Purpose To perform a process evaluation of a hospital-based work support intervention for cancer patients aimed at enhancing return to work and quality of life. The intervention involves the delivery of patient education and support at the hospital and involves the improvement of the communication between the treating physician and the occupational physician. In addition, the research team asked patient’s occupational physician to organise a meeting with the patient and the supervisor to make a concrete gradual return-to-work plan. Methods Eligible were cancer patients treated with curative intent and who have paid work. Data were collected from patients assigned to the intervention group (N = 65) and from nurses who delivered the patient education and support at the hospital (N = 4) by means of questionnaires, nurses’ reports, and checklists. Data were quantitatively and qualitatively analysed. Results A total of 47 % of all eligible patients participated. Nurses delivered the patient education and support in 85 % of the cases according to the protocol. In 100 % of the cases at least one letter was sent to the occupational physician. In 10 % of the cases the meeting with the patient, the occupational physician and the supervisor took place. Patients found the intervention in general very useful and nurses found the intervention feasible to deliver. Conclusions We found that a hospital- based work support intervention was easily accepted in usual psycho-oncological care but that it proved difficult to involve the occupational physician. Patients were highly satisfied and nurses found the intervention feasible. Due to the increased survival rates of cancer, a growing number of cancer patients are now be able to survive many years beyond a cancer diagnosis and thus face new challenges related to survivorship. For cancer patients of working age, one challenge is their return to work. Returning to work is important as work contributes to personal  and econUnfortunately, not all cancer patients are able to return to work successfully. A meta-analysis demonstrated that the risk of unemployment was 37 % higher for cancer patients than healthy controls . MoreoveWe developed this intervention based on previous studies that had employed effective interventions for enhancing the return to work of cancer patients , and we Performing a process evaluation is important for interpreting the findings of an innovative intervention because the effectiveness partially depends on how well the intervention was implemented . ConsequProcess indicators should be measured at each level that could have an influence on the implementation process of the intervention . For insLinnan and Steckler  proposedThis process evaluation was part of a multi-centre randomised controlled trial to assess the effectiveness of a hospital-based work support intervention on the return to work and quality of life of cancer patients . PatientSix hospitals in the Netherlands participated in the study. The medical ethics committee of the Academic Medical Center approved of the study. The local medical ethics committee of each participating hospital advised positively about feasibility of the study in their hospital.Patients with a primary diagnosis of cancer, who were between 18 and 60 years of age, had paid work at the time of diagnosis, were on sick leave, had been treated with curative intent, and who had been treated at one of the participating hospital departments were eligible to participate. Treatment with curative intent was defined as an expected 1-year survival rate of approximately 80 %. We excluded patients, who were not adequately able to speak read, or write Dutch, who had a severe mental disorder or other severe co-morbidity, or those for whom the primary cancer diagnosis had been made more than 2 months ago. Patients signed informed consent forms prior to their inclusion in the study.The hospital-based work support intervention began a few weeks after patients were included in the study and was spread over a maximum of 14 months. The hospital-based intervention involves delivery of patient education and support at the hospital integrated into usual psycho-oncology care and involves improvement of the communication between the treating physician and the occupational physician. In addition, the research team asked patient’s occupational physician to organise a meeting with the patient and the supervisor to make a concrete gradual return-to-work plan . A nurseIn accordance with the key process indicators that had been proposed by Linnan and Steckler , we measData of the process indicators were collected using questionnaires, which were filled in by nurses and patients, nurses’ reports of each patient in the intervention group, and checklists that were filled in by the research team throughout the study Table .Table 1PProcess indicators were measured at three levels Table  and thesThe response rate of patients to the questionnaire was 75 % (N = 49). Reasons for not responding included cancer recurrence (N = 2), study decline (N = 3), or were unknown (N = 11) and two patients died before the intervention was completed. Nurses’ reports for 6 (10 %) patients who received at least one nurse consultation were lost and nurses’ response rate to the questionnaire was 100 %. The research team collected reach data from three hospital departments  only. The other hospital departments were not able to provide data on reach due to time constraints.Of the 8 hospital departments that participated in the study, 2 hospital departments (G and H) did not treat patients who were assigned to the intervention group  of hospitals, hospital departments, and nurses, as well as reasons for non-participation. We measured recruitment as the proportion of hospitals, hospital departments, and nurses that did participate in the study compared to the total number of hospitals, hospital departments, and nurses that had been contacted by the research team.We measured intervention implementation per department to identify whether various health care contexts directly or indirectly affected intervention implementation. Two factors were considered important during the research period: type of cancer diagnosis and occupation of the health care professional who delivered the patient education and support at the hospital.Reach was measured to identify to what extent the target population participated in the study and to identify if our procedure to reach patients was feasible. Reach was expressed as the proportion of cancer patients that did participate in the study compared to all cancer patients that were found eligible to participate. Furthermore, we registered age of the cancer patients who did and did not want to participate in order to identify if our findings apply to all age groups.We measured the proportion of the intervention that was actually delivered compared to the intervention protocol as intensity of the intervention delivered for patients who started with the intervention. For each patient in the intervention group, intensity of the intervention delivered was measured as the number of meetings that were held, the number of meetings face-to-face, and their duration. We protocolised the delivery of 4 meetings of at least 10 min each of which at least two meetings were face-to-face unless a patient reached sustainable return to work before the intervention was completed. At least one initial meeting for all patients was protocolised regardless of work resumption. In case a patient was unable to complete the intervention due to medical reasons (i.e. cancer recurrence), we considered the intervention as delivered according to the protocol. In addition, drop-out of hospital departments and nurses was recorded.We measured exposure to the intervention as the extent to which the intervention was received as intended by measuring whether patients complied with the advice that was provided (yes or no). For each type of advice offered, an open-ended question was directed to patients, whereby patients could provide their source of motivation for not complying with the advice. We considered compliance with 50 % of the provided advice as sufficient. In addition, patient drop-out (yes or no) and their reason for dropping out, as well as the characteristics of the patients  were recorded in order to identify whether compliance applied to the entire population.Satisfaction with the intervention was assessed at both nurse and patient level.Nurses’ satisfaction with the training: Nurses’ satisfaction regarding the training they had received for delivering the intervention was measured and all questions (N = 5) were open-ended questions.Nurses’ perceived feasibility of the intervention: Nurses were asked whether they thought that the intervention was applicable in practice and whether they encountered barriers when applying the intervention in practice and how to best overcome these barriers in the future. Finally, we identified the nurse satisfaction with the intervention protocol and all of these questions (N = 4) were open-ended questions.Nurses’ perceived effectiveness of the intervention: Nurses were asked whether they thought the intervention was effective at enhancing the return to work of cancer patients. They were also asked which portion of the intervention they considered most useful and which not, and for which population of cancer patients. All questions (N = 14) were open-ended questions.Patients’ satisfaction with the intervention: Patient’s were asked about their satisfaction with each intervention component, the timing of each intervention component, the duration of the intervention, and the competence of the nurse and the occupational physician. Furthermore, if the intervention fulfilled their expectations, the perceived burden, and whether the timing of the intervention was adequate were also assessed, using 3- and 4-point Likert scales as well as open-ended questions.Fidelity refers to the extent to which the intervention content was carried out according to the protocol. We measured fidelity by assessing performance of nurses and occupational physicians based on the intervention protocol, i.e. protocol adherence. Six performance indicators were established a priori based on the intervention protocol. An independent researcher assessed protocol adherence by scoring each indicator as either sufficient or insufficient, or not applicable. All performance indicators were weighted equally, yielding a maximal sum score of 6.The first two performance indicators assessed nurses’ performance and were assessed based on the reports that the nurses completed after each meeting with a patient. The first performance indicator addressed whether the quality of meetings between the nurse and the patient was adequate. The second performance indicator addressed whether nurses delivered sufficient information to a patient. The third and fourth performance indicators assessed whether medical information was sent to the patient’s occupational physician (yes or no) and a score was assigned if this had taken place. The fifth and sixth performance indicators assessed occupational physicians’ performance on the basis of nurses’ reports. The fifth performance indicator assessed whether the occupational physician organised a meeting with the patient, patient’s supervisor, and him/herself, and the sixth performance indicator assessed whether a return-to-work plan was draw-up in collaboration with the patient, patient’s supervisor, and the occupational physician.All quantitative data were analysed with descriptive statics using PASW version 18 . DiffereThe open-ended questions were qualitatively analysed by the first author using content analysis [ST] and were checked by another independent researcher. Codes were derived from the open-ended questions and were categorised. Codes represent the text as closely as possible.The recruitment of hospitals and hospital departments initially occurred between September 2008 and December 2009 but the recruitment period was extended by 4 months to include as many cancer patients as possible. The onset of the study per department occurred between May 2009 (department A) and November 2010 (department H) and ended at the end of December 2010 for all hospital departments  patients received at least one consultation with the nurse to receive patient education and support about return to work, of 54 (100 %) patients at least one letter was sent to their occupational physician, and the meeting between the supervisor and the occupational physician to draw-up a return-to-work plan occurred in 5 (10 %) cases. Reasons for not receiving the patient education delivered by the nurse included logistical issues related to their treatment in another hospital department (N = 6) or a lack of interest (N = 1) Fig. .Of the 11 hospitals that were contacted by the research team, 5 hospitals did not participate in the study Fig. . ReasonsAt the onset of the study, 6 of the 8 hospital departments employed only one person who could deliver psycho-oncological care as well as the intervention, although each of these individuals were willing to deliver the intervention. In hospital departments where more than one person delivered psycho-oncological care, the supervisor of each department decided which persons would be able to deliver the intervention based on their years of experience. All nurses, who were eligible to deliver the intervention, were willing to participate.Five hospital departments (83 %) treated breast cancer patients and one department (17 %) treated gynaecological cancer patients. Breast-care nurses delivered the intervention in three hospital departments (50 %), an oncology nurse in one department (17 %), a nurse practitioner in one department (17 %), and a medical social worker in another (17 %).p = 0.2).Based on the findings from three hospital departments , an average of 47 % of the eligible cancer patients participated in the study Fig. . ReasonsNone of the 6 hospital departments dropped out of the study, although one of the nurses dropped out of the study due to a career change. This nurse’s tasks related to delivering the intervention were completed by one of the other nurses, and as such, the intensity of the intervention delivered was not affected. Fifty-seven percent of the patients had 4 meetings, 66 % three meetings, 76 % two meetings, and 88 % had one meeting Table . In addiEighty-one percent of the patients had the first meeting face-to-face, 63 % had the second meeting face-to-face, 38 % had the third meeting face-to-face, and 19 % had the fourth meeting face-to-face (Table Patient compliance with the advice to keep in contact with employer (79 %), to keep in contact with co-workers (79 %), and the advice to start with return to work before full recovery (75 %) were complied with the most Table . The advFrom the open-ended questions of the patients we inferred that non-compliance with the advice to schedule a meeting with the occupational physician, to keep in contact with employer, and to keep in contact with co-workers was caused by either the fact that it was common practice (N = 10) or because a patient did not have an employer anymore (N = 1). In addition, the open-ended questions revealed that patients’ did not comply with the advice to make a return-to-work plan for various reasons, including did not have an employer anymore (N = 1), already made a return-to-work plan (N = 1), or still have to make a return-to-work plan (N = 1). Not complying with the advice to draw up a second return-to-work plan was caused by not seeing the use of doing it (N = 3).p = 0.3–0.8). All but one nurse received the training for how to deliver the intervention and this nurse did not receive the training due to a time constraint.The education and income level of patients who demonstrated at least 50 % compliance versus those who demonstrated less than 50 % compliance did not differ statistically  to 10 (very good). The open-ended question responses indicated that some nurses (N = 3) would have preferred to receive the training material before the start of the training and that some nurses thought the period between the training and the start of the intervention was too long (N = 2).All nurses (N = 4) were satisfied with the intervention protocol and stated that it provided a clear overview of the content of the intervention. In general, nurses (N = 4) believed that the intervention was feasible to carry out in practice and that the burden associated with the delivery of the intervention was manageable. Nevertheless, the following barriers for applying the intervention to practice were mentioned: (1) delivering the intervention for patients who did not receive usual psycho-oncological care; (2) delivering the intervention by telephone; and (3) integrating the intervention into usual care. For the first barrier, nurses mentioned (N = 3) that the intervention was not as feasible to deliver to patients who did not receive usual psycho-oncological care. This situation may have occurred for patients, who did not receive follow-up care at the hospital, but for the delivery of the intervention in these cases, an extra consultation was planned or meetings were held by telephone.Second, delivering the intervention by telephone was perceived as less feasible because it was time consuming to reach patients by telephone and it was difficult to assess the patient’s situation and gain patient’s trust over the telephone. Third, nurses (N = 4) stated that the intervention should have been integrated into usual care according to the following adaptations: (1) meetings needed to be planned at the right time and for the proper length of time; (2) all meetings should have been face-to-face; and (3) to be able to deliver all meetings face-to-face it may mean that the intervention should be handed on to another health care professional who would be able to conduct longer follow-up consultations.Although all nurses (N = 4) believed that most patients benefited from the intervention, some nurses expected (N = 2) the intervention to be only moderately effective because they felt that their advice and support may not have uniquely impacted the return to work of cancer patients, as these patients typically arrange their return to work at the workplace with their supervisor and occupational physician. However, nurses (N = 4) did consider the intervention to be useful for all cancer patients of working age.Patient satisfaction regarding the various intervention components and their timing is shown in Table The median sum score of the performance indicators that met the a priori formulated criteria was 4 and ranged between 0 and 6. The performance indicator for sending medical information to the occupational physician (100 %), the indicator for satisfactory quality of meetings between the nurse and the patient (88 %), and the indicator for the delivery of sufficient information to the patients (83 %) were met in most cases  and nurses delivered patient education and support according to the protocol in 85 % of the cases (fidelity). In 100 % of the cases, at least one letter was sent to the occupational physician (fidelity) and in 10 % of the cases, the meeting with the patient, the occupational physician, and the supervisor took place (fidelity). We found that a hospital-based work support intervention was easily accepted into usual psycho-oncological care but that it was difficult to involve the occupational physician. Overall, patients were highly satisfied, and nurses found the intervention to be feasible.The strength of our study was the thorough analysis of the process indicators at the department, nurse, and patient level, which was based on a previously established framework for process evaluations .One limitation of our study was that we did not include occupational physicians in the data collection process. However, the key aspects of the hospital-based work support intervention were both the patient education and support delivered by a nurse at the hospital, and communication with patient’s occupational physician concerning patient’s diagnosis and treatment. Because earlier research had shown that occupational physicians appreciated receiving this type of information from the hospital , 17 and Another limitation of our study was the method that was used to measure fidelity. We measured fidelity by scoring performance indicators based on self-reports of nurses and we do not know how valid these self-reports are in comparison to independent observations. Thus, bias could have been introduced by the recording of socially desirable answers in the reports. However, independent observation may have introduced another form of bias as well, as nurses may have performed differently if they knew they were being observed. Another limitation of the study was the potential for recall bias, as the participants’ compliance and satisfaction with the intervention were assessed at the end of the follow-up period. However, we could not have evaluated these aspects directly after the consultation, because this may have influenced the effect of the intervention in cases in which the patient did not receive the information during the consultation but rather received the information as during the response to the questionnaire. Finally, selection bias may also have occurred, as not all patients responded to the questionnaire. We do not know whether reasons for not completing the questionnaire were related to patient satisfaction or compliance with the intervention. Therefore, it is possible, that these results represent either an overestimation or underestimation.Nieuwenhuijsen et al.  studied Almost 50 % of eligible patients participated in our study, which was considered an adequate result because it should be taken into account that participants had been diagnosed with cancer only a few weeks before the start of the study and therefore experienced higher levels of insecurity. Similar response rates were reported for the inclusion of recently diagnosed cancer patients in a life-style intervention trial . For othOther comparable trials for work support interventions among cancer and other patients have also reported the results of process evaluations –22. ThesOur study showed that the various health care contexts  did not influence the intervention implementation. This finding indicates that our intervention could be successfully adapted to various health care contexts, provided that some form of psycho-oncological care is available. This means that our intervention might be successfully adapted to other countries, despite the variation between the social security systems. However, the content and timing of the intervention should be adapted to each social security system.The intensity of the present intervention delivered was high and was also concurrent with what we protocolised. Few drop-outs were noted, and nurses were able to extend their consultation to deliver the intervention. In contrast, the number of patients who did not start with the intervention was higher than anticipated, which was mainly caused by the fact that those patients did not receive usual psycho-oncological care from nurses who delivered the intervention. For these patients, nurses encountered problems and either and extra consultation was required or the intervention had to be delivered completely over the telephone. Nurses considered this form of delivery to be less effective and more difficult. We believe that this situation would be remediated if the intervention could be implemented over a wider scale, which would provide usual psycho-oncological care to all patients and better integrate the intervention with patient care.Patients and nurses were in general very satisfied with the various intervention components and found that the timing of the intervention components was appropriate. However, encouraging the occupational physicians to organise a meeting between the patient, the supervisor and him/herself in order to draw-up a return-to-work plan proved difficult, which was likely the result of not actively involving the occupational physician into the hospital-based work support intervention.As expected, patient compliance with each type of advice provided was high. Only patients with a temporary employment contract that could not be extended were unable to comply with the delivered advices, as they no longer had an employer/occupational physician.In terms of clinical practice, this study demonstrated that psycho-oncological care can address the work concerns of cancer patients at an early treatment phase as well as during follow-up, according to the reported satisfaction of patients and nurses who provided the intervention. However, for further improvement, nurses suggested the following adaptations: 1) meetings should be planned at the right time for the proper length of time; 2) meetings should be conducted face-to-face; and 3) to be able to deliver all meetings face-to-face it may mean that the intervention should be hand on to another health care professional who have longer follow-up consultations in usual cancer care.Our study was restricted to breast and gynaecological cancer patients. However, nurses who delivered the intervention indicated that all cancer patients of working age would likely benefit from this type of intervention. Thus, evaluation studies of patients with other types of cancer are needed.It proved difficult to involve the occupational physician and the supervisor in the intervention. As these individuals are relevant to return to work of cancer patients , 23, furBecause patients with a temporary employment contract could not comply with the advices provided, the intervention should be adapted for patients with this type of employment by assessing the specific needs and concerns of this population. This approach is especially important, as patients with a temporary employment contract have a higher risk of becoming unemployed in comparison to patients with a permanent employment contract , 25 and


We study the impact of coil orientation on the motor threshold (MT) and present an optimal coil orientation for stimulation of the foot. The result can be compared to results of models that predict this orientation from electrodynamic properties of the media in the skull and from orientations of cells, respectively. We used a robotized TMS system for precise coil placement and recorded motor-evoked potentials with surface electrodes on the abductor hallucis muscle of the right foot in 8 healthy control subjects. First, we performed a hot-spot search in standard  orientation and then rotated the coil in steps of 10° or 20°. At each step we estimated the MT. For navigated stimulation and for correlation with the underlying anatomy a structural MRI scan was obtained. Optimal coil orientation was 33.1±18.3° anteriorly in relation to the standard lateral orientation. In this orientation the threshold was 54±18% in units of maximum stimulator output. There was a significant difference of 8.0±5.9% between the MTs at optimal and at standard orientation. The optimal coil orientations were significantly correlated with the direction perpendicular to the postcentral gyrus ( Transcranial magnetic stimulation (TMS) non-invasively activates cortical neurons that in turn, when targeting the motor cortex, cause muscle contraction The neurons are stimulated by a current distribution that is induced by a transient magnetic field. This magnetic field is generated by a short current pulse that is sent through a stimulation coil. For a given position of the stimulation coil on the head, the magnetic field penetrates the whole skull and induces a current density distribution that is characterized by a direction and magnitude that both vary within the skull. These quantities are determined by the coil position and geometry, and by the geometry and electrical conductivity of the tissue. An MEP will ensue if the current density at the position of a target neuron, that directly or indirectly is wired with the muscle, exceeds a threshold value to depolarize the axon membrane For a figure-8 coil, the largest current density is attained directly below the center of the coil. Thus, it is assumed that the center of the coil indicates the position of the target cells that control a given muscle. However, this is only valid when the conductivity inhomogeneities are ignored and the threshold is minimal with respect to surrounding coil positions.In addition to coil position, coil orientation also influences thresholds and MEP amplitudes in TMS. In clinical routine and experimental treatments with repetitive TMS, this is considered by recommending standard orientations The recordings of the motor threshold (MT) as a function of coil orientation that are available in the literature are not very precise with steps at least as large as 45°. Muscles in the hand have been the most frequent targets for motor cortex research For stimulation of the leg motor area , Terao et al. additionally investigated the MEP amplitudes and latencies for different coil orientations with 45°-steps. They confirmed that a lateral coil orientation produced the highest MEP amplitudes and shortest latencies Implications of optimal coil orientation for the underlying physiology were discussed by Fox et al. who proposed a cortical column cosine  is one of the deepest structures in M1. Thus, it is located directly at the medial wall of the hemisphere, making the estimation of the alignment of the cortical columns easier than for the hand motor cortex which has the shape of a knob and thus, columns in many different directions For TMS in general, precise coil positioning is a prerequisite for accurate recordings. Neuro-navigation combines a three-dimensional (3D) scan of the patient’s head with a real time tracking system and is applied with increasing frequency In this study, we investigate the impact of coil orientation with respect to the alignment of the underlying precentral gyrus on the stimulation result. In contrast and in addition to previous studies,we use a robotized TMS system to precisely place and rotate the TMS coil and to ensure that the coil maintains tangential orientation to the scalp;we use small coil-rotation steps of 10° to accurately measure the optimal coil orientation angle;we record MEPs on the AHM as the alignment of the precentral gyrus for the AHM is easier to estimate in contrast to the ATM or even the hand area; andwe use structural MRI images to locate the stimulation target in the precentral gyrus and to estimate its alignment.Applying this setup, we are able to show that.the optimal coil orientation angle for stimulation of the foot is 30° posterior than the common standard coil orientation;the inter-subject variability is much smaller than reported in previous studies; andthe optimal coil orientation angle correlates to the alignment of the precentral gyrus which will be discussed with respect to model and simulations.Preliminary results of this study have been already presented as a conference abstract We used an MC-B70 Butterfly coil with a slight bend and a MagPro X100 stimulator with MagOption  for focused biphasic stimulation. To reach sufficiently high stimulation intensity the ‘power mode’ of the device was used, which allowed a 1.4 times higher stimulation power compared to the standard mode. Recording of MEPs was accomplished using a 2-channel DanTec Keypoint Portable  with surface electrodes. For placing and holding the coil precisely, we used a robotized system that is based on an Adept Viper s850 serial six joint robot  and a Polaris infrared stereo-optical tracking system  This study was approved by the local ethics committee:Ethikkommission der Universität zu Lübeck (Ethics committee of the University of Luebeck)Ratzeburger Allee 160, Building 21, D-23562 LuebeckChairman: Prof. Dr. med. Dr. phil. H. RaspeThe recordings were performed on eight healthy male subjects with no history of neurologic disease aged 24 to 31 years after written informed consent had been obtained.As the MEP amplitude has a high variance μV (for the resting muscle). The MT is reported as a percentage of maximum stimulator output (MSO).In general, the MT is defined as the stimulation intensity at which a muscle contraction occurs with a probability of 50%. In our case, we classified the MEP signal as a muscle contraction if the base-to-negative peak amplitude exceeded 50 To accurately and systematically estimate the MT for a given coil orientation, we employed the threshold hunting method We stimulated the motor cortex of the left hemisphere and recorded MEPs on the AHM of the right foot.For each subject, two stimulation sessions were performed on different days. The sessions were designed such that coil orientation in session 1 is opposite to session 2. As we were using biphasic stimulation, we expected two threshold minima (at slightly different stimulation intensities) occurring at coil orientations differing by 180°. This way, we could further verify the optimal coil orientation in terms of stability within the subjects. For session 1 we used a right-to-left coil orientation as reference , which iFor each session, we first performed a hot-spot search. We used the median in MEP amplitude of 5 subsequent stimulations, in standard orientation and opposite orientation, respectively. A grid of positions with a distance of 1 cm was used and stimuli were applied with fixed stimulation intensity . The hot-spot was defined as the optimal stimulation site that was surrounded by four other stimulation points with smaller MEP amplitudes. Thus, depending on the starting point, at least five stimulation points were used. Consequently, not less than 25 MEPs were employed for each hot-spot definition.Subsequently, we placed the coil at the hot-spot again and rotated the coil to different orientations. At each coil orientation, we performed a motor threshold estimation and afterwards rotated the coil to the next orientation. For session 1, we rotated the coil clockwise from −20° to 80°, where 0° denotes the reference (left-to-right) coil orientation. For session 2, we used orientations from 160° to 280°, where 180° denotes the right-to-left coil orientation, used as reference for session 2. In the range of the minimum MT, we used orientations in steps of 10°. In the outer range, we employed a step size of 20° so that a clear curve with a distinct minimum could be recorded.Note that we split the investigation into two sessions to limit effects of varying vigilance. For the same reason, we used steps of 20° and 10° to not unnecessarily prolong the session, although we are able to use very small coil rotation steps with the robotized TMS system. With our setup, each session lasted approximately 1.5 hours. In sessions with duration less than 1.5 h, we repeated the motor threshold estimation for the first orientation at the end of the stimulation series. The difference between the two recordings serves as a measure for coil positioning accuracy and for the influence of changes in vigilance.The coil orientations and the sessions were randomized. The MT estimation was performed in a double-blind way: The robot operator but not subject and investigator were aware of the current coil orientation.r between first and repeated MT estimations. Subsequently, we evaluated the recorded MT curves for each subject.First of all, we analyzed the stability of the MT recordings based on the repeated MT estimations at the end of the session. Stable MTs in the first and in the repeated estimation suggest that the measurements have been performed correctly and accurately. In addition to the average MT difference, we calculated the correlation coefficient Based on the recorded MTs, we estimated the optimal coil orientation angle. Minimal thresholds and thresholds at standard orientation were compared with a repeated measures t-test, using MATLAB . Similarly, the optimal coil orientation angle was compared to the standard coil orientation angle.s and coil orientation α as:s.Since motor thresholds vary considerably between subjects , we also calculate the standardized MT values for each subject. In our case, we compute the standardized MT value for subject Cohens dd.To quantify effect sizes in our results, we calculated In general, the waveform of biphasic stimulation is cosine-shaped with the second halfwave having the largest amplitude. Thus, the second phase in biphasic stimulation is physiologically most effective In total, we can therefore expect a sinusoidal for biphasic stimulation with two minima between coil orientation angle Therefore, the sinusoidal relation should have the formFor every subject and for the group averages, we fitted the experimental data to this sinusoidal relation with nonlinear regression and estimated the error of the fit. The fitting was performed using MATLAB.i, As a quantitative measure for the goodness of the sinusoidal fitting, we used the coefficient of determination r with a repeated measures t-test on n denotes the number of subjects.Finally, we investigated whether the orientation of the underlying gyrus that has been stimulated correlates with the optimal coil orientation. To this end, we used a transversal plane of the individual MRI images at that level where the foot area is suggested in the precentral gyrus. With our TMS navigation and robot control software, we are able to precisely determine the coil’s spatial position and orientation with respect to the subject’s head contour and thus with the subject’s brain anatomy . For determination of the stimulation point in the precentral gyrus, we first selected a coronal view in the navigation software. We then went through the coronal slices from the back to the front until we met the plane where the hot-spot on the skull was located. Then, we followed the normal of the head surface at the hot spot into the brain until we reached the gyrus at the medial surface of the brain cf. . At thisThe stimulator’s ‘power mode’ was mostly well accepted by the subjects. However, two subjects felt inconvenient due to the strong muscle twitching and the impact on the skin. Therefore, subjects ‘Ti’ and ‘Pa’ only participated in one of the two sessions. For subject ‘La’ we performed session 1 twice (‘La1’ and ‘La2’). As for both trials no minimum could be found, subject ‘La’ was excluded from further analysis. Thus, we have six full recordings for each session for evaluation.r between first and repeated MT estimation was 0.99. This very small MT difference and the very high correlation coefficient support that the effect of fatigue was minimal and that we positioned the coil very accurately.In total, we were able to repeat the MT estimation of the first coil orientation at the end of the stimulation in 8 sessions. On average, the MT difference was 1.88±0.83% of MSO. The correlation coefficient The hot-spot was located close to midline over the medial lip of the precentral gyrus for all subjects and for both sessions which also suggest accurate coil positioning.For the opposite coil orientation (coil handle towards the left hemisphere), the minimum is located at 210° and results in a motor threshold of The average coil orientation for the minimum threshold was 33.1°±18.3° for session 1 and 213.3°±12.1° for session 2. The mean MT difference between optimal orientation and reference orientation was Cohens d was 0.47. As this is commonly regarded as an intermediate effect size, it indicates that our results are relevant even though the number of subjects is rather small.With our results, After fitting the average recordings to the model sinusoidal, the resulting curve had the form:The coefficient of determination, r) between angle of the precentral gyrus and the optimal coil orientation was 0.78. The correlation was therefore significant (The orientation of the gyrus underneath the hot-spot estimated in the MRI scans is presented in The monotonicity in our measurements documents that we have identified reliable minima with our setup. However, for one subject, we have not been able to estimate a clear minimum in two sessions. A reason for this might be the variation in structural anatomy, especially in the primary motor cortex Furthermore, our recordings support the assumption of a sinusoidal relationship between coil orientation and stimulation outcome – in this case with the motor threshold as quantitative parameter. The fit result cf.  however Although the optimal coil orientation in our recordings differed between subjects, the inter-individual variability was essentially smaller than reported by Balslev et al. for the hand region. In our study the variability was 30° whereas Balslev et al. reported a variability of 63° With respect to the interaction of electrical field and cells, Fox et al. suggest that the effect of the induced electrical field depends on the orientation of the cortical column In addition to the uncertainty of the orientation of the cells influenced by TMS the orientation there is also some degree of uncertainty about the orientation of the cortical columns. We assumed that the target area for the stimulation of the leg is located at the medial surface of the brain see . This isModels that simulate the propagation of electromagnetic fields in the complex distribution of different conductivities in the skull predict optimal stimulation for a coil handle perpendicular to the crown of the gyrus In conclusion, we can assume that the precentral gyrus orientation is the key factor for an optimal current direction and therefore for an optimal coil orientation. This is in analogy with the work by Terao et al., where the shortest MEP latencies were found when stimulating almost perpendicular to the underlying gyrus As a more direct test of the macroscopic models optimal directions for hand and foot stimulation could be determined in the same subjects. If these were identical an interaction with a larger structure can be assumed that in turn influences smaller parts of cortex. The robotized TMS system is a powerful and sufficient tool for this purpose as it can rotate the coil very precisely and in small steps while keeping the coil in a tangential orientation to the head.


In this article, we investigate composite media which present both a local resonance and a periodic structure. We numerically and experimentally consider the case of a very academic and simplified system that is a quasi-one dimensional split ring resonator medium. We modify its periodicity to shift the position of the Bragg bandgap relative to the local resonance one. We observe that for a well-chosen lattice constant, the local resonance frequency matches the Bragg frequency thus opening a single bandgap which is at the same time very wide and strongly attenuating. We explain this interesting phenomenon by the dispersive nature of the unit cell of the medium, using an analogy with the concept of white light cavities. Our results provide new ways to design wide and efficient bandgap materials. V) chain  chain . This scpω. To mimic this property but at macroscopic scales, some composite materials generally made out of subwavelength resonant inclusions have initially been proposed by Pendry151718202122232526272829f0, an incident plane wave at f > f0 results in a resonance response of the resonator in anti-phase(ϕ = −π) with the continuum exactly like a mechanical mass-spring that cannot follow a too fast excitation. For a monopolar resonator, this results in destructive interferences that give birth to a bandgap while cascading the resonators. This mechanism involves the coupling between the incident plane wave and a local resonance so that the bandgap of such materials can be interpreted as a hybridization bandgap333435f0 which allows very subwavelength organizations as long as no near field interaction occurs directly between the unit cells. The gap extension and efficiency depend on the quality factor of the resonant unit cell and on the density of resonators. We have shown that in the limit of no near field coupling, the hybridization bandgap is understood to result from interferences. Consequenlty, analogous to photonic/phononic crystals, we have recently demonstrated that it is possible to locally modify such metamaterials to design very subwavelength components such as waveguides or cavitiesAnother kind of natural materials constitutes a very good mirror for electromagnetic waves: metals. They possess free electrons which reply in antiphase to an incoming electromagnetic wave, hence cancelling the latter on very short distances. In other words, metals present a negative permittivity and consequently a high reflectivity, below their characteristic plasma frequency f0 and Bf. These can be independently shifted by changing either the frequency of the constitutive unit cell or the periodicity a and an overlap between the Bragg and hybridization bandgaps has been experimentally observed in phononic crystals made out of nylon rods3539From this brief review of composite materials, one naturally wonders what happens for materials presenting both a periodicity and a subwavelength resonant unit cell. It is known3538394041f0 and Bf perfectly match  of an infinite 1D chain of resonators  is the complex transmission coefficient, f is the frequency, a is the periodicity of the infinite chain and c is the speed of light (k obtained in (1) gives the propagating modes of the system, while its imaginary part corresponds to the attenuation, which in this lossless system relates only to the bandgaps. This is the quantity that is of interest for our study. To understand how the lattice constant influences the dispersion relation of a locally resonant quasi-1D metamaterial, we compute k for a set of lattice constants a using (1). We display its imaginary part as a function of the frequency and the periodicity , its shape is symmetric and its attenuation is limited, it is related to Bragg scatteringa0 = nλ0/2 (where n is an integer and λ0 is the wavelength in the empty waveguide) but we observe a slight shift from this theoretical value due to the finite quality factor of one resonator. We expect the theoretical value to be reached for very high Q resonators. We note that as expected intuitively, far from the resonance f0, the classical Bragg scattering is not affected since the resonators act like non-dispersive scatterers. To experimentally observe and investigate the very interesting properties of the hybrid Bragg/hybridization bandgap enlightened by the simulation results, we realize an experiment that mimics as much as possible this simplified theoretical system.We start our study by simplifying the problem as much as possible and to do so we consider a quasi-1D system consisting of a linear chain of “atoms” enclosed in a single mode waveguide. The “atoms” are split ring resonators (SRR) which are illuminated by a transverse magnetic field and whose dimensions, noted in sonators . This caof light . The reaiodicity . From FiL = 4.4 mm, ge = 1 mm, e = 0.9 mm). The coupling occurs because the magnetic field lines created by the transmission line cross the SRR in the out-of-plane dimension, providing the good symmetry for the SRR to be excited. The strength of the coupling Γ can be tuned by adjusting the distance between the line and the resonators. We choose the latter (d = 0.5 mm) so that the SRRs couple much faster to the line than to free space, hence mitigating radiation losses. Thus, the relaxation of the SRRs occurs mostly through the microstrip. We stress here that the split rings have no direct capacitive or inductive interaction since they are distant enough. This setup ressembles Coupled Resonator Optical Waveguides (CROWS)51Q ones and are coupled through a transmission line rather than evanescently. The transmission line is terminated on both sides with SMA type 50 Ω connectors, and we measure its transmission coefficient S12 by connecting it to a network analyzer. We first measure the transmission of a sample which contains a single SRR  which is near field coupled to SRRs . For all samples except for the middle one  is relatively symmetric and is significantly shifted with the periodicity. It corresponds to the expected Bragg bandgap. Those two bandgaps arise from completely different phenomena and display different characteristics, mostly in terms of dispersion and group velocity39We then experimentally study one dimensional chains of ddle one , we cleaf0. We now focus on the third sample  to the output point (x = L). The faster decrease occurs naturally for f0, where the bandgap is the most efficient  connectors were soldered at each side of the samples in order to plug them to the network analyzer or to an impedance matching load. The network analyser Agilent N5230C PNA) was set to its maximum number of points, 20000, and we used a reasonable power output of 5 dBm. No averaging was used since the dynamic of the measurements was very good, and the sweeping time was set to 20 ms. All the transmission measurements were obtained by measuring the S parameters between the two ports of the network analyser. The near-field measurements of the sample at the Bragg condition were realized by matching it on one side using a 50 Ohms load while the other side was connected to port 1 of the analyser. The port 2 of the analyser was connected to a small magnetic near field probe, i.e., a 2 mm diameter loop realized using the core of a SMA coaxial cable. We performed 40 by 200 measurements using this small magnetic loop 1 mm on top of the sample measuring 5 cm by 20 cm. The maps of 230C PNA G.L. initiated and supervised the project, N.K. performed the simulations and experiments, G.L and N.K. analyzed the results and developed the theory, G.L., N.K. and M.F. discussed the results and wrote the manuscript.Supplementary information


Shrimp trawling represents an important fishing métier in South India, generating high levels of employment and economic value. It is also a contested métier, ostensibly contributing to environmental degradation and social inequality. This paper investigates the job satisfaction of crew members (captains and workers) on board the shrimp trawlers of Chennai (former Madras). Research took place in 2007 and 2008 (N = 137). Results suggest a general satisfaction with being in the fishery. However, a little over three-fifths of fishers said they would be willing to change fishing métier and about one-half said they would leave the occupation. About one-half also said they would not advise a young person to enter the occupation. The tendency to move away from the fishery is argued to reflect a growing pessimism about the future of the shrimp trawl fisheries, but also an increasing awareness of other economic opportunities. Most of these studies deal with fisheries in North America . The social scientists involved focus on perhaps the most human of values: the extent to which various fisheries generate wellbeing for those who participate  is the capital of the state of Tamil Nadu. Although it boasts several fishing neighbourhoods, most of its fishing industry is concentrated in the fishing harbour of Royapuram, in the north of the city. Royapuram is a boisterous and rough area, largely inhabited by people working in the fishing sector Bavinck . The fisThe construction and operation of the Chennai fishing harbour is closely connected to the Blue Revolution in India, which fundamentally reshaped the fisheries of Tamil Nadu in the decades after Independence in 1947, and created new tensions that revolved around issues of social justice and environmental sustainability  still carry out trawling, a growing number of owners—the Fisheries Department registered 173 of such units in 2008—have converted their craft for gillnet and long line fishing. This is a result of the declining price of shrimp on the world market and the perceived availability of high-value pelagic fish in offshore waters. In addition, there is a difference between richer boat owners and those at the lower end of the socioeconomic status hierarchy. Whereas richer boat owners often possess several craft capable of long-distance fishing, their poorer colleagues generally make do with a single, small craft (known as ‘day boats’). Moreover, because the boats belonging to poorer owners are often old and in need of frequent repair, they are not popular among potential crew members, who prefer to serve on large and better equipped boats. This research has focused on the more profitable long-distance shrimp trawl fishery of Chennai, leaving the small-scale fishery, the so-called day boat fishery, and other varieties of mechanised boat operations aside.Compared with small-scale fishing operations, the mechanised boat fishery of Chennai is capitalist in nature. Ownership of equipment is concentrated in a few hands and boat owners generally do not go out fishing themselves. The captain—locally known as the ‘driver’—is in charge of daily operations and responsible for recruiting a crew of up to eight persons. Crew members do shifts in order to minimise the time spent in the harbour and receive a share of the total proceeds. Boat owners rely heavily on merchant loans and experience heavy pressure to keep their craft in continuous operation.Higher oil prices and declining prices of seafood have plunged the mechanised boat fisheries of Tamil Nadu into a deep and prolonged crisis. Although Chennai has experienced difficult times, particularly in the first years of the new millennium, the crisis now seems to have diminished. One of the indications is that boat building has recommenced after years of recession. At the same time, mechanised boat fishers generally agree that a severe resource crisis is affecting the fisheries. This is why they have also agreed to a 45-day closed season, first announced by the government in 2000 and implemented in April and May of every year thereafter  spent the mornings of Days 4–6 in the harbour area, identifying respondents and conducting interviews. Respondents were selected using snowball sampling, with each survey team commencing work in a different part of the harbour area. The researcher stayed in the vicinity and attended a number of interview sessions. Questions or problems were discussed in the evenings. The inability of having a private conversation was one of the recurring problems. In many cases, the interviews attracted bystanders who involved themselves in the discussion. The students spent Day 7 analysing the results of their efforts, which were subsequently presented to and discussed with an external academic audience on Day 8.The 2007 research group administered 90 surveys and the 2008 group 47 surveys in Royapuram fishing harbour. The difference in the number of surveys conducted was a result of the smaller number of students participating in 2008. The procedure was the same in both years: the survey teams spread out through the harbour area in the morning hours and conducted interviews with trawl fishers on the dock as they took a break from loading, unloading and cleaning the boats. In many cases, other fishers congregated around. The interview period coincided with a relatively low fishing season, which may have negatively influenced opinions on job satisfaction.Table The central tendencies for job satisfaction items are in Table The choice of lowest scoring items is confirmed by qualitative information gathered in this fishery. The decline of catches and shrimp prices and the increase of running costs have tended to reduce earnings in the shrimp fishery in the past decade. Dissatisfaction about the landing site is related to its congestion and lack of cleanliness. Finally, there is widespread frustration with the perceived partiality and corruption of officials of the Fisheries Department and their perceived inability to address the serious problems affecting the fishing sector.The highest scoring items can also be explained by the context. Once at sea, fishers the world over appreciate the ability to be their own boss and the healthfulness of the occupation Binkley . SatisfaFigure As a first step in the analysis we look at the relationships between basic background social data and the job satisfaction categories Table . As can Tables Previous studies of job satisfaction did not include the items in the Management and Nature categories. Hence, we thought it would be worthwhile to examine relationships between these two categories and the other three categories that have traditionally been included in job satisfaction research. The results of this analysis are found in Table Table This section of the paper examines factors influencing willingness to change fishing métier, leave the occupation of fishing or advise a young person to fish. A little over three-fifths of fishers said they would be willing to change fishing métier and about one-half said they would leave the occupation Tables , 9, 10. The tendency to move away from the fishery reflects a growing pessimism about the future of the fisheries in Royapuram, but also an increasing awareness of other economic opportunities. The latter correlates with the gradual breakdown of caste barriers in matters of occupation Fuller , and locTables Turning to an examination of these responses in relation to background social variables Tables , 12, 13,2 = 3.532, df = 1 p > 0.05). Sixty per cent of the captains versus 66 % of the crew report they would change fishing métier—another difference that is not statistically significant . Marital status  and crew status  are not statistically significantly related to willingness to leave the occupation of fishing. Finally, neither marital status  nor crew status  are statistically significantly related to willingness to advise a young person to become a fisher. An explanation for this lack of social differentiation did not emerge from the study.Next, we turn to the relationships between willingness to change fishing métier, leave the occupation of fishing and advise a young person to fish and two other social variables: marital status and crew status. None of the obvious comparisons show any statistical significance, not single versus married or captain versus driver versus crew, in relation to any of the three willingness to change variables. Forty-eight per cent of the single fishers versus 68 % of married fishers say they would change fishing métier—a difference that is not statistically significant (χWillingness to change is expected to be related to levels of job satisfaction—the higher the satisfaction, the less willing a fisher should be to change fishing métier or leave the occupation of fishing, and the more willing they should be to advise a young person to fish. Mean values on job satisfaction categories in relation to responses to these questions are examined in Tables Table métier for the state of the modern, in contrast to the small-scale, fisheries.This paper reports on the results of a job satisfaction survey among coastal shrimp trawl fishers in Chennai, India. This fishery spearheaded the Blue Revolution that was initiated in the decades after independence and can be taken as a flagship ‘Willingness to change’ is perhaps the most noteworthy topic of the survey, linking up to the widespread need among fisheries scientists and policymakers to investigate and promote alternative employment among fishers Pauly . The surmétier. A smaller majority indicate a willingness to move out of the fishing profession altogether, while almost half of the respondents would advise against a young person entering fishing. These results suggest that, if alternative employment would be available and other conditions are appropriate, a significant number of trawl fishers might leave the sector. A downsizing of the trawl fleet in Tamil Nadu, as investigated by Sathyapalan et al. (As a result of the situation of the shrimp trawl fishery, a large majority of respondents express a willingness to change fishing n et al. , might tWeighing against this conclusion is the fact that most respondents express satisfaction with many of the working conditions in their fishery. It is therefore not unlikely that if management succeeds in addressing the problems that affect the fishery and its waning economic performance, crew members will adjust their opinions. Moreover, whether fishers actually take the step of moving out of the profession depends in large part on the alternatives available. In the context of South India, these are likely to remain scarce for some decades to come.


We conclude that the alterations in respiratory control induced during early ventilatory acclimatization to hypoxia better reflect those associated with hypothesis 2 rather than hypothesis 1.Hypoxic exposure lasting a few hours results in an elevation of ventilation and a lowering of end-tidal  If there is an increase in In Section 22.1Ten healthy subjects  consented to take part in this study. All were non-smoking and none had a history of cardiovascular or respiratory disease. The study was approved by the Oxfordshire Clinical Research Ethics Committee and followed the guidelines set in the Declaration of Helsinki.2.2Each subject undertook two protocols. The protocols were undertaken on separate days and the order in which each subject undertook the two protocols was random. There was always an interval of at least 1 week between protocols to ensure that the protocols had no effect on each other. Protocols always started at the same time of day. To reduce variability, female subjects were either always studied 1 week after the onset of menstruation or, if using a monophasic oral contraceptive, during a period when they were taking the active component.The subject's resting d of 8 h . In the Before and after the 8-h period in the chamber, the subject undertook an incremental exercise test to exhaustion during which measurements of respiratory function were made. All subjects rested quietly breathing room air for 30 min after leaving the chamber prior to undertaking the second exercise test. This was to allow the subject time to recover from all rapidly reversible effects of the exposure to hypoxia whilst retaining the acclimatization response .2.3To determine the subject's air-breathing values for he mouth .−1 using a coloured light display mounted on the handlebars which indicated pedal rate. The protocol for the incremental exercise test was as follows: subjects pedaled at 0 W for 1 min, after which the load was increased by 15 W every minute until exhaustion. Exhaustion was considered as the point when either the subject stopped voluntarily or was unable to maintain a pedal rate of 60 rpm, and was told to stop.Subjects undertook the incremental exercise seated upright on a electrically braked cycle ergometer (Mijnhardt KEM3). During exercise, subjects were asked to keep the pedalling frequency constant at 60 minDuring the incremental exercise test, the subject breathed through a mouthpiece assembly with their nose occluded. The respired gas was sampled via a fine catheter from a port in the mouthpiece close to the subject's mouth and analysed continuously by mass spectrometry. Respiratory volumes were measured by means of a turbine volume-measuring device incorporated in the mouthpiece assembly. Respiratory flows and timing information were recorded using a pneumotachograph. The gas signals and the inspiratory and expiratory volume signals were passed to a data acquisition computer. This apparatus has been described in detail elsewhere .Both the hypoxia protocol and the control protocol were undertaken in a custom-built chamber large enough to allow the subject to move around comfortably during the experiment. The subject wore a nasal catheter at all times whilst in the chamber, through which respired gases were continuously sampled and analyzed for lsewhere . Subject2.4p < 0.05 for this study. The statistical package SPSS was used for the analysis.The breath-by-breath data for the incremental exercise tests were averaged for each minute of exercise. The values were interpolated at percentages of maximal work rate, starting at 0% of maximal work rate with increments of 5%. This generated an equal number of data points for each volunteer, 21 data points in total. The effect of the 8-h chamber exposures (hypoxia and control) on the responses in 2.52 production; The alternative hypotheses of this paper are: (i) that an 8-h exposure to hypoxia induces a fixed increment in ventilation, and (ii) that an 8-h exposure to hypoxia induces an increment in ventilation that is proportional to metabolism. This section calculates the expected effect of each hypothesis on the variation in 2.5.1Let the increment in 2.5.2k , whereas the average fall in resting Of the 10 subjects originally recruited to the study, all completed both the control protocol and the main protocols successfully and provided data that were suitable for analysis. No subject undertook the second protocol within a week of the first, and no subject took longer than 2 months to complete both protocols. p < 0.01).2 production. In this plot, a change in alveolar ventilation post-acclimatization that is fixed irrespective of metabolic rate would produce a linear relationship between the two variables that is constrained to pass through the origin. In contrast, a change in alveolar ventilation post acclimatization that is proportional to metabolic rate would produce a change that is independent of the transform of CO2 production . p < 0.005 using an F-ratio test after degrees of freedom had been corrected for the presence of auto correlation within the residuals  in humans, which should lower peripheral chemoreflex sensitivity, did not significantly alter By way of contrast, intravenous infusions of dopamine (3 μg kgorkloads  or durinorkloads .4.32 consumption/CO2 production is shown in Eqs. (14), (16) and (18) of their study together with the result in their Table 3. This arises as a consequence of the increase in the area constant of the metabolic hyperbola. Against this background, the increase in sensitivity of the peripheral chemoreflex with increasing levels of exercise may be seen as a compensatory mechanism to maintain the closed loop gain at a value that provides adequate feedback control. The interaction between VAH and metabolic rate in the present study has a similar characteristic in the sense that, as metabolic rate rises, the influence of VAH increases so that alveolar A major function of the peripheral chemoreflex is to provide feedback protection against inadequate, or indeed excessive, ventilation. For a feedback system to be effective, the closed loop gain of the system needs to be appropriate: too low, and poor control follows; too high, and instability ensues. A complication of the respiratory control system is that, as metabolic rate rises during exercise, so, in the absence of any adjustments, closed loop gain will decline and feedback will become less effective. The theory underlying this has been developed by 4.4The main finding of this study was that the absolute effect on respiration of a prior 8-h exposure to hypoxia varied with metabolic rate as this increased with exercise. This finding implies that the mechanisms underlying the initial process of ventilatory acclimatization to hypoxia interact to some degree with the mechanisms by which ventilation is increased during muscular exercise.This study was supported by the Wellcome Trust. M. Herigstad has been supported by the Norwegian State Educational Loan Fund and through a Florey EPA grant from the Queen's College, Oxford.


Diffusion plays a key role in many biochemical reaction systems seen in nature. Scenarios where diffusion behavior is critical can be seen in the cell and subcellular compartments where molecular crowding limits the interaction between particles. We investigate the application of a computational method for modeling the diffusion of molecules and macromolecules in three-dimensional solutions using agent based modeling. This method allows for realistic modeling of a system of particles with different properties such as size, diffusion coefficients, and affinity as well as the environment properties such as viscosity and geometry. Simulations using these movement probabilities yield behavior that mimics natural diffusion. Using this modeling framework, we simulate the effects of molecular crowding on effective diffusion and have validated the results of our model using Langevin dynamics simulations and note that they are in good agreement with previous experimental data. Furthermore, we investigate an extension of this framework where single discrete cells can contain multiple particles of varying size in an effort to highlight errors that can arise from discretization that lead to the unnatural behavior of particles undergoing diffusion. Subsequently, we explore various algorithms that differ in how they handle the movement of multiple particles per cell and suggest an algorithm that properly accommodates multiple particles of various sizes per cell that can replicate the natural behavior of these particles diffusing. Finally, we use the present modeling framework to investigate the effect of structural geometry on the directionality of diffusion in the cell cytoskeleton with the observation that parallel orientation in the structural geometry of actin filaments of filopodia and the branched structure of lamellipodia can give directionality to diffusion at the filopodia-lamellipodia interface. Diffusion is a key driver of many biological processes in living systems where ions and molecules move down concentration gradients as a result of their thermal motion within solutions. This phenomenon can be modeled using various computational techniques that consume varying degrees of computational resources correlated with the degree of molecular detail provided by the model. Of specific interest are modeling techniques that account for diffusion and reaction of molecules in biological systems.Current methods for modeling reaction-diffusion systems generally rely on ordinary differential equation (ODE) models in which the system is assumed to be well-mixed and molecules of interest exist in high numbers, satisfying the continuum assumption Agent based modeling is a robust computational technique used to simulate the spatiotemporal actions and interactions of real-world entities, referred to as “agents” in an effort to extract their combined effect on the system as a whole. Both space and time are discretized in an agent based model, giving these autonomous agents the ability to move and interact with other agents and their environment at each time step over a given duration. Simple behavioral rules govern the movement and interaction of each individual entity in an effort to re-create or predict more complex behavior of multiple entities. Such a model attempts to simulate the emergence of complex phenomena that may not be apparent when simply considering individual entities. Agent based modeling has seen applications in a broad range of fields ranging from artificial intelligence and gaming to modeling emergent social behavior such as the spread of disease and outcomes of financial markets different particles move throughout space in a random manner, these movements are related to particle size, and two particles tend to disfavor occupying the same space. These descriptions based on natural language can be translated into simple logic rules that govern the behavior of the system. Although ABMs seem ideal for modeling reaction-diffusion systems, existing ABM frameworks do not consider the accuracy of particle movement algorithms. Furthermore, particle movement probabilities are oftentimes selected arbitrarily by the modeler without validating that the molecules' movement behavior represents realistic diffusion rates. Subsequently, agent based modeling of biochemical systems can benefit from validated movement algorithms and movement probability selection criteria.In a physical system we can attribute the diffusion of a particle in solvent to the instantaneous imbalance of the combined forces exerted by collisions of the particle with the much smaller solvent molecules surrounding it which are moving due to random thermal motion. In an agent based model the same movement of this particle due to collisions with much smaller solvent molecules can be implicitly modeled by correlating the diffusion coefficient of the particle in the specific solvent to some movement probability for that particle. Furthermore, in a physical system, steric effects prevent two particles from coming closer than a certain distance from one another or occupying the same position. This type of behavior can also be replicated with an agent based model using governing rules that limit the number of particles per discretized space. As a result of these simplifications, the process of modeling particles diffusing throughout a space does not require computationally intensive method for simultaneously calculating velocities of particles and the effects of repulsive and attractive forces of these particles on other particles within the system (as seen in BD/LD models). Rather, we can describe diffusion and interaction in terms of natural language based on simple observations such as: We have outlined an approach for establishing the logic rules that govern particle diffusion along with methods for translating key parameters such as diffusion coefficients that have continuous and deterministic values into probabilities that can be used as inputs to a discrete and stochastic agent based model. Additionally, we validate these methods with single-particle and multi-particle simulations where normal diffusion is modeled. Furthermore, we investigate the effects of molecular crowding and high concentrations of macromolecules in the simulation volume as is seen in the cell cytoplasm along with their effect on effective diffusion coefficients, comparing our results with Brownian dynamics simulations. We then investigate the effect of allowing multiple particles to reside in a discrete cell of finite volume and quantify and discuss advantages and disadvantages of various approaches of enforcing finite cell volumes. Finally, we apply the ABM framework to investigate the role of geometry on the directionality of diffusion and show how specific geometries can promote diffusion in a particular direction while other geometries hinder the movement of macromolecules in a particular direction as seen in the filopodia and lamellipodia regions of the cell cytoplasm with regard to the diffusion of G-actin.ΔL, and dimensionality of DimensionN , the relationship between diffusion coefficient (D) and movement probability (T) for a fixed timestep of Δt is shown in Eq. (1) (see Methods for derivation).Given a lattice with discretization length of The relationship established in Eq. (1) allows us to take diffusion coefficient values that are meaningful in a continuous and deterministic framework and apply them to a discrete and stochastic agent based model via movement probabilities. The relationship between mean square displacement and time can be used to validate the relationship derived in Eq. (1) for simulating diffusion via ABM. This means that movement probability associated with the diffusion coefficient being modeled should result in displacement behavior and rate that would be seen in a physical system. The mean square displacement q is the numerical constant which depends on dimensionality, q = 2, 4 or 6 for dimensionalities of 1, 2 or 3 respectively and D is the diffusion coefficient and t is time. The exponent α is the anomalous diffusion exponent where α = 1 for normal diffusion while all other values of α represent anomalous diffusion. This means that for normal diffusion, there is a linear relationship between the mean square displacement of a particle and time. If we were to plot the calculated mean square displacement versus time in our simulation, the linearity of this plot would demonstrate whether simulated diffusion is normal or anomalous and the slope of this plot would be related to our diffusion coefficient as described by Eq. (2).Where r = 5 nm (diameter = 10 nm) that was free to diffuse in a solvent in three dimensional space with a diffusion coefficient of 2/sD = 100 µm. We ran our model for 500,000 time steps with a minimum sampling size of 300 independent runs which resulted in a linear relationship between mean square displacement and time  which implies that the model successfully reproduces normal diffusion behavior. Furthermore, when modeling multiple particles with different diffusion coefficients in very low concentration (crowding effects are negligible), it was observed that using Eq. (1) to derive movement probabilities for each particle type produced the same linear relationship between the measured mean square displacement and time  with different slopes for each particle type that corresponded to the diffusion coefficients being modeled. The deviation from linearity in this case was on the same order as that of the single particle and is most attributed to the stochastic nature of the model and the sampling size used. Additionally, it should be noted that as Δt and ΔL become larger (more coarse grained models) the error in the simulation also increases as a result of the approximations made in Eq. (1). However, this discretization error is typically negligible when compared to the variations resulting from the stochasticity of the model and more importantly, such a change in discretization will result in the loss of detailed spatial and temporal information.To validate our model for the diffusion of a single particle, we simulated a macromolecule with a Stokes radius of The relationship between crowding due to increased concentration and the effective diffusion at low time scales is shown in Eq. (3) (see Methods for derivation).D(C) is the effective diffusion coefficient as a function of concentration and D(0) is the diffusion coefficient of a particle in a low concentration system and C, elementV and AN represent concentration of crowding molecule, volume of a discrete element and Avagadro's number respectively and the product of these three terms is equivalent to the probability of finding any discrete cell to be occupied by a molecule (occ = CVelementNAP). In order to determine how higher concentrations affect particle diffusion we performed Langevin dynamics simulations utilizing the shifted force form of the Lennard-Jones potential energy function that assessed the effective diffusion coefficient of a particle as the concentration of particles in the system was increased. The analytical relationship shown in Eq. (3) is in agreement with the computational result from Langevin dynamics simulations shown in Where The higher effective diffusion coefficient of the all-neighbor attempt algorithm can be attributed to the algorithm simulating “intelligent particles” that search for vacancies rather than the behavior of “non-intelligent particles” that diffuse randomly due to Brownian motion. The behavior exhibited by the single-neighbor attempt algorithm is considered best suited for modeling the diffusion of passive “non-intelligent” molecules and macro-molecules such as proteins involved in reaction-diffusion systems. Furthermore, this phenomenon is critical for modeling macromolecular crowding and its direct effects on intracellular diffusion as well as reaction kinetics in intracellular environments. Alternatively, the all-neighbor attempt algorithm would be better suited for intelligent agents that can sense the environment around them using means other than collisions. The implementation of a single-neighbor movement algorithm is a very computationally efficient way of providing detailed spatial information for diffusing particles while enforcing steric repulsion and simulating molecular crowding. It should be noted that both the agent based and Langevin dynamics methods in this comparison neglect conservation of momentum and energy as well as hydrodynamic interactions between particles. Nevertheless, ABM simulations using the single-neighbor attempt show a linear relationship between the natural log of the effective anomalous diffusion coefficient and concentration as shown in The issue of crowding effects becomes more complex when considering systems with particles of varying size. In the simplest case where the model allows for only a single particle per cell, discretization errors can arise from small molecules saturating the available vacancies and reducing the effective diffusion coefficient, when in reality the volume density of the system has not been changed significantly. This error arises from discretization and the simplification that the smallest particles occupy the same volume as that of the largest particles. This issue can be overcome by introducing an additional layer of complexity in the agent based model where multiple particles are allowed to occupy a single cell. In this framework each particle is given a volume value, typically a fraction of the discretized cell's volume which it occupies, ranging from 0 to 1. As this framework is adopted, multiple particles are allowed to diffuse into a single cell and steric repulsion between particles is no longer intrinsically observed as it was with single particles per cell, raising concerns about individual cells' volume limits being exceeded at high concentrations of particles.The most intuitive method for ensuring that the number of particles per cell does not exceed the cell's volume is to simply enforce that the movement of any particle into a destination cell will not surpass that cell's volume limit. Although this method is seemingly straightforward and adds minimal computational cost  shown in To demonstrate a biolgoical application of the proposed agent based diffusion method, we have modeled the effect of structural geometry on diffusion directionality. In this model, we show the effect of quasi-random versus parallel structural geometries of filaments similar to what is seen in the structure of cell actin filaments in the form of lamellipodia versus filopodia X = 400nm, LY = 200nm,L and Z = 100nmL with periodic boundary conditions in the y-direction only. The model environment consists of a simulation box of size x>200 nm) as opposed to the direction of the lamellipodia (x<200 nm). The simulation was run using characteristic values for the g-actin monomer diameter and diffusion coefficient of ΔL = 5nm and 2/sD = 5.65 µmDimension = 3N with a movement probability of T = 1 given that only one particle type is diffusing in the simulation and the movement probability is maximized in order to maximize computational efficiency. Subsequently, the time step of the simulation can be determined to be Δt = 74 µs using the relationship established in Eq. (1).Actin filaments were initially generated in a non-discretized 3D environment with continuous filaments spaced a uniform distance apart and oriented parallel to one another within the filopodia region and conversely, filaments positioned randomly, with uniform density and oriented 68±2 degrees from each other in the lamellipodia region. The continuous actin polymers were then discretized into individual particles representing pairs of g-actin monomers fixed in space that occupy the full volume of each cell. It should be noted that the total number of particles (g-actin monomer pairs) in the lamellipodia and filopodia are equal to avoid obstacle concentration effects. Agent based modeling was used to investigate the effect of various actin filament densities on the directionality of free actin diffusion. As R represents the center of mass and iN represents the number of freely diffusing actin monomers at position ix.In order to show the time progression of concentration differences between the filopodia region and lamellipodia region at different fixed actin filament volume densities, we calculate the ratio of the center of mass of diffusing particles in the filopodia region to that of the lamellipodia. Eq. (4) shows the method used for calculating the center of mass for each region where ΔL = 5nm and 2/sD = 5.65 µm in a three dimensional space, Dimension = 3N with a movement probability of T = 1 given that only one particle type is diffusing in the simulation. The general trend seen from these results is that there is an initial peak in the tendency of particles to diffuse into the filopodia region  for all fixed particle densities greater than zero. Subsequently, this peak diminishes over time (ratio decreases towards 1) as particles reach the x-direction extremes and begin to distribute uniformly throughout space.In addition, it can be seen that as the density of fixed actin filaments is increased, the tendency of particles to diffuse towards the region of parallel filaments is only increased. This is most likely a result of random filaments generating a longer path that must be taken from the center of the simulation box to the left extreme whereas the parallel filaments generate the shortest possible distance that can be taken from the center of the simulation box to the right extreme which is effectively a reduction of dimensionality. Finally, sensitivity analysis was performed on the effect of varying bond angle between filaments in the lamellipodia. Simulations were performed with the original angle of 68±2 degrees as well as 90±2 and 46±2 degrees with a filament volume fraction density of 0.15. We observed the mean ratio of center of mass of particles diffused towards the filopodia to that of those diffused towards the lamellipodia at 68 degrees to fall within one standard deviation of the mean for 90 and 46 degrees. Subsequently, we conclude that the angle between bound filaments in the lamellipodia doesn't directly contribute to the directionality of diffusion at the filopodia/lamellipodia interface. Rather, the aggregation of multiple filament connections, which form a web-like network, results in the impedance of diffusion in any given direction, from which biased diffusion in the direction parallel to the filopodia emerges.Fick's second law relates the effect of diffusion on the concentration field of particles over time occP, D, t, and x in Eq. (5) represent probability of finding an occupied cell, diffusion coefficient, time, and position respectively while the variables C, particlesN, cellN, elementV, AN, and occP in Eq. (6) represent concentration, number of particles, number of cells, volume of each element, Avagadro's number and the probability of finding an occupied cell respectively.Note that the variables The diffusion term in Eq. (5) is a factor dependent on temperature of the solvent, size and shape of the particle, and viscosity of the solvent that quantifies the ratio of Brownian forces to drag forces. Factors such as force and velocity are not explicitly calculated in a simple agent based model and the coarse discretization of space that limits the direction of movement would make such calculations meaningless. Rather, in an agent based model, diffusion can be simulated by assigning a probability of movement to each particle agent. The relation between movement probability and a physically meaningful diffusion coefficient is derived below.ΔL as shown in nX at time t+Δt as:We consider a one-dimensional lattice with discretized segments of length n,tP, n-ΔL,tP and n+ΔL,tP represent the probability of finding the particle at position nX, n-ΔLX and n+ ΔLX respectively at time t; TR and TL represent the probability of the particle moving to the right or left respectively. Note that unless otherwise noted, all probability terms represent the probability of the respective cell being occupied. Eq. (7) states that the probability of a particle being found at nX at time t+Δt can be determined based on the probability that the particle was initially in that position and remained there (first term) less the probability that the particle started in that position and moved to either the right or left cells (second and third term) plus the probability that the particle was initially to the left or right of that cell and moved to the right or left respectively (fourth and fifth term).Where Taylor expansion of the terms in Eq. (7) as L+TR = 2TT). Note that the T/2 factor would translate to T/4 and T/6 for two-dimensional and three-dimensional cases respectively. Eq. (8) relates how the transition probability affects the spatial distribution of particles with time, similar to Eq. (5). Thus we can relate diffusion (D) to movement probability (T), using discretization length (ΔL) and time (Δt) along with the dimensionality of the environment  as previously shown in Eq. (1) for diffusion of a particle on a discrete cubic lattice.This assumes that movement probability in both directions are equal , we can analytically derive the effective diffusion coefficient for a high concentration, multiple particle system in a stochastic agent based model. Given the same one-dimensional discretized environment from vacP represents the probability of finding the given cell to be vacant. Eq. (9) states that the probability of a particle being found at nX at time t+Δt can be determined based on the probability that the particle was initially in that position and remained there less the probability that the particle started in that position and moved to either the right or left cells plus the probability that the particle was initially to the left or right of that cell and moved to the right or left respectively if cell nX was vacant plus the probability of the particle in cell nX attempting to move to the right or left into an occupied cell resulting in the particle remaining in cell nX. Taylor series expansion of the time and position varying terms along with the relationship that vacP  =  occ1-P gives the solution shown in Eq. (10).Where occ/VelementNAC = P).Note that Eq. (10) is similar to the relationship derived for the single particle concentration field and has the same relationship relating movement probability to diffusion coefficient as the single particle with an additional term related to the probability of cells being occupied by particles. As shown in Eq. (6), this probability of cells being occupied by particles is directly related to the concentration of the system ). In this model, we incorporate a von Neumann neighborhood consisting of the six cells orthogonally surrounding an agent in 3D space. Agents in this model can only interact with other agents within their von Neumann neighborhood and can only move in the direction of von Neumann neighborhood cells.all-neighbor attempt and a single-neighbor attempt algorithm are assessed. These movement methods differ in that an all-neighbor attempt is an intelligent agent movement procedure in which all von-Neumann neighborhoods are searched at random until an empty cell is found for the agent to move to while in the single-neighbor attempt a von Neumann neighbor is selected at random, disregarding whether it is occupied or vacant. If the cell is occupied the movement is rejected and the agent remains in its current cell while movement into a vacant cell is accepted with some probability correlated to the diffusion coefficient. In this second method, rejected movements represent a collision between two particles resulting in both particles remaining in their respective cells. At higher concentrations, two methods for particle movement consisting of an The model was developed using object oriented FORTRAN to maximize computational efficiency. Agent based modeling benefits significantly from object oriented programming since the concept of an object is similar to the concept of an agent. Moreover, agent based modeling is very computationally efficient for large systems and long time scales when compared to modeling techniques such as Langevin dynamics as shown in