Population data-based federated machine learning improves automated echocardiographic quantification of cardiac structure and function: the Automatisierte Vermessung der Echokardiographie project

Aims

Machine-learning (ML)-based automated measurement of echocardiography images emerges as an option to reduce observer variability. The objective of the study is to improve the accuracy of a pre-existing automated reading tool ('original detector') by federated ML-based re-training.

Methods and results

Automatisierte Vermessung der Echokardiographie was based on the echocardiography images of n = 4965 participants of the population-based Characteristics and Course of Heart Failure Stages A-B and Determinants of Progression Cohort Study. We implemented federated ML: echocardiography images were read by the Academic Core Lab Ultrasound-based Cardiovascular Imaging at the University Hospital Würzburg (UKW). A random algorithm selected 3226 participants for re-training of the original detector. According to data protection rules, the generation of ground truth and ML training cycles took place within the UKW network. Only non-personal training weights were exchanged with the external cooperation partner for the refinement of ML algorithms. Both the original detectors as the re-trained detector were then applied to the echocardiograms of n = 563 participants not used for training. With regard to the human referent, the re-trained detector revealed (i) superior accuracy when contrasted with the original detector's performance as it arrived at significantly smaller mean differences in all but one parameter, and a (ii) smaller absolute difference between measurements when compared with a group of different human observers.

Conclusion

Population data-based ML in a federated ML set-up was feasible. The re-trained detector exhibited a much lower measurement variability than human readers. This gain in accuracy and precision strengthens the confidence in automated echocardiographic readings, which carries large potential for applications in various settings.

Deep learning assisted measurement of echocardiographic left heart parameters: improvement in interobserver variability and workflow efficiency

Machine learning techniques designed to recognize views and perform measurements are increasingly used to address the need for automation of the interpretation of echocardiographic images. The current study was designed to determine whether a recently developed and validated deep learning (DL) algorithm for automated measurements of echocardiographic parameters of left heart chamber size and function can improve the reproducibility and shorten the analysis time, compared to the conventional methodology. The DL algorithm trained to identify standard views and provide automated measurements of 20 standard parameters, was applied to images obtained in 12 randomly selected echocardiographic studies. The resultant measurements were reviewed and revised as necessary by 10 independent expert readers. The same readers also performed conventional manual measurements, which were averaged and used as the reference standard for the DL-assisted approach with and without the manual revisions. Inter-reader variability was quantified using coefficients of variation, which together with analysis times, were compared between the conventional reads and the DL-assisted approach. The fully automated DL measurements showed good agreement with the reference technique: Bland-Altman biases 0-14% of the measured values. Manual revisions resulted in only minor improvement in accuracy: biases 0-11%. This DL-assisted approach resulted in a 43% decrease in analysis time and less inter-reader variability than the conventional methodology: 2-3 times smaller coefficients of variation. In conclusion, DL-assisted approach to analysis of echocardiographic images can provide accurate left heart measurements with the added benefits of improved reproducibility and time savings, compared to conventional methodology.

Normal Values of 3D Right Ventricular Size and Function Measurements: Results of the World Alliance of Societies of Echocardiography Study

BACKGROUND

Normal values for 3D right ventricular (RV) size and function are not well established, as they originate from small studies that involved predominantly white North American and European populations, did not use RV-focused views and relied on older 3D RV analysis software . The World Alliance of Societies of Echocardiography (WASE) study was designed to generate reference ranges for normal subjects around the world. In this study, we sought to assess the world-wide capability of 3D imaging of the right ventricle and report size and function measurements, including their dependency on age, sex and ethnicity.

METHODS

Healthy subjects free of cardiac, pulmonary and renal disease were prospectively enrolled at 19 centers in 15 countries, including 6 continents. 3D wide-angle RV datasets were obtained and analyzed using dedicated RV software (Tomtec) to measure end-diastolic and end-systolic volumes (EDV, ESV), stroke volume (SV) and ejection fraction (EF). Results were categorized by sex, age (18-40, 41-65 and >65 years) and ethnicity.

RESULTS

Of the 2007 subjects with attempted 3D RV acquisitions, 1051 had adequate image quality for confident measurements. Upper and lower limits for BSA-indexed EDV (mL/m²) and ESV (mL/m²) and EF (%) were [48, 95], [19, 43] and [44, 58] for men and [42, 81], [16, 36] and [46, 61] for women. Men had significantly larger EDV, ESV and SV (even after BSA indexing) and lower EF than women (p<0.05). EDV and ESV did not show any meaningful differences between age groups. 3D RV volumes were smallest in Asians.

CONCLUSIONS

Reliability of 3D RV acquisition is low worldwide underscoring the importance for future improvements in imaging techniques. Sex and race must be taken into consideration in the assessment of both RV volumes and EF.

Normative values of the aortic valve area and Doppler measurements using two-dimensional transthoracic echocardiography: results from the Multicentre World Alliance of Societies of Echocardiography Study

AIMS

Aortic valve area (AVA) used for echocardiographic assessment of aortic stenosis (AS) has been traditionally interpreted independently of sex, age and race. As differences in normal values might impact clinical decision-making, we aimed to establish sex-, age- and race-specific normative values for AVA and Doppler parameters using data from the World Alliance Societies of Echocardiography (WASE) Study.

METHODS AND RESULTS

Two-dimensional transthoracic echocardiographic studies were obtained from 1903 healthy adult subjects (48% women). Measurements of the left ventricular outflow tract (LVOT) diameter and Doppler parameters, including AV and LVOT velocity time integrals (VTIs), AV mean pressure gradient, peak velocity, were obtained according to ASE/EACVI guidelines. AVA was calculated using the continuity equation. Compared with men, women had smaller LVOT diameters and AVA values, and higher AV peak velocities and mean gradients (all P < 0.05). LVOT and AV VTI were significantly higher in women (P < 0.05), and both parameters increased with age in both sexes. AVA differences persisted after indexing to body surface area. According to the current diagnostic criteria, 13.5% of women would have been considered to have mild AS and 1.4% moderate AS. LVOT diameter and AVA were lower in older subjects, both men and women, and were lower in Asians, compared with whites and blacks.

CONCLUSION

WASE data provide clinically relevant information about significant differences in normal AVA and Doppler parameters according to sex, age, and race. The implementation of this information into clinical practice should involve development of specific normative values for each ethnic group using standardized methodology.

Age-, Sex-, and Race-Based Normal Values for Left Ventricular Circumferential Strain from the World Alliance Societies of Echocardiography Study

BACKGROUND

Left ventricular (LV) circumferential strain has received less attention than longitudinal deformation, which has recently become part of routine clinical practice. Among other reasons, this is because of the lack of established normal values. Accordingly, the aim of this study was to establish normative values for LV circumferential strain and determine sex-, age-, and race-related differences in a large cohort of healthy adults.

METHODS

Complete two-dimensional transthoracic echocardiograms were obtained in 1,572 healthy subjects (51% men), enrolled in the World Alliance Societies of Echocardiography Normal Values Study. Subjects were divided into three age groups (<35, 35-55, and >55 years) and stratified by sex and by race. Vendor-independent semiautomated speckle-tracking software was used to determine LV regional circumferential strain and global circumferential strain (GCS) values. Limits of normal for each measurement were defined as 95% of the corresponding sex and age group falling between the 2.5th and 97.5th percentiles. Intergroup differences were analyzed using unpaired t tests.

RESULTS

Circumferential strain showed a gradient, with lower magnitude at the mitral valve level, increasing progressively toward the apex. Compared with men, women had statistically higher magnitudes of regional and global strain. Older age was associated with a stepwise increase in GCS despite an unaffected ejection fraction, a decrease in LV volume, and relatively stable global longitudinal strain in men, with a small gradual decrease in women. Asian subjects demonstrated significantly higher GCS magnitudes than whites of both sexes and blacks among women only. In contrast, no significant differences in GCS were found between white and black subjects of either sex. Importantly, despite statistical significance of these differences across sex, age, and race, circumferential strain values were similar in all groups, with variations of the order of magnitude of 1% to 2%. Notably, no differences in GCS were found among brands of imaging equipment.

CONCLUSION

This study established normal values of LV regional circumferential strain and GCS and identified sex-, age-, and race-related differences when present.

Three-Dimensional Transthoracic Static and Dynamic Normative Values of the Mitral Valve Apparatus: Results from the Multicenter World Alliance Societies of Echocardiography Study

BACKGROUND

Recent advances in mitral valve (MV) percutaneous interventions have escalated the need for a more quantitative and comprehensive assessment of the MV, which can be best achieved using three-dimensional echocardiography. Understanding normal valve size, structure, and function is essential for differentiation of healthy from disease states. The aims of this study were to establish normative values for MV apparatus size and morphology and to determine how they vary across age, sex, and race groups using data from the World Alliance Societies of Echocardiography Normal Values Study.

METHODS

Three-dimensional volumetric data sets obtained on transthoracic echocardiography in 748 normal subjects (51% men) were analyzed using commercial MV analysis software (TomTec Imaging Systems) to determine annular and leaflet dimensions and areas. The subjects were divided into groups by sex (378 men and 370 women) and age (18 to 40 years [n = 266], 41 to 65 years [n = 249], and >65 years [n = 233]) to identify sex- and age-related differences. In addition, differences among black, white, and Asian populations were studied. Inter- and intraobserver variability was assessed in a subset of 30 subjects and expressed as mean absolute difference between pairs of repeated measurements.

RESULTS

Compared with women, men had larger annular size measurements, larger tenting size parameters, and larger leaflet length and area. Compared with the black and white populations, the Asian population showed significantly smaller mitral annular size. Although many of the age, sex, and race differences in MV parameters were statistically significant, they were comparable with or smaller than the corresponding measurement variability. Indexing to body surface area and height did not eliminate these differences consistently, suggesting that parameters may need to be indexed according to their dimensionality.

CONCLUSIONS

This analysis of the World Alliance Societies of Echocardiography data provides normative values of mitral apparatus size and morphology. Although sex- and age-related differences were noted, they need to be interpreted with caution in view of the associated measurement variability.

A Novel Approach for Semi Automated 3D Quantification of Mitral Regurgitant Volume Reflects a More Physiologic Approach to MR

BACKGROUND

Quantification of mitral regurgitation (MR) by echocardiography is an integral to assessing lesion severity, and entails integration of multiple Doppler-based parameters. These methods are primarily founded upon the principle of PISA (proximal isovelocity surface area), a 2D method known to employ several assumptions regarding MR jet characteristics. We analyzed the results of a semi-automated method of 3D-based RV estimation which accounts for jet behavior throughout the cardiac cycle, and compared it to conventional 2D PISA methods for MR.

METHODS

A total of 50 patients referred for transesophageal echocardiogram (TEE) for evaluation of primary (n= 25) and secondary MR (n=25) were included for analysis. 3D full volume color data sets were acquired, along with standard 2D methods for PISA calculation. 3D semi-automated MR flow quantification algorithm was applied offline to calculate 3D regurgitant volume (RVol), with simultaneous temporal curves generated from the 3D dataset. 3DRvol was compared to 2DRVol. 3D vena contracta area was also performed in all cases.

RESULTS

There was a modest correlation between 2DRVol and 3DRVol (r = 0.60). The semi-automated 3D approach resulted in significantly lower RV values compared to 2D PISA. Real-time and dynamic flow curve patterns were used for integral estimates of 3DRVol over the cardiac cycle, with a distinct bimodal pattern in functional MR, and brief and solitary peak in primary.

CONCLUSIONS

Using a semi-automated 3D software for quantification of mitral regurgitation allows for simultaneous calculation of 3D RVol with an automated generation of dynamic flow curves characteristic of the underlying MR mechanism. Our flow curve pattern results highlight well-known differences between MR flow dynamics in degenerative MR compared to functional MR.

Normal Values of Left Ventricular Size and Function on 3D Echocardiography: Results of the World Alliance of Societies of Echocardiography Study

BACKGROUND

Echocardiography remains the most widely used modality to assess left ventricular (LV) chamber size and function. Currently this assessment is most frequently performed using 2D echocardiography (2DE). Yet, 3D echocardiography (3DE) has been shown to be more accurate and reproducible than 2DE. Current normative reference values for 3D LV analysis are predominantly based on data from North America and Europe. The World Alliance of Societies of Echocardiography (WASE) study was a designed to sample normal subjects from around the world to provide more universal global reference ranges. In this study we sought to assess the world-wide feasibility of LV 3DE and report on size and function measurements.

METHODS

2262 healthy subjects were prospectively enrolled from 19 centers in 15 countries. 3D LV full-volume datasets were obtained and analyzed offline with vendor-neutral software. Measurements included end-diastolic and end-systolic volumes (EDV, ESV), ejection fraction (EF), global longitudinal and circumferential strain (GLS and GCS). Results were categorized by age (18-40, 41-65 and >65 years), sex and race.

RESULTS

1589 subjects (feasibility 70%) had adequate LV datasets for analysis. Mean normal values for indexed EDV, ESV and EF in men and women were 70 ± 15 and 65 ± 12 mL, 28 ± 7 and 25 ± 6 mL and 60 ± 5, 62 ± 5% respectively. Men had larger LV volumes and lower EF than women. GLS and GCS were higher in magnitude in women. In both sexes, LV volumes were lower and EF tended to be higher with increasing age, especially considering the differences between the youngest and oldest age groups. While GLS was similar across age groups in men, in women, the youngest and middle-age cohorts revealed higher magnitudes of GLS when compared to the oldest age group. GCS was higher in magnitude at older age in both men and women. Finally, Asians had smaller chamber sizes and higher EF and absolute strain values than both blacks and whites.

CONCLUSIONS

Age, sex, and race should be considered when defining normal reference values for LV dimension and function parameters obtained by 3DE.

Normal Values of Left Atrial Size and Function and the Impact of Age: Results of the World Alliance Societies of Echocardiography Study

BACKGROUND

Left atrial (LA) evaluation includes volumetric and functional parameters with an abundance of diagnostic and prognostic implications. Solid normal reference ranges are compulsory for accurate interpretation in individual patients, but previous studies have yielded mixed conclusions regarding the effects of age, sex, and/or race. The present report from the World Alliance Societies of Echocardiography study focuses on two-dimensional (2D) and three-dimensional (3D) measures of LA structure and function, with subgroup analysis by age, sex, and race.

METHODS

Transthoracic 2D and 3D echocardiographic images were obtained in 1,765 healthy individuals (901 men, 864 women) evenly distributed among age subgroups: 18 to 40 years (n = 745), 41 to 65 years (n = 618), and >65 years (n = 402); the racial distribution was 38.4% white, 39.9% Asian, and 9.7% black. Images were analyzed using dedicated LA analysis software to measure LA volumes and phasic function from 3D volume and 2D strain curves.

RESULTS

Three-dimensional maximum and minimum LA volumes adjusted for body surface area were nearly identical for men and women, but women demonstrated higher 3D total and passive emptying fractions (EFs). Two-dimensional reservoir strain was similar for both sexes. Age was associated with an incremental rise in LA volumes alongside characteristic shifts in functional indices. Total 2D EF and reservoir and conduit strain varied inversely with age, counteracted by higher booster strain, with a greater magnitude of effect in women. Active 3D EF was significantly higher, while total and passive EFs decreased with age. Interracial differences were noted in LA volumes, without substantial differences in functional indices.

CONCLUSION

Although similar normal values for LA volumes and strain can be applied to both sexes, meaningful differences in LA size occur with aging. Indices of function also shift with age, with a compensatory rise in booster function, which may serve to counteract observed lower total and passive EFs. Defining age-associated normal values may help differentiate age-associated "healthy" LA aging from pathologic processes.

Two-Dimensional Echocardiographic Right Ventricular Size and Systolic Function Measurements Stratified by Sex, Age, and Ethnicity: Results of the World Alliance of Societies of Echocardiography Study

BACKGROUND

Echocardiographic assessment of right ventricular (RV) systolic function is an important component of clinical decision making. Although professional societies have worked to define normal ranges of RV size and function, their guidelines have not included the impacts of age, sex, and ethnicity on these parameters, as they have for the left ventricle. The World Alliance of Societies of Echocardiography study was designed to investigate the effects of age, sex, and ethnicity on all cardiac chambers. The aim of this study was to explore whether these differences exist for RV systolic parameters.

METHODS

Adequate two-dimensional RV-focused views for the measurement of systolic parameters, including fractional area change and global and free wall longitudinal strain, were available in 1,913 subjects (mean age, 47 ± 17 years; 51% men). Basal and mid-RV dimensions, length, tricuspid annular peak systolic excursion, tissue Doppler S' velocity, and myocardial performance index were also measured. Subjects were grouped by age (<40, 41-65, and >65 years), with results also stratified by sex and ethnicity (Asian, black, or white) and analyzed using vendor-independent software. Differences among groups were evaluated using analysis of variance.

RESULTS

Women had smaller absolute and indexed RV areas and absolute RV dimensions and higher magnitudes of fractional area change, free wall strain, and global longitudinal strain compared to men. With respect to age, most of the statistically significant differences were noted between the <40- and >65-year age groups, with RV areas and lengths smaller in older age groups and RV functional parameters (S', fractional area change, tricuspid annular plane systolic excursion, global longitudinal strain, free wall strain, and myocardial performance index) showing minimal decreases or no changes with age. Although there were no meaningful differences in functional parameters among ethnic groups, RV size was smallest in Asians.

CONCLUSIONS

These findings suggest that although two-dimensional RV parameters are age and sex dependent, association with race is less apparent, excepting that the Asian population appears to have smaller chamber sizes compared with whites and blacks.

Normal Values of Cardiac Output and Stroke Volume According to Measurement Technique, Age, Sex, and Ethnicity: Results of the World Alliance of Societies of Echocardiography Study

BACKGROUND

Assessment of cardiac output (CO) and stroke volume (SV) is essential to understand cardiac function and hemodynamics. These parameters can be examined using three echocardiographic techniques (pulsed-wave Doppler, two-dimensional [2D], and three-dimensional [3D]). Whether these methods can be used interchangeably is unclear. The influence of age, sex, and ethnicity on CO and SV has also not been examined in depth. In this report from the World Alliance of Societies of Echocardiography Normal Values Study, the authors compare CO and SV in healthy adults according to age, sex, ethnicity, and measurement techniques.

METHODS

A total of 1,450 adult subjects (53% men) free of heart, lung, and kidney disease were prospectively enrolled in 15 countries, with even distributions among age groups and sex. Subjects were divided into three age groups (young, 18-40 years; middle aged, 41-65 years; and old, >65 years) and three main racial groups (whites, blacks, and Asians). CO and SV were indexed (cardiac index [CI] and SV index [SVI], respectively) to body surface area and height and measured using three echocardiographic methods: Doppler, 2D, and 3D. Images were analyzed at two core laboratories (one each for 2D and 3D).

RESULTS

CI and SVI were significantly lower by 2D compared with both Doppler and 3D methods in both sexes. SVI was significantly lower in women than men by all three methods, while CI differed only by 2D. SVI decreased with aging by all three techniques, whereas CI declined only with 2D and 3D. CO and SV were smallest in Asians and largest in whites, and the differences persisted after normalization for body surface area.

CONCLUSIONS

The present results provide normal reference values for CO and SV, which differ by age, sex, and race. Furthermore, CI and SVI measurements by the different echocardiographic techniques are not interchangeable. All these factors need to be taken into account when evaluating cardiac function and hemodynamics in individual patients.

Normal Values of Right Atrial Size and Function According to Age, Sex, and Ethnicity: Results of the World Alliance Societies of Echocardiography Study

BACKGROUND

The World Alliance Societies of Echocardiography study is a multicenter, international, prospective, cross-sectional study whose aims were to evaluate healthy adult individuals to establish age- and sex-normative values of echocardiographic parameters and to determine whether differences exist among people from different countries and of different ethnicities. The present report focuses on two-dimensional (2D) and three-dimensional (3D) right atrial (RA) size and function.

METHODS

Transthoracic 2D and 3D echocardiographic images were obtained in 2,008 healthy adult individuals evenly distributed among subgroups according to sex (1,033 men, 975 women) and age 18 to 40 years (n = 854), 41 to 65 years (n = 653), and >65 years (n = 501). For ethnicity, 34.9% were white, 41.6% Asian, and 9.7% black. Images were analyzed in a core laboratory according to current American Society of Echocardiography/European Association of Cardiovascular Imaging guidelines. RA measurements included 2D dimensions, 2D and 3D RA volumes (RAVs) indexed to body surface area (BSA), emptying fraction (EmF), and global longitudinal strain, including total/reservoir, passive/conduit, and active/contractile phases. Differences among age and sex categories and among countries were also examined.

RESULTS

RAVs were larger in men (even after BSA indexing), while 3D total EmF and global longitudinal strain magnitudes were higher in women. For both sexes, there were no significant age-related differences in 2D RAV measurements, but 3D RAV values differed minimally with age, remaining significant after BSA indexing. RA total EmF and reservoir strain and passive EmF and conduit strain magnitude were lower in older groups for both sexes. Interestingly, whereas RA active EmF increased with age, contractile strain magnitude decreased. Considerable geographic variations were identified: Asians of both sexes had significantly lower BSA than non-Asians, and their 2D and 3D end-systolic RAVs were significantly smaller even after BSA indexing. Of note, 2D end-systolic RAVs in this group were considerably lower than normal values provided in the current guidelines.

CONCLUSIONS

There is significant sex, age, and geographic variability in normal RA size and function parameters. Current guideline-recommended normal ranges for RA size and function parameters should be adjusted geographically on the basis of the results of this study.

Mass-spring systems for simulating mitral valve repair using 3D ultrasound images

Mitral valve (MV) diseases are among the most common types of heart diseases, while heart diseases are the most common cause of death worldwide. MV repair surgery is connected to higher survival rates and fewer complications than the total replacement of the MV, but MV repair requires extensive patient-specific therapy planning. The simulation of MV repair with a patient-specific model could help to optimize surgery results and make MV repair available to more patients. However, current patient-specific simulations are difficult to transfer to clinical application because of time-constraints or prohibitive requirements on the resolution of the image data. As one possible solution to the problem of patient-specific MV modeling, we present a mass-spring MV model based on 3D transesophageal echocardiographic (TEE) images already routinely acquired for MV repair therapy planning. Our novel approach to the rest-length estimation of springs allows us to model the global support of the MV leaflets through the chordae tendinae without the need for high-resolution image data. The model is used to simulate MV annuloplasty for five patients undergoing MV repair, and the simulated results are compared to post-surgical TEE images. The comparison shows that our model is able to provide a qualitative estimate of annuloplasty surgery. In addition, the data suggests that the model might also be applied to simulating the implantation of artificial chordae.

High-resolution transthoracic real-time three-dimensional echocardiography: quantitation of cardiac volumes and function using semi-automatic border detection and comparison with cardiac magnetic resonance imaging

OBJECTIVES

We sought to validate high-resolution transthoracic real-time (RT) three-dimensional echocardiography (3DE), in combination with a novel semi-automatic contour detection algorithm, for the assessment of left ventricular (LV) volumes and function in patients.

BACKGROUND

Quantitative RT-3DE has been limited by impaired image quality and time-consuming manual data analysis.

METHODS

Twenty-four subjects with abnormal (n = 14) or normal (n = 10) LVs were investigated. The results for end-diastolic volume (EDV), end-systolic volume (ESV), and ejection fraction (EF) obtained by manual tracing were compared with the results determined by the semi-automatic border detection algorithm. Moreover, the results of the semi-automatic method were compared with volumes and EF obtained by cardiac magnetic resonance imaging (CMRI).

RESULTS

Excellent correlation coefficients (r = 0.98 to 0.99) and low variability (EDV -1.3 +/- 8.6 ml; ESV -0.2 +/- 5.4 ml; EF -0.1 +/- 2.7%; p = NS) were observed between the semi-automatically and manually assessed data. The RT-3DE data correlated highly with CMRI (r = 0.98). However, LV volumes were underestimated by RT-3DE compared with CMRI (EDV -13.6 +/- 18.9 ml, p = 0.002; ESV -12.8 +/- 20.5 ml, p = 0.005). The difference for EF was not significant between the two methods (EF 0.9 +/- 4.4%, p = NS). Observer variability was acceptable, and repeatability of the method was excellent.

CONCLUSIONS

The RT-3DE, in combination with a semi-automatic contour tracing algorithm, allows accurate determination of cardiac volumes and function compared with both manual tracing and CMRI. High repeatability suggests applicability of the method for the serial follow-up of patients with cardiac disease.

Optimizing traffic lights in a cellular automaton model for city traffic

We study the impact of global traffic light control strategies in a recently proposed cellular automaton model for vehicular traffic in city networks. The model combines basic ideas of the Biham-Middleton-Levine model for city traffic and the Nagel-Schreckenberg model for highway traffic. The city network has a simple square lattice geometry. All streets and intersections are treated equally, i.e., there are no dominant streets. Starting from a simple synchronized strategy, we show that the capacity of the network strongly depends on the cycle times of the traffic lights. Moreover, we point out that the optimal time periods are determined by the geometric characteristics of the network, i.e., the distance between the intersections. In the case of synchronized traffic lights, the derivation of the optimal cycle times in the network can be reduced to a simpler problem, the flow optimization of a single street with one traffic light operating as a bottleneck. In order to obtain an enhanced throughput in the model, improved global strategies are tested, e.g., green wave and random switching strategies, which lead to surprising results.

Stochastic boundary conditions in the deterministic Nagel-Schreckenberg traffic model

We consider open systems where cars move according to the deterministic Nagel-Schreckenberg rules [K. Nagel and M. Schreckenberg, J. Phys. I 2, 2221 (1992)] and with maximum velocity v(max)>1, which is an extension of the asymmetric exclusion process (ASEP). It turns out that the behavior of the system is dominated by two features: (a) the competition between the left and the right boundary, (b) the development of so-called "buffers" due to the hindrance that an injected car feels from the front car at the beginning of the system. As a consequence, there is a first-order phase transition between the free flow and the congested phase accompanied by the collapse of the buffers, and the phase diagram essentially differs from that for v(max)=1 (ASEP).

Nondeterministic Nagel-Schreckenberg traffic model with open boundary conditions

We study the phases of the Nagel-Schreckenberg traffic model with open boundary conditions as a function of the randomization probabilities p>0 and the maximum velocity v(max)>1. Due to the existence of "buffer sites" which enhance the free-flow region, the behavior is much richer than that of the related, parallel updated asymmetric exclusion process [(ASEP), v(max)=1]. Such sites exist for v(max)> or =3 and p<p(c) where the phase diagram is qualitatively similar to the p=0 case: there is a free flow and a jamming phase separated by a line of first-order transitions. For p>p(c) an additional maximum current phase separated by second-order transitions occurs like for the ASEP. The density profile decays in the maximum current phase algebraically with an exponent gamma approximately 2 / 3 for all v(max)> or =2 indicating that these models belong to another universality class than the ASEP where gamma=1 / 2.

Single-vehicle data of highway traffic: a statistical analysis

In the present paper, single-vehicle data of highway traffic are analyzed in great detail. By using the single-vehicle data directly, empirical time headway distributions and speed-distance relations can be established. Both quantities yield relevant information about the microscopic states. Several fundamental diagrams are also presented, which are based on time-averaged quantities and compared with earlier empirical investigations. In the remaining part, time-series analyses of the averaged as well as the single-vehicle data are carried out. The results will be used in order to propose objective criteria for an identification of the different traffic states, e.g., synchronized traffic.