Accurate calculation of protein surfaces is of critical importance in the protein structural and functional studies including ligand-protein docking and virtual screening. In contrast to analytical or parametric representation of macromolecular surfaces, triangulated mesh surfaces have been proved to be easy to describe, visualize and manipulate by computer programs. Here, we develop a new algorithm of EDTSurf for generating three major macromolecular surfaces of van der Waals surface, solvent-accessible surface and molecular surface, using the technique of fast Euclidean Distance Transform (EDT). The triangulated surfaces are constructed directly from volumetric solids by a Vertex-Connected Marching Cube algorithm that forms triangles from grid points. Compared to the analytical result, the relative error of the surface calculations by EDTSurf is <2–4% depending on the grid resolution, which is 1.5–4 times lower than the methods in the literature; and yet, the algorithm is faster and costs less computer memory than the comparative methods. The improvements in both accuracy and speed of the macromolecular surface determination should make EDTSurf a useful tool for the detailed study of protein docking and structure predictions. Both source code and the executable program of EDTSurf are freely available at  These methods can be generally categorized into two classes: analytical computation and explicit representation. For analytical computing, Connolly first presented an algorithm for calculating the smooth solvent-excluded surface of a molecule Level Set method for Molecular Surface generation) used a level-set method and achieved a very fast speed Although analytical methods have the advantage of getting accurate values of surface area and volume, they are not convenient to be employed in other applications when explicit surfaces of local atoms are required for further processing. For example, local surfaces of proteins and ligands are often used for shape comparison in the docking problem. The explicit surface generation method is a grid-based approximation which uses space-filling model where each atom is modeled as a volumetric item After the space-filling procedure, an important step is surface representation and construction. In general, macromolecular surface could be represented by parametric equations or triangular patches. Parametric representations of protein molecular surfaces are a compact way to describe a surface, and are useful for the evaluation of surface properties such as the normal vector, principal curvatures, and principal curvature directions A commonly used method to construct triangulated isosurface from 3D grid is the Marching Cube algorithm Euclidean Distance Transform (EDT). Triangulated surfaces are then constructed by a variation of the Marching Cube algorithm, which forms triangles efficiently by connecting grid points directly rather than intersections of edges.In this paper, we develop a new method of EDTSurf for the calculation of the three major macromolecular surfaces. We demonstrate that all the macromolecular surfaces can be universally connected with the theory of van der Waals surface (VWS) is the topological boundary of these spheres (see The definitions of the three surfaces are illustrated in eres see . The outsolvent-accessible surface (SAS) (see the red part of The molecular surface (MS) is a continuous sheet consisting of two parts: the contact surface and the reentrant surfacesolvent-excluded surface (SES), which is the boundary of the union of all possible probes which do not overlap with the molecule The Distance Transform (DT) is the transformation that converts a digital binary image to another gray scale image in which the value of each pixel in the object is the minimum distance from the background to that pixel by a predefined distance function. Three distance functions between two points However, in our study, we found only the Euclidean distance has a direct relation to the three macromolecular surfaces (see Eqs. 7–9 below). Therefore, our discussions will be focused on this distance.signed Euclidean Distance Transform (sEDT), which represents the displacement of a pixel from the nearest background point, is defined in Ref. Euclidean Distance Map (EDM), is useful in skeleton extraction, shortest path planning and shape description. EDT can be computed efficiently by methods such as mathematical morphology The Suppose the set of boundary points (or surface) of an object Isosurface can be extracted conveniently after the EDT. The isosurface with isovalue Obviously, if van der Waals solid, solvent-accessible solid and solvent-excluded solid covered by the van der Waals surface, the solvent-accessible surface and the molecular surface are represented by ith atom is Macromolecular solids are solid bodies which are enveloped by the macromolecular surfaces. The For points on the solvent-accessible surface, we define a subset N atoms is minimal macromolecular solidminimal macromolecular surfaceSuppose the minimum van der Waals radius of all the i equals i is larger than If the van der Waals radius of an atom The above three equations stand for a kind of space-filling methods which are the preliminary steps for grid-based macromolecular surface generation.After applying EDT to macromolecular solids as described above, the macromolecular surfaces can be treated as isosurface extracted from EDMs.Equation (7) is elucidated in Suppose the van der Waals surface , we apply EDT to the solvent-accessible solid which is enveloped by the solvent-accessible surface . Get rid of the voxels whose Euclidean distances are less than Use Vertex-Connected Marching Cube method to construct the triangulated surfaces from the volumetric models.Scale and translate the generated surface back to the original size and position.Since In step III, the propagation stops when the Euclidean distance is larger than After we get the three kinds of macromolecular solids, triangulation is needed to construct the ultimate macromolecular surfaces. We developed the dual of the traditional Marching Cube algorithm here, which is called Vertex-Connected Marching Cubes (VCMC). The difference between them is that the vertices of the triangles in the traditional Marching Cubes are surface-edge intersections while the vertices in the VCMC are the existing grid points. When the resolution of grid is very high, there is no additional cost for real-time construction and rendering of the triangular surface by VCMC. Furthermore, the triangulation result generated by VCMC contains fewer vertices and faces than that by MC.For a unit cube which has eight vertices, there are totally pace see . The verThe number of cases for each pattern is also marked in All the triangles formed in Molecular structures in the RCSB Protein Data Bank (PDB) are mainly obtained by the techniques of X-ray crystallography and nuclear magnetic resonance spectroscopy. 2. The purpose of such a high vertex density is to make the numerical volume calculation of MSMS as close as possible to the exact value. When the MSMS program fails to generate output results with such a high vertex density, however, we set the vertex density to a lower value. As a control, we also run LSMS 2. In 3. The average relative errors of these algorithms are listed in Since the area of surface can be analytically calculated by MSMS If the vertex density is very high, the difference between numerical and analytical surface calculations by MSMS is small, i.e. 0.45%. If we take the values of the analytical area and the high-accurate numerical volume by MSMS as the golden-standard, the relative errors for surface and volume are 3.96% and 1.18% for EDTSurf at the resolution Except for the accuracy of surface, an important requirement of the surface calculation programs is the increase of speed and decrease of memory cost. The time spent on computing the molecular surface in EDTSurf is composed of three parts: generation of scaled solvent-accessible solid 2 here). Both the three algorithms run on a Microsoft Windows XP machine with Intel Pentium 4 Processor at 1.9GHZ and 768 MB of RAM.For testing the computer cost, we apply our algorithm to 15 large protein molecules taken from the PDB, which have 27,375 to 97,872 atoms. This set of proteins has also been used by Can et al. to compare their algorithm LSMS with three other programs, including the MSMS, which is integrated in UCSF Chimera As shown in The speed of EDTSurf and LSMS are both dependent on the size of bounding box while that of MSMS relies on the number of atoms and vertex density. If the triangulation result contains singularities in each round, MSMS will change the radii of some atoms and perform several rounds of computations. This is partly the reason for the expensive time cost of MSMS for most of proteins in the O(Nlog(N)) , MSMS is not efficient for large supramolecular complexes. Both EDTSurf and LSMS have the computational complexity 3)O(L (L is the length of the bounding box). They will be slower than MSMS when handling molecules with a small number of atoms.Since the computational complexity of MSMS is Protein cavities can be empty or water-containing. They can be within domains, between domains, or between subunits. The buried water molecules in the internal cavities contribute to protein stability. This is because the water-filled cavities are important for modulating residues surrounding the cavities. Cavities can help us to locate the proton transport pathway in the membrane protein After the triangulated surface generation, one part of the molecular surface is in contact with outside space while the other part is buried inside the molecular solid. Cavities are those formed by the inner molecular surface. Since molecular surface is propagated from solvent-accessible surface by our method, it can be seen that the number of cavities in the molecular surface obtained is equal to that in the solvent-accessible surface.2. It is shown in In In In the left panel of 3, 643, and 1283) to see the visual effects. We also compare our generated surfaces with the molecular surface  images. On the left panel of In We also compare the efficiency of MC and VCMC algorithms on the isosurface extraction for 18 EM density maps. The average CPU time by VCMC (0.54s) is about 1.4 times faster than the MC algorithm (0.75s).As discussed in When we add one run of Laplacian smoothing to the generated surface, each mesh vertex is moved to the centroid of the surrounding mesh vertices which are topologically connected. This post-processing step will make the mesh surface closer to the smooth continuous surface in some degree.We have developed a new method, EDTSurf, for calculating three major macromolecular surfaces based on the method of Euclidean Distance Transform. Triangulated surfaces are then constructed by using Vertex-Connected Marching Cube method. The two parts of the molecular surface which are the contact surface and the reentrant surface can be efficiently distinguished. The resolution of the grid system can be controlled flexibly. The area and the volume of molecular surface are calculated accurately. Surfaces of the interior cavities and their surrounding atoms could be detected. Moreover, compared with the methods in literature, the EDTSurf algorithm is faster in speed and consumes less memory, especially when the number of atoms in the molecule is large.As an application in protein structure prediction, we have applied EDTSurf to generate the solvent-accessible surface area of each residue for all proteins in the PDB library. This provides an essential frame for matching the predicted solvent accessibility with that of template structures in our fold-recognition algorithm http://zhang.bioinformatics.ku.edu/EDTSurf. All the images have been generated by the MVP  software which is also freely downloadable at http://zhang.bioinformatics.ku.edu/MVP.Although the illustrations have been given for proteins molecules throughout the paper, the surface of any other macromolecules such as RNA or DNA can also be calculated using EDTSurf. The source code and executable package of EDTSurf are freely available at


The Framingham Heart Study, founded in 1948 to examine the epidemiology of cardiovascular disease in a small town outside of Boston, has become the worldwide standard for cardiovascular epidemiology. It is among the longest running, most comprehensively characterized multi-generational studies in the world. Such seminal findings as the effects of smoking and high cholesterol on heart disease came from the Framingham Heart Study. At the time of publication these were novel cardiovascular disease (CVD) risk factors, now they are the basis of treatment and prevention in the US. Is the Framingham study now on it's way to becoming the gold standard for genetic epidemiology of CVD? Will the novel genetic findings of today become the health care standards of tomorrow? The accompanying articles summarizing the results of genome-wide association studies (GWAS) give the reader a first glimpse into the possibilities. The Framingham Heart Study, founded in 1948 to examine the epidemiology of cardiovascular disease in a small town outside of Boston, has become the worldwide standard for cardiovascular epidemiology . It is aThe strength of the Framingham Study has always been and will always be their extensive, well-characterized, longitudinal phenotypes. In an era of human genetics where speed is of the essence, such phenotypes are hard to come by. The recent explosion of genetic information available and low-cost genotyping technology has allowed for extensive hypothesis-free genome-wide interrogation ,6. GenomNature [Replication will be critical in determining which associations are real as we begin to see the results of multiple GWAS. A paper was recently published in Nature  providinThe data presented in the accompanying papers are not optimal. The reports are based on a preliminary GWAS with a lower SNP density  and a less accurate allele calling algorithm (Dynamic modeling or DM) than is the standard today  typed inFirst, because the GWAS was performed in families, results from linkage and association can be compared. Most human geneticists are abandoning linkage in favor of the latest technology-driven methods. However, linkage can provide valuable information to aid in differentiating between real associations and false positives. It was encouraging to see that two of the inflammatory markers (MCP1 concentration and CRP levels) showed concordant linkage and association peaks . HoweverSecond, because Framingham is a cohort without disease-based ascertainment, a multitude of phenotypes can be investigated. Many of these phenotypes are correlated. This provides the opportunity to investigate pleiotropy and to begin to decipher the genetic architecture of complex diseases such as CVD. The Framingham investigators performed a first pass look at this question. They looked for overlap among the top 500 SNPs associated with phenotypes across three "working groups": glycemic/diabetes phenotypes, lipid phenotypes and obesity phenotypes. Eleven SNPs were found in more than one group, but none of these were found in all three -12. Theset al. [et al. [Third, I think it is important to note that, despite the limitations of these data, the Framingham investigators replicated several well-established candidate gene associations. Among these were SNPs in the TCF7L2 gene and diabetes , SNPs inet al.  and McPh [et al. .The analysis of such a large volume of data and presentation of results is a daunting task. The Framingham investigators have done a commendable job in getting the results out and providing the data for other investigators to use. In the process they have entered the "gold rush" to stake claims on GWAS results . AlthougThe pre-publication history for this paper can be accessed here:


Pregnancy-related low back pain is considered an important health problem and potentially leads to long-lasting pain and disability. Investigators draw particular attention to biomedical factors but there is growing evidence that psychosocial and social factors might be important. It prompted us to start a large cohort study (n = 7526) during pregnancy until one year after delivery and a nested randomized controlled intervention study in the Netherlands.A randomized controlled trial (n = 126) nested within a cohort study, of brief self-management techniques versus usual care for treatment of women with persisting non-specific pregnancy-related low back pain three weeks after delivery. Women in the intervention group were referred to a participating physiotherapist. Women in the usual care group were free to choose physiotherapy, guidance by a general practitioner or no treatment. Follow up took place at 3 months, 6 months and one year after delivery.Outcomes included change in limitations in activities (RDQ), pain (VAS), severity of main complaints (MC), global feeling of recovery (GPE), impact on participation and autonomy (IPA), pain-related fear (TSK), SF-36, EuroQol and a cost diary. For the outcome measures, series of mixed models were considered. For the outcome variable global perceived effect (GPE) a logistic regression analysis is performed.Intention-to-treat outcomes showed a statistical significant better estimated regression coefficient RDQ -1.6 {-2.9;-0.5} associated with treatment, as well as better IPA subscale autonomy in self-care -1.0 {-1.9;-0.03} and TSK -2.4 {-3.8;-1.1} but were not clinical relevant over time. Average total costs in the intervention group were much lower than in usual care, primarily due to differences in utilization of sick leave but not statistically significant.Brief self-management techniques applied in the first 3 months after delivery may be a more viable first-line approach but further research is needed to draw inference on costs and to determine whether no care is a better option in the long term.[ISRCTN08477490] Pregnancy-related low back pain is a frustrating health problem in the Netherlands and Scandinavia because of its high prevalence during pregnancy 77–84%) -5 and th4% -5 andIt prompted us to start a large longitudinal, prospective cohort study (n = 7526), which studies the prevalence, etiology, severity and prognosis of pregnancy related low back and/or pelvic girdle pain during pregnancy until one year after delivery  and a neThe aim of the trial is to determine the effectiveness and cost of brief self-management techniques versus an approach based on a pain contingent basis , after delivery.Because of the lack of a clear definition we used an extensive description of pregnancy-related low back pain including all women who experience some form of pregnancy-related pain in the lower back and/or pelvic girdle originated within the musculoskeletal system. In this study we refer to the International Classification of Functions (ICF) as a basis for describing  and bettThe trial was assigned to an international trial identification number (ISRCTN08477490).The medical ethics committee of the Maastricht University Hospital approved the intervention and cohort study that were performed in the Southeast of the Netherlands. Midwives and gynecologists recruited the women during early pregnancy (10–14 weeks). Women were included in the cohort if they were at least 18 years old, pregnant and well versed in Dutch language. They were given written information explaining the aims and contents of the cohort and intervention study before they decide to participate. A woman entered the intervention study at the moment of three weeks after delivery after signing informed consent for both the cohort and intervention study during early pregnancy and meeting the in- and exclusion criteria of the intervention study, at three weeks after delivery. Women were included when having pain in the lower back including the pelvic girdle with an onset during pregnancy or just after delivery (cohort data), were restricted in their normal daily activities because of pregnancy-related low back pain and if there was a delay in recuperation. Women diagnosed with systematic diseases or specific pathology in the region of the pelvic girdle and/or lower back, affecting pain and activities were excluded. Exclusion also occurred in case of extensive family related or psychosocial problems or when a disablement procedure was not yet finished. Final important aspects for in-/exclusion were the willingness to participate in the study or having a clear treatment preference . We onlyRandomization took place after collecting baseline data and obtaining informed consent. An independent research assistant unaware of the baseline data carried out the concealed randomization procedure using a computer-generated random numbers list. Block size was four. Women were told that to the current knowledge the both treatment options are considered to be equally effective. Participating physiotherapists were not involved in the baseline and effect measurements. Researchers dealing with the baseline and outcome data assessment were blinded to the intervention assignments.All participating physiotherapists were experienced and specialized in treating women with pregnancy-related low back pain. Prior to the trial, specialized members of the Royal Dutch Physiotherapy Association, and working in the research area (Southeastern part of the Netherlands) were contacted and asked to participate in the intervention study. After signing consent they were at random but stratified according practice residence split up in two groups. The physiotherapists providing the experimental intervention received additional training and education, preceding and during the trial. The other group received no extra training . Participating physiotherapists of both groups were asked not to communicate the contents of both treatment approaches with each other.Women, allocated to the usual care group, were free to choose usual care treatment by a physiotherapist not providing the experimental intervention, guidance by a general practitioner or do nothing. Information about the option chosen was collected by means of questionnaires during the follow-up period. When a woman chose usual care, treatment started within one week. The only interventions that were not allowed were those associated with the experimental intervention. Prior to the trial, detailed information is gathered about the contents of the current treatment options in the Netherlands. Part of the information is collected by means of group discussions with experienced physiotherapists and interviews on an individual basis with affected women out of our cohort study . The pro• An expert role of the physiotherapist in relation to the patient focusing on disease management,• A pain contingent regime of avoiding and limiting several specific day-to-day activities,• Treatment goals were focused on biomedical factors,• Stabilizing exercises of the lumbar spine and pelvic girdle.The general practitioner in the Netherlands gives some general information about the health problem concerning the prognosis after delivery. In general, this guidance is limited to one visit.Women, allocated to the experimental intervention group, were immediately referred to a participating physiotherapist in their own neighborhood. We provided an individualized self-management approach of 7–9 sessions for 30 minutes in a period of time of 12 weeks. Self-management refers to the individual's ability to manage the symptoms, treatment, physical and psychosocial consequences and life style changes inherent to living with a chronic condition -24. A re• Standardized information by means of a protocol for the therapists and booklets for the patients specially developed for this study,• Simple complaint-related problem-solving techniques that engaged women in identifying day-to-day problems or limitations related to the complaints under investigation,• Setting personal goals by action planning,• Reviewing the action plans and progress towards goals,• A shift from an expert role of the physiotherapist to an equal partnership between physiotherapists and patients. The physiotherapist becomes a teacher in the development patient's skills to manage her health problem,• A hierarchy of individual fear-eliciting movements and activities,• Specific skills such as specific stabilizing exercises of the lumber spine and pelvic girdle and building up fitness training.Measurement should take place in all relevant domains of the ICF; body functions, limitations in activities, participation restrictions and contextual factors. Movement related body functions are listed during physical examination. Pain, another body function is listed with two Visual Analog Scales ,32 and wDuring the home visit, a standardized history was taken and physical examination was performed by a research-physiotherapist. Demographic characteristics and data about life style, delivery including epidural anesthesia, education, medication, the onset of pain and functional status during pregnancy were already gathered as part of the cohort study. After history taking a short standardized clinical examination program was performed to exclude specific pathology, list the mobility of the back and lower extremities, observe daily activities such as walking, standing and sit down and test nerve root radiation. Because of the limited evidence, specific tests for pain provocation, pelvic stability and hyper mobility were not used as exclusion criteria or to discriminate between pelvic girdle and low back pain. The research-physiotherapist filled out the Pain Behavior Scale PBS ,27, afte• Beck Depression Inventory (BDI) , measure• Pain catastrophizing was measured with the Pain Catastrophizing Scale (PCS) . The PCS• Treatment expectancy  was meas• To measure the experience of negative affect we used the 14-item Negative Emotionality Scale (NEM). To measure positive affect we used the 11-item Positive Emotionality Scale (PEM). Both are subscales of the Multidimensional Personality Questionnaire . The ten• The Pain Behavior Scale (PBS) ,27 is an• Limitations in activities were measured with the Dutch translation of the 24-item Roland Disability Questionnaire (RDQ) , with a • Global Perceived Effect  (GPE) wa• The main complaints (MC) were selected by the woman herself by selecting three essential activities in a standardized way of her everyday life that at that time (baseline) difficult or impossible to perform because of low back pain and/or pelvic girdle complaints. The severity of the complaints was rated with Visual Analog rating Scales (VAS) ,30. For • Pain was measured with two 100-points Visual Analog rating Scales (VAS) of the McGill Pain Questionnaire (MPQ-DLV) ,32 to re• The impact on participation and autonomy (IPA) measured person-perceived restriction in participation and autonomy ,34. The • Fear of movement was measured by the Dutch translation of the Tampa Scale for Kinesiophobia (TSK) . The TSK• The Short-Form 36 (SF-36) ,39 evalu• The EuroQol (EQ) was used to obtain a self-description of mobility, self-care, used activities, pain/discomfort and anxiety/depression . Each di• A cost-diary  was usedWomen were asked to complete follow-up questionnaires at 3 months after randomization (short-term results), 6 months and one year after delivery. The follow-up questionnaires contained the listed outcome measures. Furthermore, items on contents, satisfaction and beneficial aspects of the  treatment were listed. Co-interventions, medication, aids, additional medical consumption, recurrence of complaints, return to gainful employment and a possible subsequent pregnancy were also registered. Besides, the follow-up questionnaires assessed also how many treatment sessions were followed in the previous period of time.Women who did not return their follow-up questionnaires were contacted by (e) – mail or phone and were asked to continue participation.The baseline status of the study groups was compared with respect to the distribution of the baseline values of all measures. For the outcome measures, series of mixed models were considered . The modA clinical important change on the primary outcome RDQ was considered a change of 2 points.Power calculations showed that to detect a difference of 2 in changes scores of the RDQ between both groups at 80% power and with alpha = 0.05 a total sample size of 124 is needed. When alpha = 0.1 with 80% power a total sample size of 90 is needed.An economic evaluation compared the costs and health effects of both treatment options from a societal perspective. Resources recorded in the cost diaries were valued by cost estimates for the year 2003. True cost estimates are available in the Dutch guidelines for pharmaco-economic studies . Costs for over the counter drugs (OTC) and aids were reported directly by the women in their diaries. Productivity costs resulting from loss of paid labor were calculated by applying the friction costs method, which limits the period of production loss to the time during the work of the person is not replaced. In 2003 the friction period was set at 22 weeks or 154 days. In this study, the regular period of maternity leave was excluded from the friction period. The length of maternity leave after delivery is set at 10 weeks in the Netherlands. Paid production was valued by the average national gross wage per hour, broken down by sex  and age category (25–44 year).t-tests for unpaired observations. Total costs are considered the primary total cost outcome.Between-group differences in outcomes of mean total costs were analyzed by Student's Self-administrated questions about limitations in activities and the perceived need for treatment among women from the cohort study (n = 7526) resulted in 869 possibly eligible participants, in the first week after delivery. On basis of history taking by telephone two weeks after delivery, 743 women were excluded from participation Figure . The majBaseline status of the participants is given in Table After randomization, 64 women were assigned to the usual care group and 62 to the experimental intervention group. For 114 women (90%) data were available for all outcome measures 3 months after randomization  all outcome measures were complete at six months and one year after delivery. The prognostic status at baseline of women who were lost to follow-up and women who filled out all the outcome measures was highly similar.Nineteen women of the usual care group did not receive any treatment in the year after delivery. Nineteen women of the same group received treatment in the follow-up period (between three months after randomization and one year after delivery). Four women in the experimental intervention group received treatment in the follow-period.In both groups a considerable number of women reported pain flare-ups after they became free of any pain. . 34 women of the usual care group and 45 of the experimental group reported return to gainful employment one year after delivery. 11 women of the usual care group and 5 of the experimental group applied for a benefit due to the disorder. Four women of the usual group and six of the experimental group did not return to gainful employment because they were out of a job. Six women (three in both study groups) reported a subsequent pregnancy one year after delivery.The outcomes of both study groups until one year after delivery are shown in table Secondary significant estimated treatment assignment effects are demonstrated in the total score of the TSK and subscale Activity Avoidance and the IPA subscale Autonomy in self-care. The estimated treatment effect in the IPA subscale Autonomy in self-care also demonstrates a significant effect for the experimental group compared to usual care. Depression measured with the BDI was a significant covariate in all models.Other estimated treatment assignment effects were not significant different although there was an extensive within-subject improvement on the primary outcome RDQ (about 10 points improvement on the RDQ from baseline to one year after delivery) in both study groups and on several secondary outcomes Tables . SubgrouWomen in both groups reported a substantial reduction in pain (VAS pain today and last week) in the year after delivery Table , but theHistograms of the changes scores of the RDQ suggested that the assumption of normal distributed scores was acceptable (range between -5 and 20). Floor or ceiling effects are considered to be present if more than 15% of the respondents achieved the lowest or highest possible score. At baseline, only one participant showed the highest possible score (24) on the RDQ and no one the lowest possible score (range 23). With a mean of 13.4, SD 4.4 for the total group and inspection of the histogram, the normal distribution of the baseline variable was also acceptable. There were no floor or ceiling effects of the RDQ to be present at baseline. Histograms of the residuals of the linear mixed models suggested that the assumptions of normality distributed variables were acceptable.The sessions of the experimental intervention (7–9) were included in the total amount of physiotherapists' sessions. Costs were listed in table Calculation of cost-effectiveness ratios was not relevant because both the effectiveness of the primary and secondary outcomes and reduction in costs were in favor of the experimental intervention.In spite of the statistical significant estimated treatment effect of the RDQ for the experimental group compared to the usual care group, the difference is too small to be clinically relevant over time (one year after delivery). Nevertheless, subgroup analyses indicated that women with more severe limitations in activities benefited more from the experimental intervention compared to women in the usual care group on the primary outcome RDQ.In spite of the large confidence intervals of costs due to sick leave within both study groups, the mean costs of sick leave in the usual care group were about doubled compared to the experimental intervention group; however not statistically significant. Differences remained stable in the subgroup analyses. Maybe, the experimental intervention has some influence on sick leave. Physiotherapists of the experimental intervention were instructed in detail about the advice return to work. They were not allowed to advice against return to work but were asked to encourage the women in their intention to return to work with the support of goal-orientated action plans. In the usual care group, return to work was a regular topic of conversation but left to the appraisal of the physiotherapist to advice a woman. At the same time, there were still many other unknown reasons why a considerable number of the young mothers were reluctant to return to gainful employment after finishing maternity leave. More research in this field in general and especially in the Dutch situation is necessary to investigate potential prognostic variables that influence the duration of sick leave related to pregnancy and childbirth. We did not perform mixed models in this evaluation because we had not enough information about probably influential confounders. Results of the economic evaluation in this trial were therefore of limited significance.Recurrence of pain episodes was a quite common phenomenon in the year after delivery but seems to be independent from the differences in improvement on resumption of normal activities, participation (work) and reduced fears between the both study groups. Pain flare-ups seemed to be better manageable in the experimental intervention group than in the usual care group.In-/exclusion data show extensive improvement in the first weeks after delivery preceding the enrollment in the intervention study. The improvement within both groups lasted until one year after delivery. These results indicate that pregnancy-related low back pain is a temporary albeit inconvenient condition with a good prognosis, especially in the first month after delivery.Overall, results of this trial are for the greater part in line with trials using self-management approach with chronic low back pain patients .Participating therapists were already embedded in the primary health care system. Both the educational course received by the therapists and the intervention they delivered were brief and appropriate for implementation in primary care. Therapists showed the potential to shift the model of care from a biomedical approach to a broad approach that incorporated psychosocial factors. The shift from a biomedical to a biopsychosoial approach is not to mistake or misunderstand. A biopsychosocial attitude is not a matter of "leaving or ignoring the biomedical domain" but a matter of integrating all relevant aspects and paying attention to diagnostics as well as intervention regarding impairments, activities and participation. Collaborative partnership and shared responsibility between physiotherapists and the women become important. Action planning and problem solving need training and evaluation, education alone is not enough. An example of shared responsibility is that signs and symptoms must not be ignored but physiotherapists and women have to learn to interpret then adequately. Either important is to learn which activities are helpful to become active again. Graded exposure of the activities that were avoided was integrated in the protocol. After an initial period of learning these skills, it becomes the task of the woman themselves in collaborative partnership with their physiotherapist. For both the women and the physiotherapists it was a rather new policy.Similarity of improvement between the both study groups at one year after delivery raises the question whether either approach is superior to the other or to no treatment at all. Unfortunately, it was not possible to design a study with a third group receiving no treatment after delivery because there was a strong urge to leave open the possibility of a referral to a physiotherapist already in the first month after delivery. The urge did not only come from the potential participants but also in an even greater extend from the physiotherapists. All included women in the study wanted to be referred to a physiotherapist at the moment of enrolment in the intervention study. Nevertheless, a considerable number of women of the usual care group did not visit a physiotherapist afterwards. This was quite unforeseeable and has not only influenced the primary outcome but also the huge variation in costs in the usual care group.A restriction on our study and on future studies is that the prevalence of the disorder after delivery is low. We used the maximum of participants out of the cohort (n = 7526) and still could include only 126 women. This could have influenced the power of the study.The trial had high internal validity shown by an adequate recruitment out of the cohort, remote system of randomization, blinding of the assessors and researchers involved in the measurements and analyses. Embedding the trial in a large cohort study had the advantage that it enabled us to specify more precisely not only the participants but also an optimal time-frame for the intervention. According to the prevalence figures of pain during pregnancy and after delivery, the enrolment data out of the cohort and the follow-up data of the intervention study, the transition from acute to chronic pain falls most likely within the timeframe of the first two or three months after delivery. This is a moment of special interest for more detailed diagnostics and intervention. Start of the experimental intervention shortly after delivery was reasonable well-timed.Several authors in this research field advocate an intervention study during pregnancy (11–13) with a follow-up in the first year after delivery. The high prevalence of pain during pregnancy seems to support this opinion. However, the moment of transition from acute to chronic pain seems to lie in the first two months after delivery. Second, the huge amounts of participants that will be needed to reach sufficient power speak against an intervention study during pregnancy.The findings of this study and the underpinning results of the subgroup analyses lead to a future study question including a brief self-management approach compared to a no intervention and a usual care option. A study like this will address the effectiveness of the self-management approach and cost in more highly selected groups with greater disability. Potential confounders related to return to work should be included too. The preferable time-frame of the experimental intervention is between 3–4 weeks until three months after delivery.At least six out of every seven women with pain during pregnancy make a rapid recovery in the first two weeks after delivery. Nevertheless, every woman that is seeking for help during pregnancy must be offered some form of simple guidance, in clinical practice. A stay active approach and information about the prevalence and natural course of the disorder seems to be worthwhile aspects.An important signal to actually start with an active intervention after delivery in the future is not only pain and limitations in activities but also women's own worries and needs. Evaluation of the complaints within the framework of the biopsychosocial approach turned out to be meaningful.Brief self-management techniques applied during the first 3 months after delivery are probably a viable first-line approach for the management of pregnancy-related low back pain, but further research is needed to get more insight into the interference of the costs and a comparison with a no treatment option. Secondary, results indicate that it is a temporary disorder with a good functional prognosis especially in the first months after delivery.The authors declare that they have no competing interests.All authors read and approved the final manuscript. CHGB, RAdB, JWSV, MEJBG, PMJCW, JMB, PAvdB, GGME: Study concept and design. CHGB, RAdB, PL, JMB: Analysis and interpretation of the data. CHGB, RAdB:Drafting the manuscript. RAdB, JWSV, MEJBG, PL, JMB, PAvdB, GGME: Critical revision of the manuscript for important intellectual content. CHGB, RAdB, JMB: Statistical Analysis.The pre-publication history for this paper can be accessed here:


The mathematical model, initially developed for the study of normal fracture healing, is able to capture essential aspects of the in vivo atrophic non-union model despite a number of deviations that are mainly due to simplifications in the in silico model. The mathematical model is subsequently used to test possible treatment strategies for atrophic non-unions . Preliminary in vivo experiments corroborate the numerical predictions. Finally, the mathematical model is applied to explain experimental observations and identify potentially crucial steps in the treatments and can thereby be used to optimize experimental and clinical studies in this area. This study demonstrates the potential of the combined in silico-in vivo approach and its clinical implications for the early treatment of patients with problematic fractures.Recently developed atrophic non-union models are a good representation of the clinical situation in which many non-unions develop. Based on previous experimental studies with these atrophic non-union models, it was hypothesized that in order to obtain successful fracture healing, blood vessels, growth factors, and (proliferative) precursor cells all need to be present in the callus at the same time. This study uses a combined  In light of the ageing population, the occurrence of bone fractures is expected to rise substantially in the near future. In 5 to 10% of these cases, the healing process does not succeed in repairing the bone, leading to the formation of delayed unions or even non-unions. In this study we used a combination of an animal model mimicking a clinical non-union situation and a mathematical model developed for normal fracture healing to investigate both the causes of non-union formation and potential therapeutic strategies that can be applied to restart the healing process. After showing that the mathematical model is able to simulate key aspects of the non-union formation, we have used it to investigate several treatment strategies. One of these strategies, the treatment of a non-union involving a transplantation of cells from the bone marrow to the fracture site, was also tested in a pilot animal experiment. Both the simulations and the experiments showed the formation of a bony union between the fractured bone ends. In addition, we used the mathematical model to explain some unexpected experimental observations. This study demonstrates the added value of using a combination of mathematical modelling and experimental research as well the potential of using cell transplantation for the treatment of non-unions. Atrophic non-unions, a class of non-healing fractures that display only limited external callus formation, were thought to occur as a result of impaired local blood supply in vivo-in silico approach to look at these different aspects . Furthermore, the in silico model is used to investigate the occurrence of and design possible treatment strategies for atrophic non-unions. Experimental results  are used to corroborate the numerical predictions for atrophic non-unions in particular and demonstrate the potential of both the in silico-in vivo approach and the treatment strategy of cell transplantation. Finally, the mathematical model is applied to explain experimental observations and identify potentially crucial steps in the treatments.Based on previous, purely experimental, studies with these atrophic non-union models, it was hypothesized that in order to obtain successful fracture healing, blood vessels, growth factors and (proliferative) precursor cells all need to be present in the callus at the same time Rats were kept in accordance with UK Home Office welfare guidelines and project license restrictions.ad libitum and unrestricted weight-bearing.Animals and operative procedures were carried out as previously reported A standardised circular frame external fixator Two independent senior orthopaedic trainees assessed standardized radiographs obtained after operation and every two weeks thereafter. They categorized the fractures as healing or not according to the criteria of the AO-ASIF manual Atrophic non-union was induced in 8 WKY rats as previously described Formation of callus was assessed by scanning radiographs into a Macintosh Quadra 650 computer and analyzing images . The callus outline was traced manually and the size of the outlined area was calculated. The results were expressed as a percentage change in the amount of mineralized tissue from post-operative radiographs The right lower limbs were fixed in neutral phosphate-buffered formalin (4% v/v) for 48 hours, decalcified in neutral ethylenediaminotetra-acetic acid (EDTA), embedded in paraffin wax and 6µm sections were cut and stained with haematoxylin and eosin. Wax sections for immunohistochemistry were cut onto poly-l-lysine coated slides and immunostaining was performed with the following antibodies: Transforming growth factor beta (TGF-β) , Basic Fibroblast Growth Factor (FGF basic) , Platelet-Derived Growth Factor (PDGF) , Bone Morphogenetic Proteins 2 and 4 (BMP 2/4) , and Proliferating Cell Nuclear Antigen (PCNA) . Alkaline phosphatase-conjugated anti-mouse  or anti-goat  secondary antibodies were used. Cell transplant samples labelled with BrdU were prepared as above, followed by immunostaining with antibodies against BrdU  in conjunction with an animal research kit . All antibodies were used according to the manufacturer's instructions.Sections were analyzed using a light microscope. Cytoplasmic growth factor expression was semi-quantified using a four-value intensity score  A Mann-Whitney U test was used to assess significance of the cell proliferation results. All statistical analyses were performed using the Statview software package  and significance was assumed as p<0.05.The mathematical model used in this study was originally developed to describe normal fracture healing D  are the diffusion coefficients (random motion). et al.et al.in silico experiments were conducted to design potential treatment strategies for the various non-union models The regeneration processes are described by calculating the spatiotemporal evolution of the density of mesenchymal stem cells, osteoblasts, chondrocytes, fibroblasts, endothelial cells, bone, cartilage, fibrous tissue and vascular matrix and the concentrations of three generic growth factor families . The spatiotemporal dynamics is expressed by means of a system of 12 partial differential equations of the taxis-diffusion-reaction type. The system's general structure is:A simplified (fixed) geometrical domain of a fracture callus  was cons5) while all other model parameters and initial/boundary conditions were left unchanged with respect to the normal healing case. As the initial mechanical conditions for both the healing and non-union group were equal, the influence of mechanical loading was not taken into account explicitly in this study  in the mathematical model combined with the absence of vascular growth factor production by fibroblasts, leading to a slow build-up of the vascular network. The experimentally observed decrease in number of blood vessels during bone/blood vessel remodelling at POW 8  cannot be predicted as the model does not encompass the remodelling process. Despite these limitations, the mathematical model does predict a substantial time difference in the vascularisation of the callus area as shown by the  lag in blood vessel formation between healing and non-union groups at POW 3.Similar to the experimental observations in vivo healing group, concurred well with that observed by Iwaki et al.in vivo.Cell proliferation observed in the et al.et al.et al.et alin vivo observations. Furthermore, the simulations show occurrence of the highest levels of chondrogenic and vascular growth factors in the first week, as experimentally observed. In the mathematical model chondrocytes are the only cell type capable of chondrogenic growth factor production and the main responsible for the production of vascular growth factor (upon hypertrophy). As chondrocytes are predicted to be only marginally present in the callus of the non-union group, the predicted chondrogenic and vascular growth factor concentrations further on in the healing process are very low for this group in comparison to the growth factor release at fracture induction. Furthermore, for the non-union group, initial growth factor concentrations are strongly driven by boundary conditions that were applied during the first days after fracture to mimic local and systemic reactions occurring outside of the modelling domain Growth factor expression observed experimentally during the early stages of bone healing correlated well with other studies reporting BMP Comparison of experimental and simulation results showed a number of discrepancies that could be attributed to a number of model simplifications and suggestions were made above to overcome those. Additional model simplifications were made in the framework of this study such as the use of a fixed callus size (rather than a size that varies over time) and the continuum representation of blood vessel formation, which will be dealt with in future versions of the mathematical model. For a thorough discussion on the model limitations we refer the reader to in silico – in vivo approach in this study. As blood vessel formation is delayed in the non-union group, the most suitable time point for intervention of either growth factor treatment or cell transplant, seems to be three weeks post-osteotomy, when the blood supply to the interfragmentary gap has started to recover. Injection of MSCs directly into the callus area elicited to a good healing response in silico. Experimental results confirmed that transplantation of MSCs into the interfragmentary gap at POW 3 prevented the onset of an atrophic non-union. There was significantly more bone present in the treatment group (cell transplant) than in the control group (carrier solution). Union by bridging callus had occurred in three of the four treatment animals. Yet, all of the animals treated by MSC transplantation displayed an asymmetric healing with endochondral ossification in progress in part of the intercortical callus  the fracture site. MSCs entering the callus area start differentiating under the influence of the growth factors that are present. As the cells migrate slowly into the callus area, they become differentiated before they reach the central area of the callus. Differentiated cells deposit bone matrix to replace the fibrous matrix which further decreases the migration speed of the cells that enter the callus area while the osteogenic growth factors that are expressed enhance the differentiation, resulting in a layer of bone close to the cell source while fibrous tissue persist in the major part of the callus area.The use of stem cells in the treatment of non-unions is gaining interest Click here for additional data file.Text S1This file contains a detailed description of the mathematical model used in this study including the full set of equations, parameter values, boundary & initial conditions and implementation details.(0.67 MB DOC)Click here for additional data file.


Whereas a non-operative approach for hemodynamically stable patients with free intraabdominal fluid in the presence of solid organ injury is generally accepted, the presence of free fluid in the abdomen without evidence of solid organ injury not only presents a challenge for the treating emergency physician but also for the surgeon in charge. Despite recent advances in imaging modalities, with multi-detector computed tomography (CT) (with or without contrast agent) usually the imaging method of choice, diagnosis and interpretation of the results remains difficult. While some studies conclude that CT is highly accurate and relatively specific at diagnosing mesenteric and hollow viscus injury, others studies deem CT to be unreliable. These differences may in part be due to the experience and the interpretation of the radiologist and/or the treating physician or surgeon.A search of the literature has made it apparent that there is no straightforward answer to the question what to do with patients with free intraabdominal fluid on CT scanning but without signs of solid organ injury. In hemodynamically unstable patients, free intraabdominal fluid in the absence of solid organ injury usually mandates immediate surgical intervention. For patients with blunt abdominal trauma and more than just a trace of free intraabdominal fluid or for patients with signs of peritonitis, the threshold for a surgical exploration - preferably by a laparoscopic approach - should be low. Based on the available information, we aim to provide the reader with an overview of the current literature with specific emphasis on diagnostic and therapeutic approaches to this problem and suggest a possible algorithm, which might help with the adequate treatment of such patients. The introduction of routine computed tomography (CT) in trauma exposes us to a plethora of new information, sometimes leaving us with more information than we had bargained for. Although a recent study by Huber-Wagner and colleagues was able to show a positive effect on overall survival of trauma patients with blunt injury receiving whole-body CT during emergency department resuscitation , the stuWhilst sonography and conventional radiography remain well-established techniques, CT scanning of the abdomen and pelvis is the procedure of choice to evaluate the hemodynamically stable patient who has sustained blunt or penetrating trauma. CT has replaced Diagnostic Peritoneal Lavage (DPL) as the first method of choice in many trauma centers worldwide. Its major advantage is that it is not only capable of revealing the presence of intra-abdominal or intra-thoracic hemorrhage but can to some extent also identify the organ involved .CT exhibits very high sensitivity and specificity in detecting the majority of solid organ injuries, but unfortunately misses up to 15% of small bowel and mesenteric injuries as well as some acute pancreatic injuries ,4. ProtoVarious authors have evaluated the benefits (or disadvantages) of the addition of contrast agent for CT scanning. Older studies usually base their protocols on conventional or single-detector row helical CT scan with use of oral and intravenous contrast. Although relatively rare and not always easy to detect , extravaIn centers where a CT scan is not available or limited to office hours, frequent re-evaluation of the patient's condition, repeated sonography and DPL remain the cornerstones of the diagnostic work-up of abdominal trauma. In the setting where clinical evaluation alone is relied on to determine whether or not a patient requires surgery, negative laparotomy rates may be up to 40% . In centWhere CT scanning is readily available, up to 85% of abdominal solid organ injuries are treated conservatively . FortunaBut what should be done if the "almighty CT scanner" does not provide us with a conclusive answer to our questions? One of the most difficult diagnostic challenges is the presence of free fluid in the abdomen without evidence of solid organ injury. In order to find an answer to our question as to what should be done for patients in this setting, we searched Pubmed for "free fluid (without) solid organ injury".The literature on this topic, which cites more than 50 publications in English alone - mostly retrospective reviews of patient data - gives us an abundance of options to deal with this dilemma. Recommendations vary from sole observation with serial abdominal examinations, to further evaluation with additional radiological studies, DPL and/or surgical intervention -28.A major limitation of all the published studies is the inclusion of only a small number of full thickness hollow organ injuries, which can be the source of the free abdominal fluid. In some studies, the number of patients with blunt  trauma presenting with free fluid but without obvious organ injury is as low as 0.5%, especially if the study population has a high ratio of male patients, which is often the case in trauma patients . The lowOne of the largest systematic reviews, conducted by Rodriguez and co-workers, found 10 articles in which isolated free abdominal fluid was seen without organ injury . The stuAlthough the preferred surgical access still is mainly via quick and easy laparotomy, diagnostic laparoscopy, especially in the more stable patient, provides all the advantages of minimally invasive elective surgery. A recent study from Cherkasov and coauthors, although retrospective, was able to demonstrate the advantages of the less traumatic, safe and feasible technique of video-assisted minimally invasive surgery .In a more recent single centre review of 2651 trauma admissions, 14 (0.5%) patients had free intraabdominal fluid without solid organ injury in the initial CT scan . Eleven Some authors suggest that traces of free fluid in the pelvis, even so for male patients, with no other signs of injury are not associated with significant intra-abdominal injury and can be safely managed non-operatively . The preOthers, like Malhotra and colleagues, concentrate their evaluation more on the number of additional positive findings, rather than the actual amount of free fluid, which can be used to increase the accuracy of the CT scan . In a seWhilst surgically important bowel and/or mesenteric injuries are usually accurately revealed using multi-detector CT imaging , these iEven improvements in diagnostic equipment, such as contrast-enhanced ultrasound or new generation multi-detector CT scanners, have not been able to prove their efficacy yet. Both ultrasound and CT-based diagnostic algorithms have been proposed, but unfortunately hollow viscus injuries can be missed by both radiological examinations. Neither repeated clinical follow-up nor repetitive CT scan imaging revealed hollow viscus injury in the case series of Permentier et al. . The autIn alert and non-comatose patient, physical examination (presence of peritonitis) is the method of choice to rule out significant abdominal injury. However, signs of peritonitis may take hours before becoming clinically evident, which is an important downside of this strategy. If the patient is intubated, intoxicated or suffers from impaired neurological function (e.g. tetraplegia), any clinical examination loses its value and the decision to carry out a surgical intervention (or not) based solely on clinical findings becomes unreliable ,41. In hIn a study by Chandler et al., 117 victims involved in a motor vehicle accident were evaluated for the use of seatbelts and the presence or absence of a seatbelt mark . 14 of 1In an older study, Appleby and co-workers investigated 36 patients with seatbelt marks who underwent laparotomy after a motor vehicle accident . A high In accordance with the literature and to the best of our knowledge, we suggest an algorithm  obviously depends on the surgeon's experience and the overall hospital culture. In Europe laparoscopy is considered the surgical technique of choice, although it has it downsides . It is eWhilst evaluating the patient we suggest distinguishing between a trace , and larger amounts of free fluid . According to the literature, over 70% of patients will fall into the first category, and conservative treatment of these patients is thought to be safe in the vast majority of cases . As mighQuestion number five, whether or not the CT scan has been interpreted correctly is probably the most challenging question to answer and problem to solve.A thorough literature search has made it apparent that there is no straightforward answer to the question of what to do with patients with free fluid on CT scanning but without signs of organ injury. All studies, whether they are prospective or retrospective, lack the statistical power to provide a definite answer. Furthermore, the studies are difficult to compare, as there are significant differences in imaging equipment, laboratory workup and surgical experience. The majority of the studies investigated inhomogeneous groups of patients or had methodological or statistical problems.Fortunately this type of injury is very rare. This in turn, however means that exposure to such cases in the course of one's career is infrequent, making it difficult to rely on general experience alone to correctly diagnose and adequately treat such injuries.The authors declare that they have no competing interests.VB designed the study and drafted the manuscript, HZ coordinated and helped to draft the manuscript, MB helped conceive the study and contributed to the revisions, VJ helped revise the manuscript and designed Figures


It is important that the introduction of breast screening is closely monitored. The anticipated effect on breast cancer mortality will take 10 years or more fully to emerge, and will only occur if a succession of more short-term end points are met. Data from the Swedish two-county randomised trial provide targets that should be achieved, following a logical progression of compliance with the initial invitation, prevalence and stage distribution at the prevalence screen, the rate of interval cancers after the initial screen, the pick-up rate and stage distribution at later screening tests, the rate of interval cancers after later tests, the absolute rate of advanced cancer and finally the breast cancer mortality rate. For evaluation purposes, historical data on stage at diagnosis is desirable; it is suggested that tumour size is probably the most relevant variable available in most cases.


An indirect approach is usually used to estimate the metabolic fluxes of an organism: couple the available measurements with known biological constraints (e.g. stoichiometry). Typically this estimation is done under a static point of view. Therefore, the fluxes so obtained are only valid while the environmental conditions and the cell state remain stable. However, estimating the evolution over time of the metabolic fluxes is valuable to investigate the dynamic behaviour of an organism and also to monitor industrial processes. Although Metabolic Flux Analysis can be successively applied with this aim, this approach has two drawbacks: i) sometimes it cannot be used because there is a lack of measurable fluxes, and ii) the uncertainty of experimental measurements cannot be considered. The Flux Balance Analysis could be used instead, but the assumption of optimal behaviour of the organism brings other difficulties.We propose a procedure to estimate the evolution of the metabolic fluxes that is structured as follows: 1) measure the concentrations of extracellular species and biomass, 2) convert this data to measured fluxes and 3) estimate the non-measured fluxes using the Flux Spectrum Approach, a variant of Metabolic Flux Analysis that overcomes the difficulties mentioned above without assuming optimal behaviour. We apply the procedure to a real problem taken from the literature: estimate the metabolic fluxes during a cultivation of CHO cells in batch mode. We show that it provides a reliable and rich estimation of the non-measured fluxes, thanks to considering measurements uncertainty and reversibility constraints. We also demonstrate that this procedure can estimate the non-measured fluxes even when there is a lack of measurable species. In addition, it offers a new method to deal with inconsistency.This work introduces a procedure to estimate time-varying metabolic fluxes that copes with the insufficiency of measured species and with its intrinsic uncertainty. The procedure can be used as an off-line analysis of previously collected data, providing an insight into the dynamic behaviour of the organism. It can be also profitable to the on-line monitoring of a running process, mitigating the traditional lack of reliable on-line sensors in industrial environments. Fostered by the importance of studying the cell metabolism under a system-level approach ,2, the sExperimental measurements of fluxes can be incorporated as constraints, in order to determine the actual flux distribution or at least to reduce the space of possible flux distributions. However, it must be taken into account that measurements are not invariant constraints, but specific condition constraints . There aMetabolic Flux Analysis (MFA) provides a methodology to uniquely determine the actual flux distribution by using a metabolic network and a set of measured fluxes . It has The Flux Balance Analysis (FBA) can be used to predict metabolic flux distributions ,16. FirsCorynebacterium glutamicum at different temporal phases of fermentation. Elementary modes are also employed in 21], the loyed in , where tloyed in , on-lineloyed in  use a siloyed in  has presTo calculate the succession of flux distributions, it is usually assumed that intracellular fluxes are in quasi-steady state within each measurement step. However, that does not mean that the intrinsic dynamic nature of the cultivation is being disregarded. Instead, the intracellular fluxes will follow the change of environmental conditions as mediated by the measured fluxes (e.g. substrate uptakes). Hence, steady states may undergo shifting from one state to another depending on the evolution of the measured fluxes . Such asi) It cannot be used when measurements are scant (i.e. when the system is underdetermined). This happens very often due to the lack of measurable fluxes. ii) The uncertainty of the measured fluxes cannot be considered. Not only gross errors may appear -which could be managed only in case there are redundant measured fluxes- but also most sources of measurements are intrinsically uncertain and the propagation of this uncertainty to the estimated fluxes is not controlled, and iii) only equalities can be used as constraints. For instance, reversibility constraints or maximum flux values cannot be taken into account. FBA solves the first difficulty and provides a framework to deal with the other ones. But the use of FBA in this context could be problematic due to the appearance of a time-variant metabolic objective . The size of the intervals (i.e. the imprecision of the estimation) depends on the number of non-measured fluxes, the irreversible reactions, the available measurements and the degree of uncertainty considered. Of course, the more constraints are available, the tighter intervals are obtained. If uncertainty is not considered, reversibility constraints are not used, and the system (2) is determined, FSA gives the same unique solution as MFA . Accordingly, each equation of (2) is substituted by two inequalities. The resultant constraints define a region where the actual flux distribution may live.1. Impose the set of constraints given by (2) and the reversibility constraints for the irreversible reactions, vuj, by solving a set of min/max linear programming problems (nu minimizations and nu maximizations):2. Calculate the minimum and maximum values within the region for each non-measured flux nu is the number of unknown fluxes, vu is the vector of non-measured fluxes, vi represents each irreversible flux and [vm] represents the two vectors  formed with the uncertain representation of the measured fluxes. {-Sm·[vm]}min and {-Sm·[vm]}max are vectors formed with the maximum and minimum row values of the product -Sm· [vm]. To calculate each row, maximum and minimum values of vm need to be combined taking into account the signs of the elements of the corresponding row of Sm  = .The obtained ne extracellular fluxes can be linked with the intracellular fluxes by using a matrix Sξ fulfilling:A set of vξ is the vector of extracellular fluxes and v the vector of intracellular fluxes. Eq. 11 can be easily joined with eq. 1 as follows:where Hence, the extended system holds the structure of a homogeneous system of linear equations.A redundant system will be consistent if it fulfils the consistency condition:R is the redundancy matrix and Su# the Penrose pseudo-inverse of Su. In case inconsistency is detected, the method described in [h as follows:where ribed in ,39 can bRr is the reduced redundancy matrix and F the variances-covariances matrix of the measurements in vm. If a given set of measured fluxes vm fails the consistency check (h>χ2), then there is a (confidence level)% chance that either vm contains gross errors or the assumed stoichiometric matrix is incorrect. The χ2 values for two confidence levels are given in Table where Rr# denoted the Penrose pseudo-inverse of the matrix Rr. This equation provides the adjusted values for the balanceable fluxes and the original values for the non-balanceable ones.where Su:When the system (2) is determined but not redundant the unique solution can be calculated by using the inverse matrix of Su is not invertible so the Penrose pseudo-inverse is used instead (providing a least squares solution):When the system is determined but redundant, matrix Finally, if system (2) is underdetermined, Metabolic Flux Analysis cannot be used. Only some fluxes may be uniquely calculable by using the method explained in .MFA: Metabolic flux analysisFSA: Flux spectrum approachFBA: Flux balance analysisCHO: Chinese hamster ovary (cells)AIS: Average along time of the interval size of an estimated flux.FL and JP designed the research, analyzed the results and conceptualized the manuscript. FL performed the estimation of non-measured fluxes and drafted the manuscript. JP supervised and coordinated the project. All the authors read and approved the final manuscript.Conversion of measured concentrations to measured fluxes. Example of the calculation of the measured fluxes when the measurements of concentration are obtained at a high sample rate.Click here for fileFlux spectrum approach in the underdetermined and redundant case. Example of the estimation of fluxes with the Flux Spectrum Approach in an Underdetermined and redundant case.Click here for fileMetabolic network description. List of metabolites, reactions and stoichiometric matrixes.Click here for fileMathematical model (SBML and matlab). The zip file contains the mathematical model of the metabolism of CHO cells in three different formats: a matlab script, an SBML model and a metatool file.Click here for fileAdditional figures and tables. Additional figures cited in the manuscript.Click here for fileAnalysis of the unbalanced propagation of the uncertainty. Dataset with the interval size of the estimations of each non-measured flux at each time instant.Click here for fileAnalysis of the effect of the uncertainty of each measured flux. Details and datasets of the indirect and direct analysis of the effect of the uncertainty of each measured flux.Click here for fileImplementation of the Flux Spectrum Approach. The zip file contains a matlab script which implements the method to estimate the non-measured fluxes with the Flux Spectrum Approach and a simple example that illustrates how to use it.Click here for file


Aged patients with coronary heart disease (CHD) have a high prevalence of co-morbidity associated with poor quality of life, high health care costs, and increased risk for adverse outcomes. These patients are often lacking an optimal home care which may result in subsequent readmissions. However, a specific case management programme for elderly patients with myocardial infarction (MI) is not yet available. The objective of this trial is to examine the effectiveness of a nurse-based case management in patients aged 65 years and older discharged after treatment of an acute MI in hospital. The programme is expected to influence patient readmission, mortality and quality of life, and thus to reduce health care costs compared with usual care. In this paper the study protocol is described.The KORINNA (Koronarinfarkt Nachbehandlung im Alter) study is designed as a single-center randomized two-armed parallel group trial. KORINNA is conducted in the framework of KORA . Patients assigned to the intervention group receive a nurse-based follow-up for one year including home visits and telephone calls. Key elements of the intervention are to detect problems or risks, to give advice regarding a broad range of aspects of disease management and to refer to the general practitioner, if necessary. The control group receives usual care. Twelve months after the index hospitalization all patients are re-assessed. The study has started in September 2008. According to sample size estimation a total number of 338 patients will be recruited. The primary endpoint of the study is time to first readmission to hospital or out of hospital death. Secondary endpoints are functional status, participation, quality of life, compliance, and cost-effectiveness of the intervention. For the economic evaluation cost data is retrospectively assessed by the patients. The incremental cost-effectiveness ratio (ICER) will be calculated.The KORINNA study will contribute to the evidence regarding the effectiveness of case management programmes in aged people with MI. The results can be an important basis for clinicians, administrators and health policy makers to decide on the provision of high-quality care to older patients with CHD.ISRCTN02893746 The aging of the population and the increasing prevalence of chronic diseases imply great challenges to the health systems of developed countries. CHD is the leading cause of mortality and morbidity in the industrialized world. The treatment of acute myocardial infarction (MI) has improved dramatically over the last 10 to 20 years and nowadays, aged patients with an acute MI are receiving treatment that had been limited to mainly younger patients about a decade ago [Patients with CHD, in particular aged patients, have a high prevalence of co-morbidity associated with poor quality of life, physical disability, high health care costs, multiple medications, and increased risk for adverse outcomes. Common co-morbidities among patients with CHD are diabetes, chronic heart failure (CHF), chronic obstructive pulmonary disease (COPD), and depression -3. CHD iDue to changes in the German health care system, in particular the establishment of the diagnosis related groups (DRG) system, older patients with complex health care needs are nowadays discharged earlier from hospital than a few years ago . For manMany hospital admissions among aged patients with CHD can be attributed to behavioural and social factors rather than to deteriorating cardiac function or an intercurrent cardiac event . Thus, aA number of intervention trials investigated whether a nurse-based case management may influence patient readmission and other outcomes in CHD ,15. In aIn another review McAlister et al. examined whether case management programmes for patients with established CHD improve the process of care and reduce mortality . In totaAlthough the results of both studies, the meta-analysis and the review, are promising, these findings can not be generalized to higher age-groups. Very few studies reported on case management programmes in people older than 65 years. The studies by Naylor et al ,17 examiRegarding cost-effectiveness of the case management programmes it is notable that only seven of the 63 trials included in the meta-analysis by Clark et al.  describeOverall, the review of the literature showed that studies on case management programmes mostly included participants with CHD younger than 70 years  or inclu1c in patients with type 2 diabetes, and maintenance of body weight in patients with CHF.The primary objective of the study is to assess whether a case management intervention by trained nurses can reduce time to first readmission or out-of-hospital death in aged patients with MI. Secondary objectives are the estimation of the cost-utility ratio of this case management intervention and to compare case management vs. routine care with respect to secondary out-comes such as functional capacity, participation, quality of life, and compliance with medication. For patients with specific comorbidity, additional outcome criteria will be compared between the two groups, e.g. adjustment of blood glucose values and hemoglobin-AThe aim of this paper is to describe the study protocol of the KORINNA (Koronarinfarkt-Nachbehandlung im Alter) study. Patient recruitment in the KORINNA study has started by September 2008. This detailed description of the study background and protocol is published as a reference for forthcoming papers on the study results.The study is designed as a single-centre randomized two-armed parallel group trial. The study is carried out within the framework of KORA . All patients receive a baseline assessment after giving their informed consent. The baseline assessment is carried out by the study physician and a study nurse. Those who are subsequently randomized to the intervention group receive the intervention starting with the initial session shortly before discharge  which makes rehospitalization within the next months necessary or is associated with a life expectancy of less than one year, and patients who are not able to communicate in German language are excluded. Finally, patients who are unable or unwilling to give written informed consent (e.g. patients with dementia) cannot be included in the study. The number of patients not included in the study as well as reasons for exclusion will be documented.The study protocol and its amendment were approved by the Ethics Committee at the Bavarian Chamber of Physicians . Furthermore, the study is conducted in accordance to German privacy law and in compliance with the Helsinki Declaration.All patients meeting the inclusion criteria and giving informed consent are randomly assigned to the intervention or control group. The allocation ratio is 1:1. To ensure the concealment of the allocation, randomization is provided per telephone call to the biostatistical center at the Helmholtz Zentrum München, German Research Center for Environmental Health, where a randomization list is kept. A minimization procedure is used which tries to achieve balanced treatment groups with respect to gender, age (< 70 vs. 70-79 vs. 80+), and number of comorbidities (diabetes and CHF).The intervention consists of a nurse-led individualized home-follow up programme with a duration of one year. The control group receives usual care. Patients can use or apply for all available services in the area.The intervention programme starts with an initial information session (approximate duration 1 hour) which takes place one or two days before hospital discharge  and telephone calls (at least every 3 months) are carried out according to patient need and patient risk level. At the first home visit the specific problems of the patient are identified and documented. An individual plan for each patient is set up. The risk level is assessed by the study nurse during the first home visit based on compliance, the social network, and the comorbidities. The higher the risk level the more contacts (telephone and home visits) are arranged by the study nurse. The activities are planned in agreement with the patient in order to improve compliance.The first home visit is scheduled to take place 7 to 14 days after discharge. If the patient stays in a rehabilitation hospital immediately after discharge from the Augsburg hospital, the first home visit will be postponed accordingly. At the home visits patients are instructed how the prescribed drugs have to be taken and what would happen in the case of non-compliance with medication. Furthermore, to patients with diabetes advice is given regarding nutrition and physical activity, and patients with CHF are encouraged to regular weight control. During the visits, measurements of blood glucose, blood pressure, and weight are performed. The duration of the visit should be between 60 and 90 minutes. The key elements of both the home visits and the telephone calls are: to detect problems (e.g. regarding intake of medication) or risks, to give advice regarding a broad range of aspects of disease management  and to refer to the general practitioner, if necessary. The content and structure of home visits and telephone calls are comparable, and primarily differ regarding location and type of contact between the patient and nurse, and the possibility to measure blood glucose, blood pressure, and weight.In August 2008, a training of the three study nurses and the study physician was performed lasting several days. The following topics and diseases were intensively discussed with the study nurses: CHD, MI, angina pectoris, heart failure, treatment of MI, risk factors of cardiovascular diseases, action of particular drugs, diabetes mellitus, psychological factors and MI. Furthermore, the structure and the contents of the "Heart book" handed out to the patients in the intervention group at discharge were discussed.Regarding the study implementation, both study physician and study nurses received a training on patient recruitment. The study physician was instructed on patient information and obtaining informed consent. Moreover, the procedure of the clinical examination and personal interview was trained.Finally, study nurses were introduced in the performance of personal interviews in the hospital, of home visits, and of telephone interviews, the use of the intervention modules, the data extraction from patients' records, documentation, and data entry.The primary endpoint of readmission is measured as time between initial hospital discharge and first unplanned readmission to hospital (at least for 24 hours). Out of hospital death from any cause is counted as an event.The instruments used to assess secondary outcomes are shown in Table Twelve months after the index hospitalization all patients who are still alive are invited for a final assessment in the hospital or, if necessary, at home. This examination includes a personal interview with an assessment of functional capacity, mental status and quality of life, adherence to medication, health care utilization, and the measurement of blood pressure and body weight. The study physician and nurse who are involved in the final assessment are not aware whether the respective patient was assigned to the intervention- or control group.Data on resource utilization as well as on quality of life are collected at baseline, at interim telephone contacts, and during the final assessment.Data for the economic analysis is collected via patients and from hospital records. Table Within the last years, standardized instruments measuring the resource use were developed such as the RAI (Resident Assessment Instrument)  or the RThe valuation of the resource use will be based on the valuation rates calculated by Krauth et al. . As the Especially in the economic evaluation of interventions with the elderly informal care plays an important role. However, as the assessment is very time consuming and the interview time should be minimized we refrained from assessing informal care time. To estimate the cost of informal care we use the information on a care level declared by the long term care insurance. If the patient is allowed to receive nursing care and does not receive formal care, it is assumed that the patient has an informal caregiver. In that case, the maximum amount for care at home paid by the long term care insurance will be used as cost for informal care.Cost for the intervention excluding the costs caused by the study will be considered. Cost components will include labor costs, travel expenses, telephone costs etc.In order to calculate quality-adjusted life years (QALYs), the EQ-5D questionnaire  is appliIt is planned to perform a cost-utility-analysis from the societal perspective. This means that incremental costs of the intervention (vs. control) are set in relation to the number of QALYs gained. The resulting incremental cost-effectiveness ratio (ICER) is an international standard for reporting results of economical evaluation studies. In addition, we will calculate additional costs per life year saved and per year without event. For the estimated ICER value a 95% confidence interval will be calculated based on bootstrap methods.The statistical analysis for the primary endpoint will focus on the null hypothesis that there is no difference between intervention and control with respect to the distribution of time to un-planned readmission . This hypothesis will be statistically tested using a Cox proportional hazards model including age, gender, and comorbidity as covariates.Statistical analyses for secondary outcomes will be based on  linear models depending on the type and distribution of the outcome variable. Since these will be multiple tests for which control of the overall error level cannot be achieved, these will be regarded as exploratory analyses. All analyses will be done according to the intent-to-treat approach.Based on a comparable study by Young and colleagues  with patThis paper describes the study design of the KORINNA study, an innovative randomized controlled trial evaluating the effectiveness of a nurse-based case management programme for old-aged patients with MI. The KORINNA study is unique in a twofold way.First, the nurse-led case management is tailored to the specific needs of old-aged people with MI. The interventions specifically address common challenges and risks associated with the MI management in elderly people such as multi-morbidity and compliance with medication. Further, the programme is flexible regarding frequency and location of the intervention. Thus, when deciding on the number of interventions necessary or whether a home-visit or telephone call is more appropriate, the nurse can take the individual health and living condition of a patient into account. Our experiences gathered from approximately 100 patients who have already received interventions within the study, confirm the need for a highly individualized intervention programme. Until now, a broad range of health states and impairments among the study participants could be observed which necessitates a variable intervention intensity.Second, a particular strength of this study relates to the planned economic evaluation. In view of scarce financial resources within the German health system it is essential that innovative models of care not only demonstrate positive effects on clinical and patient-related outcomes but also cost-effectiveness. Since cost savings have already been shown in comparable studies in other countries, the economic results of this study are highly anticipated.A possible limitation of the study design refers to the relatively short follow-up interval of one year. It is still unclear whether the expected positive intervention effects on readmission to hospital or death can already be observed within this time interval. Hence, a prolongation of the study with a follow-up interval of 3 years is already taken into consideration. A further limitation of the study is its single center design.So far, we have experienced an unexpected challenge regarding the number of eligible patients aged 75 years and older. Some months after starting recruitment it became apparent that the planned sample size cannot be reached within the expected time frame. We discussed this problem with the members of the studies' advisory board and decided to decrease the minimum age of study participants from 75 years to 65 years. As a consequence of the initially low number of patients who could be included in the study, the recruitment phase will be extended by several months. In addition, the number of patients who could not be included due to severe concomitant diseases or dementia (20%), or since they were already nursing home residents (10%), was higher than expected. On the other hand, the number of study patients who were lost to follow-up within the one-year treatment course currently is 7% and therefore even lower than initially expected. In addition, we have noticed that the home visits as well as telephone calls are very well accepted by the patients. These findings indicate a good acceptance and feasibility of the study.In summary, the KORINNA study is expected to contribute to the evidence regarding the effectiveness of nurse-based case management programmes for aged patients with MI. The results can be an important basis for clinicians, administrators and health policy makers to decide on the provision of high-quality care to older patients with MI.The authors declare that they have no competing interests.CM, BK and RH initiated the study and raised the research grant. CM and BK are principal clinical investigators, RH is principal statistical investigator. CM and BK developed the case-management programme. CM, RH, BK, RW, HS contributed to conception and design of the study. HS is responsible for the economic evaluation and for study monitoring. RW is study physician and responsible for patient recruitment and clinical examination/assessment. IK is in charge of the local coordination of the study and wrote the manuscript. All authors critically revised and approved the final manuscript.The pre-publication history for this paper can be accessed here:http://www.biomedcentral.com/1471-2318/10/29/prepub