Its efficient computation is essential in many tasks, as in approximate computation or as a measure of error when learning a probability. In high dimensional probabilities, as the ones associated with Bayesian networks, a direct computation can be unfeasible. This paper considers the case of efficiently computing the Kullback–Leibler divergence of two probability distributions, each one of them coming from a different Bayesian network, which might have different structures. The paper is based on an auxiliary deletion algorithm to compute the necessary marginal distributions, but using a cache of operations with potentials in order to reuse past computations whenever they are necessary. The algorithms are tested with Bayesian networks from the bnlearn repository. Computer code in Python is provided taking as basis pgmpy, a library for working with probabilistic graphical models.Kullback–Leibler divergence  When experimentally testing Bayesian network learning algorithms, in most of the cases, the performance is evaluated looking at structural differences between the graphs of the original Bayesian network and the learned one , as in tNaive Bayes classifier, which obtains very good results in classification problems, despite the fact that the structure is not the correct one. So, in this situation, structural graphical differences are not a good measure of performance.However, in most cases the aim of learning a Bayesian network is to estimate a joint probability for the variables in the problem. In that situation the error of a learning procedure should be computed by measuring the difference between the probability associated with the learned network and the original joint probability distribution. Therefore, it can be useful to estimate a network that is less dense than the original one, but in which parameters can have a more accurate estimation. This is the case of the The basic measure to determine the divergence between an estimated distribution and a true one is the so-called Kullback–Leibler divergence . Some paPython and integrated into the pgmpy [Elvira system [The aim of this work is to improve existing methods for computing Kullback–Leibler divergence in Bayesian networks and to provide a basic algorithm for this task using he pgmpy  environma system  is basedThe paper is organized as follows: N be a Bayesian network defined on a set of variables N. Let A configuration or assignment of values to a set of variables A partial configuration involving a subset of variables The set of configurations for variables If The conditional probability distribution for In our example, there are three potentials and Multiplication. If W, then W in Marginalization. If Selection. If There are three basic operations that can be performed on potentials:N the joint probability distribution of the variables in N, p, is a potential that decomposes as the product of the potentials included in The family of all the conditional distributions is denoted as p for a set of variables Considering the example, The aim of this paper is to compute the Kullback–Leibler divergence LL  KL diverWe have designed a procedure to compute each one of the required marginals N. In  our case the family We have implemented a general procedure to calculate the marginal for a family networks . Let us K: Our algorithm assumes that the subsets in In fact, two repositories are employed: one for potentials , the operations are planned (using symbolic propagation) and detecting repeated operations. It is assumed that there are two basic functions CondSCombineCondSMarginalizeUpdateTimet otherwise in repository We will also consider that there are two conditional versions of these operations: if the operation already exists, only the DeleteIft).Observe that the first part of Algorithm 2 (lines 2–26) just determines the necessary operations for the deletion algorithm for for all the marginals, while the second part (lines 27–32) carries out the numerical computations in the order that was established in the first part. After each operation, the potentials that are no longer necessary are removed from As mentioned above, the analysis of the operation sequence will be carried out using symbolic operations and taking into account the scopes of potentials but without numerical computations. This allows an efficient analysis. The result of the analysis will be used as an operation planning for the posterior numerical computation.Assume the same example considered in previous sections for the networks in A has been omitted in order to simplify the notation.Algorithm 2 Computation of marginals of p for subsets 1:function Marginal. This library provides all the functions required for the process described below. Given a certain Bayesian network as defined in the repository:rbn function. As explained in the library documentation, this function simulates random samples from a Bayesian network, using forward/backward sampling.A dataset is generated using the tabu function is employed using the default setting (a dataset as unique argument). It is one of the structural learning methods available on bnlearn. Since the learned model could have unoriented links, the cextend function is required, which results in a Bayesian network consistent with the model passed as argument. Any other different learning algorithm could have been used, since the goal is to have an alternative Bayesian network that will be used later to calculate the Kullback–Leibler divergence with the methods described in Algorithms 1 and 2.The dataset is used for learning a Bayesian network. For this step, the In order to compare the computation approaches presented in the paper the experimentation uses a set of Bayesian networks available in the bnlearn  repositoNetwork name.nodes.Number of arcs.Number of parameters required for quantifying the uncertainty of the network.Number of time1: Runtime using the algorithm without cache (Algorithm 1).time2: Runtime using the algorithm with cache (Algorithm 2).ops: Number of elementary operations stored in the operations repository rep: Number of operations that are repeated and that, thanks to the use of del: Number of factors that were removed from the For each network, the Kullback–Leibler divergence is computed with the procedures presented using evidence propagation (see Algorithm 1) and using operations cache (described in Algorithm 2). The main purpose of the experiment is to get an estimation of the computation times required for both approaches. The obtained results are included in The experiments have been run in a desktop computer with an Intel(R) Xeon(R) Gold 6230 CPU working at 3.60GHz (80 cores). It has 312 Gb of RAM memory. The operating system is Linux Fedora Core 34.water, mildew, and barley. Moreover, the computational overhead required to manage operations and factor repositories is beneficial as it avoids the repetition of a significant number of operations and enables unnecessary potentials to be released, especially in the most complex networks.It is observed that the calculation with the second method always offers shorter runtimes than the first one. The shortest runtimes are presented in the table with bold style. It is noteworthy that the case of three networks in which the method based on the use of evidence cannot be completed because the available memory capacity is exceeded: Computing the KL divergence between the joint probabilities associated with two Bayesian networks is an important task that is relevant for many problems, for example assessing the accuracy of Bayesian network learning algorithms. However, in general, it is not possible to find this function implemented in software packages for probabilistic graphical models. In this paper, we provide an algorithm that uses local computation to calculate the KL divergence between two Bayesian networks. The algorithm is based in a procedure with two stages. The first one plans the operations determining the repeated operations and the times in which potentials are no longer necessary, while the second one carries out the numerical operations, taking care to reuse the results of repeated operations instead of repeating them and deallocating the memory space associated with useless potentials. Experiments show that this strategy saves time and space, especially in complex networks.pgmpy software package and are available in the github repository: https://github.com/mgomez-olmedo/KL-pgmpy, accessed on 24 August 2021. The README file of the project offers details about the implementation and the methods available for reproducing the experiments.The functions have been implemented in Python taking as basis In the future, we plan to further improve the efficiency of the algorithms. The main line will be to invest more time in the planning stage looking for deletion orderings minimizing the total number of operations or optimizing the order of combinations, when several potentials have to be multiplied.


Network meta-analysis estimates all relative effects between competing treatments and can produce a treatment hierarchy from the most to the least desirable option according to a health outcome. While about half of the published network meta-analyses present such a hierarchy, it is rarely the case that it is related to a clinically relevant decision question.We first define treatment hierarchy and treatment ranking in a network meta-analysis and suggest a simulation method to estimate the probability of each possible hierarchy to occur. We then propose a stepwise approach to express clinically relevant decision questions as hierarchy questions and quantify the uncertainty of the criteria that constitute them. The steps of the approach are summarized as follows: a) a question of clinical relevance is defined, b) the hierarchies that satisfy the defined question are collected and c) the frequencies of the respective hierarchies are added; the resulted sum expresses the certainty of the defined set of criteria to hold. We then show how the frequencies of all possible hierarchies relate to common ranking metrics.We exemplify the method and its implementation using two networks. The first is a network of four treatments for chronic obstructive pulmonary disease where the most probable hierarchy has a frequency of 28%. The second is a network of 18 antidepressants, among which Vortioxetine, Bupropion and Escitalopram occupy the first three ranks with frequency 19%.The developed method offers a generalised approach of producing treatment hierarchies in network meta-analysis, which moves towards attaching treatment ranking to a clear decision question, relevant to all or a subset of competing treatments. Providing a treatment hierarchy is often one of the objectives of systematic reviews that contain multiple interventions . To thisDespite the plethora of ranking metrics and the popularity of deriving a treatment hierarchy in NMA, relying on such a treatment hierarchy is insufficient. Limitations of ranking treatments include the fact that small differences in outcome values could lead to different hierarchies even if these differences are not clinically relevant, the difficulty in interpreting the values of the ranking metrics and the lack of consideration of multiple outcomes , 7. ThisHowever, the hierarchy questions of interest are not limited to those that can be answered by the available ranking metrics. Often, more complex research questions are posed; in such a case, hierarchy should still depend on these questions, so that its interpretation is relevant and meaningful. In this paper, we suggest an approach for translating clinically relevant questions into hierarchy questions and quantify their uncertainty. To this aim, we use simulations to derive the relative frequency of all possible hierarchies in a network of interventions. Then, we define the set of all possible hierarchies that satisfy a specified criterion, for example that a specific order among treatments is retained in the network and/or a treatment is in a specific position, and the sum of their frequencies constitute the certainty around the criterion.T treatments. NMA aims to estimate the set of titj denotes the treatment contrast  nmarank, In the first step of the approach, investigators set a question that is considered clinically important. Different users of NMA would normally consider different questions to be of clinical importance; e.g. clinicians might be interested in general questions that capture the entire population of patients, policy decision makers might ask specialized questions while patients might seek answers to research questions focused on their specific patient group. Also, questions may include all treatments in the network or focus on a subset of them, as it is often the case in a clinical setting.ti has better outcome than another (possibly effective but more expensive) treatment tj. Alternatively, clinicians might be interested to know the top three treatments in the network. Other examples of questions include that a specific order ti, tj, tk is retained anywhere in the hierarchy, that a treatment ti occupies a specific rank r or that it is among the best two ranks. It is also possible that we are interested in the case that a treatment ti has better outcome than treatment tj, but against a clinically important value c ti is first or second and tj has better mean outcome value than that of treatment tk plus a clinically important value c = 0.5. As a special case of a clinically relevant question could be that a specific treatment hierarchy occurs, for example that imposed by the estimated relative treatment effects, expressed as ti is first, tj is second, tk is third and so on.For example, a question of clinical relevance to a decision maker might be whether a treatment T! hierarchies that satisfy the criteria set in Step 1. This is done by selecting those hierarchies in the sample of Step 3.After setting the decision question of interest, the aim is to define the set of possible hierarchies out of all ti is first or second and tj has better mean outcome value than that of treatment tk plus a clinically important value c = 0.5, then we need to differentiate between the two types of hierarchies: those where in the sampling the condition If we are interested in a question involving a clinically important value c, then the respective criteria need to be applied to mark the hierarchies that satisfy them in the sampling process of Step 3 of the framework, we add the frequencies of the hierarchies Step 2 that satisfy the decision criterion set in Step 1. In our example from Fig. t1 is at higher rank as t2 is the sum of the frequencies of h1, h4 and h6 hierarchies which amounts to 50% . Below we show a hypothetical example with three treatments, t1, t2, t3, of a network with three treatments where h1 differs from the hierarchy imposed by the NMA estimated relative treatment effects.The estimated t3, t2, t1}. Fig. T !  = 6 possible hierarchies are represented by the regions separated by the straight lines in Fig.t3, t2, t1} includes the point estimate , noted as the black dot. However, this is not the most probable hierarchy (frequency 15%) as the probability mass is smaller than for other regions; hierarchies {t3, t1, t2} and {t2, t1, t3} are more probable than that of the mean effects, each one having 25% probability of occurring.Figure The first column of the ranking matrix shows the frequency that each treatment occupies the highest rank and has been frequently used as a ranking metric usually referred as “probability of being best”. “Probability of being best”, however, has been recently indicated as an inaccurate name for the particular ranking metric as “being the best” may have a large variety of meanings and interpretations . “Probabt3 has a probability of producing the best value 45%, followed by t2 with a probability of 30%, while t1 is associated with 25% probability of producing the best value. However, hierarchy {t3, t1, t2} is equally probable with {t2, t1, t3} (25%) and hierarchies {t3, t2, t1} and {t1, t2, t3} are also equally probable (20%). The hierarchy matrix highlights that given that one of the three treatments is second, the other two have equal estimated probabilities of being first or third. The large tails of the distributions of relative treatment effects of t3 versus the other two treatments make it improbable that it ranks on the second position, rendering hierarchies {t2, t3, t1} and {t1, t3, t2} occurring each in 5% of the simulations.The hypothetical triangular network of Fig. mentclass2pt{minimmentclass2pt{minimt1 produces the best value is the sum of probabilities of the hierarchies {t1, t2, t3} and {t1, t3, t2} which is 25%. Similarly, the SUCRAs or P-scores can also be derived from the hierarchy matrix. Consider for example the SUCRA (or P-score) for treatment t1 in the hypothetical triangular network of Fig. As shown in the example of section T !  = 24) along with their frequency of occurring.We illustrate the process using a network comparing mortality rates in four treatments for chronic obstructive pulmonary disease: SFC , Salmeterol, Fluticasone and Placebo . Direct estimate . The hieentclass1pt{minimaentclass1pt{minimaCriterion A: Hierarchy is exactly ‘SFC, Salmeterol, Fluticasone, Placebo’Criterion B: Order ‘SFC, Fluticasone, Placebo’ is retained anywhere in the hierarchyCriterion C: Fluticasone is among the best two optionsCriterion D: SFC and Salmeterol are the two best optionsCriterion E: Both criteria B and C are satisfiedWe consider the following alternative hierarchy questions of interest as Step 1 of the suggested approach:In Step 2 of the approach, we identify the hierarchies that satisfy the above criteria and in Step 3 we add their estimated probabilities  is 9%. The estimated probability that these three treatments occupy any of the first three ranks (criterion B) is obviously higher; 19% of times Vortioxetine, Bupropion and Escitalopram were the three treatments with the highest odds ratios. The relative order of the first three treatments is also quite precise; in one third of simulations (33%), Vortioxetine performed better than Bupropion and Bupropion performed better than Escitalopram (criterion C).Comparisons with a clinically important value are often more of interest than comparisons to the null effect. In the original NMA, an odds ratio of 0.8 and its reciprocal 1.25 was used for the examined outcome to judge upon imprecision of treatment effects and assess the confidence in NMA results. The estimated probability that all three treatments Vortioxetine, Bupropion and Escitalopram have an odds ratio of 1.25 or higher against the old, standard treatment Fluoxetine (criterion D) is 45%, while judging against the null (criterion E) the respective estimated probability is 92%.In this paper, we suggest an approach to answer complex hierarchy questions in NMA and define the certainty around them. The approach that we took moves away from producing a plain, non-meaningful and difficult to interpret hierarchy and towards attaching treatment ranking to a clear decision question, relevant to all or a subset of competing treatments.T! possible hierarchies have probability 1/T!, the precision is the minimum possible. Precision can be reflected by the magnitude of hl). Alternatively, the rate at which ratios of frequencies as those calculated in Table The work presented in this paper is somehow related to the precision in the treatment hierarchy from a NMA as a whole. Preliminary suggestions have associated the uncertainty of the entire treatment hierarchy with the shape of the rankograms: rankograms which show large differences between each treatment being at each rank indicate a precise treatment hierarchy, while flat rankograms reflect uncertainty in the treatment hierarchy . This suentclass1pt{minimaHowever, all these approaches suffer from the drawback that they are dependent on the number of treatments and thus cannot be used as a universal way to judge the precision of the entire treatment hierarchy. In contrast, looking at the certainty of the specified criteria of interest to hold is more meaningful and relevant and constitutes an alternative way of judging imprecision of NMA treatment effects and treatment ranking. Even examples with relatively imprecise results  may be associated with considerable certainty around specific criteria, relevant for decision making. Thus, carefully choosing criteria based on which to judge the imprecision of NMA results is particularly important.nmarank package [The proposed method has several limitations. In decision making multiple outcomes are often of interest and the current approach cannot take this into consideration. Moreover, benefit-risk assessments between different outcomes may be of interest to decision makers but cannot currently be appropriately handled. It would be potentially helpful that the derived frequencies are accompanied by 95% confidence intervals; as, however, the interpretation of such intervals would be unclear, they are not incorporated in the current version of the  package .The method presented in this paper can be extended to adapt to decision questions related to more than one outcome. For example, we could sample from two or more outcomes and measure the frequency for each combination of hierarchies for the considered outcomes. Taking for example a network with two outcomes, O1 and O2 we would calculate lsewhere , 29. As Medical societies, national and international agencies, guideline panels and clinicians very often use evidence synthesis to make informed decisions and recommendations about the clinical effectiveness of alternative treatment options . Given t


Demographic change is leading to an increase in the number of osteoporotic patients, so a rethink is required in implantology in order to be able to guarantee adequate anchoring stability in the bone. The functional modification of conventional standard screw implants using superelastic, structured Ti6Al4V anchoring elements promises great potential for increasing anchoring stability.For this purpose, conventional screw implants were mechanically machined and extended so that structured-superelastic-positionable-Ti6Al4V anchoring elements could be used. The novel implants were investigated with three tests. The setup of the anchoring elements was investigated in CT studies in an artificial bone. In a subsequent simplified handling test, the handling of the functional samples was evaluated under surgical conditions. The anchorage stability compared to standard screw implants was investigated in a final pullout test according to ASTM F543—the international for the standard specification and test methods for metallic medical bone screws.The functionalization of conventional screw implants with structured superelastic Ti6Al4V anchoring elements is technically realizable. It was demonstrated that the anchoring elements can be set up in the artificial bone without any problems. The anchorage mechanism is easy to handle under operating conditions. The first simplified handling test showed that at the current point of the investigations, the anchoring elements have no negative influence on the surgical procedure . Compared to conventional standard screws, more mechanical work is required to remove the functional patterns completely from the bone.In summary, it was shown that conventional standard screw implants can be functionalized with Ti6Al4V-structured NiTi anchoring elements and the new type of screws are suitable for orthopedic and neurosurgical use. A first biomechanical test showed that the anchoring stability could be increased by the anchoring elements. Demographic change is leading to an increase in patients with spinal disorders and therefore to an older population with greater and degenerative comorbidities . Thus, the number of spine procedures has increased. This circumstance makes it difficult for patients to enable optimal and stable implant fixation in the bone –3. ThereInitial approaches showed that the use of thermally activated NiTi as an anchoring element has great potential for increasing anchorage stability .A deficit of thermal NiTi anchoring elements is a complex and expensive temperature management  . FurtherTo address this, anchoring elements were manufactured with superelastic Nitinol and structured with medical titanium grade alloy Ti6Al4V elements. The structuring of the NiTi sheets is produced by using the laser powder bed fusion (LPBF) technology manufacturing process, which is already established in medical technology , 9. In tThe use of superelastic instead of thermally activated NiTi eliminates the need for complex temperature management. In addition, the revision process  is improved and the level of change in geometry of the anchoring elements is increased due to the superelasticity.The aim of the present study was to functionalize standard screw implants in order to increase anchorage stability in bone and revision capability by using superelastic, structured anchoring elements and to investigate them with regard to their handling under surgical conditions in artificial and human bone.ø 3 mm) and two opposing identical pockets were eroded from the base body. In addition, a M3.5 thread with a depth of 5 mm was countersunk into the hole  were drilled with a 40-mm-long hole  inside the base body, titanium guide sleeves (yellow) were additively manufactured ; see Fig. The setup mechanisms of the NiTi anchoring elements in artificial bone were successfully demonstrated in a CT Fig. .Fig. 2CTThe evaluation of the questionnaire showed that there were no haptic differences in the handling and feel of the NiTi screws during implantation compared to conventional, unmachined screw implants. The eroded pockets do not affect the stability of the screw in the bone. Despite the absence of a thread, no differences in the haptic and objective evaluation of the anchorage stability compared to a conventional screw were observed after implantation (before the setup) of the functionalized screw. The haptic comparison of the primary stability, after the setup of the NiTi screws, compared to the cement augmentation was rated by one of the two neurosurgeons with 7 out of 10 possible points (10 = high primary stability) and a noticeable improvement was observed. Neurosurgeon two abstained from comment.The additional effort to set up the anchoring elements due to the rotation mechanism can be negligible.The rotation mechanism for positioning the anchoring elements was rated as intuitive, so that very good haptic feedback was felt when the anchoring elements were applied to the bone. The torque was also rated as just right. It was not too low and not too high to allow optimal adjustment that allows the user to feel when the anchoring element is applied to the bone and compresses without having to apply too much force. It was well adjusted especially for osteoporotic bone tissue.To check the position of the screws a C-arm  was used. Clear imaging without artifacts of the NiTi screws as a whole as well as of the individual anchoring elements was demonstrated with this Fig. .Fig. 3HaPreliminary results of the pullout test in artificial bone showed a tendency for anchorage stability increase of the NiTi screw compared to standard screws.The pullout force of the standard screws was 57.22 N  ±  17.13 N and the pullout force of the NiTi screws was 62.36 N  ±  18.55 N Fig. Fig. 4PulThe mechanical work (energy that must be applied to break out the screw) of the standard screws was 4241.541 Nm  ±  42.549 Nm and that of the newly developed screws was 5464.796 Nm  ±  435.508 Nm , so that no further special tools were required. These process steps are currently already applicable for serial production . It woulThe sleeves, which are additively manufactured for assembly, are of significant advantage for guiding the NiTi elements, as they align the elements and fix them against twisting during implementation.The sleeves have a recess that can accommodate two NiTi anchoring elements and hold them hold them parallelly aligned A clearance fit allows them to be inserted into the screw and rotate, so that the anchoring elements shift into the correct position with regard to the pockets.Serial production is possible because of the small components and the associated large batch size on the build plate –20. MoreIn addition, the geometry of the sleeves can be made and adapted to the given implants without additional tools and complex design planning , 21. Adds = 17.7 mm .However, this is limited by the applied Ti6Al4V structures, which have a lower elasticity and can flake-off if the deflection is too large . TherefoFurthermore, the superelastic properties improve revision surgery. It allows for a more bone-sparing revision therapy (compared to bone cement augmentation), because by releasing the anchoring mechanism, the anchoring elements return to the screw without plastic deformation and occupy their original position at implantation (inside the screw). This unsets the cross-sectional enlargement and allows a more bone-sparing revision. In addition, there is no need for complex temperature management compared to thermally activated NiTi elements.The structuring of the NiTi anchoring elements with Ti6Al4V by the LSM process can be implemented satisfactorily and the fabrication over large areas is possible . In a prThe structuring of the anchoring elements was chosen so that the greatest possible interlocking can take place. The larger the surface of the structure, the greater the interlocking effect , 29. In Our investigation showed that the NiTi anchoring elements could be inserted and set up in the artificial bone. This served to prove that even with surrounding harder tissue, the anchoring elements could be placed without complications and that no tilting occurred during placement.In a further step, it was shown that the anchoring elements could also be placed in a human specimen without any problems. Surrounding bone and tissue structures did not cause disruption of the mechanism. One advantage of the mechanical setup was that it was haptically detected when the anchoring element was applied to the bone (increase in torque). The surgeon thus has direct feedback on the anchorage status, which was considered positive.At the same time, the experiments showed that the NiTi elements did not affect the imaging. No radiation overlaps occurred, they were easily controllable in lateral X-rays and the setup mechanisms could be evaluated without restrictions. This is particularly important for neurosurgical and orthopedic use, as the screw implants and their anchoring elements must not over-radiate surrounding tissue structures because of proximity to the spinal canal –32.Furthermore, the simplified handling test and the evaluation of the functional samples by the surgeons showed that the NiTi screws—despite the missing thread due to the eroded pockets—could be compared with standard screws during implantation (compressed spongiosa in the pedicle) and that there was no haptic difference. This is particularly important for users, as they can continue to rely on their typical haptic feel and experience when screwing in screw implants.The haptic feel is also important for the correct torque when setting up the anchoring elements and it could be optimally reproduced with the present mechanism. In this way, the surgeon can already detect an increase in stability during setup. For an initial assessment at this stage of development and the associated small number of available functional samples, only a small number of test implantations could be carried out. Further investigations in human and animal bone structures are planned in order to be able to make a more statistical statement.The screw extraction test according to ASTM F543  showed tIn summary, conventional monoaxial standard screws can be functionalized with Ti6Al4V-structured NiTi anchoring elements. The fabrication of the screw base body and integration of the NiTi anchoring elements is suitable for series production and the handling does not differ from standard screws. A first biomechanical test showed that the anchoring stability can be increased by the anchoring elements.The aim of the present study was to functionalize standard screw implants to increase anchorage stability in bone and revision capability by using superelastic, structured anchorage elements.To functionalize the screw implants, standard monoaxial pedicle screws were refined, mechanically processed and anchoring elements were used along the principles of the dowel and based on our own preliminary work . SuperelThe aim of the study was to investigate the increase of anchorage stability of screw implants by using superelastic anchorage elements with pyramid structure made of Ti6Al4V with regard to their manufacturing, handling and biomechanical pullout test.The setup mechanisms of the structured NiTi anchoring elements were tested in an artificial bone. For this purpose, the screw functional samples were implanted in a pre-drilled artificial bone cube with unset anchoring elements. Subsequently, the anchoring elements were set up so that a diameter increase of 2 mm results in the non-implanted state. For the evaluation and verification of the setup of the anchoring elements, the artificial bone cuboid with setup anchoring structure was analyzed in a µCT .In a following evaluation, an experienced neurosurgeon and orthopedic surgeon assessed the handling of the functional samples and the anchoring mechanism on human specimens of the lumbar spine Fig. . The focDifferences in handling and feeling during implantation and anchorage in the bone after implantation (before placement of the anchoring elements) compared to conventional standing screws.The anchorage situation after placement of the anchorage elements in comparison to cement augmentation.The additional work involved in setting up the anchoring mechanisms during implantation.The handling of the rotation mechanism for setting up the anchoring elements.The intraoperative imaging.A questionnaire was developed to evaluate the handling, which had to be completed by the two experienced neurosurgeons. The following aspects were evaluated:A screw pullout test according to “ASTM F543_ Specification and Test methods for Metallic Medical Bone Screws”  in artifN = 12 standard and N = 12 NiTi screw implants were examined. For each screw implant, a separate artificial bone test block with a size of 400 × 400 × 800 mm was used. The artificial bone blocks were all from the same production batch .For the pullout test, The evaluation of the results was carried out by means of a descriptive static analysis, evaluated using the median.For implantation and revision, conventional screwdrivers must be extended to mechanically set up the anchoring elements.Furthermore, there is currently no locking mechanism installed for the maximum setup mechanisms of the anchoring elements, which prevents the elements from bending too much. This must take place in further adjustments to prevent the Ti6Al4V structures from flaking.For further statements regarding the anchorage stability, toggle tests (ASTM 1717-15 ) must be


Stroke can impose a heavy burden on caregivers. Caring for stroke patients at home is more challenging than in hospitals with facilities. The purpose of this study was to evaluate the effect of a supportive home care program on caregiver burden with stroke patients.This was an experimental study. One hundred sixteen caregivers of stroke patients were recruited using convenience sampling from two university-affiliated hospitals in Tehran from June 2019 to February 2020. They were randomly allocated into two groups  using a randomized block design. The supportive home care program included eight educational sessions delivered in the hospital before discharge, and with home visits after hospital discharge. Caregiver burden was measured using Caregiver Burden Inventory. The data were analyzed using independent samples t-test and Analysis of Covariance.p = 0.055). There was a significant difference between the two groups regarding caregiver burden scores after the intervention period .Caregiver burden in the routine education group increased significantly after 2 weeks, from 52.27 ± 23.95 to 62.63 ± 22.68. The mean of caregiver burden scores in the supportive home care program decreased from 44.75 ± 17.21 to 40.46 ± 17.28. The difference between the scores of the two groups before the intervention was not significantly different (t = 1.941, df = 114, Caregiver burden increased significantly after the discharge without proper interventions in the caregivers of stroke patients. Providing support for home care providers can help to decrease or prevent the intensification of caregiver burden. Caregiver Burden (CB) is the negative effect of caregiving tasks that caregivers perceive , in termSensory and motor disabilities are major complications of a stroke that cause various degrees of dependence in patients . These cIn developing countries like Iran, there are very few public support and care centers that provide post-discharge education and care in stroke patients , 20. MorThe number of interventional studies in the field of CB reduction in caregivers of stroke patients is limited. A study investigated the effect of social problem-solving telephone partnerships on primary family caregiver burden after stroke survivors are discharged home from a rehabilitation facility . Their rThe family needs a proper understanding of the disease and comprehensive support during the care of a patient after discharge. The nurse must provide proper information and support for the family in addition to caring for the patient , 30. SupIn many developing countries, including Iran, the family provides care after the discharge of stroke patients , 11. AltThis experimental study was a part of mixed-method research. One hundred sixteen caregivers were randomly assigned to two groups. The primary outcome was caregiver burden, which was assessed by Caregiver Burden Inventory.The convenience sampling method was used to enroll the study subjects. All patients who were admitted to the hospital during the study period were approached by the first author. The caregivers of patients were assessed for eligibility. If they had inclusion criteria, they were randomly assigned to one of the two groups, with a randomized block design. The inclusion criteria were  being anThe minimum sample size was determined using the following equation Barthel Index was used for Activities of Daily Living to assess the mobility function and self-care activities such as eating, bathing, and dressing . This InThe first author explained the purpose of the study and procedures to caregivers with a full description of the study intervention and routine care. Then, written informed consent was obtained from them. The block randomization was performed using a computer-generated permuted block randomization scheme (blocks of four). Subjects were randomly assigned to supportive home care programs and routine hospital education program groups by the statistician who was not involved in determining the eligibility of the subjects and had no information from the persons included in the experiment and no influence on the assignment sequence.Eligible subjects were chosen from patients with Stroke in the ward who was stable and ready to discharge. Barthel Index of Activities of Daily Living (BI) was completed for each eligible patient. After the allocation of eligible subjects, they completed the socio-demographic questionnaire and CBI (Pre-test). Caregivers in the routine hospital education program group received routine educations about CVA and caring for patients with CVA, which was programmed and performed in the hospitals before this study. They completed the study questionnaires 2 weeks after discharge. Subjects in the intervention group received an eight-session intervention program. The first two sessions of the program in the intervention group were planned and conducted at the hospital after the stabilization of the patient’s condition. The remaining six sessions of the program were performed at the patient’s home in 2 weeks. They completed post-tests after the intervention. Each session lasts between 45 to 60 min, and the intervention was finalized 2 weeks after discharge from the hospital. The Content of the sessions is presented in Table The main outcome of the study was the caregiver burden, which was measured by Caregiver Burden Inventory (CBI). This 24-item is scaled with Likert-format scoring from 0 to 4 with five dimensions, including time dependence –5, develThe data were entered into SPSS 16. The normality of the distribution of CBI scores was tested using the Kolmogorov-Smirnov test. The CBI score was reported as Mean ± Standard Deviation (SD). The difference in the scores of CBI and its domains between the two groups was tested by the independent samples t-test. Analysis of Covariance (ANCOVA) was used to compare the scores of CBI and its domains between the two groups after the intervention period. CBI and its domain scores before the intervention were used as a covariate in the ANCOVA. Linear regression was used to assess the effect of socio-demographic characteristics on the results.The study protocol was approved by the Ethics Committee of the Iran University of Medical Sciences (IR.). All study subjects completed the informed written consent. All study subjects could withdraw from the study whenever they desired. The information on all research units was confidential.p = 0.106). The mean ± SD of the age of patients was 68.50 ± 13.16 years in the supportive home care program group and 64.65 ± 12.20 in the routine hospital education program group . The Sociodemographic characteristics of the study subjects are presented in Table One hundred sixteen caregivers were enrolled in the study and finished the post-test. The mean ± SD of the age of study subjects was 43.98 ± 13.80 years and 43.41 ± 11.25 years in the supportive home care program and routine hospital education program groups, respectively . The scores of CBI and all its domains increased significantly in the control group (p < 0.05). It means that the caregivers felt a higher level of CB. Caregiver Burden scores in the intervention group decreased significantly. It means that caregivers felt a lower level of CB. In the intervention group, the mean scores of time-dependences (p < 0.05), physical (p > 0.05), and emotional (p < 0.05) domains were decreased, and the mean scores of developmental (p > 0.05) and social domains (p > 0.05) were increased. It means that the intervention was more successful in the prevention of physical and emotional burdens along with time dependence activities.Caregiver Burden and its domain scores are presented and compared in Table p > 0.05). The difference became significant after the intervention period and the control group had a higher score of time dependence caregiver burden (P < 0.001) Time dependence domain mean score in the intervention group was decreased while it was increased in the control group. The difference in the developmental domain between the two groups was not significant before the intervention period (p > 0.05). The control group had a significantly higher score of developmental domain score after the intervention period (P < 0.001). The developmental score increased in both groups but the increase in the control group was significantly higher (P < 0.001) There was a significant difference between the two groups in terms of the physical domain before the intervention period and the intervention group had a higher score (p < 0.05). The physical domain score decreased in the control group and increased in the control group and the difference remained significant with opposite direction, where the control group received higher scores (p < 0.05). There was no significant difference between the two groups in terms of the social domain before the intervention period (p > 0.05). The difference became significant after the intervention period and the control group had a higher score of social caregiver burden (P < 0.001) Social domain mean score in both groups was increased. The difference in the emotional domain between the two groups was not significant before the intervention period (p > 0.05). ANCOVA showed that the significant difference between two groups remained after the intervention period (p > 0.05). There was no significant difference between the two groups in terms of CB score before the intervention period (p > 0.05). The difference became significant after the intervention period and the control group had a higher score of caregiver burden (P < 0.001). CB mean score in the intervention group was decreased while it was increased in the control group (P < 0.001).There was no significant difference between the two groups in terms of time dependence domain before the intervention period (The results showed that the program is effective in reducing caregiver burden and its domains. The CB increased in the routine hospital education program and decreased in the supportive home care program.The level of care burden in caregivers of stroke patients is very high. The research has shown that their caregiver burden is very frustrating, especially in the first few weeks. This is a factor that can have very negative effects on patients’ outcomes. Insufficient knowledge about the nature of the disease and its severe effects can lead to severe frustration in caregivers. Failure to follow up on primary care, such as providing general hygiene and physiotherapy can lead to serious complications, such as infection and deformity of the limbs , 35. TheCaregiver Burden is a multidimensional phenomenon whose dimensions are time-dependence, developmental, physical, social, and emotional burden. The results showed that the intervention significantly affects the score of the time-dependence domain. Time-dependence is the perceived burden attributable to restrictions on a caregiver’s time forced by the demands of caring for the patient . A patieWhile the change in the developmental burden score in the control group was significantly positive, it was negative in the intervention group. The developmental burden is the perceived feelings that caregivers have. They are “out of sync” with their peers or feelings of missing out on life . The decThe results showed that the increase of physical burden, which describes chronic fatigue and damage to the physical health of caregivers is significant in the control group. The physical burden also increased in the intervention group, but the increase was not significant. Primary skills training was effective in this outcome . AlthougA supportive homecare program is also effective in the prevention of an increase in the social burden of care. Social burden refers to conflicts with other family members about care decisions, or feelings of isolation such as not having time to maintain social relationships . The eduOur study evalutes the effect of Home Care Program on Caregiver Burden with Stroke patients in Iran. While the evidence showed that stroke survivors are completely focused on physical recovery in the 1-month post discharge, the caregiver burden begins in the hospital and it increase through time , 8, 10. This was an experimental study that was conducted on eligible caregivers who had the mentioned inclusion criteria. The small sample size can reduce the generalization of the results. It is recommended to perform larger studies on a wider range of caregivers. Another limitation of this study was the significant difference in scores between the two groups before the intervention. ANCOVA is used to modify the effect of scores before the intervention, which showed that the supportive home care program was effective in the reduction of caregiver burden despite the higher scores in the control group before the intervention. However, it is recommended to use caregiver burden scores as a matching criterion in future studies.Stroke is a condition that has long-term effects on the patients and his/her caregivers. The family has a lot of problems coping with the new life that the disease imposes on them after the acute phase in the hospital. Caregiver Burden can increase after the discharge of stroke patients in the caregivers. The burden also can increase significantly on people who are caring for their patients at home. Providing support for home care providers along with proper and relative education can help to decrease or prevent the increase of caregiver burden. Future studies can help to further understand the methods that can help in the decrease of caregiver burden.


Social buffering occurs when the presence of one animal attenuates another’s stress response during a stressful event and/or helps the subject to recover more quickly after a stressful event. Inconsistent previous results might reflect previously unrecognised contextual influences, such as the nature of the stimulus presented or social factors. We addressed these issues in a two-part study of horses paired with familiar (16 subjects) or unfamiliar (16 subjects) companions. Each subject performed 4 tests in a counterbalanced order: novel object test —alone or with companion; and umbrella opening test—alone or with companion. Social buffering was significantly influenced by the nature of the stimulus presented, but not by companion’s habituation status or familiarity. Importantly, the stimulus used produced differential effects on behavioural and physiological measures of buffering. A companion significantly reduced behavioural response (reactivity) in the novel object test but not in the umbrella test. However, heart rate recovered more quickly for subjects with a companion in the umbrella test but not in the novel object test. We propose that circumstances which permit greater contextual processing may facilitate demonstration of behavioural effects of social buffering, whereas buffering in response to startling events may be manifest only during post-event physiological recovery. There are two predominant, but not mutually exclusive, models relating to social support, and these make slightly different predictions. The first “direct effects” model predicts that companions will provide beneficial effects to the subject, regardless of whether the subject is stressed or not1. For example, in wild chimpanzees, a close social companion, i.e. a companion with whom the subject exchanges high rates of affiliative and cooperative behaviours, can help to reduce the activation of a subject’s hypothalamic-pituitary-adrenocortical (HPA) axis within a stressful context (intergroup encounters) but also throughout daily life (everyday affiliation)2. The second “social buffering” model focuses on discrete contexts only where the subject experiences a negative or stressful life event, and the companion has the potential to attenuate the stress response in one or more ways in these circumstances. The latter is the focus of the current paper.The concept of social support applies to a diversity of situations whereby an individual subject benefits, physically or emotionally, from the presence or behaviour of a companion5. For example, marmosets exposed to novelty show fewer behavioural signs of distress and agitation, and do not have significantly increased levels of urinary cortisol if accompanied by a companion6. The effects of social buffering can be further distinguished according to whether the companion is present during or after the stressful event experienced by the subject. In both cases, the presence of a companion seems to have a positive impact on the subject’s response. For example, the presence of a conspecific rat can reduce behavioural signs of stress when a subject rat is exposed to a conditioned stimulus7. In a similar way, rats housed with a littermate after experiencing social defeat show more exploratory behaviour in an elevated plus maze test than those housed alone8.There are many examples of social buffering in the literature where conspecific animals have been shown to reduce the subject’s stress response during a stressful event5. Similarly, measures of social buffering are very diverse, and include the return of corticosteroid levels to baseline, heart rate, body temperature and Fos gene expression and/or behavioural measures of vocalization, escape attempts, immobility, defecation rate and motivation to seek social contact depending on the study5. This diversity in both stressful stimuli and measurement parameters has resulted in studies with very different objectives  but such diversity also hinders the development of a coherent understanding of important sources of variability in the social buffering process.The qualitative properties of stressful stimuli that have been used to examine social buffering vary from novel objects or environments to the appearance of a sudden stimulus, white noise, electric shocks, social defeat and social separation and/or isolation12; marmoset:13; rat:15; Siberian dwarf hamster:17), while others indicate that unfamiliar animals are better (19) and some report no effect . Moreover, many researchers have demonstrated that the arousal status of the companion can affect its efficiency as a social buffer . Companions that have previously experienced or that anticipate the arrival of a stressor do not appear to be good social buffers in cattle22 or rats25. However, in horses26 and mice27, if companion arousal is reduced by prior habituation to a novel but harmless stimulus then this can increase the companion’s effectiveness as a social buffer.This is especially apparent when trying to draw conclusions about the impact of familiarity and/or companion’s arousal state on social buffering. Indeed, contradictory results about the role of companion familiarity abound, with some studies showing familiar animals are better buffers , confounding factors (e.g. lack of standard definitions and measures of subject-partner association level) as well as gaps in our knowledge. For example, individual studies of social buffering effects have all focussed on one stressor at a time, so it is not possible to known from any individual study whether the impact of the companion on the subject’s stress response is context-dependent. To our knowledge, only one study has compared the impact of different stressors30 and increasing evidence of the sophistication of their social cognition. Horses are, for example, able to exchange information through subtle communication32 and can perceive the emotional state of their conspecifics33. We also used both behavioural and physiological measures to assess the extent of social buffering.Our aim is to contribute to the development of a general model of social buffering by investigating, for the first time, whether the effectiveness of factors such as companion arousal and familiarity are influenced by stimulus context. We used horses as a study species because of their complex social systemIn two studies involving two different groups of subjects, we tested if a companion can attenuate the subject’s stress response. In the first study, we also tested whether the impact of companion arousal on the subject’s stress responses was context-dependent by exposing subjects to two distinct stressful events while using pairs of subjects with a high level of consistent familiarity. The hypotheses were that the companion will help to reduce the behavioural and physiological responses across different stressful contexts, and that a habituated companion will be more efficient at buffering the subject’s stress responses than a naïve one. We then evaluated in a second study whether similar effects of companion arousal and the nature of the stressful event were obtained when individuals were not familiar with their companions. The hypothesis was that a familiar companion would be more effective in reducing behavioural and physiological responses than an unfamiliar companion.This research was carried out in compliance with the ARRIVE guidelines. The delegated authority of the University of Lincoln Research Ethics Committee approved this research (CosREC433) and all methods were carried out in accordance with the university Research Ethics Policy and with the ethical guidelines of ISAE. Written informed consent was obtained from the owner of the horses.The first study took place between May and June 2018 in the riding school of Haras de Jardy . 32 horses  of various breeds, aged 6–24 years old  representing 10 geldings and 22 females which belong to a busy riding school environment. Each pair (n = 16) consisted of a focal subject and a companion and the roles were not reversed during the experiment.The second study was undertaken at the same location as the previous experiment, from April to June 2019. 32 horses of different breeds, consisting of 16 pairs of unfamiliar horses  were used, aged 4–23 years old  representing 19 geldings and 13 females. Among the 32 horses, 7 were used in both studies and played the role of habituated companion on both occasions. As in the first study, each pair (n = 16) consisted of a focal subject and a companion. Within a pair the roles were not reversed during the experiment.34 was built with wooden poles  with free access during the test. The distance between the buckets and the novel object or the umbrella was 1 m.A rectangular test arena (6 m × 3 m) with a starting area (3m × 3m)36.Two different types of novel stimuli were presented in a counterbalanced order to control for prior exposure effects. One was a novel unchanging stimulus , the other a novel suddenly changing stimulus . These different stimuli were presented in front of the horses by an experimenter26. The horses were considered ready for use when they met the following criteria: the horses entered the arena voluntarily and walked directly to the bucket to eat for at least 90 s out of a total of 120 s. During this habituation process, the novel object was absent, the umbrella was closed and the person who would open the umbrella stood still behind it to habituate the horse to their presence. The umbrella and associated individual  were present throughout every experiment (novel object and umbrella test).Each horse was habituated individually to the test arena prior to the experiment to reduce the risk of stress due to a new environment, using the same principles of habituation described by Christensen et al.26. The horse which required fewer trials was selected as the companion, with the other horse being the subject. If the two horses required the same number of trials, then the fastest responding horse within the trials was made the companion: it was reasoned that a faster-responding horse spending less time examining its environment would be more confident and therefore potentially a better social buffer.The allocation of experimental roles (subject or companion) within a pair was done by measuring the time taken by individuals to go to the bucket and eat during the habituation period and by the number of habituations achieved per horse26. Following Christensen et al.26, they underwent up to 13 trials. If they had not reached the habituation criteria after the 13th trial, they would have been dropped from the study. To ensure that they remained habituated, the procedure was repeated to the stimulus  once, less than 10 min before performing the test with the subject.In the first study, half of the companions (n = 8) were habituated to the test stimuli (novel object test and umbrella test), these are referred to as habituated companions. They were regarded as habituated when they met the following predefined criteria during the stimulus exposure: little (reactivity score of 1) or no behavioural reaction (reactivity score of 0) to the stimulus and no greater increase in heart rate than 20 beats/min during stimulus exposureThe other eight companions were not habituated to the test stimulus, they are referred to as naïve (control) companions.26). In addition, eight horses that did not participate previously in the study were used as naïve companions.In the second study, the same eight habituated companions from the first study were scheduled for use, however one horse had to be replaced because it had been retired. These companions did further habituation sessions to the test stimuli (novel object test and umbrella test), following the same procedure as before  was measured from the time it took for the subject’s heart rate to return to within 15% of this pre-test heart rate value (bpm) after being exposed to the test stimulus39. The threshold for determining recovery of pre-test heart rate value plus 15% was chosen as it represents a substantial degree of decline and accommodates individual variability in baseline values based on the pre-test heart rate value; as a result, most horses recovered during the allocated time (5 min). If a horse escaped from the test arena in response to the presentation of the stimulus during the test, it was assigned a value of 300 s which corresponds to the maximum duration of the testing session. The heart rate data was checked for artefacts. In the analysis, all recordings with more than 5% heart beat errors were excluded 39.The heart rate was only recorded for the focal subjects. These were habituated to a Polar Equine H7 heart rate monitor, and heart rate data analysed with the software Kubios HRV 3.0.2. The settings of the heart rate monitor were such that the sampling occurred 1/s, with the monitor always sending the current heart rate, not the rolling average. The week before the tests, the focal subject’s heart rate was measured for two minutes in the test arena with the same conditions as in the test (i.e. when the subject was eating from the bucket) but without being exposed to any test stimuli (i.e. pre-test heart rate)Behaviours were recorded by two cameras during testing which had been present throughout habituation.26. Two evaluators separately watched and rated the same videos in order to assure a reliable reporting of the behavioural data  and the opening of the umbrella were evaluated by assigning a score , called reactivity score (RS) —alone or with companion; and umbrella test—alone or with companion. Each horse did only one test per week. To control for order effects, the 16 pairs were randomly allocated into 4 groups; each group contained 2 pairs of subjects with habituated companions and 2 pairs of subjects with naïve companions. With each group performing the tests in a different order to control for order, the potential effect of test order was minimised, but it was still considered in the statistical model.41.The software R (version 3.5.2) was used for all analysesFor each study, the data from one pair was removed because the companion stayed in the starting area during the umbrella test. The companion was therefore not considered able to play the role of social buffer. For this case, only the data obtained in the novel object test alone and by pair were kept in the analyses.For the population level data, we first we established that there was no order effect on either the behavioural or physiological responses of subjects . In order to compare the median values of the pre-test heart rate with the heart rate obtained when the subject was alone in the novel object and umbrella test, a Wilcoxon test was used. This determined if the horse’s heart rate was significantly higher when the stimulus was presented.ordinal) were used for the data on reactivity score and linear mixed effect models (LMM) in the R-package lmerTest used for the data on heart rate recovery, with companion (absent vs. present) as a fixed factor and the identity of the subjects as a random factor.For the next stage of analysis, since our focus was on factors affecting the occurrence of social buffering, all subjects with a reactivity score of 0 when they performed the test alone were excluded from the behavioural analyses as there was no potential to show a social buffering effect on their responses. Subjects who did not show a change in heart rate (obtained 0 s recovery time) when they were alone were excluded from the physiological analyses. Exclusion for one of the analyses did not necessitate exclusion from other analyses. To examine if the companion reduced the behavioural and/or physiological responses of subjects during stressful situations, the reactivity score and the heart rate recovery were compared between when the subject was alone or with a companion for each test. Cumulative link mixed models (CLMM) using the adaptive Gauss-Hermite quadrature (AGQ)  and heart rate recovery time  were both compared as a function of the types of companion (naïve vs. habituated) for each test. The data on reactivity score were analysed with a cumulative link model (CLM) and the data of heart rate recovery with a linear effects model (LM). Similar models were used for each dependent variable, with type of companion (habituated vs. naïve) as fixed factors. In addition, companion reactivity score was added as a fixed factor in the CLM of reactivity score.The significance of the results was assessed at a threshold of p < 0.05.Reactivity scores were analysed for 16 pairs for the novel object test. In this test, subjects in pairs had significantly lower reactivity scores than those alone (Cumulative link mixed models (CLMM): estimate ± S.E.: − 2.12 ± 0.88, P = 0.016)  and significantly increased to 48.33 (SD = 12.54) during the novel object test .The analyses of heart rate recovery were run on 12 pairs in the novel object test. The difference in time to recover obtained from the subjects in pairs and when alone was not significantly different (Linear mixed effect models (LMM): t-value, df: − 1.336, 11, P = 0.208) : estimate ± S.E.: 0.31 ± 0.51, P = 0.535).For the umbrella test, reactivity scores were analysed for 14 pairs. Considering only subjects who showed a reaction, the reactivity score for the subjects in pairs was not significantly lower than that obtained from those alone  see Fig. a.Figure The mean value of the subject’s pre-test heart rate was 41.50 (SD = 3.66) and significantly increased to 50.68 (SD = 8.66) during the umbrella test .The data on heart rate recovery were analysed for 14 pairs for the umbrella test. The presence of a companion was associated with quicker heart rate recovery  .The median value of the companion’s reactivity score in the novel object test was 0.5 (Quartile 1 (Q1) = 0; Quartile 3 (Q3) = 1) for habituated companions  versus 1  for naïve companions. These values were not significantly different . In the umbrella test, the median value of the companion’s reactivity score was significantly lower at 1  for habituated companions compared to 2  for naïve companions .The difference in reactivity scores and heart rate recovery were not significantly different between subjects with habituated companions and subjects with naïve companions regardless of the test (Reactivity score (RS), CLM: Novel object test (NO), estimate ± S.E.: 0.36 ± 0.95, P = 0.705; Umbrella test (UM), estimate ± S.E.: 0.20 ± 1.36, P = 0.881; Heart rate recovery (HRR), Linear effect model (LM): NO, t-value, df: − 1.027, 10, P = 0.329; UM, t-value, df: 0.216, 12, P = 0.833).For the novel object test, the analysis of reactivity scores was run on 12 pairs. The subject’s reactivity score in the novel object test for paired subjects was significantly lower than when alone  see Fig. a.Figure The mean value of the subject’s pre-test heart rate measurement was 48.34 (SD = 4.73) versus 50.53 (SD = 10.52) for the novel object test. These values are not significantly different .The data on heart rate recovery were analysed for 11 pairs in the novel object test. The time to recover for the subjects in pairs was not significantly different to those alone  .In the umbrella test, the reactivity scores were analysed for 15 pairs. The reactivity score for the subjects in pairs was not significantly lower than that obtained from those alone   versus 71.54 (SD = 33.04) during the umbrella test .The data on heart rate recovery were analysed for 15 pairs for the umbrella test. Subjects in pairs had significantly quicker recovery times compared to those alone  .The median value of the companion’s reactivity score in the novel object test was 0 for habituated  and naïve companions . These values are not significantly different .In the umbrella test, the median value of the companion’s reactivity score was significantly lower at 1  for habituated companions versus 4  for naïve companions . Only one subject investigated the umbrella and this was an individual with a companion. During the tests 11 pairs had agonistic exchanges such as head threat when they ate, i.e. one of the horses turned its heard toward the other with the ears pinned back.Regardless of the test, there were no significant differences in reactivity scores and heart rate recovery, between subjects with a habituated companion and subjects with a naïve companion .5, there is inconsistency in the conclusions drawn about general effects42. These relate to variability in the stimuli and measurements assessed; our work allows the development of a framework for rationalising these inconsistencies. Our results show that while the nature of the stressor produces a differential effect on behavioural and physiological measures of buffering, the characteristics of the companion such as its arousal status or familiarity, did not have a significant effect. A companion significantly reduced the subjects’ behavioural response (reactivity) in the novel object test but not in the umbrella test; the converse was found in relation to heart rate recovery time. This interaction between stimulus type and behavioural versus physiological buffering effect has not been noted before. Moreover, the consistency of the effects in the two studies show the robustness of the phenomenon.Among the many examples of social buffering44). Although theoretically, this might simply relate to the umbrella being larger, for example, Bulens et al.44 suggested that the large size of an opened umbrella makes it difficult to ignore compared to the cone and plastic ball used in their test. However, stimulus size alone does not seem to be a full explanation as horses have been observed to react similarly to a stationery umbrella and a stationery but larger plastic tarp (5 m × 6 m)45. Another possibility, evident in our study, is that stimulus movement played an important role on the subsequent response: the umbrella was a novel, suddenly changing stimulus which led to a rapid change in the environment at a given distance from the subjects, unlike the ball. The sudden change provoked a more dramatic reaction  and ensure that responses were directly comparable.The differential impact of the companion on the subject’s behavioural response might relate to the emotional quality and intensity of the response provoked by the two stimuli . Like others, we found a greater reaction to an umbrella than to a ball  effect was reported for a strange object on mean heart rate compared with a marked increase in heart rate during a surprise test (bucket dropped). However, as already noted, their study examined group size effects and not social buffering effects since there was no condition where individuals were alone. Consequently, it seems a middle stressor, such as a novel object, has a relatively small impact on a subject’s physiology which could explain the lack of physiological social buffering effect in the ball, novel object effect. The more gradual mental processing52 may facilitate greater social buffering of the behavioural response in these circumstances.Heart rate recovered more quickly for subjects with a companion in the umbrella test but this was not the case in the novel object test. It is possible that in the umbrella test, the immediacy and mental focus of the startle response meant the behavioural reaction was not susceptible to social buffering; however, having moved away from the umbrella, it might be that the companion can act as a social buffer during the recovery phase. In this situation, it would be predicted that the effect of the companion would only be manifest physiologically (e.g. in heart rate recovery). In addition, it could be argued that the intensity of the emotional response  rather than its quality (anxiety versus fear) differentiates the two conditions. In the former case, the opening of the umbrella may have increased heart rate to a greater peak, more readily permitting a reduction by the companion, which is not the case with the novel object test. In both of our studies, the mean heart rate obtained during the 5 min of the umbrella test alone was significantly different from the pre-test heart rate measurement. The same result was found in Study 1, for the novel object test alone. By contrast, in Study 2 mean heart rate was not significantly higher than the pre-test heart rate measurement. Our result for Study 2 is consistent with that found by Takeda et al.52. The differing social buffering effects that we noted with the two stimuli can be explained by the fact that the animal needs time to process relevant information such as a companion’s behaviours, however during sudden changes this mental process is focused on the immediate, rapid response that might be necessary to protect the individual from harm.Thus we postulate that the ball caused a state of lower level increased arousal and possibly anxiety, while the sudden opening of the umbrella resulted in a fear state with a discernible startle response27. Christensen et al.27 found that a habituated demonstrator horse reduced the fear reactions of unrelated young horses facing an opening umbrella. This difference in results between our study and that of Christensen might be explained by the age of the horses. Our horses being older were more experienced and therefore potentially more likely to have habituated to a wider range of sudden changes in the environment54. In the study of Christensen et al.27, the horses were just two years old, relatively inexperienced, and more likely to show flight responses. As the behavioural response is not always correlated with the physiological response56, it would be useful, in future, to record the behavioural and the physiological responses of the companion as well as the focal subjects in order to have greater insight into their arousal state57.The arousal status of the companion (i.e. companion’s habituation or not to the stimuli) did not affect the subject’s reaction and recovery time in either of our studies. This is not surprising for the novel stimulus test, given that the behavioural response of habituated and naïve companions was similar. Indeed, only 4 horses from the first study and 2 from the second study produced a reaction score higher than that allowed for a habituated companion (and one of these horses in each study was a habituated companion). However, in the sudden stimulus test, the behavioural response was different between the two types of companion, with habituated companions showing less reaction than naïve companions. This finding is in contrast to some others who have reported that companions are more effective social buffers if their arousal is reduced by prior habituation to a novel but harmless stimulus5. Some20 have found that after social isolation, reunion with any conspecific (familiar or unfamiliar) helped to reduce behavioural responses; while others28 found that a familiar companion was a more efficient buffer of the behavioural response during a novelty test and surprise test, and the physiological response during a surprise test and conflict test. The importance of familiarity between individuals seems to vary with age, potentially being less important with older subjects58. In adult cattle, after a separation from the group, any form of conspecific could help to reduce the subject’s behavioural responses during the reunion period20. However, in calves, it has been found that a familiar conspecific was more effective than an unfamiliar conspecific in reducing the behavioural response during a separation from the group58. The results of these studies are potentially consistent with the lack of effect of familiarity in our own study as the horses used are older (mean age 13.2 years in the first study and 14.2 in the second one). Whether or not these results apply to younger or less experienced horses needs to be investigated.Our results also showed that in horses, familiarity between the subject and companion also had no effect on the subject’s stress responses. In the literature, the role of companion familiarity varies with factors such as the nature of the stressor and also with the species studied60; but does not imply any form of social bond. We suggest that future studies should investigate the potentially separate effects of social bond and familiarity on social buffering effects.It is important to highlight that the familiarity of a subject is not the same as its relationship. Familiarity implies recognition of an individual, i.e. an individual is able to identify another whom it has previously met based on distinctive characteristicsIn conclusion, neither the arousal status nor the familiarity of a companion influenced the responses of adult subjects in our study. However, we found strong effects of stimulus context. We propose that when the risks of referencing another individual in a stressful situation are low, social buffering of the initial behavioural response will be evident; however when there is a high potential risk from the initial immediate response, social buffering effects will only be evident in the physiological recovery of the horse after the event.Supplementary Information