The main objective of this systematic review was to collect the pre-existing scales for assessing the difficulty of third molar extraction. The secondary objective was to design a proposal for a preoperative evaluation protocol for the difficulty of third molar extraction. Two independent researchers conducted an electronic search in Pubmed (MEDLINE), Cochrane, and Scopus databases during March 2021. Included studies evaluated the prediction of the difficulty of surgical removal of impacted upper or lower third molars using new indices/scales or pre-existing scales with or without modifications. Articles referring to coronectomies or assessing pre-surgical difficulty using other tools were excluded. Neither language nor publication date restrictions were applied. Out of 242 articles, 13 prospective cohort studies were finally selected. Seven developed new indices/scales, and 6 assessed the predictive ability of some pre-existing scales. Most of the indices/scales contained radiological variables and few added any patient-related variables. We proposed a preoperative assessment protocol of the difficulty of third molar extraction to facilitate treatment planning and/or considerate referral in cases of high difficulty. This proposal used patient-related, radiological and surgical variables. Using a preoperative protocol to evaluate the surgical difficulty, including different patient-specific, radiological and surgical variables, could facilitate treatment planning, help clinicians prevent complications and assess the possibility of referral. Key words:Wisdom teeth, patient characteristics, radiological variables, surgeon experience, assessment form. Pre-operative evaluation of surgical difficulty can help the practitioner plan the surgical technique, estimate the operating time and foresee possible complications . In addiM is one The ability to predict surgical difficulty based on the surgeon's experience is controversial, as in the published literature some studies find no difference , while oThe fact that most 3M difficulty scales are mainly based on radiological criteria constitutes a gap between the impact that patient or surgeon factors can have on actual surgical difficulty . In thisIn the field of oral surgery there is no form to determine the difficulty and assess the ability to perform surgery or to refer the case to a specialist according to the different variables involved, such as patient, radiological and operative factors, as determined by a recently published systematic review . ConsideThe main objective of this systematic review was to collect the pre-existing scales to assess the difficulty of 3M extraction. The secondary objective was to design a 3M difficulty assessment form, based on the previously demonstrated influencing factors, to assist clinicians, whether they are students, recent graduates or even oral surgery specialists, to make a correct treatment plan or to make a referral decision.This systematic review was carried out according to Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) guidelines  and the Inclusion criteria were studies assessing the preoperative prediction of the difficulty of impacted upper or lower 3M removal using new indices/scales or pre-existing scales with or without modifications. Articles referring to coronectomies or that had only evaluated the preoperative difficulty by means of visual analogue scales or operating time were excluded. Neither language nor publication date restrictions were applied.Two independent researchers  performed an electronic search in Pubmed (MEDLINE), Cochrane, and Scopus databases during March 2021. The search strategy used was “(wisdom tooth OR third molar) AND ”. Articles were first selected by reading titles and abstracts, and finally, those that met the eligibility criteria were read in full text. A third researcher resolved any discrepancies (CGE). Moreover, a manual search into the references of the selected studies was also conducted to ensure that all studies related to the area of interest were collected. We calculated the degree of agreement between the researchers for article selection after the full text reading using Cohen's Kappa index.Data was recorded in Tables to collect the following information: author and year, number of patients and third molars treated, objective of the use of a scale or index , name of the index or scale, type of variables  and individual items recorded by the index/scale, objective post-operative variables that help determine the difficulty, evaluator of the index/scale, surgeon(s) experience and main results. Based on this information and the factors that determine an increase in difficulty according to a previous systematic review , the autThe electronic search yielded 242 articles, of which 20 were selected to be read in full text. After reading, 7 articles were excluded because they did not assess the predictive ability of the indexes/scales -15. Finaet al.  as a post-operative variable indicating the degree of difficulty -21,24-28All studies showed an improvement on the prediction of the surgical difficulty when using the new indices/scales or the proposed modifications of the pre-existing ones in comparison with pre-existing indices. Only 1 study failed to demonstrate improvement of a new index with respect to the modified Parant scale .The form includes 3 groups of variables: features of the patient, and radiological and surgical features. It classifies each clinical case into 1 out of 3 categories of difficulty. The scoring was adopted from the ‘Endodontic Case Difficulty Assessment Form and Guidelines’. Each item is scored with 1 point for low difficulty, 2 points for moderate difficulty and 5 points for high difficulty. If the sum of the points is less than 20, the case has a low difficulty, suggesting an easy surgical case, that is, a conventional extraction that can be performed by a supervised student or by a general dentist. If the sum is between 20 and 40 points, the case is classified as moderately difficult and should be operated by a dentist with training in oral surgery over 3 years or by a qualified generalist dentist with specific continuing education and over 5 years experience in oral surgery. In cases over 40 points, considered to be highly difficult, the surgical intervention should be reserved for senior surgeons with more than 10 years of experience.This study aimed to collect pre-existing scales assessing the difficulty of third molars in order to design a difficulty assessment form to help professionals and to be used in an educational setting. The importance of having indices/scales that indicate the degree of surgical difficulty lies in a correct treatment planning to avoid underestimation of the difficulty and to minimize the number of intra- and post-operative complications . Some scet al. (Juodzbalys and Daugela  carried et al.  shows a The results obtained in the present systematic review show that most of the existing indices/scales include radiological variables collected from panoramic radiographs, and only some contain variables or characteristics of the patient himself, such as age or BMI, among others. However, taking into account the results of a recently published systematic review , these set al. (Surgical factors are usually treated separately from other factors. There are indices/scales that assess difficulty only by the type of surgical technique, such as the modified Parant scale . Howeveret al.  determinet al. ,35 or noet al. , as wellIn the field of oral and maxillofacial surgery there are no studies to assess the learning curve of the extraction of impacted 3M. The learning curve is the time and/or number of surgical interventions that a novice surgeon needs to be able to perform a procedure independently and with a good result, thus becoming a competent surgeon . Therefoet al. (However, although the more experienced surgeons have fewer post-operative complications, the less experienced ones may also have a low number of complications, provided that their learning curve is good and progressive . In the et al.  studied et al. .In our opinion, the learning curve on difficulty assessment has to be developed also during the first years of clinical practice, both for generalists and for specialists in oral and maxillofacial surgery. Correctly predicting the difficulty of the impacted 3M removal is relevant in order to avoid iatrogeny in less expert surgeons and perform a progressive learning curve.Therefore, the development of the present form for assessing the difficulty of surgical extraction of 3Ms based on the available scientific evidence and the clinical experience of the authors is an opportunity to improve the training of students and to guide recent graduates and even oral surgery specialists. It is intended to help reduce intra- and post-operative complications and to assist with referral to an experienced surgeon.The existing indices/scales are mainly based on radiological variables that can be evaluated in a panoramic radiography. Very few authors introduce variables related to the patient's own clinical characteristics. The few scales that evaluate surgical variables only include the type of surgical technique. None of them values the surgeon's experience.The use of a protocol designed to evaluate the difficulty of 3Ms removal that includes patient-specific, radiological and surgical variables can facilitate treatment planning, help the professional foresee possible complications and decide whether to refer the patient to a specialist with proven knowledge and experience.


Electromagnetic forming (EMF) is one of the most popular high-speed forming processes for sheet metals. However, modeling this process in 3D often requires huge computational time since it deals with a strongly coupled multi-physics problem. The numerical tools that are capable of modeling this process rely either on shell elements-based approaches or on full 3D elements-based approaches. The former leads to reduced computational time at the expense of the accuracy, while the latter favors accuracy over computation time. Herein, a novel approach was developed to reduce CPU time while maintaining reasonable accuracy through building upon a 3D finite element analysis toolbox which was developed in CEMEF. This toolbox was used to solve magnetic pulse forming (MPF) of thin sheets. The problem was simulated under different conditions and the results were analyzed in-depth. Innovative techniques, such as developing a termination criterion and using adaptive re-meshing, were devised to overcome the encountered problems. Moreover, a solid shell element was implemented and tested for thin structure problems and its applicability was verified. The results of this element type were comparable to the results of the standard tetrahedral MINI element but with reduced simulation time. Lightweight structures have many applications, especially in aerospace and automotive industries. The huge demand on lightweight structures requires improvements in the forming processes that would lead to cost reduction while maintaining structural resistance. High-speed forming processes, such as explosive forming discussed by Mynors and Zhang , electroMulti-physics simulation is a wide domain that contains various problems, including fluid-structure , thermalThe electromagnetic forming (EMF) process applies an intense electromagnetic pulse on a metallic component, inducing plastic deformations. It is a high-speed forming process that has strain rates ranging from k et al.  discussek et al. . Unger eRecently, many endeavors have been made to simulate this problem. Most of these approaches were mainly restricted to axisymmetric geometries or small deformation problems. Fenton and Daehn  tackled Additionally, many multi-physics commercial software already exist in the market, such as LS-DYNA . The eleThe main novelty of this work is the study of an application of the EMF processes, which is the magnetic pulse forming (MPF) of thin sheets. This process can be used in either direct forming, used with highly conductive materials, or indirect forming, used with less conductive materials. Although the magnetic pulse forming problem can be simulated using axisymmetric model , we haveThe paper is divided as follows: Multi-physics simulations, including electromagnetic simulations, can be very computationally expensive. Additionally, design processes that include multiple simulation iterations and optimization processes require high computational power to be carried out. Thus, it is important to select the most appropriate numerical method to solve these problems in a reasonable time while maintaining good accuracy.A numerical toolbox based on finite elements methods for the electromagnetic forming applications has been developed to solve electromagnetic forming problems ,32. ThisThe electromagnetic solver is based on the well-known Maxwell’s electromagnetic field equations:Equation :   where A→Combining Equation  with EquSince for any scalar function Finally, after substitution of  element  and an eFor the MINI element, the strong form of the mechanical problem is defined by conservation equation along with the boundary conditions. Considering the decomposition of the stress tensor into spherical and deviatoric parts, the mechanical problem is represented on the domain The system of equations representing the mechanical problem can be summarized as follows:The first two equations represent the conservation of momentum in the system. Although, the representation used here is divided to deviatoric stress and pressure that will help later in developing the mixed formulation element approach.Third equation represents Dirichlet boundary condition and fourth equation represents Neumann boundary condition.The weak form is based on a mixed velocity-pressure formulation. The formulation is written for test functions  and SteBoundary conditions: In the direct forming, the Aluminum workpiece is the only part in the mechanical solver. Thus, there is no contact condition added in this simulation. However, there is a bilateral sticking condition between the green ring manipulator shown in This section is fully dedicated to discussing the results of the MPF problem in the utmost details possible. The following subsections will tackle two basic types of the MPF process: direct forming and indirect forming. The former, a 160 mm diameter disc-shaped workpiece, is formed by MPF directly, whereas the latter, an Aluminum disc, is placed between the coil and the Steel workpiece since Al has a much higher electrical conductivity than Steel and will help better form the Steel material . Many teIn this subsection, the results of the direct forming process are presented. Two different workpieces were tested under direct forming: 0.5 mm thick Al and 1 mm thick Steel. Equivalent strains of both Steel and Al at 7 kV and 3 kV are shown in More investigations have been conducted on the deformed shapes. The final deformation of the Steel material is very small and cannot be shaped through direct forming due to insufficient electrical conductivity and, consequently, not enough deformation range. Therefore, the rest of the work is focused on indirect forming in order to obtain more deformation with the help of an aluminum hammer, which is the same workpiece used in direct forming (0.5 mm thick).The indirect forming process results will be the main focus of this section. More in-depth investigation will be tackled in this subsection. Likewise, numerical simulations are carried out for the indirect case using two elements: MINI and SHB. More deformation has been noticed for the Steel when used with Al since it makes use of the electrical conductivity of Al to gain more force to shape the Steel.Overall, the results of the recently implemented element SHB showed very good agreement with its counterpart MINI element. These results are very encouraging to use this element in such complicated simulations as it proved its precision and efficiency. Although, more investigation is required to better compare the two elements, which will be introduced in the following section.The aim of implementing the new element SHB is to use a special element for bending-dominated problems and obtain accurate results with a low number of elements. The usage of this element was very remarkable as the simulation time was greatly affected. Similarly, the CPU time of the direct forming process represents the same trend. Finding a way to reduce the simulation time of the magnetic pulse forming is tremendously important, especially in the optimization processes. Optimization iterations have to be run to optimize the shape of the workpiece, study the effect of the workpiece’s thickness and carry out the material parameter identification process. This is considered a crucial milestone in the simulation of MPF processes and similar problems.This section is dedicated to giving a better insight of the results, along with discussing other results that explain the physical intuition of the process. Nevertheless, some challenges have been encountered while simulating the problem. Therefore, some of these problems are mentioned in the following subsections along with the proposed solutions. These problems include determining the final forming time, remeshing of the electromagnetic domain mesh and the effect of the mechanical mesh on the results. In the following subsections, the energy notion will be used to explain some of the difficulties that have been encountered while solving the problem. Therefore, it is important to explain the energy components that exist in this problem.The initial energy input in the electromagnetic system is as follows:This energy is equal to the total energy that exists in the system:In our case, we are not considering the One of the main issues with all these models is determining the final forming time. At the beginning, the simulation time was set to To better understand this, At the beginning, the numerical simulations were carried out using a fixed but fine mesh in the electromagnetic domain, as shown in On the other hand, Therefore, all the results in the previous subsections are obtained with remeshing activated. Although this increased the total simulation time, the obtained results can be trusted and a negligible amount of energy is lost.One of the questions that was intriguing while studying this process was the effect of mechanical mesh on the accuracy of the results. Thus, the indirect forming process has been simulated again with coarser mesh of the MINI element and its results have been compared to both the MINI fine mesh and SHB element. However, more insight has been given to the mechanical energy of the three cases. An efficient approach for the simulation of the magnetic pulse forming process of thin sheet metals was developed by combining an electromagnetic solver, relying on Maxwell’s equations, with a mechanical solver, based on the conservation of momentum equations. In-depth analysis of the types of the magnetic pulse forming processes was carried out, namely on direct forming and indirect forming. Tetrahedral element (MINI) and solid-shell prism element were employed to solve the mechanical problem and quantitative comparisons were carried out to assess their performance in such applications. The overall results showed that the accuracy obtained with a low resolution SHB approach (low number of elements) was comparable to that of a high resolution MINI element based technique (high number of elements). The SHB element was shown to be less stiff than the MINI element. Finally, a computational cost study was carried out and demonstrated a higher computational efficiency for the SHB element since a smaller number of elements could be used while maintaining comparable accuracy to that of the MINI element. These results are very promising to study the performance of the SHB element, not only in MPF application but also in other applications. Many challenges were encountered during the simulation of this multi-physics problem and some solutions to overcome them were devised. First, the final forming time. It was very challenging to determine the exact final simulation time since the deformation takes place in the order of magnitude of milliseconds. Consequently, criteria based on measuring the change in the mechanical energy variation were adopted to find the termination time at which the energy variation is minimum. Second, the electromagnetic mesh had to be adjusted to consider the new mechanical deformation since the electromagnetic solution is highly dependent on the spatio-temporal evolution of the deformation of the workpiece in the mechanical problem. Hence, a remeshing strategy was utilized for the electromagnetic mesh and the results were compared to those conducted without the remeshing step.


At the beginning of a sprint, the acceleration of the body center of mass (COM) is driven mostly forward and vertically in order to move from an initial crouched position to a more forward-leaning position. Individual muscle contributions to COM accelerations have not been previously studied in a sprint with induced acceleration analysis, nor have muscle contributions to the mediolateral COM accelerations received much attention. This study aimed to analyze major lower-limb muscle contributions to the body COM in the three global planes during the first step of a sprint start. We also investigated the influence of step width on muscle contributions in both naturally wide sprint starts  and in sprint starts in which the step width was restricted .Motion data from four competitive sprinters  were collected in their natural sprint style and in trials with a restricted step width. An induced acceleration analysis was performed to study the contribution from eight major lower limb muscles  to acceleration of the body COM.In natural trials, soleus was the main contributor to forward (propulsion) and vertical (support) COM acceleration and the three vasti  were the main contributors to medial COM acceleration. In the narrow trials, soleus was still the major contributor to COM propulsion, though its contribution was considerably decreased. Likewise, the three vasti were still the main contributors to support and to medial COM acceleration, though their contribution was lower than in the natural trials. Overall, most muscle contributions to COM acceleration in the sagittal plane were reduced. At the joint level, muscles contributed overall more to COM support than to propulsion in the first step of sprinting. In the narrow trials, reduced COM propulsion and particularly support were observed compared to the natural trials.The natural wide steps provide a preferable body configuration to propel and support the COM in the sprint starts. No advantage in muscular contributions to support or propel the COM was found in narrower step widths. The best results in sprint running are achieved by developing high forward acceleration, reaching the maximal speed, and keeping that speed over the remainder of the run . AccordiMuscles are the major contributors to COM motion and are in charge of accelerating all joints in the body . PreviouAnalyses of muscle contributions to COM acceleration have practically only focused on the sagittal plane. There is, however, motion outside of the sagittal plane; this is particularly evidenced by the variation of the step width over a sprint run . Even thFour  competitive sprinters  participated in the study. The personal best for 100 m for two male sprinters is 10.98 and 11.30 s, and 11.47 and 11.93 s for two female sprinters. The sprinters are a sub-cohort of a previous study . The StoEach athlete performed a total of ten sprint start trials with 74 reflective markers placed on the body. Each sprinter performed five sprint trials in their natural style and other five trials during which they were asked to stay within a 30-cm lane, indicated by ropes on the floor . For eacMarker trajectories were sampled at 250 Hz with a twelve-camera motion capture system . A force platform  was embedded in the floor and covered with a running tartan surface. GRF during the stance phase of the first step was recorded at 1500 Hz and a force threshold of 10 N was defined in the vertical direction. Kinematics and kinetics data were low-pass filtered at 50 Hz with a fourth-order Butterworth filter using custom designed scripts . The high cut-off frequency (12 Hz) was used for both data in order to avoid the development of artificial peaks in joint moments due to the loss of the high frequency content in the kinematic data, which was usually filtered at a lower cut-off frequency. Electromyography (EMG) patterns were measured with surface electrodes  placed bilaterally over six lower-limb muscles: soleus, gastrocnemius medialis, biceps femoris (caput longum), vastus lateralis, gluteus medius, and gluteus maximus. The raw EMG signals were recorded at 1500 Hz, band-pass filtered between 30 and 300 Hz, rectified, low-pass filtered with a cut-off frequency of 6 Hz, and normalized to the maximal value found during the whole recording . Second-Musculoskeletal simulations were performed [OpenSim v3.3 ] based oThe simulation was performed using a dynamic simulation pipeline which consisted of steps for scaling, inverse kinematics, inverse dynamics, residual reduction, computed muscle control and IAA . The genThe cumulative contributions of individual muscles to COM acceleration were calculated by summing the induced acceleration between 14 and 82% of the stance phase. The induced accelerations at the joint level were then computed by summing the cumulative accelerations induced by all muscles spanning that joint. The summed contributions of all muscles spanning the ankle, knee, and hip joint were thus computed.Step width and COM velocity were calculated with a 15 segment  model . Step width was calculated as the mediolateral distance between the midpoints of markers located at the first and fifth metatarsal head on the right and left feet when the front foot was on the starting blocks and the rear foot contacted the ground for the first time . COM velAveraged measured GRF was plotted in the The spatio-temporal characteristics in the natural and narrow trials are summarized in the The summed acceleration from all muscle contributions agreed with the measured acceleration, i.e., the summed muscle induced accelerations agreed with each sprinter’s GRF divided by body mass . IndividAt the joint level, muscles around the ankle joint contributed most to propulsion and support followed by muscles around the knee and hip . The cumCompared to the natural trials, all muscles in general contributed less to propulsion in the narrow trials. The soleus had a distinctly smaller contribution to propulsion starting from approximately 25% of stance phase and the decreasing throughout the rest of stance. The gastrocnemius likewise contributed distinctly less to propulsion from approximately 59% of stance phase . The vasAt the joint level, muscles spanning all joints induced less support and propulsion in the narrow trials with only one exception, that muscles spanning the knee induced slightly propulsion. Muscles spanning the knee contributed more to medial COM acceleration, and muscles spanning the ankle contributed to more lateral COM acceleration. Muscles spanning the hip induced a small medial COM acceleration in the narrow trials, rather than a lateral COM acceleration as in the natural trials.The objectives of this study were to study individual muscle contributions to COM acceleration during a sprint start and to analyze whether the step width at the onset of sprint influenced the muscles’ induced accelerations. Muscle induced COM accelerations were computed from trials with the widest and the narrowest step width in four competitive sprinters. The results indicate that ankle plantarflexors, i.e., the soleus and the gastrocnemius, were the principal contributors to forward (propulsion) and vertical (support) COM acceleration, and that the vasti group was the dominant contributor to medial COM acceleration when athletes performed their natural wide sprint start. At the joint level, muscles contributed overall more to support than to propulsion in the first step of sprinting. When the step width was restricted, all muscles generally diminished their contributions to support and propulsion COM acceleration, most notably the ankle plantarflexors. The differences at the joint level were mostly evident in decreased contribution to support. The natural wide steps apparently provided a preferable body configuration to for the muscles to most effectively propel and support the COM in the sprint starts.Our finding of dominance of the ankle plantarflexors in propulsion, not hip extensors intuitively, during the first stance of sprint running is in agreement with other studies , 2015. TWhen the step width was reduced, all muscles’ contributions to COM propulsion and support were lower. Ankle plantarflexors and vasti were still the main contributors to anterior and medial COM acceleration, respectively. However, the vasti became the major contributors to support. This implies that in the narrower step position, the COM was lifted more through knee extension than through ankle plantarflexion. The spatio-temporal characteristics observed  agree wiAt the joint level, muscles spanning the ankle contributed somewhat more to propulsion than to support, whereas muscles spanning knee and ankle joint contributed more to support than propulsion. This observation agrees with findings from There are several limitations in this study. First, there are computational limits when executing the computed muscle control and the induced acceleration analysis tools. The accelerations induced could not be analyzed during the first 0.03 s and the final 0.04 s, i.e., the first 14% and the last 18% of the stance phase, due to the abrupt changes in muscle forces and external forces in these phases. Secondly, the musculoskeletal model in OpenSim has several limitations. For instance, the generic model was a male model and there were two female sprinters in the participants; the knee joint is modeled as a hinge joint, which may affect the results; and the metatarsophalangeal (MTP) joint motion had to be ignored even though Ankle plantarflexors, in particular the soleus, were the main contributors to propulsion regardless of step width. Ankle plantarflexors and knee extensors were the primary contributors to support. The vasti contributed most to medial COM acceleration, regardless of step width. Hip extensors and hip adductors had relatively small contributions to COM acceleration in any direction, regardless of step width, although the gluteus medius was found to contribute more in the narrow than in the natural trials. At the joint level, muscles spanning the ankle contributed mostly to propulsion, while muscles spanning the ankle and knee joint were the dominant contributors to support. When step width was restricted, practically all muscles contributed less to propulsion and support, which implies that narrow steps might inhibit the muscles spanning the ankle and particularly the knee to maximize their performance in sprint start. Based on our simulation, no muscular advantage was found with narrower step width.The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.The studies involving human participants were reviewed and approved by the Stockholm Regional Ethical Committee. The patients/participants provided their written informed consent to participate in this study.RW participated in the study design, interpretation of results and drafted the manuscript. LM performed the simulation and drafted the manuscript. PS initiated the project, and collected the motion data and participated in the interpretation of results. AA initiated the project and participated in the study design and interpretation of results. EG-F participated in the study design and interpretation of results. All authors contributed to the manuscript writing. All authors have read and approved the final version of the manuscript.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


Due to the increasing number of vehicles equipped with millimeter wave (mmWave) radars, interference among automotive radars is becoming a major issue. This paper explores the automotive radar interference in both two-lane and multi-lane scenarios using stochastic geometry. We derive closed-form expressions for mean and variance of interference power considering directional antenna with constant and Gaussian decaying gains. In view of the sensitivity of mmWave radar signals to the blockages, we propose a blockage model including partially and completely blocking, and then calculate the effective number of the interferers. By means of modeling randomness for interferers and blockages as Poisson point process, we characterize the statistics of radar interference under different conditions. We further utilize the interference characterization to estimate the successful ranging probability of automotive radars. These theoretical analyses are verified by using Monte Carlo simulations. The results show that the increasing interfering density and ranging distance largely degrade the radar detection performance, whereas the interference levels decrease as blockage intensity increases. Millimeter wave (mmWave) radars are being widely used in modern vehicles for supporting the applications of advanced driver assistance systems (ADAS) and autonomous driving, thus providing comfort and safety functions, such as adaptive cruise control (ACC), blind spot detection (BSD), lane change assist (LCA), emergency braking and collision avoidance ,2. To daThere have been many studies analyzing the interference of mmWave automotive radars. In , mutual Although the above studies deeply analyzed and investigated the mutual interference for most automotive radar waveforms in simple two-node topologies, the work on quantifying the interference problem in realistic traffic scenarios is still limited. In , a simulHowever, in the above studies, the gain of directional antenna in the main lobe is always assumed to be a constant, regardless of the locations of interferers relative to the victim, which is equivalent to the case of omnidirectional radiation pattern or completely aligned main beam. Employing such a flat main lobe, the results of the interference analysis may be significantly larger than actual ones. In addition, these studies do not consider the effects of blockage on radar interference among multiple vehicles, ultimately resulting in exaggerated interference. The authors in  derived As the directional beam of the mmWave signal is quite sensitive to blocking, many works for analyzing the impact of blockage on interference in mmWave cellular networks have been carried out ,20,21,22We derive the mean and variance of the aggregated interference power of the victim radar equipped with constant directional gain antenna, under no-fading, Rayleigh-fading and Nakagami-fading cases with any path-loss exponent;Employing the directional antenna with Gaussian attenuation gain in the main lobe, we first derive closed-form expressions of the mean and variance of interference in the two-lane scenario and then extend the work to multi-lane one;We propose a blockage model considering both complete and partial blocking, and calculate the corresponding blockage probabilities. The expected number of active interferers is obtained by computing its probability-generating function (PGF). Based on this blockage model, we compare the levels of automotive radar interference with and without considering blockage;The above theoretical analysis and derivation are verified by using Monte Carlo simulations. We validate the supposed distribution model of aggregated interference, and then provide radar performance estimation based on the interference statistics.In this paper, we propose an analytical framework of interference power for automotive radars in both two-lane and multi-lane scenarios. Considering different directional angles between interferers and victim, we adopt a directional antenna whose radiation pattern in the main lobe is modeled by a Gaussian decaying function. The influence of blockage on the interference signal was taken into consideration to evaluate the levels of aggregated interference among multiple radars. Utilizing the stochastic geometry method to characterize the randomness of locations and number of vehicles and blockages, we then derive the signal-to-interference-and-noise ratio (SINR)-based successful ranging probability of automotive radar. Our main contributions can be summarized as follows.The rest of this paper is organized as follows. The system and signal models are described in The common setup of a modern vehicle is a forward looking radar (FR) to enable ACC, two sideward left and right looking radars  and two backward left and right looking radars  to provide BSD and LCA, respectively, ,2, as shWe consider a population of FMCW mmWave automotive radars, modeling the geometry distribution of vehicular nodes as a homogeneous one-dimensional Poisson point process (1-D PPP) with intensity ollision . Let ρ dThe typical radar will receive two kinds of signals composed of target echo signals and interference signals except for the noise signal. The target echo signal is the desired signal for the typical receiver, which is reflected by the target being tracked and primarily used to realize ranging and positioning. Most of interference signals come from the automotive radars operating at the same frequency with the typical radar. In this paper, we mainly investigate the direct incident interference caused by the oncoming vehicles moving in the opposite direction, where the interfering radars have an overlapping beam with the typical radar.c is speed of light and For a target vehicle with a radar cross section (RCS) ith interferer is given byith interferer and the typical radar, in which We assume all automotive radars have the same transmit power and the interference effects caused by these radars on the victim are independent of each other. The interference power of the L is lane spacing, We consider a mutual interference scenario with direct interference from the oncoming vehicles driving in the opposite direction to the typical vehicle (victim), as illustrated in In this section, we first derive the general expressions of the mean and the variance of the aggregated interference power with constant antenna gain for no-fading, Nakagmi fading and Rayleigh fading cases with different path-loss exponents. Subsequently, employing the directional antenna with Gaussian waveform gain, we derive the closed-form expressions for statistical characteristics of interference power. Finally, the above analysis methodology and work are extended to the considering blockage case.N of interfering vehicles located at the interval D, has the same probability density fuction (PDF) for any interferer i:The mean interference power can be solved in two ways, either by utilizing the Campbell’s theorem , or by tith interfering radar with a constant antenna gain is expressed asWe start the interference analysis applying a flat-top directional antenna, which has constant gain within its beamwidth and zero gain outside the beamwidth, like in the literature ,14,15,16According to The aggregated interference of the typical radar depends on the interference levels of the individual radars, and the effects from these interfering radars are independent. Hence, the mean value of the aggregated interference at the typical vehicle can be calculated asIf the average channel gain tituting  and 7)  Ehi is atituting  we obtaiith interfering radar is given byThe variance value of the interference power of the  Formula  replacinSimilarly, the variance value of the aggregated interference power is:The second moment of the total interference is given byFinally, the variance is formulated asSubstituting , 6) and and6) anIn this part, we employ a widely used directional antenna model  to calcuessed by  in unitsThe constant side lobe gain can be obtained by i is omitted for notational simplicity and the parameter For simplicity, we take the no-fading case with the path-loss exponent of 2, for example, to characterize the interference statistics based on the above directional antenna model. The analysis methodology can also be applied to different channel fading cases with any path-loss exponent. The interference power of the individual interfering radar with the Gaussian decaying antenna gain is rewritten asSimilarly, the variance value of total interference power considering the above directional radiation pattern is obtained by -4.6cm0cmThe beamwidth  Formula . erfi· iThe signals of mmWave automotive radars are blocked, which is mainly caused by the vehicles running on the road. We consider these blocking vehicles modeled as a 1-D PPP with intensity The signal from an interferer is completely blocked, if at least one blockage is presented and located at a distance of less than N follows Poisson distribution with density K is expressed asith interferer is not blocked with probability The number of the interferers K is derived asSuppose whether each interferer is blocked or not is independent of each other, and the PGF of K is also a Poisson random variable with parameter K in the interval The result of Formula  shows thth EK in  and 20)K is alsoIn this section, we extend the interference analysis to multiple lanes scenario, where the mean value of the total interference for the victim vehicle at any lane is derived firstly without consideration of the blockage, and then the blockage probability is formulated based on the proposed blocking model to assess the impact of blockage on interference.n lanes in the opposite direction and m lanes in same direction with that of the victim vehicle. From the innermost lane to the outermost lane, the interfering lanes are marked as We assume there are jth interfering lane with mean We do not consider the blockage impact on automotive radar signal in this part. The interference is caused by the interfering FRs on vehicles from the lanes i can be solved by Formula Interference to SRL from SRRs and SRLs: the interfering SRRs are on vehicles from the lanes (2)Interference to SRR from SRLs: the interfering SRLs are on vehicles from the lanes (3)Interference to BRL from BRLs: the interfering BRLs are on vehicles from the lanes We can explore the interference level of mmWave automotive radars including BR and SR as a function of vehicle density and signal beamwidth, as well as the radar on-vehicle mounting location. Suppose that the typical vehicle is located at lane The above analysis is on account of the prerequisite that different types of radars operate at a different frequency. The characterization of the interference extents for SR and BR can be obtained according to the solution method of FR.We consider both the complete and partial blockage cases in the multi-lane scenario and model the blocking vehicles on each lane as 1-D PPP with the same line intensity (1) Complete blockage: the interfering signal is completely blocked by the vehicle ahead moving in the same lane as the given interferer. In each interfering lane exists the complete blockage case, where the blockage probability can be calculated byj and the typical vehicle in lane i, the transmit beam of the interferer–victim pair is partially obstructed by the blockages including the vehicles from the lanes kth interferer in lane j blocked by the vehicles in one of the blockage lanes is denoted asi and j are the lane marks where the victim and the interferer are located, respectively, the directional angle kth interferer and the victim.(2) Partial blockage: assume the interfering vehicle in lane kth interferer on the jth lane being blocked by the vehicles on its left lanes is Consequently, the partial blockage probability of the apply to . Figure uired by .j expressed as Finally, we obtain the blockage probability of the interferers on lane  Formula , most ofjth interfering lane is Based on the analysis result of Formula , the aver ENj in .The performance of mmWave automotive radars is likely to be limited by interference and noise. We leveraged the ranging and detection success probability as the metric to evaluate radar performance. The successful ranging probability In order to calculate the above probability, we rearrange the parameters in  and obtaX on account of its MGF There are two ways to obtain the CDF of the aggregated interference power. In the first approach, using Gil-Pelaez’s inversion formula :35)FPIFPI(35)FPIn what follows, we describe another approach to find Consequently, the closed-form expression of the automotive radar ranging success probability for the path-loss exponent of 2 is expressed byIn this section, simulations are carried out to verify the derived analytical results presented in this paper. We first explore the interference levels of automotive radar in terms of interfering vehicle density, directional antenna pattern, channel fading, path-loss exponent, as well as blockage effect. Subsequently, we validate the proposed interference distribution from the empirical model and the histogram obtained by numerical statistics. At last, the successful ranging probability N of interferers obeying Poisson distribution with intensity N. The channel fading and the path-loss exponent are simulated following the description in We consider a 1000 m-long straight segment for the two-lane scenario, whereas the length of the road segment is related to the lane location of the typical vehicle for a multi-lane scenario, e.g., the victim on lane 1, de1 = 1000 m and the victim on lane 2, de2 = 2000 m. In order to obtain the statistic of interference, 100,000 Monte Carlo trails are conducted for plotting each line in simulations. Simulation parameter settings are listed in In this part, the interference levels of automotive FR in both two-lane and multi-lane scenarios are presented, which are affected by different parameters. As it was illustrated in The mean interference at the typical vehicle in multi-lane scenarios is presented in In the proposed analytical method of radar performance, the critical assumption is the gamma distribution of total interference. To validate the method, we simulate the deployment scenarios, described in the above section. We first obtain the interference statistic histograms from simulated data, and then based on the histograms, we compare the analytical and empirical PDFs for different We numerically evaluate the successful ranging probability nd d0 in  for the In this paper, we developed an analytical method for the mmWave automotive radar interference using stochastic geometry. Directional antennas with constant and Gaussian decaying gain were included in the analysis. Furthermore, the effect of blockages on mmWave radar signals was also taken into consideration. We first derived the closed-form expressions for the mean and variance of interference power at the typical radar receiver in two-lane scenarios and then extended the work to multi-lane ones. Based on the interference characterization, we formulated the radar performance evaluation method utilizing the successful ranging probability. Finally, we verified the proposed interference analysis method by simulation in the presence of a Poisson field of interferers and blockages. The results show that considering the directional antenna gain related with the directional angle between the victim and interferer pair is more reasonable for the interference analysis. In addition, considering blocking factors makes the interference analysis more accurate. As expected, the interference level with blockage is more tally with the actual one. This paper provides the insights to understand the interference levels in automotive radars, which is necessary to design the effective mitigating or avoiding an algorithm in the future.


Nonverbal synchrony between individuals has a robust relation to the positive aspects of relationships. In psychotherapy, where talking is the cure, nonverbal synchrony has been related to a positive outcome of therapy and to a stronger therapeutic alliance between therapist and client in dyadic settings. Only a few studies have focused on nonverbal synchrony in multi-actor therapy conversations. Here, we studied the synchrony of head and body movements in couple therapy, with four participants present (spouses and two therapists). We analyzed more than 2000min of couple therapy videos from 11 couple therapy cases using Motion Energy Analysis and a Surrogate Synchrony (SUSY), a procedure used earlier in dyadic psychotherapy settings. SUSY was calculated for all six dyads per session, leading to synchrony computations for 66 different dyads. Significant synchrony occurred in all 29 analyzed sessions and between the majority of dyads. Complex models were used to determine the relations between nonverbal synchrony and the clients’ well-being and all participants’ evaluations of the therapeutic alliance. The clients’ well-being was related to body synchronies in the sessions. Differences were found between the clients’ and therapists’ alliance evaluations: the clients’ alliance evaluations were related to synchrony between both dyads of opposite gender, whereas the therapists’ alliance evaluations were related to synchrony between dyads of the same gender, but opposite to themselves. With four participants present, our study introduces a new aspect of nonverbal synchrony, since as a dyad synchronizes, the other two participants are observing it. Nonverbal synchrony seems to be as important in couple therapy as in individual psychotherapy, but the presence of multiple participants makes the patterns more complex. Synchrony is an elementary part of human interaction. Synchrony occurs automatically during conversations as we regulate turn-taking or adjust our nonverbal behaviors, including movement, pitch, and facial expressions, to each other. Synchrony can occur in many domains, from physiological arousal to body movements. In this article, we concentrate solely on the coordination of body movements, hereafter nonverbal synchrony. The tendency to synchronize in human interactions has been studied quite extensively using different research methods, including conceptualizations and computations .Even though research methods and computations vary, nonverbal synchrony has generally been related to positive aspects of the interpersonal relationship. Synchrony increases when participants like each other , are in On a social level, nonverbal synchrony enhances social bonding and contributes to a prosocial orientation , making What is the essence of nonverbal synchrony? According to the Russian-doll model of empathy , nonverbIn the context of psychotherapy, nonverbal synchrony has been proposed as a marker of therapeutic alliance . The theEmpirical evidence shows that more synchrony leads to better outcomes—that is, the clients having fewer symptoms at the end of therapy—and to a stronger therapeutic alliance—that is, a better quality of the relationship better between client and therapist . InteresHigh synchrony between therapist and client has not always been found to be beneficial. A high level of synchrony between the therapist and client at the beginning of therapy has been related to poor therapy outcomes , and higClient characteristics related to nonverbal synchrony have been studied. Depressed clients were found to be less in synchrony with others  as well via therapist interventions). Nonverbal synchrony was not associated with problem actuation (the activation of avoided experiences and behavior guided by the therapist) or motivational clarification (the therapist’s ability to guide the client through a process of exploration to gain insight into needs and motives). It is fair to say that research on nonverbal synchrony in psychotherapy is still quite novel, and only some aspects of the effect of nonverbal synchrony on the psychotherapy process have been studied.More nonverbal synchrony was found in cognitive behavioral therapy, especially in the automated version, than in manualized psychodynamic therapy . Prinz eMany studies have replicated the finding that nonverbal synchrony occurs above chance level in psychotherapy . As it sEven though nonverbal synchrony in psychotherapy has become a growing research area, nonverbal synchrony in couple therapy is still unexamined. In couple therapy, research on nonverbal synchrony is more complex given the presence of multiple participants and relationships. There is the relationship between the therapist and each spouse, and the relationship between the spouses , and in the cases studied here, also the relationship between the therapists.Here, we explored dyadic patterns of nonverbal synchrony in couple therapy. The data originated from a research project , 2018 thResearch on nonverbal synchrony between romantic couples is sparse. Synchrony of immediacy behaviors  between spouses has been reported to be more prevalent in satisfied couples . SynchroResearch on nonverbal synchrony between the therapist and the couple is even more scarce. One study investigated body movements, but not synchrony, in couple therapy. Therapeutic alliance was related to predictable and recurring patterns of bodily movements  between the couple and the therapist . PreviouEven though couple therapy is an ecologically valid naturalistic context for studying nonverbal synchrony, causal inferences cannot be made due to the many confounding variables that might affect synchrony and the way it is felt or interpreted by each participant. Therapists and the couple have different roles within the situation; the therapists are in their professional roles, acting accordingly, and are highly familiarized with the context. To the clients seeking help because of issues in their relationships, couple therapy may be a novel situation that could also be threatening. Further, the couple have their own relationship history, which makes them react to each other in predisposed ways. Moreover, in couple therapy, both spouses react to the situation separately but also as a part of their couple system. In couple therapy, there can be hidden variables or agendas that presumably affect how the participants synchronize with each other. We aimed to study whether nonverbal synchrony in couple therapy occurred between all the possible dyads and whether it was related to the clients’ well-being, the therapeutic alliance in the sessions, and to the outcome of therapy.A strong alliance has been related to a positive outcome in individual psychotherapy , but alsDifferent factors influence the relationship between alliance and outcome in couple therapy. For instance, the relationship between alliance and outcome becomes stronger when both spouses agree on the strength of the alliance . Even geNonverbal synchrony could also be a method for studying alliance in couple therapy, as it has been suggested to be a marker of therapeutic alliance in individual therapy . DiffereRQ 1: We hypothesized that nonverbal synchrony of head and body movements occurred above chance level in the whole dataset. More specifically, there would be significant synchrony between all dyads in all sessions. We were also interested in whether there was a mean difference between head and body synchrony between three different types of dyads .RQ 2: We hypothesized that the well-being of the clients, the alliance, and the outcome of therapy would be related to the nonverbal synchrony patterns in the session.The couple therapy data were collected in the research project Relational Mind in Events of Change in Multi-actor Dialogues, which took place at the Psychotherapy Training and Research Centre of the Department of Psychology at the University of Jyväskylä . At the The overall Relational Mind data consisted of 12 couple therapy cases, of which 11 consisted of man and woman. For all therapies, two therapists were present. Ten therapists worked with the couples; that is, many of the therapists worked on more than one couple therapy case. Normally, the therapist dyads varied, but one dyad worked on two cases. The therapists were between 31 and 64years old, mainly with a degree in family therapy (7 out of 10 therapists). All but one therapist had over 10years of experience from clinical work. Six of the 10 therapists were female.The therapy sessions were recorded using six cameras: one camera focused on each participant’s face and one camera recorded the full bodies of the two therapists and the couple. The couple and the therapists were seated in chairs around a round table: The clients sat next to each other, and the two therapists sat next to each other on the opposite side of the table.Because of the research group’s interest in autonomous nervous system responses, all participants’ autonomous nervous system reactions were usually recorded in the second and sixth session. In these measurement sessions, heart rate monitors were attached to the chest, two skin conductance electrodes were attached to the palm of the nondominant hand, and a respiration rate belt was fastened around the lower chest. The skin conductance electrodes were attached to the chair in which the participant sat and thus restricted the movement of the non-dominant arm to a range of approximately 25cm from the chair.The well-being (outcome) and alliance were assessed using the ultra-brief forms of the Outcome Rating Scale (ORS) and the Session Rating Scale SRS; , and theThe outcome of the therapy was assessed with the CORE-OM questionnaire , adminisThe research procedure was approved by the University of Jyväskylä Ethical Committee. All participants gave their written informed consent to participate in the research project.M=6.27, Mdn=6), and duration varied between cases .For the movement analysis, one couple therapy case was omitted, since one of the spouses suffered from obsessive movement patterns, which affected the data. Videos from 11 couple therapy cases were used. Of the 11 couples, seven were married (one registered partnership), three were living together, and one couple lived separately. All of the couples had been together for over a year and almost all of them had been together for several years. The mean age of the female clients was 41 (range=27–54), and the mean age of the male clients was 44 (range=34 to 61). Mean psychotherapy duration per couple was six sessions  needed to be visible in the video at all times. For MEA, videos showing the full bodies of the participants in a split-screen format were used.M=2.6, SD=0.7, Mdn=3). Out of the qualified videos, 17 were from measurement sessions, and 12 were from regular sessions.SD=8.29min, Min=52min, Max=90min).From a pool of 69 videos, 29 met these criteria, which indicates one to three sessions per case . SUSY allows dyadic synchrony to be computed: head and movement synchrony for six dyads  was calculated. SUSY divided the time series of the MEA individual movement raw data into segments of 30s. In each segment, all the cross-correlations were calculated up to time lags of +/− 5s by shifting one of the time series stepwise (in 0.1s steps because of the sampling rate of 10 frames/s) in relation to the other one. The cross-correlations were standardized using Fisher’s Z, which were then aggregated to a mean Z value of nonverbal synchrony for all lags separately in each segment. The mean Z values of all segments were averaged, resulting in a mean Z value of nonverbal synchrony for the whole therapy session for each dyad and synchrony type (head and body). SUSY calculates the mean Z synchrony using both absolute values from the cross-correlations (Zabs), by converting negative values of cross-correlations into positive ones, and the original positive and negative  values of the cross-correlations (Znoabs). Using non-absolute values (Znoabs) enables distinguishing between in-phase synchrony  and anti-phase synchrony . Both absolute and non-absolute cross-correlations and in-phase and anti-phase synchrony of datasets have been interpreted by After obtaining the raw data from the MEA, movement synchrony between different ROIs was computed using the Surrogate Synchrony (SUSY) procedure (abs) and non-absolute values (ESnoabs). We used the non-absolute effect sizes (ESnoabs) for all statistical calculations, since they allow for the distinction of in-phase and anti-phase synchrony.To investigate whether synchrony occurred above chance level, surrogate datasets were created by shuffling the segments of the original data from the two time series, aligning segments that never occurred at the same time. Many surrogate datasets can be generated from the data of a session, for example, in a 50-min session containing 100 segments, 100×99=9,900 surrogate datasets. A value of the pseudo synchrony of each surrogate dataset was then computed in the same way as the synchrony computations described above. Lastly, the empirically obtained synchrony calculations were standardized using pseudo-synchronies by comparing the mean value of the surrogate data to the same value of the empirically collected synchrony, giving the effect size for each dyadic head and body synchrony in the session. The effect size was obtained for both absolute values (ESnoabs) of each of the six dyads  were obtained from all sessions, resulting in 12 dyadic nonverbal synchrony effect sizes (ESnoabs) per session. Contrary to the earlier research, we used the movement data from the whole session for the synchrony computations, resulting in a more valid value of nonverbal synchrony between participants. We used the gender of the participants to distinguish between the four participants in each situation.The head and body synchrony effect sizes  were computed to determine whether the data were indeed hierarchical . The ICCs were calculated in MPlus version 8.4 using two-level models  with Maximum Likelihood with robust standard errors (MLR) as estimator. Six models with two variables in each model were calculated.p. The small dataset and the small number of clusters restricted the number of estimated parameters in one model. Thus, several one-level complex models were used for estimating correlational relations and for comparing means. The number of models is specified below for each computation. The models were all computed using MLR as estimator, and case was used as the cluster variable. All models were saturated, meaning that all degrees of freedom were used, and thus fitted the data perfectly. All complex models were computed using MPlus version 8.4.Due to the hierarchical data set, and thus the non-independence of the nonverbal synchrony effect sizes (which were nested within cases), complex models were used for the majority of the statistical analyses. Complex models have been developed for analyzing clustered data . ComplexWe studied the individual movements of each participant to gain a full picture of the data used for the nonverbal synchrony calculations. The individual amount of movement of head and body per participant in each session was obtained with MEA, and the data were organized according to gender. The amount of movement was adjusted to the length of the session, providing comparable values. Six complex models were calculated to estimate the difference between how much the participants moved their head and body. The following three pairs were compared: female client vs. male client (head and body in separate models), female therapist vs. male therapist (head and body in separate models), and the mean of both clients vs. the mean of both therapists (head and body in separate models). The nonverbal synchrony effect sizes were designated as dependent variables and their means were compared.To assess potential influence of wearing measurement equipment on the participants’ movement patterns, three complex models were used to estimate the differences in how much the participants moved in regular vs. measurement sessions: The first model included the mean of all participants’ head movements, the second model included the mean of all participants’ body movements, and the third model included the mean of all participants’ head and body movements. Session type was designated as the independent variable and movement as the dependent variable. As for the comparison of nonverbal synchronies in regular sessions vs. measurement sessions two complex models (head and body separately) were calculated for each dyad type  with session type as independent variable and synchrony as the dependent variable. For the client–therapist dyad, a mean of nonverbal synchrony of all four possible dyads  was used.d was calculated according to the procedure described by Znoabs of all N sessions and the mean Znoabs-pseudo of the surrogate dataset of all N sessions was divided by the standard deviation of the Znoabs-pseudo for the surrogate data set. Cohen’s d is thus an effect size at the level of all N sessions.To study whether nonverbal synchrony in the whole data set occurred above chance level as expected, Cohen’s noabs) of each dyadic synchrony value (N=12) per session were computed using one-sample t-tests.To calculate whether the head and body synchrony between each of the six dyads was significant in each session, the effect sizes  were compared using six complex models: (1) client–client vs. client–therapist head synchrony, (2) client–client vs. client–therapist body synchrony, (3) client–client vs. therapist–therapist head synchrony, (4) client–client vs. therapist–therapist body synchrony, (5) therapist–therapist vs. client–therapist head synchrony, and (6) therapist–therapist vs. client–therapist body synchrony. The synchrony value for the client–therapist dyad consisted of the mean of nonverbal synchrony of all the four different dyads . The nonverbal synchrony effect sizes were designated as dependent variables.The relationship between the clients’ self-reported well-being (ORS) and nonverbal synchrony was calculated with complex models. Six complex models were used for both female and male clients to calculate the relationship between the client’s ORS and all six dyadic  head and body synchronies. Two additional complex models, one per client, were calculated to find out the relationship between ORS and nonverbal synchrony between one of the spouses and both therapists . In these eight aforementioned models, both ORS and nonverbal synchrony were designated as dependent variables.To study the relation between the mean of both clients’ ORS and the mean of all head and body synchronies two complex models were calculated, where ORS was designated as the independent variable and synchrony as the dependent variable. One model included the mean of both clients’ ORS and the mean of all head synchronies, and the other model included the mean of both clients’ ORS and the mean of all body synchronies.To calculate whether taking part in synchrony or observing had any impact on the relationship between ORS and nonverbal synchrony two new aggregated variables per client were computed: one variable for the mean of all dyadic synchronies in which the client participated, and another variable for the mean of the nonverbal synchronies that the client observed. The new variables were used in one complex model per client, where all variables were treated as dependent variables.The relationship between all participants’ evaluations of the alliance (SRS) and the non-absolute effect sizes of nonverbal synchronies was calculated almost identically as the relationship between ORS and nonverbal synchrony: First, the relationship between all participants’ SRS evaluations and the nonverbal synchrony of the six dyads were calculated separately for each participant. One complex model included the SRS evaluation of one participant and head and body synchrony of one dyad, thus six complex models for each participant were calculated . Second, the relation between the mean of both clients’ SRS and the mean of both therapists’ SRS with the mean of all participants’ head synchrony (one complex model) and body synchrony (one complex model). The two mean SRSs were designated as independent variables and the mean of synchrony as the dependent variable. Third, we studied the relationship between each participant’s SRS and the nonverbal synchronies in which they participated or observed. One complex model per participant was calculated with the SRS and the two new variables  as dependent variables.N=6). Spearman’s rank order correlations were used . Bootstrapping was not used because of the small N possibly distorting the bootstrapped sample. The calculations were performed using IBM SPSS Statistics version 26. First Spearman’s rank order correlations were computed for the six dyads’ head and body synchronies and the basic CORE-OM change scores  for each client separately. Second, a mean of all the participants’ head synchronies and a mean of all body synchronies were correlated with the participants’ CORE-OM change scores. Third, the mean of both clients’ CORE-OM scores was correlated with all the dyadic nonverbal synchronies.CORE-OM was filled by all participants at the beginning and end of therapy, and after a 6month follow up. The relationship between the outcome (change in CORE-OM) and nonverbal synchrony was calculated using one aggregated head synchrony value and one aggregated body synchrony value for each case and dyad. The aggregation was done because of CORE-OM only giving three change values  for each client to represent the whole therapy process. There was unfortunately a large amount of missing data in the CORE-OM because clients failed to return their questionnaires, which resulted in an extremely small sample size (noabs) to establish if the data was hierarchical. After this we studied the individual movement patterns of each participant to get an overview of the data used to compute the dyadic nonverbal synchronies. We investigated the validity of the data, that is, whether wearing measurement equipment affected individual movement patterns or nonverbal synchrony patterns.First, we explored the basic characters of the data, and computed ICCs of all dyadic nonverbal synchronies (ESnoabs) using 60 two-level models . The majority (58%) of the dyadic nonverbal synchrony effect sizes (ESnoabs) had significantly more variance between cases than within cases, pointing to the data being hierarchical. All results are provided in The ICCs show how many percent of the whole variance is between cases. ICCs were calculated for each dyadic nonverbal synchrony value . No other significant differences were found. All results are provided in The amount of individual movement of each participants’ head and body adjusted by the length of the sessions were calculated to understand the data underlying the dyadic nonverbal synchrony patterns. A significant difference was found between all head movement means between all dyads , as shown in β=−1.15, p=0.91), body movements , or all movements .There was no difference between individual movements in the regular vs measurement sessions. No significant differences were found for head movements . All results are provided in For the nonverbal synchrony, the only significant relation was that there was less therapists’ head synchrony in the measurement sessions (N=29) by using the method described earlier (d=1.36) met d>0.80).We hypothesized that there would be significant dyadic nonverbal synchrony in the whole data set. To obtain the effect size of the overall synchrony of the whole data set, Cohen’s d was calculated based on all the effect sizes of all dyads (6×2×29) in all sessions ( earlier . The effnoabs) in all sessions and between the majority of dyads. Twelve values of nonverbal synchrony per session were obtained, head synchrony for each dyad (N=6), and body synchrony for each dyad (N=6). For all cases and dyads, this resulted in 348 different synchrony values. However, 32 values were treated as missing because some of the cases were not gendered balanced . We did not omit any synchrony values from the client-client and therapist-therapist dyads. This resulted in 316 synchrony values. Using one-sample t-tests on the effect sizes of each dyadic synchrony, the significance of the nonverbal synchronies was calculated for all synchrony values (N=316). Of all nonverbal synchrony effect sizes 97% (N=307) were significant and 3% were not significant (N=9). Out of the effect sizes 189 were positive, indicating in-phase synchrony, and 127 effect sizes were negative, indicating anti-phase synchrony. A summary of the significances is provided in We also hypothesized that there would be significant nonverbal synchrony (ESNonsignificant in-phase synchrony was found for two body movement synchrony effect sizes (of the 189 effect sizes) between two different dyads  in two different cases. Nonsignificant anti-phase synchrony was found for seven nonverbal synchrony effect sizes (of the 127 effect sizes): five head movement synchronies and two movement body synchronies. Nonsignificant anti-phase head synchrony between clients was found in three different cases and sessions. Anti-phase head movement synchrony between the male client and the male therapist was nonsignificant in two different cases and sessions . In one session, anti-phase body movement synchrony was nonsignificant in two dyads: between the male client and the male therapist and between the female client and the female therapist.In-phase and anti-phase synchrony can be distinguished by the effect size being positive (in-phase synchrony) or negative (anti-phase synchrony). noabs) between the three different types of dyads . The nonverbal synchrony effect size of the client–therapist dyad was the mean of the four client–therapist dyads. All comparisons were significant except for head movement synchrony between the client–client dyad and the client–therapist dyad . All estimates and the mean of synchrony of each dyad type can be seen in We further assessed potential differences in means between the synchrony of head and body movements , the post hoc power was 0.279 for head synchrony, and 0.496 for body synchrony. All post hoc powers are shown in Out of interest to find out whether the sample size was too small especially when using the mean value for the client–therapist dyad, a noabs) across the whole data , whereas the relationship of ORS to the mean of head synchronies (ESnoabs) was not significant . All relationships between the female and male client’s ORS and the dyadic synchronies (ESnoabs) are shown in The relationships between the clients’ well-being (ORS) and head and body synchronies were calculated using several complex models (see method section). ORS was administered to the clients before each session, which meant that we tested whether the well-being of the clients at the beginning of the session was related to the synchronies later on in the session. The mean of both clients’ ORS was significantly related to the mean of all body synchronies .Complex models were computed to determine whether there was a difference in the relationships between ORS and the synchronies in which a client participated or observed. For ORS, no significant relations were found for either of the clients concerning nonverbal synchronies in which they participated or observed  and the head and body synchronies were calculated using complex models. The alliance was evaluated by all participants filling out the SRS after each session. All relations between the participants’ SRSs and the dyadic nonverbal synchronies are displayed in β=0.532, p<0.001), but not to the mean of all head synchronies . The mean of both therapists’ SRS was significantly related to both the mean of all head synchronies  and body synchronies .The mean of both clients’ SRS evaluations was significantly related to the mean of all body synchronies , but not to the mean of head synchronies . As for the therapists, the female therapists’ SRS evaluations were significantly related to the mean of both body  and head  synchrony. For the male therapists, no significant relations were found between their SRS evaluations and the mean of all body  or head synchronies .For both clients, their SRS evaluations were related to the mean of all body synchronies in the sessions , but not to the synchronies in which they participated . For male clients, the opposite result was found: Their SRS was significantly related to synchronies in which they participated , but not to synchronies that they observed .For female clients, their SRS was significantly related to the mean of the synchronies that they observed  or observed . The male therapists’ SRS evaluations were significantly related to the synchronies in which they participated  but not to the synchronies that they observed .For female therapists, no significant relationships were found between their SRS evaluations and the synchronies in which they participated (r(4)=0.829, p=0.0041, and the female clients’ CORE-OM change scores from end to 6months were significantly related to head synchrony between the female client and male therapist r(4)=1.000. No significant relations between the male clients CORE-OM change scores and the dyadic nonverbal synchrony effect sizes were found.The relation between CORE-OM and the dyadic nonverbal synchronies was calculated using data where the dyadic nonverbal synchronies were case wise aggregated, i.e., calculating the mean of head synchrony and the mean of body synchrony for each dyad in each case. Spearman’s rank order correlations were used. First, both client’s CORE-OM change scores were correlated with all dyadic nonverbal synchrony effect sizes. The female clients’ CORE-OM change scores from beginning to end were significantly related to body synchrony between the male client and female therapist r(4)=0.829, p=0.0042. No other significant correlations with the mean of head or body synchrony were found.Second, both clients’ CORE-OM change scores were correlated with the mean of all head and body synchronies. The male clients’ CORE-OM change score beginning to 6months was significantly correlated with the mean of all head synchronies r(4)=0.886, p=0.0019. No other significant correlations were found.Third, the mean of both clients’ CORE-OM change scores was correlated with all dyadic head and body synchronies. The mean of both clients’ CORE-OM change score from the beginning to the end was significantly correlated with body synchrony between the male client and the female therapist We explored whether nonverbal synchrony occurred in couple therapy, and if it was related to the well-being of the clients, and to the therapeutic alliance and therapy outcome. Nonverbal synchrony occurred above chance level in all sessions, and usually between all dyads. Importantly, significant nonverbal synchrony occurred between all possible dyads, meaning that all participants were included in the nonverbal synchronies. Nonsignificant synchrony was rare and occurred mostly between spouses . This was consistent with expectations, since nonverbal synchrony between spouses has been related to satisfaction in the relationship , and spocf. It is noteworthy that almost all of the synchronies showing in-phase, where both participants’ movements were positively correlated, were significant, as well as the majority of the anti-phase synchronies, where one participant moved more when the other one moved less cf. . Most ofComparing the three different types of dyads  revealed that the co-therapists had indeed more head and body synchrony than the other kinds of dyads. Previous research on the same data also found a large amount of physiological synchrony  between co-therapists . The larIn the couple therapy it is important to detect both in-phase and anti-phase synchrony, since as multiple participants are present it makes the movement patterns more diverse. It is for instance usual that one dyad is talking and moving more, whereas the other dyad is listening and remaining quite still. Qualitative inspection of the couple therapy videos revealed that there could be long instances where one of the participants sat quite still listening to others talking. Thus, we assessed differences between how much the participants moved. Clients moved their heads and bodies more than therapists did, which is contrary to earlier findings in individual psychotherapy . Female As the data originated from a research project studying the participants’ autonomous nervous system responses, the participants wore autonomous nervous system equipment in some of the sessions. We wanted to know if these altered the movement patterns of the participants. No differences were found for individual movements. For nonverbal synchrony, the only difference was that there was less head movement synchrony between the therapists in the measurement sessions. All of the therapists’ head synchronies were in-phase synchronies, meaning that they both moved their head more (or less) when synchrony occurred. It might be that wearing measurement equipment made the situation novel even for the therapists and made them concentrate more on their own thoughts and bodily reactions, thus affecting how they worked together but not how they nonverbally related to the clients.cf. The clients evaluated their well-being with ORS at the beginning of each session , whereas male clients and male therapists evaluated the alliance to be stronger when they participated in nonverbal synchronies. For female therapists, no such associations were found. It appears possible that when the female clients saw other persons synchronizing together, they implicitly felt that something important was being worked on. Research on physiological synchrony using the same data revealed that female clients also made increasingly better evaluations of the alliance when the physiological synchrony between their spouse and the male therapist increased .A detailed examination of the relation between nonverbal synchrony and alliance revealed that for both female and male clients’ alliance evaluations, synchrony between male client and female therapist, and female client and male therapist, were of importance. It is interesting that synchrony between the same dyads were relevant for clients of both genders. It seems that both clients implicitly felt the importance of all participants being included in the dyadic synchrony patterns for them to evaluate the working relationship to be of good quality. This pattern of dyadic synchrony between the opposite genders was not seen in the psychotherapists’ alliance evaluations. On the contrary, both therapists evaluated the alliance to be stronger when there was more synchrony between the two participants of the same gender but opposite to themselves (the other therapist and one of the spouses). For female therapists, head and body synchrony between the male client and male therapist were significant. For the male therapists, body synchrony between the female client and female therapist was significant. Head synchrony between the co-therapists was related to the male therapists’ but not the female therapists’ evaluations of the alliance. We found such a difference interesting, as it could suggest that female and male therapists implicitly concentrated on different aspects of co-working. It might not be gender related but having to do with the male therapists being more experienced family therapists than the female therapists.For female therapists, more head synchrony between clients was related to them evaluating the alliance to be stronger. It might be that the female therapists implicitly evaluated synchrony between clients as a positive marker of their relationship as previous research has suggested . But surEven though the results have been presented by gender, it is important to keep in mind that as the data were quite small, generalizations based on the gender cannot be made. The gender was needed in the statistical computations to distinguish between the two therapists and the two clients. To summarize, the significant nonverbal patterns for the alliance differed between the therapists and clients, suggesting that they implicitly experienced different nonverbal synchrony patterns as relevant. For clients, nonverbal synchrony by dyads of the opposite gender was related to their alliance evaluations, whereas for the therapists, nonverbal synchrony by dyads of the same gender but opposite to their own were related to their evaluations of the alliance.The relationship between the CORE-OM outcome measurement and nonverbal synchronies must be considered precursory, since the data set was extremely small. It is noteworthy that some of the relationships between the outcome change scores and nonverbal synchrony were similar to the relationships between the therapeutic alliance evaluations and nonverbal synchrony. For instance, for female client, changes from the beginning of therapy to the end of therapy were related to body synchrony between the male client and the female therapist, and her six-month follow-up was related to head synchrony between herself and the male therapist. These same dyads were related to her alliance evaluations. For male clients, head synchrony among all participants was related to his outcome 6months after the therapy ended.The study presented here is the first to study nonverbal synchrony in couple therapy. In spite of the small amount of data, nonverbal synchrony was significant between the majority of dyads, and we found significant relations between nonverbal synchrony and the clients’ well-being, alliance, and therapy outcome.One important finding was the difference between therapists and clients, concerning which dyads were related to their alliance evaluations. For clients, synchrony between dyads of the opposite gender was relevant, and that all participants were included in the nonverbal synchronies. In particular, synchrony between the male client and female therapist was related to both clients’ well-being, to both clients’ evaluations of the alliance, and to the therapy outcome for the clients. For therapists, other patterns were found, such as synchrony in same-gender dyads relating to their alliance evaluations. The results were reported gender-wise to distinguish between the four participants, but other unknown variables could lie behind the associations.Our findings suggest that nonverbal synchrony is a potential marker of therapeutic alliance in couple therapy, albeit with some restrictions. The relationship between nonverbal synchrony, alliance, and outcome is more complex in a multi-actor context, where there are multiple relationships and alliances at play compared to individual psychotherapy. The couple therapy conducted in our data was not manualized, and the therapists used dialogical and system-therapeutic ways of working. The fact that there was nonverbal synchrony in all sessions and among almost all dyads is in line with earlier research that have demonstrated nonverbal synchrony during interactions and in the therapeutic context, especially in non-manualized therapies . But theNonverbal synchrony can be seen as a process variable influencing the outcome of therapy , as nonvOur results indicate that the relation between nonverbal synchrony and alliance and outcome in couple therapy is not straightforward but affects spouses and therapists  in different ways. It is crucial for the therapist to be attentive to the nonverbal synchrony patterns in the sessions since they can be related to the well-being of the clients, to therapeutic alliance, and even outcome. But conclusions cannot be made based on this study alone, more research is needed.There is for instance some evidence from research on individual psychotherapy that a curvilinear model of nonverbal synchrony would be best, where a medium-level synchrony may offer better outcomes than low or high synchrony . ResearcThe result that synchrony of head movements between the spouses was negatively related to the female clients’ alliance evaluations suggests that nonverbal synchrony might not always serve a good purpose in couple therapy. Previous research has also hinted that it is equally important to be able to withdraw from synchronizing with others in some situations. For clients, not synchronizing with others might help in the self-regulation of affect . For theThe dyadic nonverbal synchrony data were based on 29 sessions, and it comprised data from only 11 couple therapy cases, thus generalizations cannot be made. Because of the limited number of cases, we obtained nonverbal synchrony from the entire therapy sessions, something that is not common. Nevertheless, the results from this study should be regarded as exploratory. The presence of four participants resulted in six different dyads that could synchronize in either head or body movements. Dyadic synchrony is the most common form of nonverbal synchrony studied in psychotherapy settings. Couple therapy with four participants would provide a good context for studying triadic and quadratic synchrony, which was not done in the study presented here. In the future, the procedure of calculating triadic synchrony  or the mAnother shortcoming of the study presented here is that it was not possible to use multilevel modeling because of the small amount of data within clusters. The statistical methods chosen were the best option for overcoming this difficulty.The use of self-report measures for the evaluation of subjective well-being, the therapeutic alliance, and outcome can be criticized. In particular, the ultra-brief forms of ORS and SRS could be criticized for not giving a detailed enough account of the evaluations. For instance, the alliance was evaluated holistically by the participants, meaning that both spouses evaluated the therapists as a team, and the therapists evaluated the alliance to both spouses simultaneously. However, the use of ultra-brief forms is clinically sound, since filling out the forms is convenient, even in a standard therapy setting. The large amount of missing data in the CORE-OM form was unfortunate, and the results should be read with caution.In the future, research with a larger dataset is needed to confirm the results. It would also be interesting to study what variables affect nonverbal synchrony in the couple therapy context. For example, does the content of the discussion affect the synchrony patterns? What variables induce in-phase or anti-phase synchrony? Do the synchrony patterns reveal the participants’ views or attitudes towards the topic spoken of? Does nonverbal synchrony signal like-mindedness or empathy in the couple therapy context? It would also be interesting to further elaborate on the relationship between nonverbal synchrony and alliance based on the In-sync model . An alliN, we are not comfortable with sharing it openly. Requests to access the datasets should be directed to PN-S, petra.nyman-salonen@jyu.fi.The datasets presented in this article are not readily available because the data is confidential psychotherapy data from 11 couple therapy cases, with data organized by gender. Even though the data is anonymized, because of the small The studies involving human participants were reviewed and approved by University of Jyväskylä Ethical Committee. The patients/participants provided their written informed consent to participate in this study.PN-S: first authorship. V-LK: senior authorship, research design, and collecting of the data. WT: senior authorship and synchrony computation. JM: statistical methods. AT: research design and collecting of the data. MP: research design and collecting of the data. JS: last authorship, research design, and collecting of the data. All authors contributed to the article and approved the submitted version.Academy of Finland, grant number 265492 . Kone foundation, grant number 201710524 .The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.