Rodents are characterised by a distinctive masticatory apparatus which includes a single pair of enlarged and continually growing incisors. This morphology, termed diprotodonty, has also independently evolved in a number of other mammals, including the aye-aye. This study examined the functional significance of the internal “root” of the elongated rodent-like incisor. The mandibles of four rodents and an aye-aye were modelled to exhibit incrementally shorter incisor roots. Finite element analysis was used to predict stress and strain patterns across the jaw to determine whether the length of the incisor root contributes to the resistance of mechanical forces encountered in the mandible during incision. It was found that von Mises stresses increase in the region of the mandible local to where the incisor is removed, but that the stress distribution across the wider mandible is only minimally affected. Thus, the long internal incisor appears to play a small role in resisting bending forces close to the incisor alveolus, and may act with the arch-like mandibular shape to strengthen the mandible in this region. However, the impact across the whole mandible is relatively limited, suggesting the highly elongate incisor in diprotodont mammals may be principally driven by other factors such as rapid incisor wear. This condition, known as diprotodonty, is not, however, unique to rodents, having evolved independently in a number of other mammalian groups including lagomorphs, hyraxes, marsupials, and primates3. The aye-aye (Primates) in particular has a masticatory apparatus very similar to that of rodents, with a pair of continually growing incisors that lack enamel on their lingual side and form a sharp chisel-like groove with wear4. These are used to gnaw through bark to obtain xylophagous insect larvae6. The skull and mandible of the aye-aye have been shown to be morphologically convergent with rodents, specifically squirrels7. This may indicate strong functional drivers of morphology in these taxa, in particular, the need to produce high bite forces at the incisors, which themselves exhibit features related to the resistance of forces encountered during gnawing10. Whether the presence of a long rodent-like incisor within the mandibular body, in conjunction with bony adaptations of the mandible, plays a role in the mechanical adaptation of the mandible to resisting bending during incisal biting is of key interest in understanding the success of rodents, and the independent evolution of diprotodonty in other non-rodent taxa.Rodentia is the most speciose order of mammals, containing over 2500 extant species11, and, in order to function, incisors must be able to resist the forces encountered. Such a need to resist bending means that diprotodont incisor morphology varies in a way that is largely predictable from ecology and mechanics14. During a bite, forces encountered at the tooth tip lead to stresses and strains in the root, the periodontal ligament (PDL), and the surrounding bone17. Rodent incisors are very long and deep rooted, and possess only labial enamel, with just their embedded lingual side covered by PDL18. It has been proposed that a longer incisor may play a role in the dissipation of stresses within the rodent mandible19. However, it would not be expected that forces propagate along the entire incisor length, as rodent incisors are continually growing (hypselodont) teeth, and therefore technically rootless, with the apical portion of the incisor consisting principally of newly formed unmineralised tissues18. For simplicity the portion of the tooth which projects into the bone is referred to as the root in this paper. The question of whether a deep tooth root plays a mechanical role in the resistance of forces encountered during biting has been tested in Thylacosmilus atrox, with their long-rooted maxillary canines, and found to have a very minor impact on the cranial biomechanics in a series of simulated bite scenarios20. The impact of an elongated tooth root on the resistance of forces however has not been tested in the mandible, which is both more compliant than the cranium and, in the case of rodents, can occupy most of the mandibular corpus.During gnawing, the incisors of diprotodonts are exposed to bending and shearing stresses9, occasionally extending as far as, or into, the condylar process21. It has previously been suggested that the deep internal projection of the incisor within the rodent mandibular body is responsible for the arch-like shape of the mandible visible in many rodents and a reduction in the bending moment by up to 25% compared to a beam-like mandible22. In addition, other biological curved structures such as long bones have been proposed to make the location and orientation of strains more predictable24.In rodents, the unerupted portion of the incisor typically extends distally to the end of the tooth row or just beyond25) to assess the resulting differences in stress and strain distributions. The core aim of this study is to determine whether the length of the incisor root is functionally significant for the resistance of mechanical forces encountered during incision. Three main hypotheses will be tested:Reduction in the length of the incisor root will result in an increase in stress across the mandible. Specifically, we expect to see this most clearly in von Mises stresses along the ventral surface of the mandible based on the assumptions that the rodent-like mandible operates in a manner similar to an arch22, and that an arch operates in compression. We will test this by comparing the stress magnitudes predicted by the FE models with complete incisors and those with virtually shortened roots.The incisor grows through an area of naturally low strain. This will be assessed by creating FE models in which the incisor length is reduced and the resulting space filled with bone. In particular, we wish to explore whether the area from which the incisor has been removed will experience lower strains than the area immediately around it, and whether the path that would have been filled by the incisor is visually apparent in the strain contour maps. We predict that the path through which the incisor grows will directly coincide with a region of reduced strains, and therefore bone resorption, to accommodate the growth of an elongated structure.The non-rodent diprotodont aye-aye will perform in a mechanically similar way to the rodents, but will produce more extreme results. We anticipate the aye-aye will exhibit patterns of stress similar to those observed in other examined diprotodonts, in particular the grey squirrel, but that it will experience stress magnitudes that are far higher than in any of the rodent taxa. We predict similarity with the grey squirrel based on previous results which indicate the aye-aye has convergently evolved a masticatory apparatus resembling sciurid rodents7, and expect a finding of more extreme stress values based on previous results that indicate the aye-aye mandible follows the same pattern of variation in incisor form as rodents but does so in a more exaggerated manner9.The principal focus of this study is whether, in the mandibles of diprotodont mammals, the replacement of bone with the relatively stiffer dental tissues of the incisor acts to increase the mandible’s ability to resist bending. A series of four rodents representing the major morphological and phylogenetic groups, and one non-rodent diprotodont, the aye-aye, will be modelled with incrementally shorter incisor roots and examined using finite element analysis , Rattus norvegicus , Sciurus carolinensis , Castor canadensis , and Daubentonia madagascariensis . These were chosen based on the length of their incisor roots, the availability of information about their masticatory musculature, and the quality of the available microCT scans, as well as to ensure that the three extant suborders and the major muscle morphotypes  of rodents were represented alongside a non-rodent diprotodont.One specimen of each of the following taxa was selected: 29. No live specimens were used in this study. Further details on specimen scanning parameters and the institutions from which they were borrowed are given in Supplementary Table 32. All models were produced in this way, keeping any decreases in strain consistent between specimens. Furthermore, creating solid models enabled the variations in incisor length and in-filling of the alveolar space to be achieved in a repeatable manner between specimens.Specimens were obtained and microCT scanned as part of previous projectsFive models were made for each specimen, with variations in the length of the incisor root, and in the presence or absence of an incisal crypt Fig. . The fir33. All models were assigned the same material properties based on previously published data for rodent bone and teeth. Cortical bone was assigned a Young’s modulus of 17 GPa28 and Poisson’s ratio of 0.334. The incisor was assigned a Young’s modulus of 55 GPA and a Poisson’s ratio of 0.32. These values were averages of the published values for rodent enamel and dentine28 as the two tissues were not distinguished during the segmentation process as a consequence of insufficient CT resolution in some specimens. Furthermore, it has been noted that representation of separate dental tissues in FE models has very limited impact on overall stress distributions35. Post-incisor dentition was not segmented as a separate material from bone as the focus of this study was directly on variation in mechanical strength of the mandible as a result of changes in incisor length.After segmentation of the mandibles was completed, the models were exported as bitmap stacks and converted into a mesh of eight-noded linear cubic elements by direct voxel conversion. This FE mesh was then imported into the non-commercial voxel-based FEA software VOX-FE37. The muscles applied to all specimens were the superficial masseter, deep masseter, ZM, temporalis, and medial pterygoid. In the crested porcupine two additional muscles, the lateral pterygoid and the infraorbital part of the ZM were added; and in the beaver the posterior masseter was added, whilst the deep masseter was separated into anterior and posterior portions38. The lateral pterygoid was included only in the crested porcupine as in other specimens the muscle properties were either not noted, or produced only very small forces  of each muscle was calculated by converting muscle mass to volume (assuming a muscle density of 1.0564 g cm−339) and dividing by fibre length. Muscle force estimates 44. Using Avizo, landmarks were placed at the centroid of each muscle attachment site on a virtual reconstruction of the cranium, and these landmarks were imported into VOX-FE to orient the muscle vectors. The models were aligned to the molar occlusal plane and constrained in all three axes at the left and right temporomandibular joints (TMJ). The tips of both incisors were constrained in the direction of the bite .Muscle attachment sites were determined based on published descriptions of attachment sites and muscle originsFE models were solved using VOX-FE. Results were compared via a visual assessment of coloured contour plots representing von Mises stress distributions across the whole mandible. Quantitative comparisons of stress across the mandible were performed via the recording of von Mises stress values at each of 20 landmarks located along the ventral margin of the mandible Fig. , the regFigure Plotting of the stress values extracted from the landmarks across the ventral surface of the mandible Fig.  providesFor all biting simulations, high stresses were exhibited around areas of muscle attachment, particularly on the thinner material of the coronoid process, and around the angular process. Visual examination reveals that even with the increased stresses as a result of the removal of incisor material, stresses along the ventral margin are still much lower than those seen at the muscle insertions.Overall, it can be seen that hypothesis 1, that reduction in the length of the incisor root will result in an increase in stress across the mandible, was partially supported. However, increases in stress are mostly localised to areas close to the incisor alveolus.With the mandible aligned to the occlusal plane of the post-incisor dentition and a perpendicular dorso-ventral slice taken through the solved FE model, the model was viewed in cross-section Figs. , 5. FromPlotting of the von Mises stress values extracted from the landmarks across the ventral surface of the mandible shows similar patterns across all five specimens Fig. . HoweverOverall, the aye-aye appears comparable to the rodent sample; although it experiences much higher stresses than the rodents as its internal incisor length is reduced, it produces patterns of strain similar to those observed in other examined diprotodonts. Thus hypothesis 3, that the non-rodent diprotodont aye-aye will perform in a mechanically similar, albeit more extreme, way to the rodents is supported.3. The mechanical significance of an arch is its ability to withstand a greater load than an otherwise materially equivalent horizontal beam can support. Vassallo22 found that as the mandible is exposed to three-point bending, its curved, arched shape reduces the bending moment by up to 25% more than in a beam-like mandible and argued this to be a functional adaptation for the resistance of forces encountered during gnawing. The curvature of the mandibular corpus, associated with the curvature of the underlying incisor, together with the increase in vertical height of the mandibular corpus are more effective ways of providing resistance to this sort of bending than increasing the medio-lateral thickness of the corpus48. It is possible these two features are not unrelated, as proposed by Druzinsky3. It may be, then, that the growth of a large internal incisor not only serves as a means of stress reduction along the ventral mandibular margin, by increasing the overall stiffness of the mandible, but also allows for the development of a morphology (an arch) that markedly reduces the moment of bending. The two in tandem may be key to the mechanical strength of the rodent-like mandible.Hypothesis 1 proposed that, by reducing the internal length of the incisor, an increase in stress across the mandible would be observed. This hypothesis was partially supported by the above results in that a reduction in the amount of internal incisor material resulted in an increase in stress local to the incisor alveolus in all five specimens. However, it was noted that von Mises stresses in regions further from the incisor  were broadly constant across all variant models within each taxon. The increases in stress are most pronounced along the ventral margin of the mandible, an area which would be under high compressive strain in an arch-like structure. It has been proposed that the growth of the rodent mandible follows the course of the rodent incisor, producing an arch-like shape19. Teeth are composed of a composite of nearly inelastic materials and are among the most deformation resistant biological materials49. In the models tested here, the reduction in the length of the incisor reduces both incisor surface area through which to dissipate the forces encountered during incision and the volume of stiff material to resist bending. This predictably results in increased stress along the mandible in the areas previously occupied by the stiffer incisor material, notably across the ventral margin of mandible. That the amount by which stress increase was related to the volume of material in the model replaced with cortical bone or air , which could require a long incisor to ensure that the tooth is fully mineralised by the time it erupts from the alveolus. Alternatively, there may be a developmental and geometric constraint that requires the incisor to have a long internal root in order that the erupted section emerges at the correct angle from the jaw50. Indirect evidence for this second theory is provided by chisel-tooth digging rodents which show longer, and more procumbent, incisors55.Despite the increases in stress related to removal of incisor material noted above, the stress changes from model to model are highly localised. Stress patterns in many parts of the mandible are seemingly unaffected by changes in incisor length, implying that, while it has some impact on stress, the length of the diprotodont incisor could be principally driven by factors other than bone stress reduction. Such drivers could include the rapid replacement rates seen in many rodents . The similarly large stress increases in the aye-aye and squirrel may be related to the convergence in mandibular shape seen in these two species8. Overall, it appears that the aye-aye has a rodent-like masticatory apparatus and form of diprotodonty that behaves in a mechanically similar way to that seen in rodents, especially squirrels, thus supporting hypothesis 3.Previous studies have demonstrated that the incisor morphology of the aye-aye is well-adapted to resist the forces encountered during gnawing behaviours, and that its specialised ecology has driven the evolution of an incisor morphology that is similar to, but more extreme than, that seen in rodents59. Furthermore, in reality, diprotodont incisors are only attached to the mandible on their labial side, whereas due to model resolution and the limitations of a voxel-based model the modelled incisor attaches to the mandible wherever voxels meet all along the internal length. However, both of these simplifications were consistent across all five models, allowing us to compare relative changes between variant models.As with all finite element studies, the models here are subject to a series of assumptions and simplifications to try and reflect a complex biological reality. In this study we did not model the PDL owing to limitations of scan resolution and a lack of consensus on the impact on strain distributions in FE models from the inclusion of PDL60) to robust bony fusion (e.g. in beavers38). Soft tissue connections at the symphysis may provide some degree of shock absorbance61, thus reducing overall mandibular stress. Thus, the FE models produced in this analysis will have overestimated mandibular stiffness, and potentially stress62, in those taxa with reduced symphyseal fusion. However, given that overall stress patterns did not change greatly between variant models, and that our interpretations were based on relative changes between models of the same taxa, we believe that the representation of symphyseal morphology as complete bony fusion in all taxa is a simplification that will not have changed our overall conclusions.The fusion of the hemimandibles during the modelling process may have introduced some error into the FEA results. Rodents show varied symphyseal morphologies from very loose ligamentous connections  resulted in an increase in deformation, but that overall the effect on stress magnitudes was very minor. In that instance, other bony features of the skull such as the postorbital bar appeared to be more key to the resistance of forces when biting, rather than the deep tooth root, which appeared to be more important for anchoring the long canine63. It would be interesting to determine whether the enlarged upper incisors of rodents perform a similar role or if they assume greater importance in resisting masticatory forces.Future work would benefit from the exploration of whether the crania of rodents and rodent-like diprotodonts produce similar results to more compliant mandibles. Janis et al.9 and finds that the aye-aye also resembles rodents in its biomechanical response to incisal biting.Here we examined whether the relatively stiff and elongated incisor, seen in rodents and aye-ayes, acts as a strengthening structure within the relatively less stiff bony mandible during incision. The FE models demonstrated that shortening the internal incisor root and replacing it with bony material or an empty space results in an increase in stress local to the incisor alveolus, but that the overall stress distribution across the mandible remained largely constant. This study found that the long incisor root may play a role in resisting bending forces, and may act in tandem with an arch-like mandibular shape to aid in strengthening of the mandible. However, the localised nature of stress reduction indicates that the principal driver of the elongate incisor may not be mechanical, and could be related to tooth wear or development. The incisor and mandible of the non-rodent diprotodont aye-aye appear to behave in a mechanically similar manner to those examined in rodents, particularly other hard-object biting species, albeit showing more extreme results and greater increases in stress as a consequence of modifications to its dental morphology. This result supports earlier findings that the aye-aye has converged upon a rodent-like mandibular and incisor morphologySupplementary Information.


According to the basic structure and working principle of the excitation signal sensors of a diesel engine electronic control unit (ECU), a segmentation model of an ECU excitation signal based on characteristic parameters (ESCP-SM) is proposed. In the ESCP-SM, the ECU excitation signal is divided into several parts, and each part has its characteristic parameters model. By using the same global parameters and strictly controlling each part’s proportional parameters, the ESCP-SM can achieve signal alignment and dynamic frequency modulation. Based on the simulation experiment, spectrum analysis proves that this modeling method ensures that the original signal’s effective information is not lost. Pearson similarity analysis shows that the similarity between the simulation signal and practical signal reaches 74%, exhibiting strong correlation. In addition, we set up a physical testing environment. ESCP-SM is realized based on virtual instrument technology, and provides excitation signals for a Komatsu 8 ECU. By modifying the parameter configuration, the ECU can drive the injector to work correctly. Infrastructure construction plays an essential role in the development of a regional economy. The most often utilized equipment in infrastructure building is engineering vehicles . Diesel The ECU obtains real-time engine status during engine operation by collecting various excitation signals via the sensor, including the crankshaft position (CKP) signal, the camshaft position (CMP) signal, the knock signal, and the throttle signal ,10. AmonThe research on ECU excitation signal simulation is primarily focused on two factors: Hardware circuit simulation  and the The characteristic parameters of crankshaft position sensor (CKP) signals and camshaft position sensor (CMP) signals were analyzed. The signal type can be distinguished by detecting the threshold value of the difference between adjacent points of the signal. Fast Fourier transform (FFT) was used to obtain the frequency parameters of the original signal;A segmentation model of the ECU excitation signal based on characteristic parameters (ESCP-SM) is proposed. By the mathematical modeling of crankshaft and camshaft signals, high-precision analog signals were generated. Different CKP and CMP signals were generated by setting the characteristic parameters of the signals;The design of the ESCP-SM ensures a high signal accuracy and significantly increases signal diversity. We released the source code so that other researchers can better understand the control characteristics and operational parameters of the ECU. It provides a large quantity of valuable data for the research and evaluation of ECU simulation software. The LabVIEW source code used in this study can be found on GitHub .This paper proposes a segmentation model based on characteristic parameters for easily and quickly simulating various CKP and CMP signals. In contrast to the prior method, which concentrated only on the precision of the analogue signal, we sought to improve the signal’s variety while maintaining its accuracy and synchronization. To pursue a higher signal accuracy, we adopted the following design. Firstly, the characteristic parameters of the CKP and CMP signals were analyzed so that the signals could be modeled piecewise. Subsequently, the proportional coefficient was set to strictly control the periodic relationship of each piecewise function. Finally, the analogue signal was output through the high precision synchronous data acquisition (DAQ) card. The DAQ card is only responsible for the digital-to-analogue conversion to output analogue signals, so the model’s design can ensure the high precision of the signals. To ensure the synchronization of the CKP and CMP signals, we extracted and set the frequency of the signals. The characteristic parameters control the relative position between the missing teeth of the CKP signal and the gear shaping the CMP signal. To increase the diversity of signals, we simulated different crankshaft and camshaft signals by setting the characteristic parameters of the signals. The experimental results show that the similarity between the simulated ESCP-SM signal and the original signal is up to 74%, and the accuracy is improved by 26% compared with the hardware HBS-EED signal. This study makes the following contributions:The rest of the paper is organized as follows. In In recent years, hardware-in-the-loop simulation (HIL) technology has been widely used in engine ECU testing . The sigIn the traditional engine signal simulation platform, multiple signal generators are combined, and the signal is changed by manual adjustment. The operation is complicated, and the actual working condition cannot be simulated accurately. For example, the motor drives the optical hole disk to produce the crankshaft signal. The signal type is fixed and cannot be applied to the simulation of other kinds of engines. As the signal’s speed change can only be regulated slowly by hand and cannot accurately imitate a failure condition such as the engine speed being out of control, this solution has difficulty meeting the requirements for real-time control. To solve the problems existing in the above traditional methods, A. Z. Jidin et al. ,22 used To solve the problem that parameters are difficult to adjust, I. J. Oleagordia Aguirre et al.  used a dIn order to simplify the complexity of the circuit and improve the accuracy of the signal, Zhao Futang et al.  selectedThe hardware-in-the-loop simulation links a portion of the real system equipment to the computer, simulates a portion of the real system equipment using the mathematical model, and simultaneously assures the function of the whole system. Krzysztof Wiecławski et al. ,32 introf can simulate the remaining multitooth waveform. For the Hall CKP signal, the missing part can be simulated by the square wave function with a duty ratio of 100%, while the square wave function simulates the other teeth with a duty ratio of 50%. The characteristic parameters of the CKP signal are shown in The CKP signal is a kind of waveform signal that is used to determine the engine’s speed and crank angle. The CKP signal types The CMP signal is a kind of waveform signal composed of a few pulses synchronized with the CKP signal. The CMP signal types To mitigate the effect of individual noise spots on the overall amplitude of the waveform, the data must be normalized. We chose min-max normalization to change the data to a decimal between 0, 1), as shown in Equation  is used to extract the frequency domain features of the signal. The formula for the DFT is shown below:k in the spectrum, the more frequencies corresponding to this k value are contained in the signal. However, the k value is not the actual signal’s frequency, and the relationship between them is shown in Equation f=kFk is 100. Therefore, the frequency of the actual signal can be calculated as 1000 HZ.As shown in T and duty cycle The CKP signal modeling process is detailed in T and duty cycle L) of the horizontal line waveform The CMP signal modeling process is detailed in f is the number of points in a single period.The magnetoelectric CKP signal can be divided into a missing teeth CKP waveform and no-missing-teeth CKP waveform according to the number of missing teeth. The magnetoelectric CKP signal can also be generally divided into two sections: The multitooth waveform and the missing tooth waveform. Usually, the waveform generated by the function is continuous, but the data sent to the data acquisition card are discrete. It is necessary to multiply the independent variable of the function by reciprocating the sampling rate to generate discrete waveforms at equal intervals. The ratio of the sampling rate The no-missing-teeth CKP signal comprises two sections: The multitooth signal and the marked tooth signal.x represents a sequence of sampling points. Stage 1: Multitooth Modeling. A sinusoidal waveform of Equation :(5)ymk_zStage 2: Marked tooth Modeling. The two sinusoidal waveforms, the period of which is half of the sinusoidal waveform of the multitooth signal, generate the marked tooth signal, as shown in Equation :(6)ymaryf_siStage 3: Front missing tooth arc modeling. The sinusoidal part and arc part of the missing tooth waveform are r, then the center coordinate of the circle is b.f is cancelled out:The sinusoidal part and the horizontal line part of the missing teeth waveform are connected smoothly by the circular part. Suppose the radius of the circle is For the front arc part of the missing teeth CKP signal, the arc waveform of Equation :(12)yf_aThe first half of the missing teeth waveform is generated by Equations  and 12)12). In FStage 4: Middle missing tooth line modeling. For the middle horizontal line of the missing teeth CKP signal, the horizontal line with Equation :(13)ym_lStage 5: Behind missing tooth arc modeling. For the behind arc part of the missing teeth CKP signal, the center coordinate of the circle is Equation :(14)yb_aStage 6: Behind missing tooth sine modeling. For the behind sinusoidal part of the missing teeth CKP signal, the sinusoidal waveform of Equation .(15)yb_The posterior part of the missing tooth waveform is generated by Equations  and 15)15). In FThe complete missing teeth magnetoelectric CKP signal is shown in As shown in The function Stage 1: Multitooth modeling. In the first stage of the Hall CKP signal, the square multitooth waveform part with Equation .(17)yhkStage 2: Missing teeth modeling. In the second stage of the Hall CKP signal, the square missing tooth waveform part with (Equation :(18)yhk_The magnetoelectric CMP signal consists of three parts: A sinusoidal pulse waveform, horizontal line waveform, and sinusoidal marked pulse waveform.Stage 1: Sine pulse modeling. The period of the sinusoidal pulse waveform in the CMP signal is Equation .(19)ymmStage 2: Horizontal line modeling. The horizontal line waveform is generated according to Equation .(20)ymmL of the horizontal line is calculated according to Equation (The length Equation :(21)L=NtStage 3: Sinusoidal marked pulse modeling. One of the sinusoidal waveforms is the marked pulse waveform, and the interval length between the other sinusoidal waveforms is the same. The sinusoidal marked pulse waveform is generated according to Equation .(22)ymmThe complete magnetoelectric CMP signal is shown in The Hall CMP signal consists of three parts: Rectangular pulse waveform, horizontal line waveform, and square marked pulse waveform.Stage 1: Rectangular pulse Modeling. The front part of the rectangular pulse consists of a square wave with a duty ratio When Equation :(23)yhm_The rectangular pulse is shown in Stage 2: Horizontal line Modeling. The voltage amplitude of the horizontal line is 0. The length of the horizontal line and the marked pulse signal’s position parameters are the same as that of the magnetoelectric CMP signal.The horizontal line waveform is generated according to Equation .(24)yhmStage 3: Marked pulse modeling. The rectangular marked pulse waveform is generated according to Equation :(25)yhm_The complete Hall CMP signal is shown in According to the above modeling method, we designed a signal generator software. This software included four functional modules: The loading parameter file module, output channel selection module, rotating speed frequency modulation module, and simulation signal display module. The software can generate a variety of CKP and CMP signals so that the construction vehicle’s ECU can be detected offline. To improve the software’s extensibility, we designed the signal parameter editing page to meet the actual test requirements. The main interface of the signal generator software is shown in The ECU excitation signal segment model with the above characteristic parameter configuration was realized by programming the previously mentioned computer software. The magnetoelectric CKP signal was taken as an example to generate the signal of the corresponding parameter configuration. In terms of the hardware circuit simulation, the HBs-EED method was selected to compare with the real vehicle signal. In relation to the virtual instrument simulation, the MSS-AS method was chosen to compare with the actual collected signal.In In In In X and Y represent two groups of data, X, and Y.To verify the parameter configuration model’s accuracy, the Pearson similarity formula  was usedEquation :(26)ρX,YAccording to the Pearson correlation coefficient’s value, we can estimate the degree of similarity between the two. By comparing the similarity between the ESCP-SM simulation CKP signals and the actual CKP signals, the final result was 0.74, which indicated a strong correlation. By comparing the similarity between the HBS-EED-simulated CKP signal and the actual CKP signal, the final result was 0.48. In the HBS-EED simulation, the CKP signal vibration is large due to the voltage instability of circuit components. The amplitude stabilizing circuit leads to difficulty in controlling the positive feedback, resulting in the amplitude of the sine wave fluctuating. Compared to the HBS-EED simulation method, our ESCP-SM simulation based on the modeling technique improved the accuracy by 26%. By comparing the similarity between the MSS-AS simulated CKP signal and actual CKP signal, the final result is 0.68. The MSS-AS method uses the arcsine function to generate the missing tooth waveform signal, which is relatively steep. Compared with the proposed ESCP-SM method, the signal accuracy is improved by 6%.Since the environment of the engine test bench is difficult to build, we can only go to the real vehicle to collect signal data. The real vehicle data usually collected is easily affected by noise and uneven engine speed and other factors, resulting in a certain deviation of our simulated signal when compared. In fact, our simulated signal is much closer to the ideal signal, with an accuracy of more than 74%.To verify that the simulation CKP signal’s effective information was not lost, the actual CKP signals and simulation CKP signals were analyzed with a fast Fourier spectrum . ObservaThe experimental environment was set up. The ESCP-SM was realized based on virtual instrument technology and provided an excitation signal for the ECU through the data acquisition (DAQ) card. The voltage-stabilized source supplied the ECU with power and the ignition switch signal. The experimental environment is shown in Collecting the injection pulse signal output by the ECU with an oscilloscope can detect whether the ECU can recognize the simulated CKP and CMP signals. The ECU can recognize the signal normally and issue the injection instruction after the actual test. The injection waveform output of the ECU is shown in This study analyzed the characteristic parameters of the ECU excitation signal, and a segmentation model of the ECU excitation signal based on characteristic parameters is proposed in this paper. The ESCP-SM is more dynamic and scalable, which leads to an improved complex excitation signal simulation. The experimental results show that the proposed ESCP-SM method is much better than the hardware simulation HBS-EED model in the similarity detection of signals collected from actual vehicle sensors. By the parameterized configuration, the diversity of signals is significantly increased.The model can not only be applied to diesel vehicles but can also be extended to gasoline vehicles by adjusting the parameters. For part of the automotive camshaft signal, additional parameters of the proportional relationship between different protruding pulses are needed. For other excitation signals of ECUs, such as oxygen sensor signals, we need to add some additional uniform white noise signals to simulate actual sensor signals while adjusting characteristic parameters. Researchers in related fields can draw on the ideas of this model to develop corresponding simulation signals. First, the intrinsic characteristic parameters of the signals are extracted and abstracted, and then appropriate mathematical functions are used to piecemeal fit local signals. The accuracy of the simulation signal can be significantly improved by using this model.When applied to the actual ECU test of engineering vehicles in the later stage, we need to burn the program into the development board and separately design the corresponding data acquisition card to reduce the test cost. The released open source code can help researchers in related fields to provide some ideas for reference when designing multi-type and complex parameter simulation signals. In future studies, we can further use more accurate characteristic parameters to simulate irregular signals.


This is explained by the substitution of international activities by local circular activities. This comparative analysis advocates for the consumption approach to assess the CE’s impact on CO2 equivalent emissions.This paper investigates the economy-wide impact of the uptake of circular economy (CE) measures for the small open economy (SOE) of Belgium, in particular the impact of fiscal policies in support of lifetime extension through repair activities of household appliances. The impact assessment is completed by means of a computable general equilibrium model as this allows quantification of both the direct and indirect economic and environmental impact of simulated shocks. The results show that different fiscal policy types can steer an economy into a more circular direction. However, depending on the policy type, the impact on the SOE’s macroeconomic structure and level of circularity differs. Furthermore, common claims attributed to a CE  can be, but are not always, valid. Hence, policy-makers must prioritize their most important macroeconomic goals and opt for an according fiscal policy. Finally, this paper finds that the COThe online version contains supplementary material available at 10.1007/s00168-021-01079-6. The circular economy (CE) is gaining momentum as an alternative to traditional linear economic systems that rely on a take–make–dispose approach, e.g. as part of the European Green Deal  model to investigate the economy-wide impact of the uptake of CE measures for the small open economy (SOE) of Belgium. Specifically, it assesses the impact of fiscal policies in support of repair activities to extend the lifetime of household appliances. In addition, the CGE also determines the environmental impact of the policies and increased circularity in terms of COAs a hot topic, the CE has received ample attention in recent literature, but a meta-analysis by Kirchherr and van Santen  on 160 pThis is problematic for two reasons. First, services contributed 73.2% of the EU-28’s total gross value added in 2018 EUROSTAT . Hence, 2 equivalent emissions. This allows policy-makers to balance economic and environmental costs and benefits in the context of a CE, beyond recycling.The CGE model presented in this paper addresses several of the issues mentioned above. First, a CGE model bridges the gap between theoretical and empirical research Franck . The theThe use of CGE models is common practice whenever there is a need to quantify the effect of change in one part of the economy upon the rest as CGE models capture both the direct and indirect effect of simulated shocks . As stated by Winning et al. , the anaThe extraction of these two additional sectors requires the extraction of additional (competing) products and services. First, the ‘repair of household appliances’ services is extracted and subsequently added as a separate service to the CGE model, produced by the circular activity  provide monetary information on the supply and use of goods per sector. The original SUTs are published by the Belgian Federal Planning Bureau  and contThe aim of this paper is to assess the impact of the uptake of CE measures. Therefore, prior to the aggregation of the SUT sector and product groups, two industries and three product groups closely related to the CE were split up using additional data sources. The purpose here was to isolate certain industries and products of particular relevance to the CE. Specifically, we isolate the retail trade of new household appliances from the general retail trade industry (NACE 2 rev.47), and the repair of household appliances is isolated from the repair of computers and consumer goods (NACE 2 rev. 95). As such, the SAM distinguishes the current conventional (and predominantly linear) retail activity from the circular repair activity.To isolate the retail trade of new household appliances from the general retail trade industry, we rely on data from Eurostat’s Structural Business Statistics (SBS). Specifically, we collect data on the sales of the CPA 470,054 ‘Retail trade services of electrical appliances’, which we use as a proxy for output. Next, we assume the same supply and use structure as that of the general retail trade industry, which is rescaled according to the relative size of CPA 470,054 to the retail trade industry (NACE 47). We proceed similarly using available SBS data to isolate the repair of household goods from NACE 2 rev.95. Finally, the isolation of the retail trade and repair industry as well allowed for calibration of the CGE model.On the product side, we divide manufactured electrical goods into household goods excluding spare parts, on the one hand, and manufactured spare parts of household appliances, on the other hand. To estimate the total amount of both products produced, we use the import and export flows of household appliances and the parts thereof as well as the total consumption of these goods in Belgium obtained through the Household Budget Survey  and conventional (more linear) activities to be modelled as substitutable consumption products. This rationale allows for the design of policy scenarios in support of the CE, and the assessment and comparison of these scenarios’ results.CGE models computationally derive the impact of policy at economy-wide level. Following the calibration of the CGE model , the model is run a first time to compute the baseline scenario, which represents the economy’s pre-policy situation. As the model is calibrated by making use of 2015 data, the baseline represents the structure of the Belgian economy in 2015.Restrictive fiscal policy increased taxes to discourage the consumption and production of unsustainable products and services. The tax rate on linear purchases of new household appliances via the retail sector is increased in a stepwise process. Specifically, the original tax rate on new (linear) purchases is repeatedly increased by 0.3 percentage points. The increase is repeated 15 times to assess the economy’s evolution.Expansionary fiscal policy taxes are cut to encourage the consumption of sustainable (i.e. circular) products and services. The original tax rate on circular repair services is repeatedly (15 times) decreased by 0.3 percentage points. The evolution of the economy is monitored throughout this stepwise process.Hybrid fiscal policy combination of the restrictive fiscal policy and the expansionary fiscal policy. This results in a simultaneous decrease in the tax rate on repair services (− 0.3 percentage points) and tax rate increase on new purchases (+ 0.3 percentage points). Both policy types can address different sectors simultaneously to assess their combined impact.Generic green fiscal reform a tax cut (− 0.3 percentage points) on all services in addition to the restrictive fiscal policy on retail of new household appliances (+ 0.3 percentage points). This kind of tax cut on services is advocated by numerous stakeholders (e.g. Meuleman and Parker (d Parker  and Eurod Parker ) as a prThis paper investigates the impact of fiscal policies and taxation as Stahel  describeThe presented CGE model is comparative static by nature and hence does not introduce dynamics or future developments. This allows the impact assessment of different policy options, with little deviation in the economy’s underlying structure, compared to the baseline scenario . Figure As shown in Fig. Simultaneously, all tax policies manage to discourage the conventional retail activities , albeit in different magnitudes. Retail of new household appliances is least affected by the expansionary tax policy (decreased traded volume of 0.03%) and most affected by the green fiscal reform policy, which manages to decrease sales by 1.9%. The impact on the spare parts follows the evolution of the impact on the repair services in the restrictive, expansionary and hybrid scenario. This is not the case in the green fiscal reform scenario, as this policy does not solely target the repair sector, but favours other sectors as well.In addition to the directly targeted products and services, the policies also indirectly impact all other products and services. These indirect impacts are presented in Table In the hybrid and restrictive scenarios, the traded volumes increased for all products and services, except for the industrial products, construction products and services, and the market services. The opposite situation is observed for the expansionary scenario: the traded volume of the non-targeted products and services decreased, except for the construction sector. Finally, the green fiscal reform scenario’s impact on the non-targeted products and services is most comparable to the expansionary scenario’s impact. Most traded volumes decreases, except for the market services, air transport services, trade services and construction products and services. For the latter category, the magnitude of change (+ 10.79%) surpasses the impact in the expansionary scenario (+ 0.0017%) considerably, however. The considerable impact in the green fiscal reform scenario is explained by the observation that the construction sector makes relatively more use of services compared to other sectors. As the green fiscal reform favours all types of services, this allows the construction sector to benefit most.While Table The evolution of household income is not related to the job creation. The households provide more labour in the restrictive, hybrid and green policy scenario  while they provide less labour in the expansionary scenario (− 0.0005%). Hence, the restrictive and hybrid policies manage to create more jobs but offer lower wages. Note that the economy’s production processes’ demand for logistical services evolves in line with the evolution in labour requirements per policy scenario .In accordance with the policies’ impact on household income level, the restrictive and hybrid policy scenarios are characterized by a decrease in the investment level , a decreased government budget  and a decreasing gross domestic product (GDP) . The magnitude of change for these three parameters does not differ considerably among these two policy scenarios. On the other hand, the expansionary and green fiscal reform policies manage to achieve a growth in the investment level , government budget  and GDP (+ 0.0004% and + 1.5672%). However, the magnitude of change differs considerably for these policies; the green fiscal reform has a much more elevated impact on these three parameters.Note that the policies’ overall impact on the available government budget consists of both a direct and an indirect part. The direct impact relates to the policies properties (i.e. taxes generate revenues while subsidies generate expenditures). However, this direct impact is partially levelled out by an indirect impact. This is explained by the CGE model’s assumption that the government’s utility level is fixed compared to the baseline situation. Hence, the direct impact of tax incomes is compensated by shifts in other governmental revenues and expenditures. Because of this reason, the policies’ overall impact on the government budget strongly correlates to the policies’ impact on GDP (as the government’s revenues stem from a taxation on economic activities).In addition, it is worthwhile considering the origin of the products and services that are traded in this SOE. The restrictive and hybrid policy increase the importance of domestically produced products and services , at the expense of products imported from the EU  or the ROW . Again, the magnitude of change in the origin of the traded products and services is highly comparable for the restrictive and hybrid policies. The expansionary policy, on the other hand, increases the importance of products and services imported from the EU (+ 0.0003%) and the ROW (+ 0.0002%), while domestically produced products and services are traded less (− 0.0008%) within the SOE. These finding on import dependence are in line with common economic theory. The green fiscal reform policy finally increases the traded volume of products from all origins.The penultimate column in Table 2 equivalent emissions. However, these emissions are calculated using two different perspectives: the production perspective and the consumption perspective.Since the different policies affect the economy differently, it can also be expected that the policies entail a different environmental impact. The environmental impact is estimated by means of the COFollowing the EEA , the proTable These findings tend to suggest that it is preferable to assess emissions by means of the consumption approach, as this approach provides a complete picture on a region’s contribution to global emissions. The production approach on the other hand only provides a partial view on these emissions. However, limited data availability often prevent the use of the consumption perspective, as data on emissions abroad are not always available.  to a minimum level of 0.9. This minimum level is determined as 0.9 is also the elasticity of substitution between household appliances and other goods in the model  of the circular  product is more distinctive and linear. A stepwise decrease in the elasticity of substitution to a minimum level of 0.9 resulted in a lower but limited decrease in the consumption of new household appliances in both the restrictive and expansionary scenario. In case the minimum elasticity of substitution is reached, the consumption of new household appliances is 0.024% and 0.033% above the consumption levels in case of the initial elasticity of substitution for the restrictive and the expansionary scenario, respectively. It is especially the consumption of repair services which is impacted. In case of the minimum elasticity of substitution, the consumption of repair services is 3.8% and 5.16% below consumption levels in case of the initial elasticity of substitution for the restrictive and the expansionary scenario, respectively. Hence, in particular the consumption levels of the circular alternative appear sensitive to the chosen elasticity of substitution. However, due to the limited importance of this activity (e.g. as part of the GDP), the overall economic trends and impact of the proposed policies are not affected by changing levels of substitution between the conventional and circular activities.The changes in traded volume per product or service Table  and the The economic impact of the fiscal policy and the uptake of the CE is remarkable because of the limited magnitude of the imposed shock and the limited economic importance of the targeted repair sector. While the policies manage to increase the repair activities of household appliances by 4.00% to 12.42%, their impact indirectly trickles down to all other sectors. As a result, the aggregate impact surpasses the size of the repair sector for household appliances by twelve times and changes the SOE’s GDP considerably. Thus, the generic impact of the policies outweighs the relative economic importance of the niche repair sector for household appliances.At product/service level, the restrictive and hybrid policies manage to increase or decrease the traded volume for all products and services  by more than 0.004% . The expansionary policy has the smallest impact on the traded volumes of all products and services while the green fiscal reform policy has the largest impact. This is a consequence of the latter policy’s broader scope, which goes beyond the retail, repair and production of service parts for household appliances sectors.Apart from the repair and retail of new household appliances and the spare parts of household appliances, the products and services whose traded volume is affected the most by the policies, in decreasing order of magnitude, are: ‘Construction products and services’, ‘Logistical services and mail’, and ‘Water transport services’. This indicates that the construction sector is more responsive to changes in the retail sector, while the water transport, logistics and mail sectors are more responsive to the repair sector.The expansionary policy is more positive in nature as it aims to encourage circular activities. For this reason, this policy also manages to achieve a higher level of circularity (measured in terms of traded repair services) in comparison to the purely restrictive policy. On the other hand, the expansionary policy is least effective in discouraging sales of new household appliances . To decrease the undesirable linear activities, it appears necessary to also implement a discouraging and restrictive tax regime. Note, however, that the restrictive policy tends to decrease the GDP . Therefore, in the current set-up, a trade-off is required between the ambition to limit unwanted environmental externalities and the need to maintain (linear) economic activity. Alternatively, governments can also aim to increase consumers’ interest in repair services of household appliances as opposed to the purchase of new appliances. In the CGE model, this would manifest itself in increased cross-price elasticities between repair and retail and an upsurge in the extent to which consumers switch to repair following price increases in the retail price of new appliances.The hybrid policy, like the restrictive policy, is characterized by decreasing economic parameters . Hence, the restrictive element in the hybrid policy is not fully compensated by the expansionary elements.The green fiscal reform manages to increase the repair activities more than the purely expansionary policy targeted at the repair sector. So, it appears as if there is an element of truth in the claim to cut taxes on services in order to stimulate the CE as suggested by Stahel  or the EHowever, the extent to which the policies increase (decrease) the circular (linear) activities differs considerably. On the one hand, expansionary fiscal policies are more effective in the promotion of circular activities compared to restrictive fiscal policies. On the other hand, the restrictive fiscal policies are more effective in reducing the existing linear activities. Policy-makers should reflect on their priorities: encourage circularity or discourage less circular activities.In addition, the analysis demonstrates that the impact of the different fiscal policies is considerable but not sufficient to achieve a full circularity. Achieving full circularity will require a more holistic approach and a set of accompanying policies in addition to fiscal policies. As such, the paper provides empirical evidence for findings by Hartley et al.  and NohrThe CE is increasingly perceived as stimulus for local job creation Stahel . This paIn any case, the analysis shows that a transition towards a more CE will simultaneously lead to job creation in some sectors and job destruction in other sectors. Governments can anticipate this process and avoid unemployment because of a discrepancy between the available and the required skills on the labour market. This can be achieved by proactively providing education and training and encouraging inter-sectoral labour movement. The latter policy recommendation supports the findings by Burger et al.  who claiAdvocates of the CE also claim that it decreases a nation’s import dependence as more resources remain present in its economy , the analysis demonstrates that the economic gains related to increased circularity also achieve environmental gains at global level.This observation calls for a careful analysis of the environmental impact of policies which aim to increase an economy’s circularity levels, especially because it can be expected that increased circularity encourages local economic activities within the economy. The more holistic consumption perspective is likely to provide a more robust assessment of an economy’s contribution to climate change. This finding fits in a dynamic discussion on this topic and conflicts with earlier research findings on the need for a consumption perspective by, for example, Barrett et al. . This coThe presented analysis is prone to some limitations. First, the model departs from, and maintains, the current SOE’s structure and mechanisms. The fiscal policies are not supported by any other transitionary policy in support of the CE. Consequently, the competitiveness of the CE sector over its conventional (linear) counterpart in this CGE model is not strengthened by more structural measures . This rather conservative approach cautions against hasty conclusions and results in a moderate increase in the circularity. In reality, however, the uptake of the CE most likely requires a more integrated and comprehensive policy framework . This robustness check confirmed all findings, but no further sensitivity is run on external parameters. These external parameters might impact the responsiveness of the economy to the CE and supportive fiscal policies. Important examples of external parameters are the price stickiness and the monetary policy conduct . For an overview of CGE models and other types of models with the inclusion of environmental aspects , see Ciarli and Savona . Because of the importance of the indirect impact on other sectors, the aggregate economy-wide effect of the CE measures surpasses the size of the niche repair sector for household appliances considerably.This paper shows different  policy paths for promoting more repair of household appliances, leading towards a more CE. However, the extent to which the policies increase (decrease) the circular (linear) activities differs considerably. On the one hand, expansionary fiscal policies are more effective in the promotion of circular activities compared to restrictive fiscal policies. On the other hand, the restrictive fiscal policies are more effective in reducing the existing linear activities. Policy-makers should reflect on their priorities.2 equivalent emissions from a consumer perspective while it increases these emissions from a production  perspective. Hence, the environmental gains are mainly realized at global level since the CE stimulates local economic activities. This also stresses the importance of the selection of the correct perspective while assessing the environmental impact of circular activities. This paper advocates the consumption approach, as this approach provides a more complete picture on a region’s contribution to global emissions. Put differently, the consumption approach accounts for the substitution of less circular international activities by circular local activities. Hence, the strength of the consumption approach in this context is not that it accounts for submissions caused abroad, but that it instead it accounts for emissions avoided abroad. The production approach fails to account for this substitution and hence potentially leads to incorrect conclusions on the environmental impact of circular activities.Finally, the uptake of circular activities manages to decrease COSupplementary file1 (DOCX 69 KB)Below is the link to the electronic supplementary material.


Background: In 2010, Sweden opened up for establishment of privately owned primary health care providers, as part of a national Free Choice in Primary Health Care reform. The reform has been highly debated, and evidence on its effects is scarce. The present study therefore sought to evaluate whether the reform have impacted on primary health care service performance.Methods: This ecological register-based study used a natural experimental approach through an interrupted time series design. Data comprised the total adult population of the 21 counties of Sweden 2001–2009 (pre-intervention period) and 2010–2016 (post-intervention period). Hospitalizations and emergency department visits for ambulatory care sensitive conditions (ACSC) were used as indicators of primary health care performance. Segmented regression analysis was used to assess the effects of the reform, in Sweden as a whole, as well as compared between counties grouped by (i) change in private provision pre- to post reform; (ii) the timing of the implementation; and (iii) sustained presence of private providers both pre- and post-reform.Results: The results suggest that, following the introduction of the reform in Sweden as a whole, the trends in total hospitalizations rates were slowed down by 1.0% albeit acute emergency visits increased 1.1% more rapidly after the introduction of the reform. However, we found no evidence of more beneficial effects in counties where the reform had been implemented more ambitiously, specifically those with a larger increase in private primary care providers, or where the reform was introduced early and thus had longer time effects to emerge. Lastly, counties with a sustained high presence of private primary care providers displayed the least favorable development when it comes to ACSC.Conclusion: Taken together, the present study does not support that the Swedish Free Choice reform has improved performance of the primary care delivery system in Sweden, and suggests that high degree of private provision may involve worse performance and higher care burden for specialized health care. Further evaluations of the consequences of the reform are dire needed to provide a comprehensive picture of its intended and unintended impact on health care provision, delivery and results. The Swedish health care system has historically been predominantly public, managed and provided by the 21 county councils, but has since the 1990s gradually increased its market-orientation, particularly within primary health care .The FCPHC reform consisted of two main parts, directed at providers and patients, respectively. First, the reform allowed all PHC providers that met certain basic requirements to establish a health care center at a geographical location of their choice; and second, it allowed patients to choose their PHC provider, which in turn served as a basis for capitation payment to the providers . The refThe reform has been a matter of contention even since before its implementation. One reason for this is that the introduction of the reform embodies an underlying ideological shift from a more egalitarian to a more libertarian view of health care organization . Other cThe introduction of similar choice policies and market competition in other European health systems has, like in Sweden, been controversial. The accumulated evidence on the effects is so far insufficient and inconclusive, and has been limited to outcomes related to health service provision such as waiting times and patient satisfaction , 12–14. While there are many alternative approaches to evaluate policies and interventions, there is a growing interest from epidemiologists and public health researchers in using natural experiments. Natural experiment is an approach referring to empirical studies that evaluate the effects of interventions through detailed comparisons of contrasting cases , where the intervention is not allocated by the researcher but naturally occurring –19. In tThe present study sought to utilize a natural experiment design to evaluate whether the reform have impacted PHC service performance at the national level, and if the impact varied by regional differences in the de facto implementation of the reform. We measured ambulatory care sensitive conditions (ACSC), which are widely used to assess overall access, quality and performance of the primary care delivery system , 21. HosWith these hypotheses as a point of departure, the present study aimed to examine: (1) whether the FCPHC reform has led to national decreased rates of avoidable hospitalizations and emergency visits in Sweden 2001–2016, and (2) whether the effects of the reform shows regional variations depending on (a) increase in public/private ratio (b) timing of implementation of the reform, and (c) sustained presence of private PHC providers.This ecological register-based study was based on data on the total adult population of the 21 counties of Sweden aged 20 years and older for the time period 2001–2016. As a majority of young Swedes still go to secondary school and lives with their parents up to the age of 19 years, 20 years was chosen as the youngest age. We employed a natural experimental approach to assess the effects of the FCPHC reform; specifically, an interrupted time series design with segmented regression analysis.Interrupted time series analysis (ITSA) is the strongest quasi-experimental approach for evaluating longitudinal effect of public health policies introduced at a population level over a clearly defined period of time –19. A siIn the present study we used single-group ITSA to test the overall national reform effects, and a series of multiple-group ITSA comparing counties with different levels of the de facto implementation of the reform, in order to more specifically attribute any effects to the FCPHC reform.Aggregated county-level data was collected for each year of observation 2001–2016. Outcome data stratified by sex and 5-year age groups was retrieved from the National Patient Register of the National Board of Health and Welfare. Total population numbers (for denominators) were retrieved from publicly available data from Statistics Sweden; and information on numbers of annual private and public PHC centers per county and hospital beds per 1,000 population were gathered from the Swedish Association of Local Authorities and Regions.The studies involving human participants were reviewed and approved by The Regional Ethical Review Board in Umeå . Written informed consent for participation was not required for this study in accordance with the national legislation and the institutional requirements.To operationalize the FCPHC reform, contrasting groups of counties were created according to three characteristics of the de facto implementation of the reform , 8.While the reform covered the entire Sweden from January 1st 2010, the regional context varies when it comes to the attractiveness for private health care providers to establish , and a contrasting population for whom the reform has not involved any major change in this regard (low magnitude of implementation). First, the proportion of private PHC centers was calculated for each county . Second, the change in the proportion of PHC from before to after the reform was calculated for each county, using the year before the implementation of the reform  as the baseline proportion, and the average proportion across the years following the reform  as the post-reform proportion. As absolute and relative changes may capture different aspects of increased/decreased privatization, both the absolute (before – after) and relative (before/after) change in the proportion of private PHC centers from before to after the reform were calculated separately. Third, the 21 counties were ranked according to the absolute and relative changes, respectively, and then a mean of the two rankings was calculated. Fourth and last, the mean rank was divided into tertiles. The top tertile encompassing the seven counties with greatest increase in the private proportion from before to after the reform (>10% absolute increase and >60% relative increase) was categorized as high magnitude (=1); the lowest tertile of the seven counties with the smallest increase (or even a decrease) in the private proportion (<6% absolute increase and <15% relative increase) was categorized as low magnitude (=0). To ensure a clear contrast for the comparison, the middle tertile consisting of counties with a moderate change in the private proportion was excluded of the comparison , 2008 (Stockholm and Västmanland) and 2009  . The popA third group of counties was identified based on sustained high presence of private PHC providers over the entire observation period. These counties had in effect already exemplified a model prescribed by the reform. They were special in that they were highly exposed to private health care provision both in time and magnitude, but at the same time a saturated market may have diminished opportunities for incremental changes in the establishment of private providers following the reform. Three counties had a private/public proportion above the national mean both before (28.5%) and after (41.4%) the reform, and were therefore categorized as having a sustained presence (=1), while 13 counties with a lower than national average in private/public proportion both before and after the reform were categorized as having a low presence of private providers (=0). Counties that did not have consistently higher or lower proportions than national averages were excluded of the comparison.Hospitalizations and emergency department visits for ambulatory care sensitive conditions (ACSC) were used as outcomes. ACSC are a set of acute and chronic health conditions that potentially can be managed with timely and effective primary health care, reducing the need for or avoiding secondary care such as hospitalization and emergency department visits , 21. TheThe identification of ACSC was done through International Classification of Disease (ICD-10) codes and categorized by the Swedish National Board of Health and Welfare classification of avoidable hospitalizations. This classification has been used for monitoring and research on primary care performance and quality in Sweden , 25 and Chronic ACSC include diabetes complications, hypertension, heart failure, chronic obstructive pulmonary disease, angina, anemia and asthma. Acute ACSC include diarrhea, bleeding ulcers, epileptic seizures, pelvic inflammatory diseases, pyelonephritis and ear, nose and throat infection . HospitaAge-standardized hospitalization and emergency visits rates  were calculated across the period 2001–2016, using Swedish total population 2016 as standard.Corresponding to the first aim, we first estimated the change in trends of ACSC-H and ACSC-EV in Sweden as a whole through single-group ITSA. Corresponding to the second aim we subsequently performed multiple-group ITSA for comparisons between contrasting groups of counties with different levels of the de facto implementation of the reform as follows: (a) High vs. low magnitude of implementation; (b) Early vs. late timing of implementation; and (c) High vs. low sustained presence of private providers. The pre-intervention period was defined as 2001–2009 and post-intervention period 2010–2016. Time series for each outcome  were plotted by 6-month periods, giving 18 points before and 14 points after the reform implementation. Analysis for each outcome was done by total number of cases as well as separately by acute and chronic conditions, totaling six single-group and eighteen multiple-group ITSA models.Preliminary analysis suggested that our data was moderately overdispersed, and we therefore fit our segmented regression analysis with negative binomial regression models, which is an approach that has been shown to be appropriate for modeling time series of counts data when there is evidence of overdispersion . The preSince the number of available hospital beds could be a particularly important confounder for hospitalization rates , ACSC-H In addition to the six single-group ITSA and 18 multiple-group ITSA carried out as the main analyses, a number of additional analyses were run. First, the models were rerun stratified by sex  and broad age groups , to explore whether the overall results were valid across gender and age.Moreover, to explore the sensitivity of the results to the choice of cut-offs for the intervention operationalization and the time point to evaluate the reform, a series of analyses were carried out using alternative cut-offs. For the intervention operationalization, the cut-off for early implementation was changed to at least 1 year before 2010 , and for the magnitude of implementation the cut-off was changed to the national average, including all counties . For the time point to evaluate the reform, the year was changed to 2011 instead of 2010, allowing for a longer period of implementation .Since the auxiliary analyses comprised a large set of models and led to similar conclusions as the main analyses, a summary of the results are reported in the Results section, and details are available on request.A summary of results of the single-group ITSA, corresponding to the first aim of estimating the overall impact of the FCPHC reform on ACSC outcomes in Sweden as a whole, are reported in The 9 years prior to the introduction of the reform (the “pre-trend”), saw a universal increase in ACSC outcomes, both for hospitalizations and emergency visits, and for chronic as well as acute ACSC. These trends were significant for all outcomes except for chronic ACSC hospitalization, and the largest increases were seen for acute ACSC hospitalizations and emergency visits, corresponding to an estimated 2.2 and 1.7% average semi-annual increase in the age-adjusted rates, respectively.Upon the introduction of the reform in 2010, the trends changed for the different outcomes. The trend of total ACSC hospitalization flattened out after introducing the reform (2011–2016), as seen in insubstantial and non-significant 0.1% decrease (post-trend). This shift in trend from before to after the introduction of the reform was significant (pre-post trend), estimated at an average 1% lower increase in the semi-annual hospitalization rate, relative to the pre-intervention trend. This effect seemed to be driven by post-reform reductions in hospitalizations due to chronic, rather than acute, ACSC.In contrast to hospitalization rates, the increasing trend in total ACSC emergency visits before the reform continued even after the introduction of the reform, at a comparable pace and with no significant break in the trend (post-trend). A similar pattern was seen specifically for chronic ACSC emergency visits. In contrast, the increasing trend of acute ACSC emergency visits rather accelerated after the reform, estimated at a significant 1.1% higher increase after compared to before the reform (pre-post trend).Auxiliary analyses  by age specific groups and stratified by sex, overall pointed in the same direction as in the total population. For example, there was a significant decrease pre-post trend in total ACSC hospitalizations  and in chronic ACSC hospitalizations , and a significant increase in acute emergency visits . In addition, pre-post trends were also significant for acute hospitalizations in men  and chronic emergency visits in men and <65 years .Based on the overall impact of the reform on ACSC outcomes in Sweden described above, the subsequent series of analyses report variations in the impact across counties who differed with respect to increases in the proportion of private PHC providers following the introduction of the reform , the year of introduction of the reform , and a long-term presence of private providers .The comparisons between counties which introduced the free choice earlier than the FCPHC reform was implemented nationally displayed a more complex pattern depending on the outcomes; see For all ACSC hospitalization outcomes , the early adopters of the reform showed a less promising development, with a significantly worse trends before the reform (pre-trend difference). The universal introduction of the reform in 2010 did however not change this pattern, with similarly sized but non-significantly worse trends among the early compared to late implementers (post-trend difference), and a non-significant pre-post trend difference as a result.In contrast, the early implementers displayed a less pronounced increase in the acute ACSC emergency visits compared to the late implementers before the reform (pre-trend difference), but a similar increase after the reform (post-trend difference). This resulted in a significantly more unfavorable impact of the reform among the early implementers (pre-post trend difference), amounting to a 1.4% accelerated rates among early compared to late implementers. This overall pattern was in the same direction but non-significant for total and chronic ACSC emergency visits.The impact of the reform on ACSC outcomes differed consistently between counties with a high-sustained presence of private providers compared to those with a consistently low presence, both before and after the introduction of the reform; see For hospitalizations outcomes, this was explained by significantly more steeply increasing pre-reform trends among the counties with high compared to low sustained presence of private providers (pre-trend difference), in combination with increasing trends after the reform (post-trend difference), which resulted in a significant 0.8–0.9% less favorable impact of the reform among the counties with sustained presence (pre-post trend difference).A more sizable less favorable impact of the reform among the counties with high compared to low sustained presence of private providers was also seen for emergency visit outcomes amounting to a 2.2–2.4% difference (pre-post-trend difference). This was the result of less pronounced increasing trends before the implementation (pre-trend difference) in combination with steeper increasing trends after the reform in the counties with sustained presence of private providers (post-trend difference).Analyses stratified by sex and age (results available on request) led to the same overall conclusions as in the total population. Specifically, there were no variation in impact of the reform by magnitude of implementation either by gender or age; an unfavorable impact of the reform in acute emergency visits among the early compared to late implementers ; and an overall negative impact of the reform in both, hospitalizations  and emergency visits  among the counties with high compared to low sustained presence of private providers.The series of sensitivity analysis (results available on request) using different cut-off points for intervention operationalization and timing of the intervention confirmed the inferences from the main analysis, only with slightly larger pre-post trend differences observed for certain comparisons when the time point to evaluate the reform was changed to 2011 instead of 2010, thereby allowing for a longer period of implementation. Specifically, the pre-post trend differences were more pronounced for hospitalizations in the high compared to low sustained presence counties  and for emergency visits in the early compared to late implementers .This study set out to evaluate the impact of the 2010 Swedish Free Choice in Primary Health Care reform on PHC performance as indicated by rates of hospital admissions and emergency visits for chronic and acute Ambulatory Care Sensitive Conditions. The results suggest that, following the introduction of the reform in Sweden as a whole, the trends in total hospitalizations rates were slowed down and for chronic conditions even turned to a downward trend, which marks a break from the pre-reform secular trend. On the other hand, acute emergency visits increased more rapidly after the introduction of the reform. However, we found no evidence of more beneficial effects in counties where the reform had been implemented more ambitiously, specifically those with a larger increase in private primary care providers, or where the reform was introduced early and thus had longer time effects to emerge. This suggests that the overall changes in Sweden as a whole are not to be attributed to the reform itself. Lastly, counties with a sustained high presence of private primary care providers displayed the least favorable development when it comes to ACSC. Taken together, our study does not provide evidence that the FCPHC reform has had the expected positive impact on ACSC, and instead tentatively suggests that widespread private PHC provision could, in the long run, negatively affect PHC performance.The pattern of slightly increasing trends in hospitalizations for chronic ACSC turning toward downward trend after 2010 have been noted before , and hasComplementary interventions implemented together or as a consequence of the reform could have also played a role on the observed results. For example, it is possible that the reduction of hospitalizations would be a reflection of guideline adaptations made at county-level to improve quality indicators. i.e., the ACSC have been used as quality performance indicators  and therWhen it comes to the between-county comparisons, it is possible that other characteristics than changes in the proportion of private provision have led to the estimated effects of the reform. For example, whereas most of the county councils have a mixed reimbursement system largely based on capitation and a small part on fee-for-service , each coThe observation that counties with sustained presence of private providers showed the worst development when it comes to ACSC was a notable and surprising finding. This comparison does not directly reflect the impact of the 2010 national reform, but should instead be seen as an illustration of the possible long-term outcome of the reform in Sweden as a whole, if all counties were to develop a persistent dominance of private primary care providers. A lot of controversy surrounds the role of the private (for-profit) sector in health services delivery. Indeed previous research have cautioned policymakers of possible negative effects, such as the potential of the private sector to strip away the workforce from the public sector, and their tendency to focus on advantaged groups and over treat patients to generate more profits . Some evWhereas impact on equity in PHC performance was not part of the scope of the present report, it is important to note that failures to meet the needs of underserved population groups, as has been found in previous research in Sweden , could hThe main strengths of the present study are the longitudinal design spanning over 16 years of follow up; the use of a comprehensive set of outcomes retrieved from Swedish total population registers of good quality; and the interrupted time series designs, which is considered the best available mean of assessing an intervention impact , 36.Some potential limitations should be considered when interpreting our results. First, the analyses were done using population-level rates and can therefore not be used to make individual-level inferences . FurtherAlthough the single-group ITSA does not require to have a comparison group to obtain association between an intervention and outcome , 38, it Moreover, it is possible that the lack of effect in counties where the reform had been implemented more ambitiously is due to the chosen operationalization of the reform, and that the results therefore also may conceal differential developments in specific sub-groups . However, in this paper, we tried various analyses stratified by sex and age subgroups with different cut-off points for magnitude and timing, yet none of them led to a different result. Nonetheless, it should be noted that using other aspects rather than the public/private proportions to operationalize the reform and other specific subgroups for the analysis could possibly yield different inferences.It is also possible that the reform needs a longer time to produce an impact on PHC performance, perhaps beyond the period of this study. For example, in the shorter term, the reform would be expected primarily to increase the number of providers; while in the medium term, the benefit might be in access to primary care and only in the long term, a clearer benefit in reducing the burden of secondary and tertiary care would be seen. In this analysis, we included 18 observations points (9 years) before and 14 points (7 years) after the reform implementation, which would be considered sufficient to statistically evaluate changes . NeverthLastly, it is difficult to isolate the independent impact of the reform in a dynamic ever-changing health system and society. In fact, to identify competing or complementary interventions to the reform that could be responsible for shifting the time series of the evaluated outcomes is challenging by itself, as there could be national preventive efforts and particular county level interventions, as well variations in reimbursement systems as discussed above, that could be expected to have a similar effect as the reform itself. Relatedly, considering the long study period over 16 years, a change in unconsidered population or health system characteristics could also potentially confound the analyses, as long as the change coincides with the introduction of the reform. Even though the ITS design is based on both within- and between-group comparisons of trends, and the threat to internal validity is considerably lower than for a weaker study design, confounding cannot be ruled out. In preliminary analyses, sociodemographic characteristics did not differ between the comparison groups, but other unobserved potential confounders include for example regional health system differences, such as variations in clinical practice, and also healthcare seeking behavior. Another potential confounder is the actual prevalence and incidence of chronic disease. There are unfortunately no national register data on disease prevalence in Sweden outside the patient registers that were used as outcomes in the study.These considerations illustrate the inherent challenges of performing population-wide evaluations in real-world settings, which are relevant for future research on the impact of health system changes on PHC performance. The choice of evaluation design is a key methodological issue that may be restricted by the availability of appropriate data. Controlled designs are preferred but formulation of the comparison population requires careful consideration, which poses a challenge also for regionally implemented interventions . The isThe present study contributes to evidence on the effects of a major health care reform, driven by libertarian goals rather than the egalitarian principles that traditionally have been central to Swedish health care system.Taken together, the present study does not support that the Swedish Choice in PHC reform has improved the overall quality and performance of the primary care delivery system in Sweden, and suggests that high degree of private provision in PHC may lead to worse PHC performance and higher care burden for specialized health care.The results illustrate the value of using population-level approaches and counterfactual evaluation designs to assess interventions through attributable impact. While evidence-based policy-making free from ideological or ethical guiding principles may neither be realistic nor desirable, rigorous evidence as provided by the present study represents an important aspect for assessing, tailoring and designing effective health policy. Further evaluations of the consequences of the reform are direly needed to provide a comprehensive picture of its intended and unintended impact on health care provision, delivery and results.The raw data supporting the conclusions of this article will be made available by the authors upon request, without undue reservation.The studies involving human participants were reviewed and approved by The Regional Ethical Review Board in Umeå . The study is based on aggregated data on a large scale, and thus does not process any personal data. The Regional Ethical Review Board in Umeå waived the requirement for written informed consent for participants in this study in accordance with Swedish national regulations , as the study only retrieved and utilized secondary register data.PM, PG, and MS conceived the study. PM conducted the data analysis, interpretation of the data and drafted the manuscript, with support from PG. PG and MS contributed to the analysis and interpretation of the data and revised the manuscript. BB and AKH participated in the interpretation of the data and revised the manuscript. All authors approved the final draft.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.