may also be related to unfavorable trajectories of prognostic factors over time. Further longitudinal studies are needed to examine these mechanisms in detail.

Study limitations

In interpreting the present results, it is important to note some limitations. First, this cohort of civil servants did not include blue collar workers, unemployed or individuals with precarious jobs and younger adults; thus it is not representative of the general population, which may limit the generalisability of our findings. Second, we assessed depressive symptoms rather than clinical depression. However, it has been suggested that significant depressive symptomatology could be a risk factor for clinical depression . Finally, as we had only 15 [START_REF] Radloff | The CES-D Scale: A Self-Report Depression Scale for Research in the General Population[END_REF] all-cause and 5 CVD deaths in the group of participants with both depressive symptoms and CHD, lack of statistical power is likely to be the main reason why the RERI values, though large, did not reach statistical significance.

Conclusions and implications

Despite these potential limitations, the present findings remain important by providing evidence that depressive symptoms are associated with an increased risk of all-cause and CVD death and that this risk is particularly marked in depressive participants with co-morbid CHD. A major implication of these results is the need for health care professionals to pay more attention to depression in their

  are drawn from the Whitehall II study, established in 1985 as a longitudinal study to examine the socioeconomic gradient in health and disease among 10,308 civil servants (6,895 men and 3,413 women). All civil servants aged 35 55 years in 20 London based departments were invited to participate by letter, and 73 agreed. Baseline screening (Phase 1) took place during 1985 1988, and involved % a clinical examination and a self-administered questionnaire. Subsequent phases of data collection have alternated between postal questionnaire alone Phases 2 (1989 1990), 4 (1995 1996), 6 (2001) and 8 (2006) and postal questionnaire accompanied by a clinical

[ 15 ]

 15 Disease) was based on electrocardiograms, markers of myocardial necrosis, and chest pain history from medical records. Angina was assessed based on participant s reports of symptoms with corroboration in medical records or abnormalities on a resting electrocardiogram, ' an exercise electrocardiogram, or a coronary angiogram.

  cardiac patients. Approximately 20 of participants with a history of CHD in our study had depressive symptoms, a figure consistent with % those from previous studies estimating the prevalence of minor and major depression in patients with established CHD to be 27 and 20 , stress the importance of developing interventions that are effective in reducing mortality due to [28 29 ] depression. It should be noted that the mechanisms through which depressive symptoms increase mortality need to be better understood before evidence-based interventions can be developed.

Figure 1 Figure 2

 12 Figure 1Hazard ratios of mortality for participants with both CHD and depressive symptoms comparatively to those with depressive symptoms but without CHD A: All-cause mortality B: Cardiovascular mortality

  attenuation of the association was related to controlling for biobehavioural risk factors. The fully-adjusted HR was highest in the group with both depression and CHD (HR 2.94, 95 CI 1.63 5.34) but the group with CHD but no depression was not robust to successiveThe results for CVD mortality are essentially similar to those obtained for all-cause mortality. The age-and sex-adjusted HRs were 2.52 (95 CI, 1.17 5.43) for depressive participants without CHD, 2.29 (95 CI 1.02 5.14) for those with CHD but not depression and .54 17.54) for those with both depression and CHD. The fully adjusted HRs attenuated by 49 in the group with both CHD and -% depression (HR 3.91, 95 CI 1.34 11.43), and by 74 for participants with CHD but not depression (HR 1.33, 95 CI 0.54 3.28). For

			=	%	-
	adjustment for covariates (HR 1.10, 95 CI 0.66 1.82). = % -
	%	-			%	-
	6.69 (2=	%	-	%		=	%	-

10, 95 CI % -% 1.47 3.13), and those with depression and CHD (4.99, 95 CI 2.89 8.62). After successive adjustments for sociodemographic -% characteristics (model 2), biobehavioural risk factors (model 3), antidepressant and CVD medications (model 4) and for all of these covariates (model 5), the magnitude of the associations was substantially reduced except in the depressed but no CHD group. Almost all " "

Table 1

 1 Baseline characteristics by presence or absence of CHD and depressive symptoms at phase 7

	Variables	N total	No CHD, not depressed	No CHD, Depressed	CHD, not depressed	CHD, depressed	P value/trend
	Sex						0.161
	Male	4268	3359 (72.9)	491 (63.2)	350 (79.0)	68 (63.0)
	Female	1668	1259 (27.1)	286 (36.8)	93 (21.0)	40 (37.0)
	Age in years						< 0.001
	< 54	1110	873 (18.9)	203 (26.1)	25 (5.6)	9 (8.3)
	54 59 -	1822	1453 (31.5)	251 (32.3)	97 (21.9)	21 (19.4)
	60 64 -	1259	998 (21.7)	140 (18.0)	98 (22.1)	23 (21.3)
	64 69 -	1196	896 (19.4)	129 (16.6)	137 (30.9)	34 (31.5)
	70 74 -	549	388 (8.4)	54 (6.9)	86 (19.4)	21 (19.4)
	SEP						< 0.001
	High	2040	1661 (36.0)	181 (23.3)	178 (40.2)	20 (18.5)
	Middle	3032	2361 (51.2)	415 (53.4)	202 (45.6)	54 (50.0)
	Low	864	586 (12.7)	181 (23.3)	63 (14.2)	34 (31.5)
	Ethnicity						< 0.001
	White	5485	4355 (94.3)	669 (86.1)	397 (89.6)	74 (68.5)
	Other	451	263 (5.7)	108 (13.9)	46 (10.4)	34 (31.5)
	Antidepressant drugs						< 0.001
	No	5728	4505 (97.8)	690 (88.8)	437 (98.6)	96 (88.9)
	Yes	208	103 (2.2)	87 (11.2)	6 (1.4)	12 (11.1)
	Smoking status						0.001
	Never smoker	2678	2129 (46.2)	334 (43.0)	172 (38.8)	43 (39.8)
	Ex smoker	2282	1780 (38.6)	255 (32.8)	205 (46.3)	42 (38.9)
	Current smoker	680	490 (10.6)	132 (17.0)	45 (10.2)	13 (12.0)
	Missing	296	209 (4.5)	56 (7.2)	21 (4.7)	10 (9.3)
	Alcohol consumption						0.994
	Abstainers	973	662 (14.4)	179 (23.0)	91 (20.5)	41 (38.0)
	Moderate	3725	2983 (64.7)	437 (56.2)	258 (58.2)	47 (43.5)
	High	1158	920 (20.0)	137 (17.6)	85 (19.2)	16 (14.8)
	Missing	80	43 (0.9)	24 (3.1)	9 (2.0)	4 (3.7)
	Exercise						< 0.001
	≥ 1.5 h/week	5152	4074 (88.4)	625 (80.4)	379 (85.6)	74 (68.5)
	< 1.5 h/week	784	534 (11.6)	152 (19.6)	64 (14.4)	34 (31.5)
	Hypertension						< 0.106
	No	4521	3590 (76.4)	603 (77.6)	324 (73.2)	74 (68.5)
	Yes	1410	1084 (23.5)	174 (22.4)	118 (26.6)	34 (31.5)
	Missing	5	4 (0.1)	0 (0.0)	1 (0.2)	0 (0.0)
	BMI (kg/m ) 2						< 0.001

[START_REF] Dickens | Depression is a risk factor for mortality after myocardial infarction: fact or artifact?[END_REF]

29.9, or 30 kg/m ) and diabetes, assessed via glucose tolerance test at the medical screening or self-report of doctor diagnosis.

[START_REF] Dickens | Depression is a risk factor for mortality after myocardial infarction: fact or artifact?[END_REF]

[START_REF] Dickens | Depression is a risk factor for mortality after myocardial infarction: fact or artifact?[END_REF]

[START_REF] Dickens | Depression is a risk factor for mortality after myocardial infarction: fact or artifact?[END_REF]

[START_REF] Dickens | Depression is a risk factor for mortality after myocardial infarction: fact or artifact?[END_REF]

Recovery in Coronary Heart Disease Patients (ENRICHD) Randomized Trial . Jama . 2003 ; 289 : 3106 -16

[START_REF] Dickens | Depression is a risk factor for mortality after myocardial infarction: fact or artifact?[END_REF]

[START_REF] Dickens | Depression is a risk factor for mortality after myocardial infarction: fact or artifact?[END_REF]

[START_REF] Dickens | Depression is a risk factor for mortality after myocardial infarction: fact or artifact?[END_REF]

Ackowledgements:

We thank all participating civil service departments and their welfare personnel, and establishment officers; the Occupational Health and Safety Agency; the Council of Civil Service Unions; all participating civil servants in the Whitehall II study; all members of the Whitehall II study team. The Whitehall II Study team comprises research scientists, statisticians, study coordinators, nurses, data managers, administrative assistants and data entry staff, who make the study possible. The Whitehall II study is supported by grants from the Medical Research Council; British Heart Foundation; Health and Safety Executive; Department of Health; National Heart Lung and Blood Institute (R01HL036310), US, NIH: National Institute on Aging (R01AG013196 and R01AG034454), US, NIH; Agency for Health Care Policy Research (HS06516); and the John D and Catherine T MacArthur Foundation

Research Networks on Successful Midlife Development and Socio-economic Status and Health. MK and JV are supported by the Academy of Finland (projects 124271, 124322, 129262 and 132944) and EU New OSH ERA Programme and MK is additionally supported by the BUPA Foundation, UK, the National Heart, Lung, and Blood Institute and the National Institute on Aging, USA. MJS is supported by a grant from the British Heart Foundation. AS-M is supported by a European Young Investigator Award from the European Science Foundation.

" "

Footnotes:

None.

DECLARATION OF INTERESTS:

References: : all aforementioned Model 5 ** n events/n total is the same in all models.