Enhancing risk prediction capabilities in patients with carotid artery disease using a 2-level computational approach.

One of the main causes of death worldwide is carotid artery disease, which causes increasing arterial stenosis and may induce a stroke. To address this problem, the scientific community aims to improve our understanding of the underlying atherosclerotic mechanisms, as well as to make it possible to forecast the progression of atherosclerosis. Additionally, over the past several years, developments in the field of cardiovascular modeling have made it possible to create precise three-dimensional models of patient-specific main carotid arteries. The aforementioned 3D models are then implemented by computational models to forecast either the progression of atherosclerotic plaque or several flow-related metrics which are correlated to risk evaluation. A precise representation of both the blood flow and the fundamental atherosclerotic process within the arterial wall is made possible by computational models, therefore, allowing for the prediction of future lumen stenoses, plaque areas and risk prediction. This work presents an attempt to integrate the outcomes of a novel plaque growth model with advanced blood flow dynamics where the deformed luminal shape derived from the plaque growth model is compared to the actual patient-specific luminal model in terms of several hemodynamic metrics, to identify the prediction accuracy of the aforementioned model. Pressure drop ratios had a mean difference of <3%, whereas OSI-derived metrics were identical in 2/3 cases.Clinical Relevance-This establishes the accuracy of our plaque growth model in predicting the arterial geometry after the desired timeline.

TAXINOMISIS: A cloud - based platform for risk profiling and patient specific management of the carotid artery disease.

Carotid Artery Disease is a complex multi-disciplinary medical condition causing strokes and several other disfunctions to individuals. Within this work, a cloud - based platform is proposed for clinicians and medical doctors that provides a comprehensive risk assessment tool for carotid artery disease. It includes three modeling levels: baseline data-driven risk assessment, blood flow simulations and plaque progression modeling. The proposed models, which have been validated through a wide set of studies within the TAXINOMISIS project, are delivered to the end users through an easy-to-use cloud platform. The architecture and the deployment of this platform includes interfaces for handling the electronic patient record, the 3D arterial reconstruction, blood flow simulations and risk assessment reporting. TAXINOMISIS, compared with both similar software approaches and with the current clinical workflow, assists clinicians to treat patients more effectively and more accurately by providing innovative and validated tools.Clinical Relevance - Asymptomatic carotid artery disease is a prevalent condition that affects a significant portion of the population, leading to an increased risk of stroke and other cardiovascular events. Early detection and appropriate treatment of this condition can significantly reduce the risk of adverse outcomes and improve patient outcomes. The development of a software tool to assist clinicians in the assessment and management of asymptomatic patients with carotid artery disease is therefore of great clinical relevance. By providing a comprehensive and reliable assessment of the disease and its risk factors, this tool will enable clinicians to make informed decisions regarding patient management and treatment. The impact of this tool on patient outcomes and the reduction of healthcare costs will be of great importance to both patients and the healthcare system.

Accurate adventitia reconstruction; significant or not in atherosclerotic plaque growth simulationsƒ A comparative study.

A reform in the diagnosis and treatment process is urgently required as carotid artery disease remains a leading cause of death in the world. To this purpose, all computational techniques are now being applied to enhancing the most cutting-edge diagnosis techniques. Computational modeling of plaque generation and evolution is being refined over the past years to forecast the atherosclerotic progression and the corresponding risk in patient-specific carotid arteries. A prerequisite to their implementation is the reconstruction of the precise three-dimensional models of patient-specific main carotid arteries. Even with the most sophisticated algorithms, accurate reconstruction of the arterial vessel is frequently difficult. Furthermore, there are several works of plaque growth modeling that ignore the reconstruction of the artery's outer layer in favor of a virtual one. In this paper, we investigate the importance of an accurate adventitia layer in plaque growth modeling. This is done as a comparative study by implementing a novel plaque growth model in two reconstructed carotid arterial segments using either their realistic or virtual adventitia layer as input. The results indicate that accurate adventitia reconstruction is of minor importance regarding species distributions and plaque growth in carotid segments, which initially did not contain any plaque regions.Clinical Relevance- The findings of this comparative study emphasize the importance of precise adventitia geometry in plaque growth modeling. As a result, this work sets a higher standard for publishing new plaque growth models.

A Machine Learning Model for the prediction of the progression of carotid arterial stenoses.

Atherosclerotic carotid plaque development results in a steady narrowing of the artery lumen, which may eventually trigger catastrophic plaque rupture leading to thromboembolism and stroke. The primary cause of ischemic stroke in the EU is carotid artery disease, which increases the demand for tools for risk stratification and patient management in carotid artery disease. Additionally, advancements in cardiovascular modeling over the past few years have made it possible to build accurate three-dimensional models of patient-specific primary carotid arteries. Computational models then incorporate the aforementioned 3D models to estimate either the development of atherosclerotic plaque or a number of flow-related parameters that are linked to risk assessment. This work presents an attempt to provide a carotid artery stenosis prognostic model, utilizing non-imaging and imaging data, as well as simulated hemodynamic data. The overall methodology was trained and tested on a dataset of 41 cases with 23 carotid arteries with stable stenosis and 18 carotids with increasing stenosis degree. The highest accuracy of 71% was achieved using a neural network classifier. The novel aspect of our work is the definition of the problem that is solved, as well as the amount of simulated data that are used as input for the prognostic model.Clinical Relevance-A prognostic model for the prediction of the trajectory of carotid artery atherosclerosis is proposed, which can support physicians in critical treatment decisions.

Prediction of the atherosclerotic plaque development in carotid arteries; the effect of T-cells.

The carotid artery disease is one of the leading causes of mortality worldwide, as it leads to the progressive arterial stenosis that may result to stroke. To address this issue, the scientific community is attempting not only to enrich our knowledge on the underlying atherosclerotic mechanisms, but also to enable the prediction of the atherosclerotic progression. This study investigates the role of T-cells in the atherosclerotic plaque growth process through the implementation of a computational model in realistic geometries of carotid arteries. T-cells mediate in the inflammatory process by secreting interferon-y that enhances the activation of macrophages. In this analysis, we used 5 realistic human carotid arterial segments as input to the model. In particular, magnetic resonance imaging data, as well as, clinical data were collected from the patients at two time points. Using the baseline data, plaque growth was predicted and correlated to the follow-up arterial geometries. The results exhibited a very good agreement between them, presenting a high coefficient of determination R2=0.64.

Computational modeling of atherosclerotic plaque progression in carotid lesions with moderate degree of stenosis.

Carotid atherosclerotic plaque growth leads to the progressive luminal stenosis of the vessel, which may erode or rupture causing thromboembolism and cerebral infarction, manifested as stroke. Carotid atherosclerosis is considered the major cause of ischemic stroke in Europe and thus new imaging-based computational tools that can improve risk stratification and management of carotid artery disease patients are needed. In this work, we present a new computational approach for modeling atherosclerotic plaque progression in real patient-carotid lesions, with moderate to severe degree of stenosis (>50%). The model incorporates for the first time, the baseline 3D geometry of the plaque tissue components (e.g. Lipid Core) identified by MR imaging, in which the major biological processes of atherosclerosis are simulated in time. The simulated plaque tissue production results in the inward remodeling of the vessel wall promoting luminal stenosis which in turn predicts the region of the actual stenosis progression observed at the follow-up visit. The model aims to support clinical decision making, by identifying regions prone to plaque formation, predict carotid stenosis and plaque burden progression, and provide advice on the optimal time for patient follow-up screening.

SmartFFR, a New Functional Index of Coronary Stenosis: Comparison With Invasive FFR Data.

Aims: In this study, we evaluate the efficacy of SmartFFR, a new functional index of coronary stenosis severity compared with gold standard invasive measurement of fractional flow reserve (FFR). We also assess the influence of the type of simulation employed on smartFFR (i.e. Fluid Structure Interaction vs. rigid wall assumption). Methods and Results: In a dataset of 167 patients undergoing either computed tomography coronary angiography (CTCA) and invasive coronary angiography or only invasive coronary angiography (ICA), as well as invasive FFR measurement, SmartFFR was computed after the 3D reconstruction of the vessels of interest and the subsequent blood flow simulations. 202 vessels were analyzed with a mean total computational time of seven minutes. SmartFFR was used to process all models reconstructed by either method. The mean FFR value of the examined dataset was 0.846 ± 0.089 with 95% CI for the mean of 0.833-0.858, whereas the mean SmartFFR value was 0.853 ± 0.095 with 95% CI for the mean of 0.84-0.866. SmartFFR was significantly correlated with invasive FFR values (RCCTA = 0.86, p CCTA < 0.0001, RICA = 0.84, p ICA < 0.0001, R overall = 0.833, p overall < 0.0001), showing good agreement as depicted by the Bland-Altman method of analysis. The optimal SmartFFR threshold to diagnose ischemia was ≤0.83 for the overall dataset, ≤0.83 for the CTCA-derived dataset and ≤0.81 for the ICA-derived dataset, as defined by a ROC analysis (AUCoverall = 0.956, p < 0.001, AUCICA = 0.975, p < 0.001, AUCCCTA = 0.952, p < 0.001). Conclusion: SmartFFR is a fast and accurate on-site index of hemodynamic significance of coronary stenosis both at single coronary segment and at two or more branches level simultaneously, which can be applied to all CTCA or ICA sequences of acceptable quality.

Fluid Dynamics-Derived Parameters in Coronary Vessels.

Continued development in the field of cardiovascular modeling over the past few years has contributed to the production of precise three-dimensional models of main coronary arteries. Computational fluid dynamic-derived parameters such as smartFFR, a CT-FFR surrogate, and endothelial shear stress (ESS) can be assessed from non-invasive imaging techniques like computed tomography coronary angiography using novel 3D reconstruction methods and can be used to investigate the functional significance of an artery. The investigation of the different flow conditions for the calculation (steady state vs. transient) of the ESS presents that while there is a difference in the final values, it is not statistically significant. ESS in the whole vessel is higher compared to the lesion-specific segments and smartFFR calculated in lesion segment does not reflect accurately the flow capability of the vessel. Higher ESS is present in vessels with <0.85 smartFFR and both parameters are present higher values in vessels with abnormal PET myocardial perfusion imaging.

A deep learning oriented method for automated 3D reconstruction of carotid arterial trees from MR imaging.

The scope of this paper is to present a new carotid vessel segmentation algorithm implementing the U-net based convolutional neural network architecture. With carotid atherosclerosis being the major cause of stroke in Europe, new methods that can provide more accurate image segmentation of the carotid arterial tree and plaque tissue can help improve early diagnosis, prevention and treatment of carotid disease. Herein, we present a novel methodology combining the U-net model and morphological active contours in an iterative framework that accurately segments the carotid lumen and outer wall. The method automatically produces a 3D meshed model of the carotid bifurcation and smaller branches, using multispectral MR image series obtained from two clinical centres of the TAXINOMISIS study. As indicated by a validation study, the algorithm succeeds high accuracy (99.1% for lumen area and 92.6% for the perimeter) for lumen segmentation. The proposed algorithm will be used in the TAXINOMISIS study to obtain more accurate 3D vessel models for improved computational fluid dynamics simulations and the development of models of atherosclerotic plaque progression.

The effect of the degree and location of coronary stenosis on the hemodynamic status of a coronary vessel.

The ongoing advances in the field of cardiovascular modelling during the past years have allowed for the creation of accurate three-dimensional models of the major coronary arteries. The aforementioned 3D models can accurately mimic the human coronary vasculature if they are combined with sophisticated computational fluid dynamics algorithms and shed light to non-trivial issues that concern the clinicians. One of these issues is to define whether a coronary lesion is more dangerous to present with ischemia if it is at a proximal or a distal part of the vessel. In this work, we aim to investigate the aforementioned issue by reconstructing in 3D a coronary arterial model from a healthy subject using Computed Tomography Coronary Angiography images and by editing it to create eight diseased arterial models that contain one or two lesions of different severities. After carrying out the appropriate blood flow simulations using the finite element method, we observed that the distal lesions are more dangerous than the proximal ones in terms of hemodynamic significance. Moreover, the distal severe stenosis (i.e. 70% diameter reduction) present with the highest peak Wall Shear Stress (WSS) values in comparison to the proximal ones.

The effect of the stenosis location at a coronary arterial bifurcation: a parametric study.

The advances in cardiovascular modelling over the past two decades have given the opportunity to create accurate three dimensional models of the coronary vasculature which, combined with advanced computational fluid dynamics algorithms can shed light to intriguing matters that concern clinicians. One of these issues is the presence of a stenosis near bifurcations in one of the major coronary vessels. In this work, we try to shed light on the aforementioned matter by creating a healthy arterial bifurcation reconstructed using the fusion of Optical Coherence Tomography and X-Ray angiography images. The healthy model was edited by adding an artificial stenosis of 50% diameter reduction into three different locations after the bifurcation, thus creating three diseased models. After performing the appropriate blood flow simulations, we observed that the location of the stenosis affects the Wall Shear Stress (WSS) distribution but it does not affect the functional significance of the stenosis itself.

Characterization of functionally significant coronary artery disease by a coronary computed tomography angiography-based index: a comparison with positron emission tomography.

AIMS: To test the hypothesis that virtual functional assessment index (vFAI) is related with regional flow parameters derived by quantitative positron emission tomography (PET) and can be used to assess abnormal vasodilating capability in coronary vessels with stenotic lesions at coronary computed tomography angiography (CCTA). METHODS AND RESULTS: vFAI, stress myocardial blood flow (MBF), and myocardial flow reserve (MFR) were assessed in 78 patients (mean age 62.2 ± 7.7 years) with intermediate pre-test likelihood of coronary artery disease (CAD). Coronary stenoses ≥50% were considered angiographically significant. PET was considered positive for significant CAD, when more than one contiguous segments showed stress MBF ≤2.3 mL/g/min for 15O-water or <1.79 mL/g/min for 13N-ammonia. MFR thresholds were ≤2.5 and ≤2.0, respectively. vFAI was lower in vessels with abnormal stress MBF (0.76 ± 0.10 vs. 0.89 ± 0.07, P < 0.001) or MFR (0.80 ± 0.10 vs. 0.89 ± 0.07, P < 0.001). vFAI had an accuracy of 78.6% and 75% in unmasking abnormal stress MBF and MFR in 15O-water and 82.7% and 71.2% in 13N-ammonia studies, respectively. Addition of vFAI to anatomical CCTA data increased the ability for predicting abnormal stress MBF and MFR in 15O-water studies [AUCccta + vfai = 0.866, 95% confidence interval (CI) 0.783-0.949; P = 0.013 and AUCccta + vfai = 0.737, 95% CI 0.648-0.825; P = 0.007, respectively]. An incremental value was also demonstrated for prediction of stress MBF (AUCccta + vfai = 0.887, 95% CI 0.799-0.974; P = 0.001) in 13N-ammonia studies. A similar trend was recorded for MFR (AUCccta + vfai = 0.780, 95% CI 0.632-0.929; P = 0.13). CONCLUSION: vFAI identifies accurately the presence of impaired vasodilating capability. In combination with anatomical data, vFAI enhances the diagnostic performance of CCTA.

Virtual Functional Assessment of Coronary Stenoses Using Intravascular Ultrasound Imaging: A Proof-of-Concept Pilot Study.

AIMS: We aimed to investigate the performance of virtual functional assessment of coronary stenoses using intravascular ultrasound (IVUS)-based three-dimensional (3D) coronary artery reconstruction against the invasively measured fractional flow reserve (FFR). METHODS AND RESULTS: Twenty-two (22) patients with either typical symptoms of stable angina or a positive stress test, who underwent IVUS and FFR, were included in this study. Five (5) patients presented FFR values lower than the 0.80 threshold, indicating ischaemia. IVUS-based 3D reconstruction and blood flow simulation were performed and the virtual functional assessment index (vFAI) was calculated. A strong correlation between IVUS-based vFAI and FFR was observed (Spearman correlation coefficient [rs]=0.88, p<0.0001). There was a small overestimation of the FFR by the IVUS-based vFAI (mean difference=0.0196±0.037; p=0.023 for difference from zero). All cases with haemodynamically significant stenoses (FFR≤0.8) were correctly categorised by the IVUS-based vFAI (vFAI≤0.8). CONCLUSION: The proposed approach allows the complete and comprehensive assessment of coronary stenoses providing anatomic and physiologic information, pre- and post-intervention, using only an IVUS catheter without the use of a pressure wire.

Noninvasive CT-based hemodynamic assessment of coronary lesions derived from fast computational analysis: a comparison against fractional flow reserve.

OBJECTIVES: Application of computational fluid dynamics (CFD) to three-dimensional CTCA datasets has been shown to provide accurate assessment of the hemodynamic significance of a coronary lesion. We aim to test the feasibility of calculating a novel CTCA-based virtual functional assessment index (vFAI) of coronary stenoses > 30% and ≤ 90% by using an automated in-house-developed software and to evaluate its efficacy as compared to the invasively measured fractional flow reserve (FFR). METHODS AND RESULTS: In 63 patients with chest pain symptoms and intermediate (20-90%) pre-test likelihood of coronary artery disease undergoing CTCA and invasive coronary angiography with FFR measurement, vFAI calculations were performed after 3D reconstruction of the coronary vessels and flow simulations using the finite element method. A total of 74 vessels were analyzed. Mean CTCA processing time was 25(± 10) min. There was a strong correlation between vFAI and FFR, (R = 0.93, p < 0.001) and a very good agreement between the two parameters by the Bland-Altman method of analysis. The mean difference of measurements from the two methods was 0.03 (SD = 0.033), indicating a small systematic overestimation of the FFR by vFAI. Using a receiver-operating characteristic curve analysis, the optimal vFAI cutoff value for identifying an FFR threshold of ≤ 0.8 was ≤ 0.82 (95% CI 0.81 to 0.88). CONCLUSIONS: vFAI can be effectively derived from the application of computational fluid dynamics to three-dimensional CTCA datasets. In patients with coronary stenosis severity > 30% and ≤ 90%, vFAI performs well against FFR and may efficiently distinguish between hemodynamically significant from non-significant lesions. KEY POINTS: Virtual functional assessment index (vFAI) can be effectively derived from 3D CTCA datasets. In patients with coronary stenoses severity > 30% and ≤ 90%, vFAI performs well against FFR. vFAI may efficiently distinguish between functionally significant from non-significant lesions.

The effect of error propagation in the 3D reconstruction of coronary segments using CTCA images on crucial hemodynamic parameters.

The development of 3D reconstruction methods of the coronary vasculature has gained substantial ground during the past years. The accurate 3D reconstruction is of utmost importance because the propagation of errors caused by either equipment calibration errors, human errors or other error sources can seriously affect the computation of critical hemodynamic parameters such as Endothelial Shear Stress, intracoronary pressures etc. In this work, we present a study on how the 3D reconstruction error can affect the subsequent blood flow simulations in 3D coronary arterial models. Eight arterial segments were reconstructed, creating the control models and were then modified in order to create an underestimated and an overestimated model of the same segment using a 5% error. Cross-sectional ESS values, as well as, smartFFR values were calculated to examine the effect of the reconstruction error. As it was expected, the underestimated models presented with higher ESS values and lower smartFFR values, whereas the overestimated models presented with lower ESS values and higher smartFFR values, respectively.

A new method for the 3D reconstruction of coronary bifurcations pre and post the angioplasty procedure using the QCA.

The aim of this study is to propose a new semi-automated method for three-dimensional (3D) reconstruction of coronary bifurcations arteries using X-ray Coronary Angiographies (CA). Considering two monoplane angiographic views as the input data, the method is based on a four-step approach. In the first step, the image pre-processing and the vessel segmentation is performed. In the second step the 3D centerline is reconstructed by implementing the back-projection algorithm. In the third step, the lumen borders are reconstructed around the centerline to result to the fourth step, during which the 3D point cloud of the side branch is adjusted to the main branch, to produce the final 3D model of the coronary bifurcation artery. Imaging data from seven patients (pre and post-stenting) were reconstructed in the 3D space. The validation of the proposed methodology was based on the comparison of the 3D model with the 2D CA. Blood flow simulations were performed both for the vessels before and after the angioplasty procedure. Decreased Endothelial Shear Stress (ESS) values were observed for the vessels after the Percutaneous Transluminal Coronary Intervention (PTCI).

A comparison of three multimodality coronary 3D reconstruction methods.

The assessment of the severity of arterial stenoses is of utmost importance in clinical practice. Several image modalities invasive and non-invasive are nowadays available and can be utilized for the 3-dimensional (3D) reconstruction of the arterial geometry. Following our previous study, the present study was conducted to further strengthen the evaluation of three reconstruction methodologies, namely: (i) the Quantitative Coronary Analysis (QCA), (ii) the Virtual Histology Intravascular Ultrasound VH-IVUS-Angiography hybrid method and (iii) the Coronary Computed Tomography Angiography (CCTA). Data from 13 patients were employed to perform a quantitative analysis using specific metrics, such as, the Mean Wall Shear Stress (mWSS), the Minimum Lumen diameter (MLD), the Reference Vessel Diameter (RVD), the Degree of stenosis (DS%), and the Lesion length (LL). A high correlation was observed for the mWSS metric between the three reconstruction methods, especially between the QCA and CCTA (r=0.974, P<; 0.001).

Comparison of 3D reconstruction methods based on different cardiovascular imaging: a study of multimodality reconstruction method.

Coronary arterial imaging and the assessment of the severity of arterial stenoses can be achieved with several modalities classified mainly according to their invasive or noninvasive nature. These modalities can be further utilized for the 3-dimensional (3D) reconstruction of the arterial geometry. This study aims to determine the prediction performance of atherosclerotic disease progression using reconstructed arteries from three reconstruction methodologies: Quantitative Coronary Analysis (QCA), Virtual Histology Intravascular Ultrasound (VH)-IVUS-Angiography fusion method and Coronary Computed Tomography Angiography (CCTA). The accuracy of the reconstruction methods is assessed using several metrics such as Minimum lumen diameter (MLD), Reference vessel diameter (RVD), Lesion length (LL), Diameter stenosis (DS%) and the Mean wall shear stress (WSS). Five patients in a retrospective study who underwent X-ray angiography, VH-IVUS and CCTA are used for the method evaluation.

Art care: A multi-modality coronary 3D reconstruction and hemodynamic status assessment software.

BACKGROUND: Due to the incremental increase of clinical interest in the development of software that allows the 3-dimensional (3D) reconstruction and the functional assessment of the coronary vasculature, several software packages have been developed and are available today. OBJECTIVE: Taking this into consideration, we have developed an innovative suite of software modules that perform 3D reconstruction of coronary arterial segments using different coronary imaging modalities such as IntraVascular UltraSound (IVUS) and invasive coronary angiography images (ICA), Optical Coherence Tomography (OCT) and ICA images, or plain ICA images and can safely and accurately assess the hemodynamic status of the artery of interest. METHODS: The user can perform automated or manual segmentation of the IVUS or OCT images, visualize in 3D the reconstructed vessel and export it to formats, which are compatible with other Computer Aided Design (CAD) software systems. We employ finite elements to provide the capability to assess the hemodynamic functionality of the reconstructed vessels by calculating the virtual functional assessment index (vFAI), an index that corresponds and has been shown to correlate well to the actual fractional flow reserve (FFR) value. RESULTS: All the modules of the proposed system have been thoroughly validated. In brief, the 3D-QCA module, compared to a successful commercial software of the same genre, presented very good correlation using several validation metrics, with a Pearson's correlation coefficient (R) for the calculated volumes, vFAI, length and minimum lumen diameter of 0.99, 0.99, 0.99 and 0.88, respectively. Moreover, the automatic lumen detection modules for IVUS and OCT presented very high accuracy compared to the annotations by medical experts with the Pearson's correlation coefficient reaching the values of 0.94 and 0.99, respectively. CONCLUSIONS: In this study, we have presented a user-friendly software for the 3D reconstruction of coronary arterial segments and the accurate hemodynamic assessment of the severity of existing stenosis.

A novel hybrid approach for reconstruction of coronary bifurcations using angiography and OCT.

The aim of this study is to present a new method for three-dimensional (3D) reconstruction of coronary bifurcations using biplane Coronary Angiographies and Optical Coherence Tomography (OCT) imaging. The method is based on a five step approach by improving a previous validated work in order to reconstruct coronary arterial bifurcations. In the first step the lumen borders are detected on the Frequency Domain (FD) OCT images. In the second step a semi-automated method is implemented on two angiographies for the extraction of the 2D bifurcation coronary artery centerline. In the third step the 3D path of the bifurcation artery is extracted based on a back projection algorithm. In the fourth step the lumen borders are placed onto the 3D catheter path. Finally, in the fifth step the intersection of the main and side branches produces the reconstructed model of the coronary bifurcation artery. Data from three patients are acquired for the validation of the proposed methodology and the results are compared against a reconstruction method using quantitative coronary angiography (QCA). The comparison between the two methods is achieved using morphological measures of the vessels as well as comparison of the wall shear stress (WSS) mean values.