Jean-Pierre P Quenot

Jean-Philippe P Rigaud

Sébastien Prin

Saber Barbar

Arnaud Pavon

Mael Hamet

Nicolas Jacquiot

Bernard Blettery

Christian Hervé

Pierre Emmanuel Charles

PE Charles

G Moutel

Impact of an intensive communication strategy on end-of-life

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Since the advent of the discipline of critical care almost half a century ago, it has become clear that in some patients, there are limits to the therapeutic engagement. The use of all available resources to maintain artificial life support can sometimes border on the excessive, not to say unreasonable, given the hopeless prognosis and low quality of life expected for the patient, or the excessive economic cost [START_REF] Ferrand | Withholding and withdrawal of life support in intensive-care units in France: a prospective survey. French LATAREA Group[END_REF][START_REF] Prendergast | Increasing incidence of withholding and withdrawal of life support from the critically ill[END_REF][START_REF] Smedira | Withholding and withdrawal of life support from the critically ill[END_REF].

Early studies exploring this concept led to the proposal of a scale of therapeutic engagement [START_REF] Rapin | Palliative comfort therapy in critically ill patients][END_REF]. Further reports evaluating practices in terms of withholding and withdrawing treatment in critical care in France [START_REF] Ferrand | Withholding and withdrawal of life support in intensive-care units in France: a prospective survey. French LATAREA Group[END_REF][START_REF] Knaus | Do objective estimates of chances for survival influence decisions to withhold or withdraw treatment? The French Multicentric Group of ICU Research[END_REF] brought the medical community to a collective realisation that the conceptual framework needed to be reviewed. This ushered in an era of profound reflection on the role of the patient, their proxies, and the responsibility of physicians and paramedical staff in end-of-life decision-making. The results of this reflection have materialised in different forms in different countries, depending on the local legal and cultural context [START_REF] Lilly | An intensive communication intervention for the critically ill[END_REF][START_REF] Deliens | End-of-life decisions in medical practice in Flanders, Belgium: a nationwide survey[END_REF][START_REF] Cook | Cardiopulmonary resuscitation directives on admission to intensive-care unit: an international observational study[END_REF][START_REF] Drazen | Decisions at the end of life[END_REF][START_REF] Van Der | End-of-life decision-making in six European countries: descriptive study[END_REF][START_REF] Quill | Dying and decision making--evolution of end-of-life options[END_REF].

In France, this process of reflection led to new legislation, dating from 22 April 2005, relative to patient rights at the end-of-life, the so-called "Leonetti" law [START_REF] Baumann | Ethics review: end of life legislation--the French model[END_REF][13]. Briefly, this law gives new rights to patients and clarifies medical practices regarding end-of-life care.

We performed a before-and-after, interventional study to investigate whether an intensive communication strategy regarding end-of-life decisions, taking into account the dispositions of the law dated 22 April 2005, would have an influence on practices in terms of withholding and withdrawing treatment, and on the outcome of patients hospitalised in critical care.

Methods

This single-centre study was performed over two periods, namely before the law of [START_REF] Stricker | Family satisfaction in the intensive care unit: what makes the difference?[END_REF] Between the 2 phases, our healthcare team (physicians, nurses, nurses' aids, psychologist) developed an intensive strategy for communication on the level of therapeutic engagement for every patient in the intensive care unit (ICU) according to clinical severity and expected prognosis. The communication strategy and related structural organisation within the department is described in Table 1.

Data Collection

We examined the medical records of all patients who died in the ICU or in-hospital after discharge to another department, during the two study periods.

We recorded for all patients: age, sex, simplified acute physiological score (SAPS II) [START_REF] Azoulay | End-of-life practices in 282 intensive care units: data from the SAPS 3 database[END_REF], comorbidities and diagnosis at admission as defined by the International Classification of Disease, 9th Ed, clinical Modification (ICD-9-CM); Knaus score [START_REF] Sprung | End-of-life practices in European intensive care units: the Ethicus Study[END_REF], type of admission (medical or surgical), the person who initiated the decision-making process on withholding of withdrawal of treatment for each patient; reasons for withholding or withdrawing treatment (choice of prespecified items); whether an external expert was consulted (clinician specialist of the main disease presented by the patient); existence of any information concerning withholding or withdrawal of treatment emanating from the patient or their proxies; whether any end-of-life decisions were noted in the medical file; frequency of use of morphine and/or midazolam; whether the patient died in the ICU or in-hospital.

Withholding was defined as a planned decision not to initiate treatment that was otherwise indicated. Withdrawal was defined as interruption of ongoing treatments. Withholding or withdrawal of treatment included the possibility that a patient could be transferred to another hospital Department with instructions not be to readmitted to the ICU. For all patients who had died in the ICU or in-hospital further to discharge from the ICU to another department in period 1, we examined the medical records to identify whether death was due to limitation or withdrawal of ongoing treatment; and in cases where a decision to withhold or withdraw treatment had been made, what had been the reasons for this decision.

Overall, 99% of all deaths from both periods were analysed. Data relating to advance directives were noted as « not applicable » in period 1, since they pre-dated the 2005 legislation. Similarly, the first data on officially appointed proxies appeared in 2002, when a specific law allowing for the appointment of surrogates was introduced and put in practice in all hospitals nationwide.

It should be noted that the ICU comprised 8 beds in period 1, and 15 in period 2, with an intermediate transitional period with an incremental increase of capacity to 11 then 13 beds.

Statistical Analysis

Quantitative variables are presented as median [Interquartile range] and qualitative variables as number (percentage). Quantitative variables were compared using the Wilcoxon test and qualitative data with the Chi square test or Fisher's exact test. All tests were two-tailed and a p-value <0.05 was considered statistically significant. Bonferroni correction for multiple comparisons was applied where appropriate. All analyses were performed using SAS version 9.1 (SAS Institute, Cary, NC, USA).

Results

In total, 2478 patients were admitted in period 1, of whom 520 (21%) died in critical care, and 158 (10%) in-hospital after discharge from critical care. In period 2, 2940 patients were admitted, of whom 672 (23%) died in critical care, and 151 (5%) in-hospital.

The baseline characteristics of all patients who died in critical care or in-hospital after discharge to another department are displayed in were for medical pathologies (93% in period 1, 92% in period 2). Previous state of health as evaluated by the Knaus score did not differ significantly between periods. Similarly, no significant difference between periods was observed in admission diagnosis or comorbidities.

In period 1, a written notification of a decision to withhold or withdraw treatment was found in the medical files of 306 (45%) patients who died , versus 700 (85%) in period 2 (p<0.01). The difference was statistically significant for withholding alone, withdrawal alone, and for withholding plus withdrawal (table 1).

In the majority of cases, the decision with withhold or withdraw therapy was made in the critical care department (95% in period 1 vs 93% in period 2).

For the subsequent analyses, we considered only the 306 patients in period 1 and the 700 patients in period 2 who died further to a decision to withhold or withdraw treatment.

Time between admission to ICU and initiation of end-of-life decision-making process (Table 3)

The median time delay (in days) between admission to the ICU and the initiation of a decision-making process regarding possible withholding or withdrawal of therapy was significantly different between periods (Table 3). Similarly, the median time delay from admission to the actual decision to withhold or withdraw therapy was significantly shorter in period 2 (Table 3). We also observed a statistically significant difference between periods in median time delays [IQR] (in days) from admission to death in ICU and in-hospital, further to a decision to withhold treatment, withdraw treatment, or both.

Reasons for Withholding or Withdrawing Treatment in both periods (Table 4)

The reasons leading to a decision to withhold or withdraw treatment were documented in 68% of medical files in period 1 vs 99% in period 2 (p<0.01). There was no significant change in the main reasons cited in both periods, with the exception of expected future quality of life for the patient, which was cited significantly more frequently in period 2 as a reason for withholding or withdrawing therapy (See Electronic Supplementary Material).

Similarly, there was also a significant difference between periods in the citation rate of nonresponse to optimal therapy (Table 4).

Persons who initiated the decision-making process (Table 5)

The person(s) who initiated the decision-making process regarding the need to withhold or withdraw therapy (expressed as percent of patients) differed significantly between periods. In period 2, the process was more often initiated by close family members and non-physician staff members (nurses, nurses' aids) and this information was significantly less frequently unknown. Only four patients had prepared advance directives (all in period 2).

Use of morphine and midazolam during withholding or withdrawal of treatment (Table

6)

The pharmacological environment used for pain and anxiety relief in patients in whom a decision to withhold or withdraw treatment had been made showed significantly more frequent use of morphine and midazolam during period 2 as compared to period 1 (Table 6).

The information regarding any decision to withhold or withdraw treatment was given to the patient in 5% of cases in period 1, vs 9% in period 2 (p=NS). The same information was given to the families in 65% of patients in period 1 vs 95% in period 2 (p<0.01).

An external expert (clinician from another discipline) was consulted in an advisory capacity for 45% of decisions to withhold or withdraw therapy in period 1 vs 65% in period 2 (p<0.01).

Experts were mainly consulted by telephone in both periods (85% in period 1 vs 87% in period 2, p=NS).

Discussion

Our study shows that the number of deaths occurring further to a decision to withhold or withdraw therapy in patients hospitalised in the ICU differed significantly between the period before the new French law on patients' rights at the end-of-life (45%), and the period after the new legislation (85%), when an intensive communication strategy around the dispositions of this law had been put in place. This study mainly relates to the process of reflection and introspection concerning the ethics of end-of-life care, and how this process can and should become more consensual. The results of our intensive communication strategy have been to bring about a collective raising of awareness within the ICU. Official guidelines from national societies published in 2000 had previously made a start at laying down a framework for this difficult domain [START_REF] Ferrand | Active withholding and withdrawal of therapy in adult intensive care units[END_REF]. There was a clear need to allay the fears of caregivers who, although not trained in end-of-life care, were almost "obliged" to make difficult end-of-life decisions on a routine basis. Similarly, there was a need to communicate, in a clear and transparent manner, on the ethics of end-of-life decisions, and to allow all those involved in end-of-life care to have access to the medical and ethical knowledge that could help them to make and follow through on their decisions.

Previous studies have reported death rates of 50% to 78% after WWT decisions [START_REF] Ferrand | Withholding and withdrawal of life support in intensive-care units in France: a prospective survey. French LATAREA Group[END_REF][START_REF] Pochard | French intensivists do not apply American recommendations regarding decisions to forgo life-sustaining therapy[END_REF]. These studies were performed before the 2005 law and indeed, our results from period 1 are in line with these results, with 45% of deaths occurring further to a decision to forego therapy.

The second period of our study, after the new French legislation of 2005, saw the rate of deaths after limiting of life-sustaining therapy increase to 85% in our department, which is coherent with the rates reported in other studies conducted after 2005 [START_REF] Prendergast | Increasing incidence of withholding and withdrawal of life support from the critically ill[END_REF][START_REF] Antonelli | Year in review in Intensive Care Medicine 2009. Part III: mechanical ventilation, acute lung injury and respiratory distress syndrome, pediatrics, ethics, and miscellanea[END_REF][START_REF] Azoulay | End-of-life practices in 282 intensive care units: data from the SAPS 3 database[END_REF][START_REF] Sprung | End-of-life practices in European intensive care units: the Ethicus Study[END_REF]. It should be noted that studies conducted in different religious or geographic contexts, particularly within Europe, can give differing results. This could reflect not a true evolution in practices, but rather a better communication regarding what really happens, facilitated by the law of 2005, which rendered it easier to make such decisions and note them in the patient's file. By creating a legal framework for end-of-life decisions, the new law has helped to exculpate physicians who previously laboured in a no-man's-land of uncertainty about the ethics of end-of-life practices.

Our results further underline the importance of a clear decision-making procedure within an ICU that includes good communication and regular collegial meetings to facilitate discussion.

The new strategy we introduced comprising open communication and daily meetings with all

staff members made it possible for all relevant parties to advance their opinions and reachwithin a shorter time framea consensual decision about WWT options. Again, before the law of 22 April 2005, physicians in France had great difficulty in making decisions pertaining to suspension of life-sustaining therapies, and it was especially problematic to document such a decision in the medical file. With the legal framework created by the new law, the decision-making process has been greatly facilitated, and has been greeted with widespread relief among the medical profession. In the study by Ferrand et al [START_REF] Ferrand | Withholding and withdrawal of life support in intensive-care units in France: a prospective survey. French LATAREA Group[END_REF], among the patients in whom a decision to forego life-sustaining therapy was made, this decision was generally made within 2 days (in 40.5%), and within 30 days of admission to the ICU for 50%. In our study, the decision-making process was initiated after a median of 6-7 days in period 1, and 3-5 days in period 2, leading to a decision being made within a median of 11-13 days vs 4-6 days in period 1 vs 2 respectively. This clearly underlines that the greater communication facilitated the initiation of the decision-making process, even though the consequence was a significant reduction in the time delay to death.

The main motives cited as justification for deciding to withhold or withdraw therapy did not change significantly after the new legislation, except for quality of life and non-response to maximal medical therapy, which were more frequently cited in the later period. (See Electronic Supplementary Material). The new law specifically mentions that excessively burdensome treatment should be avoided and future quality of life taken into consideration, whereby the likelihood of a very low future quality of life would be considered suitable justification for WWT. Thus, these factors are legitimised by the law as reasons for foregoing life-sustaining therapy. In the literature, other reported reasons for suspending life-sustaining therapy include physical or psychological suffering, or economic reasons [START_REF] Ferrand | Withholding and withdrawal of life support in intensive-care units in France: a prospective survey. French LATAREA Group[END_REF][START_REF] Sprung | End-of-life practices in European intensive care units: the Ethicus Study[END_REF]. However, cost was not a factor in our study, since in the French medical health system, neither the patients nor the doctors are directly concerned by the cost of care.

eWe noted an increase in the proportion of end-of-life decisions initiated by the patient's close family or the non-physician personnel (nurses, nurses' aids). Several studies assessing the collegial nature of decisions to forego life-sustaining therapy mention the lack of communication and interaction between the caregivers and the patients' close family members when discussing the patient's future [START_REF] Baggs | The association between interdisciplinary collaboration and patient outcomes in a medical intensive care unit[END_REF][START_REF] Fagin | Collaboration between nurses and physicians: no longer a choice[END_REF][START_REF] Gramelspacher | Perceptions of ethical problems by nurses and doctors[END_REF]. Indeed, Stricker et al highlighted the need for improved emotional support, coordination of care and communication in their study of family satisfaction among the relatives of 996 Swiss ICU patients [START_REF] Antonelli | Year in review in Intensive Care Medicine 2009. Part III: mechanical ventilation, acute lung injury and respiratory distress syndrome, pediatrics, ethics, and miscellanea[END_REF][START_REF] Stricker | Family satisfaction in the intensive care unit: what makes the difference?[END_REF]. Therefore, it is of particular importance to have an intensive communication strategy involving all staff members as well as the patient's family and/or appointed surrogates. Contrary to reports that nurses are not sufficiently involved in end-of-life decisions [START_REF] Ferrand | Withholding and withdrawal of life support in intensive-care units in France: a prospective survey. French LATAREA Group[END_REF][START_REF] Pochard | French intensivists do not apply American recommendations regarding decisions to forgo life-sustaining therapy[END_REF][START_REF]A controlled trial to improve care for seriously ill hospitalized patients. The study to understand prognoses and preferences for outcomes and risks of treatments (SUPPORT). The SUPPORT Principal Investigators[END_REF][START_REF] Truog | Recommendations for end-of-life care in the intensive care unit: The Ethics Committee of the Society of Critical Care Medicine[END_REF][START_REF] Stevens | Education, ethics, and end-of-life decisions in the intensive care unit[END_REF][START_REF] Cook | Life support in the intensive care unit: a qualitative investigation of technological purposes. Canadian Critical Care Trials Group[END_REF][START_REF] Asch | Decisions to limit or continue lifesustaining treatment by critical care physicians in the United States: conflicts between physicians' practices and patients' wishes[END_REF][START_REF] Ferrand | Decision-making capacity and surrogate designation in French ICU patients[END_REF][START_REF] Sprung | Worldwide similarities and differences in the foregoing of life-sustaining treatments[END_REF][START_REF] Vincent | European attitudes towards ethical problems in intensive care medicine: results of an ethical questionnaire[END_REF][START_REF] Stanley | The Appleton International Conference: Developing guidelines for decisions to forgo life-prolonging medical treatment --Preamble, Parts I, II, III, and IV[END_REF][32][START_REF]Withholding and withdrawing life-sustaining therapy. This Official Statement of the American Thoracic Society was adopted by the ATS Board of Directors, March 1991[END_REF][START_REF] Mitchell | American Association of Critical-Care Nurses Demonstration Project: profile of excellence in critical care nursing[END_REF], we observed in our study that the intensive communication helped to increase the participation of nursing staff. Indeed, Ferrand et al previously reported that nurses often cited emotional distress as a source of dissatisfaction [START_REF] Ferrand | Discrepancies between perceptions by physicians and nursing staff of intensive care unit end-of-life decisions[END_REF], whereas in our study, the greater implication of nurses in the end-of-life decision-making process may have helped them to avoid this moral distress through greater communication.

The intensive communication strategy introduced in our department made it possible to identify at an earlier stage patients who were likely to later have withholding or withdrawal of treatment. In view of the fact that there is a now a legal basis for such decisions, perhaps it has simply become easier to reach such decisions. Despite the improvements achieved with an intensive communication strategy in our department after the new French legislation on end-of-life patient rights, there are undoubtedly several areas where there is still room for further progress. Many patients do not have officially appointed surrogates or proxies, and the level of communication regarding this possibility could likely be improved. Secondly, external consultants are often just consulted by telephone. More active involvement in grand rounds or interprofessional meetings could help to yield a more positive contribution from outside experts. Third, while the new law lays down good principles for end-of-life care, these dispositions are of little use and impossible to put into application if the whole medical and non-physician staff is not sufficiently aware and involved. Thus, regular training and constant communication are necessary, as well as psychological support. End-of-life care should be seen as extending beyond the patient to include the patient's family, and is not simply a question of treating a specific disease.

Limitations

This was a single-centre study, including mainly medical patients (90%). Thus, our results may not be extrapolated to all ICU populations, or multiple centres, as it would be difficult to obtain uniform practices. Secondly, data from period 1 were retrospective, and there were probably missing data or insufficiently exploited files. Thirdly, decisions to withhold or withdraw treatment were not generally made during the night or during the weekend, because of the absence of sufficient staff to guarantee the collegial decision-making procedures. e Fourthly, the person who initiated the decision-making process regarding endof-life options can be difficult to identify, particularly in period 1, where notations in the medical file were less frequent and less detailed. e Fifth, our strategy of intensive communication was developed as a policy in the department and is not necessarily replicable in other departments. In addition, it is not possible to conclude that the changes observed in our practices were due solely to the introduction of the new legislation. e Sixth, since the ICU capacity increased between periods, there is a possibility that the patient profile changed between periods. Lastly, while doctors in France are not directly concerned by the cost of care, we cannot exclude that economical considerations due to limited resources may have influenced their decisions to withhold or withdraw therapy.

Conclusions

The new law of 2005 in France on patient rights at end-of-life has made it possible to introduce an active communication strategy regarding end-of-life decisions, with a true legal framework, probably limiting excessively burdensome treatment.

Intensive communication makes it possible to identify earlier patients who are likely to evolve towards WWT, which brings about quicker decision-making regarding end-of-life in the ICU.

We noted greater involvement of close family and nursing staff in initiating decisions relating to end-of-life. The new law has the advantage of providing a legal framework to free physicians of the burden of unguided decision-making in this difficult context.  Create a special "Ethics" section in every patient's medical record, accessible to all members of the caregiving team, to document all discussions and decisions relating to the level of therapeutic engagement  Organise debriefing for members of caregiving team to discuss emotionally stressful cases Both Withholding and withdrawal, no (%) # 68 [START_REF] Van Der | End-of-life decision-making in six European countries: descriptive study[END_REF] 102 [START_REF] Pochard | French intensivists do not apply American recommendations regarding decisions to forgo life-sustaining therapy[END_REF] 136 [START_REF] Fagin | Collaboration between nurses and physicians: no longer a choice[END_REF] 165 [START_REF] Fagin | Collaboration between nurses and physicians: no longer a choice[END_REF] 288 [START_REF] Ferrand | Discrepancies between perceptions by physicians and nursing staff of intensive care unit end-of-life decisions[END_REF] 247 [START_REF] Vincent | European attitudes towards ethical problems in intensive care medicine: results of an ethical questionnaire[END_REF] % Decisions to withhold or withdraw made in ICU 95 93 # p<0.05 for comparison between periods; all other patients died with full support.

IQR, Interquartile range.

Table 3. Time delay between admission and initiation of end-of-life decision-making process, actual decision to withhold or withdraw therapy, and death in ICU or in-hospital in the two study periods.

  April 2005, from January 2000-March 2005 (period 1), and after the law, from January 2006 to December 2009 (period 2). The institutional review board (Comité de Protection des Personnes, Dijon) approved the protocol.

Table 1 :

 1 Description of the elements comprising the intensive communication strategy regarding end-of-life decisions implemented in the intensive care unit according to the French law of 22 April 2005 Organisation: Introduce unrestricted visiting hours  Increase availability of the caregiving team to discuss clinical evolution and therapeutic engagement  Assign a meeting room specifically reserved for meetings with patients' families  Define fixed appointments with families for meetings, without interruptions (physicians' telephones switched off)  Apprise entire caregiving team of new communication strategy (defined below)  Implement continuing medical education training in end-of-life ethics before introduction of new communication strategy Communication: Daily meetings of the caregiving team and with the patient and/or their family to : o decide on the level of therapeutic engagement (according to diagnosis, prognosis, comorbidities, previous quality of life, life expectancy, patient's wishes as expressed either directly or indirectly through advance directives) o define modalities for withholding or withdrawing treatment, in accordance with the 2005 law, and initiate collegial procedure in concert with an outside expert o discuss options for use of pain and anxiety relieving medications.

Table 2 .

 2

	Median age [IQR] was 65 [53-78] in period 1 and 66 [54-78] in period 2. Median [IQR] SAPS
	II scores were respectively 65 [57-72] and 63 [54-75] in periods 1 and 2. Most admissions

Table 2 :

 2 Main characteristics of patients who died in ICU or in-hospital during the two study

	periods
	Variable

#

Withdrawal only, no (%) #

Table 6 :

 6 Use of morphine and midazolam during withholding or withdrawal of therapy in both periods.Totals exceed 100% as both drugs could be used in the same patient. *p<0.05 for comparison period 1 vs period 2 for the three categories

	#, Median, [IQR]	6 [3-9]	7 [3-10]	7 [4-10]	3 [2-6]	5 [2-7]	5 [2-7]
	Decision # , Median [IQR]	11 [7-15]	13 [7-18]	11 [8-16]	4 [2-7]	6 [3-8]	6 [3-8]
	Death in ICU # , Median [IQR]	15 [11-21]	14 [9-17]	13 [10-19]	8 [6-13]	7 [4-9]	7 [4-9]

Totals exceed 100% as more than one reason could be cited for each decision to withhold or withdraw therapy.


Jean-Pierre P Quenot

Jean-Philippe P Rigaud

Sébastien Prin

Saber Barbar

Arnaud Pavon

Mael Hamet

Nicolas Jacquiot

Bernard Blettery

Christian Hervé

Pierre Emmanuel Charles

PE Charles

G Moutel

Suffering among carers working in critical care can be reduced by an

Keywords: ethics, critical care organisation, communication

Introduction

Burn-out syndrome (BOS) among health professionals was first described in the 1970s, and corresponds to an inability to cope with emotional stress at work, or an excessive expenditure of energy accompanied by a feeling of failure and exhaustion [START_REF] Freudenberger | The issues of staff burnout in therapeutic communities[END_REF][START_REF] Maslach | Job burnout[END_REF][START_REF] Pines | Characteristics of staff burnout in mental health settings[END_REF]. The most common symptoms of BOS are fatigue, headaches, eating disorders, insomnia, irritability, emotional instability, and excessive rigidity in interpersonal relations.

Wide variations in symptoms of BOS have been reported in different categories of healthcare workers [START_REF] Blenkin | Stress in NHS consultants[END_REF][START_REF] Caplan | Stress, anxiety, and depression in hospital consultants, general practitioners, and senior health service managers[END_REF][START_REF] Coomber | Stress in UK intensive care unit doctors[END_REF], and it would appear that it is particularly frequent among doctors [START_REF] Embriaco | High level of burnout in intensivists: prevalence and associated factors[END_REF] and nurses [START_REF] Poncet | Burnout syndrome in critical care nursing staff[END_REF] in the setting of critical care. In one multicentre French study of 2,392 nurses [START_REF] Poncet | Burnout syndrome in critical care nursing staff[END_REF],

BOS was classified as severe in 33% of participants, and predictive factors included age, organisational factors (choice of days off…), communication problems with hierarchy (head nurse, doctors), a high number of end-of-life decisions and caring for dying patients. Factors protective against BOS included participation in ICU research groups, and good quality working relations. A similar study among doctors [START_REF] Embriaco | High level of burnout in intensivists: prevalence and associated factors[END_REF] reported a prevalence of severe BOS of 46.5%, and the predictive factors identified in this study were a heavy workload or conflicts with colleagues and/or nurses, whereas good relations with the caregiving team was a protective factor.

The consequences of BOS are manifold and can be harmful for both the caregiver themselves, and the patients, with decreased well-being of caregiving staff leading to diminished quality of care [START_REF] Shanafelt | Burnout and self-reported patient care in an internal medicine residency program[END_REF][START_REF] Thomas | Resident burnout[END_REF] and poor communication with patients and families [START_REF] Shanafelt | The well-being of physicians[END_REF], high societal costs related to absenteeism and high turnover rates [START_REF] Ackerman | Retention of critical care staff[END_REF]. BOS is often reported to have its basis in communication problems, particularly in end-of-life situations [START_REF] Ferrand | Discrepancies between perceptions by physicians and nursing staff of intensive care unit end-of-life decisions[END_REF][START_REF] Puntillo | Communication between physicians and nurses as a target for improving end-of-life care in the intensive care unit: challenges and opportunities for moving forward[END_REF], and we hypothesized that an improvement in communication could help to alleviate the symptoms and consequences of BOS.

Therefore, we performed a longitudinal, before-and-after, interventional study to investigate whether an intensive communication strategy regarding end-of-life practices would have an influence on the incidence of burn-out syndrome in healthcare workers in critical care.

The results of this study were presented in part at the annual congress of the European Society of Intensive Care Medicine, Barcelona, September 2010.

Methods

This monocentric study was performed over two periods, with an initial evaluation of BOS performed in early 2007 (period 1) before the implementation of the intensive communication strategy, and a second evaluation in the second semester 2009 (period 2). The institutional review board (Comité de Protection des Personnes, Dijon) approved the protocol and all participants gave informed consent.

All caregivers who agreed to participate received a questionnaire in a sealed envelope to be completed and returned anonymously to the lead investigator. No data were recorded on caregivers who declined to participate.

Between the 2 phases of the study, our healthcare team (physicians, nurses, nurses' aids, psychologist) developed an intensive strategy for communication regarding end-of-life practices in the intensive care unit (ICU). In a preliminary study [START_REF] Chahraoui | Psychological experience of health care professionals in intensive care unit: A qualitative and exploratory study[END_REF], clinical interviews were performed with caregivers by 2 hospital psychologists in order to identify the individual components of BOS and identify areas for intervention. The communication strategy was then developed from this preliminary study, based on the questions more frequently reported to arise in the context of end-of-life decisions in the critical care unit. The main objective of this strategy was to improve communication between the triad of caregivers, patients and patients' families, in the aim of alleviating stress for the caregivers. The communication strategy was phased into routine practice over a period of 6 months.

The communication strategy and related structural organisation within the department is described in Table 1. In addition, caregivers were encouraged to participate in working groups or brainstorming groups within the ICU with a view to improving delivery of care and management of conflicts. All staff also participated regularly in congresses and meetings to remain abreast of latest developments and improve quality of care. These two approaches (working groups, conference participation) were both innovative for our unit, where such outside activities were not previously common.

Data Collection

For all participating healthcare workers, we recorded the following data : age; sex; marital status; number of children; professional status (physician, nurse, nurse's aid); number of years in practice since qualification; number of years experience in critical care; working rhythm (days only, nights only, days and nights).

To evaluate BOS, we used the Maslach Burnout Inventory (MBI) and the Centre for Epidemiologic Studies Depression Scale (CES-D) to evaluate symptoms of depression.

The MBI is a 22-item questionnaire evaluating three domains of burnout, namely the emotional exhaustion subscale (9 items), assessing feelings of being emotionally overextended and exhausted by one's work; the depersonalization subscale (5 items), measuring an unfeeling and impersonal response toward recipients of one's service, care, or treatment; and a personal accomplishment subscale (8 items); assessing feelings of competence and successful achievement in one's work with people. The scoring method used was the standard scoring method suggested by the developers. Severe burnout was defined as a score >30 on the emotional exhaustion subscale, or a score >12 on the depersonalisation subscale, or a score <33 on the personal accomplishment subscale, or a high total score [START_REF] Embriaco | High level of burnout in intensivists: prevalence and associated factors[END_REF][START_REF] Poncet | Burnout syndrome in critical care nursing staff[END_REF][START_REF] Canouï | Le burn out: le syndrome d'épuisement professionel des soignants[END_REF].

The CES-D scale evaluates symptoms of depression through 20 questions that cover domains including self-deprecation, somatic problems, sadness, apathy and persecution) [17].

Statistical analysis

Quantitative variables are presented as median [Interquartile range] and categorical variables as number (percentage). Quantitative variables were compared using the Wilcoxon

Results

Among 62 healthcare workers employed in the critical care department of our University Hospital, 53 (85%) responded to both questionnaires (MBI and CES-D) in period 1, and 49 (79%) in period 2. No questionnaire was excluded because of missing data. The main characteristics of respondents in both periods are described in table 2. In both periods, the majority of respondents were nurses (29 (55%) nurses, 20 (38%) nurses' aids, 4 (7%) physicians in period 1; 27 (55%) nurses, 18 (37%) nurses' aids, 4 (8%) physicians in period 2). Median age [Interquartile range] was 27 [START_REF] Lert | Psychological stress among hospital doctors caring for HIV patients in the late nineties[END_REF][START_REF] Weibel | Work-related stress in an emergency medical dispatch center[END_REF][START_REF] Donchin | The hostile environment of the intensive care unit[END_REF][START_REF] Bakker | Burnout contagion among intensive care nurses[END_REF][START_REF] Guntupalli | Burnout in the internist--intensivist[END_REF][START_REF] Cathebras | Burn out among French general practitioners[END_REF][START_REF] Soupios | Stress on personnel working in a critical care unit[END_REF][30][31][32][33][34][35][36][37][38] in period 1 and 26 [START_REF] Nyssen | Occupational stress and burnout in anaesthesia[END_REF][START_REF] Lert | Psychological stress among hospital doctors caring for HIV patients in the late nineties[END_REF][START_REF] Weibel | Work-related stress in an emergency medical dispatch center[END_REF][START_REF] Donchin | The hostile environment of the intensive care unit[END_REF][START_REF] Bakker | Burnout contagion among intensive care nurses[END_REF][START_REF] Guntupalli | Burnout in the internist--intensivist[END_REF][START_REF] Cathebras | Burn out among French general practitioners[END_REF][START_REF] Soupios | Stress on personnel working in a critical care unit[END_REF][30][31][32][33][34][35][36][37][38] in period 2.

The majority of participants had <5 years experience in the ICU (33 (63%) in period 1 vs 32 (65%) in period 2).

The results of the MBI and CES-D questionnaires are presented in table 3. We observed a significant difference between periods in all three components of the MBI. MBI classified burnout as severe in 15 (28%) caregivers (9 nurses, 5 nurses' aids, 1 physician) in period 1, and in 7 (14%) in period 2 (4 nurses, 3 nurses' aids, 1 physician), p<0.01 (figure 1,panel A).

This corresponds to a reduction of 50% in the relative risk of BOS between periods. All respondents with a high CES-D score also presented severe BOS.

Symptoms of depression as evaluated by the CES-D were present in 9 (17%) caregivers in period 1 (6 nurses, 2 nurses' aids, 1 physician) vs 3 (6%) in period 2 (1 nurse, 1 nurse's aid, 1 physician), p<0.05 (figure 1, panel B). The difference in CES-D between periods was statistically significant, representing a reduction of approximately 60% in the relative risk.

There was no difference in overall mortality rate in the ICU between periods (21% mortality in the ICU in period 1 vs 23% in period 2, p = NS).

Discussion

The main finding of this study is that the implementation of an intensive communication strategy regarding end-of-life practices in the ICU was associated with a reduction in the relative risk of severe BOS by 50% as measured by the MBI, and a reduction the relative risk of depression by 60%, as evaluated by the CES-D. To the best of our knowledge, this is the first longitudinal, before-and-after study to evaluate the effects of interventions aiming to reduce burnout among ICU caregiving staff.

Wide variations in the prevalence of BOS in healthcare professionals have been reported across specialities, both in doctors [START_REF] Ramirez | Mental health of hospital consultants: the effects of stress and satisfaction at work[END_REF] and in nurses [START_REF] Lu | Job satisfaction among nurses: a literature review[END_REF]. The perceived workplace climate and workload have been shown to contribute to BOS [START_REF] Mcmanus | Stress, burnout and doctors' attitudes to work are determined by personality and learning style: a twelve year longitudinal study of UK medical graduates[END_REF]. Higher levels of severe BOS have been reported in oncologists [START_REF] Lyckholm | Dealing with stress, burnout, and grief in the practice of oncology[END_REF], anaesthesiologists [START_REF] Nyssen | Occupational stress and burnout in anaesthesia[END_REF], physicians caring for patients with AIDS [START_REF] Lert | Psychological stress among hospital doctors caring for HIV patients in the late nineties[END_REF], and physicians working in emergency departments [START_REF] Weibel | Work-related stress in an emergency medical dispatch center[END_REF].

ICUs are characterized by a high level of work-related stress [START_REF] Donchin | The hostile environment of the intensive care unit[END_REF], a factor known to increase the risk of BOS [START_REF] Bakker | Burnout contagion among intensive care nurses[END_REF]. Burn-out syndrome can be difficult to identify and recognise. The results of our study underline the importance of the MBI to evaluate the level of work-related stress and suffering among caregivers.

In a study concerning 253 members the Section of Internal Medicine of the Society of Critical Care Medicine, Guntupalli reported that among the MBI subscales, the average emotional exhaustion subscale score was 22.2± 9.5, average depersonalization score was 7.1± 5.1, and average personal accomplishment score was 30.9± 6.4 [START_REF] Guntupalli | Burnout in the internist--intensivist[END_REF]. In our study, the average value on all these subscales was higher, regardless of the study period under consideration,

showing that although the level of stress may have been higher in our cohort, this was compensated by a greater feeling of personal achievement. This could explain why some caregivers continue to work in this stressful environment.

In a French study concerning 306 general practitioners, the emotional exhaustion subscale score was 21.9± 12.4, the depersonalization score was 9.1±6.7, and the personal achievement score was 38.7±7.1 [START_REF] Cathebras | Burn out among French general practitioners[END_REF]. These figures are similar to those observed in our study on the latter two scales, whereas the mean emotional exhaustion observed in our study was considerably higher, perhaps related to the high number of stressful end-of-life situations encountered in critical care.

Almost one-half of intensivists presented a high level of BOS in the one-day study in a sample of French ICUs performed by Embriaco et al [START_REF] Embriaco | High level of burnout in intensivists: prevalence and associated factors[END_REF], and one third of nursing staff had severe BOS in a similar study by Poncet [START_REF] Poncet | Burnout syndrome in critical care nursing staff[END_REF]. In our study, the low number of participating physicians precludes any formal conclusions regarding the prevalence of BOS among this category of healthcare worker, although we did observe BOS among 28% of nursing staff.

These results highlight how the ICU is a highly stressful work environment and may, therefore, be associated with a high rate of BOS in staff members [START_REF] Donchin | The hostile environment of the intensive care unit[END_REF][START_REF] Soupios | Stress on personnel working in a critical care unit[END_REF].

Based on the predictive factors of BOS in critical care previously identified in the literature [START_REF] Embriaco | High level of burnout in intensivists: prevalence and associated factors[END_REF][START_REF] Poncet | Burnout syndrome in critical care nursing staff[END_REF], such as organisational factors, communication problems in end-of-life situations, and conflicts in the workplace, we developed a BOS prevention programme by introducing a detailed strategy of intensive communication. In a preliminary study [START_REF] Chahraoui | Psychological experience of health care professionals in intensive care unit: A qualitative and exploratory study[END_REF], clinical interviews were performed with caregivers by 2 hospital psychologists in order to identify the individual components of BOS in our department, and based on the feedback from these interviews, it became clear that three main areas were suitable for intervention. The first objective was to reduce, as much as possible, the « stressors » in the working environment, in both organisational and institutional terms. We attempted to improve the integration of the workplace organisation with personal organisation (such as work schedules and family commitments), improve communication between the caregiving team, foster a climate of confidence, ensure that the hierarchical superiors were available to listen and be consulted, and to improve manifestations of gratitude on the part of our institution. The second main axis of our communication strategy was focused on each individual, and personal strategies for coping. The death of a young patient, or patients with whom the staff member had considerable personal or emotional investment, strong identification with patients or their close family, accompanying families in difficult times, and the rapport with the patient's body were just some of the points raised by the caregiving staff. In this context, the support of staff psychologists is extremely helpful for all the staff of the ICU.

Psychological adjustments for the most difficult situations helped each staff member, according to their personality, to adapt their defence strategies in order to better deal with such situations, thus reducing the ensuing stress.

The third and final orientation of our intensive communication strategy was a collective, multidisciplinary approach. The suffering of the ICU caregivers is at the crossroads of a range of areas for reflection in medical, psychological, ethical, social and ergonomic terms.

When caregivers are questioned about sources contributing to their suffering, initial responses relating to the volume of work and under-staffing rapidly give way to more philosophical questions about the overall meaning of their work, hopeless therapeutic cases, ethical questions on end-of-life matters, and quality of life. This reflection on the meaning of care was given particular attention in our department, so that the suffering endured by both caregivers and patients and their families would be given precedence. Giving greater meaning to the work of the caregivers may have contributed to the increased level of personal accomplishment observed in our study, as measured on the MBI subscale. The implementation of this active communication strategy made it possible to significantly reduce both the number of caregivers with BOS, as measured by the emotional exhaustion and depersonalization subscales of the MBI, but also to significantly increase the feeling of personal achievement.

Several perspectives exist that have the potential to improve BOS, and we tried to implement these to the best of our ability. The following are just some examples:  Improving communication within the triad of the caregiving team, the patient and the patient's family. This requires constant effort on a 24/7 basis.

 Orienting care towards the patient as a person, without any judgement or prejudice.

 Facilitating access to physicians for patients' families, and reception of families within the department, to demystify the caregiving activity in the ICU and help involve the family in the care of their relative.

 Developing palliative care, with dedicated reference personnel within the ICU.

 Improving psychological management for all concerned (i.e. caregivers, patients, families), with ICU-based psychologists.

 Widening the scope for continuing medical education and training for the caregiving staff, oriented towards ethics of care and end-of-life practices.

 Implementing standardised protocols and guidelines to be reviewed regularly by audits, in order to standardise quality of care. Random samples of patient files are regularly monitored within our hospital to verify the completeness of documentation as regards end-of-life practices, as required in the framework of a new programme for the evaluation of professional practices introduced into French legislation in 2004.

Strengths and Weaknesses of the Study

One of the main strong points of this study was the high level of participation among the staff in both periods. The project was strongly supported and even solicited by the staff members.

The communication strategy was developed after interviews between the staff members and psychologists, and after several training courses in end-of-life ethics. Furthermore, there was very little turnover in the staff between periods, with 95% of all staff members present in both periods. We aimed in particular to work on preventive strategies for BOS (such as debriefing and psychological coping strategies for difficult situations) rather than curative measures.

Conversely, the limitations of this work include the fact that it was a monocentric study with a small sample size. In particular, the observation that nurses presented more frequently with 13 BOS or depression than doctors is likely due to the low number of participating physicians as compared to nurses. We did not evaluate predictive factors for BOS in our population. Other confounding factors could have influenced our results, since the study took place over a period of 2 years, and we cannot exclude that other changes in work conditions may have occurred during this time, independently of our study measures. Similarly, symptoms of burnout may have changed over time without any relation to the intervention under study. We evaluated the level of suffering as measured by burn-out and depression, although these two measures alone are likely insufficient to fully apprehend professional suffering. Further investigations are warranted to explore more fully all the factors that comprise suffering in the workplace. Lastly, it should be noted that the same population was studied in both study periods, thus the results are not independent.

Conclusions

The implementation of an active, intensive communication strategy regarding end-of-life care in the ICU was associated with a reduction in the rate of burn-out syndrome and depression among a stable population of healthcare professionals. These preliminary data warrant confirmation in a larger population. o define modalities for withholding or withdrawing treatment, in accordance with the 2005 law, and initiate collegial procedure in concert with an outside expert o discuss palliative care options  Create a special "Ethics" section in every patient's medical record, accessible to all members of the team, to document all discussions and decisions relating to the level of therapeutic engagement  Organise debriefing for members of caregiving team to discuss emotionally stressful cases  Role-playing and round-table discussions about conflict prevention

Table 1 :

 1 Description of the elements comprising the intensive communication strategy regarding end-of-life practices implemented in the intensive care unit Organisation: Introduce unrestricted visiting hours  Increase availability of the caregiving team to discuss clinical evolution and therapeutic engagement  Assign a meeting room specifically reserved for meetings with patients' families  Define fixed appointments with families for meetings, without interruptions (physicians' telephones switched off)  Apprise entire caregiving team of new communication strategy (defined below)  Implement continuing medical education training in end-of-life ethics before introduction of new communication strategy  Availability of a staff psychologist for consultation on demand. Communication: Daily meetings of the caregiving team and with the patient and/or their family to : o decide on the level of therapeutic engagement (according to diagnosis, prognosis, comorbidities, previous quality of life, life expectancy, patient's wishes as expressed either directly or indirectly through advance directives)

Figure 1 :

 1 Figure 1: Number of physicians, nurses and nurses' aids with a high score on the Maslach

Table 2 .

 2 Characteristics of respondents in both study periods

	Variable

Table 3 :

 3 Results of the Maslach Burnout Inventory and CES-D in both periods

	Period 1	Period 2	P
	(n=53)	(n=49)

test and categorical data with the Chi square test or Fisher's exact test as appropriate. All tests were two-tailed and a p-value <0.05 was considered statistically significant. All analyses were performed using SAS version 9.1 (SAS Institute, Cary, NC, USA).


Romain Rieger

Ridha Hambli
email: ridha.hambli@univ-orleans.fr

Rachid Jennane

Modeling of biological doses and mechanical effects on bone transduction

Keywords: Osteocytes, Shear stress, Ca-PTH, NO, PGE 2 Active sensing osteocytes number Active osteocblasts number Active osteoclasts number. Ca Calcium level PTH

Shear stress, hormones like parathyroid and mineral elements like calcium mediate the amplitude of stimulus signal which affects the rate of bone remodeling. The current study investigates the theoretical effects of different metabolic doses in stimulus signal level on bone. The model was built considering the osteocyte as the sensing center mediated by coupled mechanical shear stress and some biological factors. The proposed enhanced model was developed based on previously published works dealing with different aspects of bone transduction. It describes the effects of physiological doses variations of Calcium, Parathyroid Hormone, Nitric Oxide and Prostaglandin E2 on the stimulus level sensed by osteocytes in response to applied shear stress generated by interstitial fluid flow. We retained the metabolic factors (Parathyroid Hormone, Nitric Oxide, and Prostaglandin E2) as parameters of bone cell mechanosensitivity because stimulation/inhibition of induced pathways stimulates osteogenic response in vivo. We then tested the model response in term of stimulus signal variation versus the biological factors doses to external mechanical stimuli. Despite the limitations of the model, it is consistent and has physiological bases. Biological inputs are histologically measurable.

This makes the model amenable to experimental verification.

Introduction

It is well admitted that mechanical strain is one of the main stimulus triggering bone remodeling.

Bone adaptation to its environment is influenced by both mechanical and biological stimuli [START_REF] Feskanich | Calcium, vitamin D, milk consumption, and hip fractures: a prospective study among postmenopausal women[END_REF][START_REF] Goltzman | Interactions of PTH and PTHrP with the PTH/PTHrP Receptor and with Downstream Signaling Pathways: Exceptions That Provide the Rules[END_REF][START_REF] Heldring | Estrogen Receptors: How Do They Signal and What Are Their Targets[END_REF]. Fluid flow imposes a shear stress on osteocytes that appears to deform the cells [START_REF] Weinbaum | A model for the excitation of osteocytes by mechanical loading-induced bone fluid shear stresses[END_REF]. [START_REF] Bonewald | Osteocytes, mechanosensing and Wnt signaling[END_REF] rewieved a cascades of transduction events into the osteocyte as a response to mechanical loading. Important signaling molecules like Nitric Oxide (NO) and Prostaglandin E2 (PGE 2 ) influencing bone remodeling homeostasis have been shown to be produced in the osteocyte in response to fluid flow. [START_REF] Weinbaum | A model for the excitation of osteocytes by mechanical loading-induced bone fluid shear stresses[END_REF] were one of the first to propose a theoretical model to predict the fluid shear stress and streaming potential at the surface of osteocytic process in the lacunocanalicular porosity. [START_REF] Lemaire | Multiscale analysis of the coupled effects governing the movement of interstitial fluid in cortical bone[END_REF] enhanced the model of Zeng by including mass flux. [START_REF] Lemaire | Multiscale analysis of the coupled effects governing the movement of interstitial fluid in cortical bone[END_REF] developed a more complex model based on the idea that the motion of interstitial fluid is caused by a combination of mechanical strain, electro-osmotic and osmotic actions.

Few numerical studies modeling the load-induced fluid flow have been developed [START_REF] Goulet | Influence of cortical canal architecture on lacunocanalicular pore pressure and fluid flow[END_REF][START_REF] Gururaja | Modeling Deformation-Induced Fluid Flow in Cortical Bone's Canalicular-Lacunar System[END_REF][START_REF] Steck | Fluid flow through anisotropic, poroelastic bone models in the opposite direction to that through analogous models[END_REF][START_REF] Swan | Micromechanically Based Poroelastic Modeling of Fluid Flow in Haversian Bone[END_REF]. Some other theoretical and numerical studies have been performed considering the osteocyte's tissue strain amplification [START_REF] Han | Mechanotransduction and strain amplification in osteocyte cell processes[END_REF][START_REF] Rathbonivtch | Tissue strain amplification at the osteocyte lacuna: A microstructural finite element analysis[END_REF] or the integrin function on the mechanosensation process [START_REF] Wang | A model for the role of integrins in flow induced mechanotransduction in osteocytes[END_REF][START_REF] Weinbaum | Mechanotransduction and flow across the endothelial glycocalyx[END_REF].

Recently, Adachi et al., (2010) Some studies have attempted to explore the effect of metabolic doses regarding bone remodeling or bone diseases in numerical models. [START_REF] Maldonado | Mathematical modeling and analysis of force induced bone growth[END_REF] has developed a formulation of the production of NO and PGE 2 by the osteocyte and a description of the evolution of the osteocyte cell population. The osteocyte rate growth was expressed as a function of the number of osteoblasts (some osteoblasts differentiate into osteocytes) and a fluid shear stress function (mechanical loading is involving on osteocyte viability).

Recently, enhanced mathematical model was developed by [START_REF] Peterson | A physiologically based mathematical model of integrated calcium homeostasis and bone remodeling[END_REF] to describe the bone and Calcium-Parathyroid Hormone (Ca-PTH) homeostasis. [START_REF] Komarova | Mathematical Model of Paracrine Interactions between Osteoclasts and Osteoblasts Predicts Anabolic Action of Parathyroid Hormone on Bone[END_REF] have developed a theoretical model describing the autocrine and paracrine factors which are involved in the Bone Multicellular Units (BMUs) autoregulation composed of osteoblast and osteoclast. In this work the authors studied the influence of pulsatile PTH therapy on those autocrine and paracrine factors to induce bone formation. [START_REF] Lemaire | Modeling the interactions between osteoblast and osteoclast activities in bone remodeling[END_REF] have developed a more dynamic BMUs interaction model and investigated the effects on bone remodeling of the different biological factor such as Osteoprotegerin (OPG) or Transforming Growth Factor β (TGF-β). Some others have investigated the effect of mechanical stimulus on bone remodeling without considering the metabolic factor effects [START_REF] Hambli | Multiscale methodology for bone remodelling simulation using coupled finite element and neural network computation[END_REF][START_REF] Hambli | Strain-damage coupled algorithm for cancellous bone mechano-regulation with spatial function influence[END_REF][START_REF] Mcnamara | Bone remodelling algorithms incorporating both strain and microdamage stimuli[END_REF][START_REF] Scott | A mechanistic model for internal bone remodeling exhibits different dynamic responses in disuse and overload[END_REF].

Despite of the large number of studies dealing with bone mechanotransduction, there is still a lack of mechanobiological models combining in a unified way the most observed mechanical and biological mechanisms during transduction phase on bone [START_REF] Rieger | A mechanobiological transduction model for bone remodelling[END_REF]. Such models are very useful to enhance bone remodeling predictions based on -biophysical‖ description rather than phenomenological ones.

Materials and methods

Concepts of bone transduction

A summary of the previous discussed components is presented in table 1. The integrin senses the amount of Ca and regulates PTH. In the same manner the integrin produces NO, PGE 2 and a mechanical stimulus due to fluid flow. All those components are organized into mechanical and biological normalized signals and then summed up into a full mechanobiological stimulus.

Table 1

Proposition of a transduction model

Based on Oesterhelt (2010) transduction concept combined with [START_REF] Bonewald | Osteocytes, mechanosensing and Wnt signaling[END_REF] we propose the following general block diagram representing the osteocyte transduction phase (Fig. 1): Figure 1

Mathematical description

The proposed model is based on the idea that the osteocyte is the operating center which generates the interaction between both mechanical stimulus and biological factors.

After combining both stimuli (mechanical and biological), the osteocyte triggers the signal to active BMUs to form or resorb bone.

For the signaling phase we consider the fluid flow velocity in the canaliculi due to mechanical pressure proposed by [START_REF] Lemaire | Multiscale analysis of the coupled effects governing the movement of interstitial fluid in cortical bone[END_REF]. They concluded that the fluid The biological signaling part is assumed to be triggered by Ca demands. The Ca level is considered as an input in the model (equ.

(2) which leads to PTH release .

To describe the mathematical relation between PTH release rate and level o f Ca, we propose a fitted model obtained by experiments [START_REF] Haden | The effects of age and gender on parathyroid hormone dynamics[END_REF][START_REF] Houillier | Le récepteur du calcium : un rôle central dans le métabolisme calcique[END_REF] expressed by equation ( 3) exhibiting a sigmoidale relation.

The reception phase is expressed by the fluid velocity (equ. ( 4)) where and the release of NO and PGE 2 (equ.

(5-6)), from the integrin.

The NO and PGE 2 rates growth [START_REF] Maldonado | Mathematical modeling and analysis of force induced bone growth[END_REF] depends on a fluid shear stress function (equ. 7) applied to osteocytes. If NO evolution is purely stimulated by the fluid shear stress function, PGE 2 are also dependant of the NO evolution and then the coupling is expressed in equation ( 6).

Osteocyte detects the concentration of Ca through PTH [START_REF] Langub | Parathyroid Hormone/Parathyroid Hormone-Related Peptide Type 1 Receptor in Human Bone[END_REF][START_REF] Teti | Do osteocytes contribute to bone mineral homeostasis? Osteocytic osteolysis revisited[END_REF] and responses to the fluid shear stress. Thus the Osteocyte population growth developed by [START_REF] Maldonado | Mathematical modeling and analysis of force induced bone growth[END_REF] of the digging hole and the movement of the BMUs across the bone surface. This model is biochemically more complex than the one from [START_REF] Komarova | Mathematical model predicts a critical role for osteoclast autocrine regulation in the control of bone remodeling[END_REF] and is more suited for visual bone remodeling evolution.

In order to investigate the potential in our approach to model the coupling effects on the transduction signal, the model of [START_REF] Komarova | Mathematical model predicts a critical role for osteoclast autocrine regulation in the control of bone remodeling[END_REF] has been retained here for its simplicity in the autocrine and paracrine factors description which allows us to focus on the effects of the transduction mechanism.

The integration and amplification phase ensures a normalized signals variations between 0% and 100% of their maximum expressed by the relation , (equ. 11-14). It enables to leave aside dimensional consideration of the variables since we combine mechanical dimension (MPa) and biological concentration (mM) [START_REF] Brazel | Dimensionless analysis of swelling of hydrophilic glassy polymers with subsequent drug release from relaxing structures[END_REF][START_REF] Coatanéa | Applying dimensionless indicators for the analysis of multiple constraints and compound objectives in conceptual design[END_REF][START_REF] Coatanéa | Applying dimensionless indicators for the analysis of multiple constraints and compound objectives in conceptual design[END_REF].

Finally, the mechanical and the biological signals are weighted and summed up (equ.

15-17) to generate a normalized stimulus function as a signal (varying between 0% and 100%) mediated by the biological factors (equ. 17).

, i= Mecha, Bio, MB, PTH, NO, PGE 2 : are mechanical and biological weight factors verifying: and .

Table 2 Table 3

Results

We have modeled and investigated the main important phenomena of bone transduction in a mechanical and biological point of view. The influence of metabolic doses on stimulus level has been explored in order to investigate their sensitivity on the mechanobiological stimulus. The following figures show the ability of the model to interpret mechanical effects due to bony fluid flow through the lacunocanalicular system and/or different biological effects due to the virtual injection or the basal production of different messengers such as NO and PGE 2 .

If mechanical effect is the most influenced part in bone remodeling it is also highly dependent on the biological components considered as a regulating factor. Figure 2 Figure 3 It is well known that NO and PGE 2 have an important role in bone remodeling regulation [START_REF] Brandi | Bidirectional regulation of osteoclast function by nitric oxide synthase isoforms[END_REF][START_REF] Pilbeam | Prostaglandins and Bone Metabolism[END_REF][START_REF] Wimalawansa | Skeletal Effects of Nitric Oxide: Novel Agent for Osteoporosis[END_REF]. One can notice that fluid flow gradually increases the production o f NO and PGE 2 , which results in a higher stimulus. Although this stimulus can be increased or decreased at some specific magnitude Our model incorporates the effects of the bone matrix damage. Fluid velocity is obtained by Darcy's law and is weighted by the term . The damage considered here is due to the presence of microcracks into the bone which leads to an alteration of the osteocyte's communication (Burger and K lein-Nulend, 1999;[START_REF] Prendergast | Microdamage and Osteocyte-Lacuna Strain in Bone: A Microstructural Finite Element Analysis[END_REF]. Figure 5 The disrupted communication between osteocytes increases as the damage on the lacunocanalicular network increases. This can be represented by a leakage of the bony fluid contained in the canaliculi. So the proportionality between the fluid flow and the deformation applied onto the bone is altered and the resulted signal does not match properly with the expected information. This non-proportionality is expressed by the modification of the stimulus' magnitude.

Instead

Discussion

The work presented here is an attempt to develop a dose dependent integrated transduction model incorporating both mechanical and biological reactions. The idea has arisen from the observation that actual transduction model are only based on mechanical stress neglecting the biological effects.

The current model predicts the influence of Ca concentration on the magnitude of the mechanobiological stimulus. The concentration of Ca can be a regulating factor for the stimulus increase. Low level of Ca induces an important release of PTH [START_REF] Houillier | Le récepteur du calcium : un rôle central dans le métabolisme calcique[END_REF] which stimulates bone resorption in order to deliver Ca from the bone to restore falling plasma Ca. This effect leads to a reduced level of the stimulus. On the opposite high concentration of Ca diminishes the release of PTH and as a consequence, it stimulates bone formation. This is consistent with the work of [START_REF] Chen | Strain differences in bone density and calcium metabolism between c3h/hej and c57bl/6j mice[END_REF] who have shown that there was a progressive increase in the PTH secretion as dietary Ca level decreased which would favor Ca mobilization from bone.

Experimental [START_REF] Bakker | The production of nitric oxide and prostaglandin E2 by primary bone cells is shear stress dependent[END_REF][START_REF] Klein-Nulend | Mechanobiology of bone tissue[END_REF][START_REF] Pitsillides | Mechanical strain-induced NO production by bone cells: a possible role in adaptive bone (re)modeling?[END_REF] and numerical [START_REF] Mcgarry | A comparison of strain and fluid shear stress in stimulating bone cell responses a computational and experimental study[END_REF] Other studies have proven the importance and the benefit of non-mechanical agent to enhance mechanical loading [START_REF] Jee | The benefit of combining non-mechanical agents with mechanical loading: a perspective based on the Utah Paradigm of Skeletal Physiology[END_REF]. This confirms the regulating role of biological messengers which inhibit the action of mechanical loading or improve bone adaptation responsiveness. Their action can be easily illustrated in some hormonal bone diseases by submitting patients onto drugs administration (mainly non-mechanical agents such as estrogen or growth hormone). The threshold values are then moved in order to improve mechanical loading effects.

Nevertheless, the model presents some limitations and simplifications. First, the mechanotransduction process is much more complex than the one described in this paper. Second, our model does not consider the pulsatile and the continuous injection of PTH. Many studies suggest an anabolic effect of PTH for pulsated injection [START_REF] Komarova | Mathematical Model of Paracrine Interactions between Osteoclasts and Osteoblasts Predicts Anabolic Action of Parathyroid Hormone on Bone[END_REF][START_REF] Kousteni | The cell biology of parathyroid hormone in osteoblasts[END_REF] and catabolic one for continuous injection. An extended version of the model could incorporate the pulsatile/continuous PTH dosing [START_REF] Potter | Response to continuous and pulsatile PTH dosing: A mathematical model for parathyroid hormone receptor kinetics[END_REF].

Experiments are required to further study the many parameters required for the model and the effects of biological factors dosing the mechanobiological stimulus. Further investigation of the molecular basis of mechanotransduction on bone physiology and disease is needed to confirm that the mechanobiological model can provide realistic predictions.

In spite of these limitations the model can predicts a plausible mechanobiological stimulus consistent with experimental, clinical and numerical observations. Moreover it is easily updatable regarding the block diagram architecture.

In conclusion two perspectives arise from this work. First of all we are going to link this work with a model of BMUs in order to define a complete bone remodeling algorithm [START_REF] Rieger | A mechanobiological transduction model for bone remodelling[END_REF]. Then the whole model will be implemented into finite element code in order to predict bone quality evolution for specific patients and to estimate the necessity of putting them under drugs medication.

(3)

(6) (7) (8) (5)
(10) [START_REF] Maldonado | Mathematical modeling and analysis of force induced bone growth[END_REF][START_REF] Maldonado | Mathematical modeling and analysis of force induced bone growth[END_REF][START_REF] Maldonado | Mathematical modeling and analysis of force induced bone growth[END_REF]Calc. based on Maldonado et al., 2006Calc. based on Maldonado et al., 2006[START_REF] Komarova | Mathematical model predicts a critical role for osteoclast autocrine regulation in the control of bone remodeling[END_REF]-Parfitt 1977 Osteoblasts 200 cells 3.e0 cell.day [START_REF] Komarova | Mathematical model predicts a critical role for osteoclast autocrine regulation in the control of bone remodeling[END_REF]-Parfitt 1977[START_REF] Komarova | Mathematical model predicts a critical role for osteoclast autocrine regulation in the control of bone remodeling[END_REF][START_REF] Komarova | Mathematical model predicts a critical role for osteoclast autocrine regulation in the control of bone remodeling[END_REF][START_REF] Komarova | Mathematical model predicts a critical role for osteoclast autocrine regulation in the control of bone remodeling[END_REF][START_REF] Komarova | Mathematical model predicts a critical role for osteoclast autocrine regulation in the control of bone remodeling[END_REF] Osteoclasts 20 cells 4.e0 cell.day [START_REF] Komarova | Mathematical model predicts a critical role for osteoclast autocrine regulation in the control of bone remodeling[END_REF]-Parfitt 1977[START_REF] Komarova | Mathematical model predicts a critical role for osteoclast autocrine regulation in the control of bone remodeling[END_REF][START_REF] Komarova | Mathematical model predicts a critical role for osteoclast autocrine regulation in the control of bone remodeling[END_REF][START_REF] Komarova | Mathematical model predicts a critical role for osteoclast autocrine regulation in the control of bone remodeling[END_REF][START_REF] Komarova | Mathematical model predicts a critical role for osteoclast autocrine regulation in the control of bone remodeling[END_REF]

  developed a bone remodeling finite element model based on a stimulus function expressed in term o f fluid flow in the lacunocanalicular system. The limitations of this work it that the model neglects the coupling effects with the main biological mechanisms. No biological entities were considered and the bone adaptation is purely triggered by mechanical stimulus.

  Oesterhelt (2010), proposed a general framework to describe the transduction concept based on four steps. (i) Reception of the external signals as inputs (mechanical and biological). Signals can be stimulatory or inhibitory; (ii) Integration (combination) of the signals (iii); Amplification of the signals as outputs (iv); Signals sent to the specific target. Following the transduction concept proposed by Oesterhelt (2010) the current study attempts to investigate the effect of doses in transduction signal based on a plausible theoretical model. Several physiological factors can mediate the transduction. In the present work, we retained Ca, PTH, NO and PGE 2 factors as parameters of the model because those metabolic factors are known to stimulate/inhibit osteogenic response in vivo.

  movement (equ. (1)) generated by pressure gradient is the most important driving effect in fluid flow since it accounts for 95%. The term    D  1 was added to Darcy's law to incorporate the bone matrix damage (D) where  is a damage exponent that defines the sensitivity of the damage in the fluid velocity.

  has been enhanced and is expressed by equation (8). It is directly affected by the osteoblasts population and the osteocytes. Komarova et al., 2003 developed a model describing the BMUs population dynamics (equ. 9, 10). It includes osteoblasts , osteoclasts and considers an auto-regulation between these two types of cells. Indeed the autocrine and paracrine factors are phenomenological modeled as a rate coefficient by an exponent in the model. Insulin-like Growth Factor (IGF) (g22) and Transforming Growth factor Beta (TGF-β) (g11) are autocrine factor stimulating osteoblasts and osteoclasts respectively. Whereas for the stimulation of osteoblasts the paracrine factor is modeled by an exponent (g12) representing IGF and TGF-β actions. Regarding osteoclasts the paracrine stimulation takes effects trough the exponent (g21) modeling Receptor Activator of Nuclear factor κB Ligand (RANKL) and Osteoprotegerin (OPG) actions. Ryser et al., (2009) developed a model describing the evolution of a single BMU taking into account dynamic biochemical factors such as RANKL and OPG driving osteoblasts and osteoclasts evolution. Moreover it describes temporal and spatial features

  shows the evolution of the stimulus versus of the Ca concentration for different magnitudes of the fluid flow.

Figure 2

 2 Figure 2

  of fluid flow by considering a virtual injection of continuous controlled dose (0.37 & 0.2 for the square curve; 1.6 & 0.2 for the circle curve; 1.6 & 0.85 for the triangle curve respectively for NO and PGE 2[pM]) in a specific area. By doing so the model is able to magnify or to reduce NO and PGE 2 effects in the integral domain of influence. The model is considered as dose dependent because it enables the stimulus to be adjusted by the amount of NO and PGE 2 injected or auto regulated.Since this is an original work, there is no comparable study which allows us to calibrate the appropriate values of the weighting-factors. Thus we propose two different configurations of the stimulus equations which represent the possibility of the model to match with the large adaptability of any biological system. Figure4exhibits the stimulus' responses to different combinations of weighting-factors. In fact we propose in the first case to express the stimulus to be equally responsive to the mechanical and biological part. This is expressed by assigning a weighting-factors of 0.5 (filled solid curves). In the second case the stimulus is more influenced by the biological component which is expressed by weighting by 0.8 (open dashed curves). Moreover for the second case we consider the effect of NO and PGE 2 to be more influencing than the PTH, which is represented by weighting by 0.8.

Figure 4 For

 4 Figure 4

  of an open/close communication relation we shall consider here the possibility of some degradation of the signals sent trough the lacunocanalicular network. So when the damage increases it reduces the magnitude of the mechanical signal sent to the osteocytes. The figure 5 depicts the influence of the level of damage in the mechanobiological stimulus for basal physiological evolution of NO and PGE 2 .

  studies have shown NO and PGE 2 to be increased when fluid flow grows which confirms the results of the model for two reasons. Firstly we can observe the increase of NO and PGE 2 as the fluid flow magnifies. Secondly the stimulus is amplified as the amount of NO and PGE 2 increase. Based on the work of Maldonado (2006) the kinetics of NO and PGE 2 have been integrated in the present study in order to create a more precise stimulus taking into account the influence of N O and PGE 2 .

  Vitamin D[START_REF] St-Arnaud | The direct role of vitamin D on bone homeostasis[END_REF][START_REF] Wasserman | Vitamin D and intestinal calcium transport : facts, speculations and hypotheses[END_REF], Ca homeostasis(Peterson and Riggs), age, sex, drugs treatments and nutrition should be taken under consideration in order to get an accurate model of transduction. Building such comprehensive model requires proceeding step by step and implies to develop a block diagram model in order to be easily updated.

  Adachi, T.,Kameo, Y., Hojo, M., 2010. Trabecular bone remodelling simulation considering osteocytic response to fluid-induced shear stress. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 368, 2669-2682, doi:10.1098/rsta.2010.0073.

Figure 1 :

 1 Figure 1: Block diagram describing the events cascade for bone stimulus with coupled mechanical and biological effects. Dashed arrows represent the mechanical effects and dotted ones represent the biological effects. Solid arrows denote biological reaction due to mechanical stimulation represented by NO & PGE 2 production by the osteocyte. Transduction phases (Signal, Reception, Integration & Amplification, Target) are based on Oesterhelt's concept (2010).

Figure 2 :

 2 Figure 2: Mechanobiological stimulus versus calcium conce ntration for different levels of fluid flow on basal physiological evolution of NO and PGE 2 .

Figure 3 :

 3 Figure 3: Pre dicted stimulus versus fluid velocity for different levels of NO [pM] and PGE 2 [pM].

Figure 4 :

 4 Figure 4: Pre dicted stimulus versus calcium concentration at constant fluid flow for different levels of NO [pM], PGE 2 [pM] and different configurations of the stimulus Ψ.

Figure 5 :

 5 Figure 5: Pre dicted mechanobiological stimulus at different levels of canaliculus damages for basal physiological evolution of NO [pM] and PGE 2 [pM].

Table 1 : Mechanical and biologic components used in the model.

 1

		Signal	Reception	Integration &	Target
				Amplification
	Mechanics	Fluid flow,	Production	fMecha,fNO,fPGE2
		Shear stress	of NO & PGE 2		BMUs
	Biology	Ca	PTH	fPTH,fBio
			regulation

Table 2 : Model's equations Parameter value Description

 2 Calc. based on[START_REF] Houillier | Le récepteur du calcium : un rôle central dans le métabolisme calcique[END_REF] Calc. based on Houillier et al., 2009 Calc. based on Houillier et al., 2009 Calc. based on Houillier et al., 2009 Based on Houillier et al., 2009

	Source

Table 3 : Model's parameters

 3