New Mathematical Model for the Surface Area of the Left Ventricle by the Truncated Prolate Spheroid

Domingues, José Sérgio; Vale, Marcos de Paula; Martinez, Carlos Barreira

doi:10.1155/2017/6981515

Cited by 8 publications

(7 citation statements)

References 19 publications

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“…We first used mathematical models of the idealized LV geometry to study the effect of area vs. volume estimates on LVEF. Other researchers proposed several mathematical approximations of the LV geometry: cylindrical 3 , truncated prolate spheroid (TPS) 4 , and paraboloid 5 models were published in prior literature. Of these, the TPS and paraboloid models matched the LV shapes from our US image dataset more closely, so they were used for geometric simulations to characterize and describe the left ventricle.…”

Section: Methodsmentioning

confidence: 99%

Left ventricular ejection fraction assessment: unraveling the bias between area- and volume-based estimates

Liu

Peck

Dangi

et al. 2019

Medical Imaging 2019: Ultrasonic Imaging and Tomography

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Calculating left ventricular ejection fraction (LVEF) accurately is crucial for the clinical diagnosis of cardiac disease, patient management, or other therapeutic treatment decisions. The measure of a patient’s LVEF often affects their candidacy for cardiovascular intervention. Ultrasound (US) is one of the imaging modalities used to non-invasively assess LVEF, and it is the most common and least expensive. Despite the advances in 3D US transducer technology, only limited US machines are equipped with such transducer to enable true 3D US image acquisition. Thus, 2D US images remain to be widely used by cardiologists to image the heart and their interpretation is inherently based on two dimensional information immediately available in the US images. Past knowledge indicates that visual estimation of the LVEF based on the area changes of the left ventricle blood pool between systole and diastole (as depicted in 2D ultrasound images) may significantly underestimate the ejection fraction, rendering some patients as suitable candidates for potentially unnecessary interventions or implantation of assistive devices. True LVEF should be calculated based on changes in LV volumes, but equipment and time constraint limit the current technique to assess 3D LV geometry. The estimation of the systolic and diastolic blood pool volumes requires additional work beyond a simple visual assessment of the blood pool area changed in the 2D US images. Specifically, following the manual segmentation of the endocardial LV border, 3D volume would be assessed by reconstructing a LV volume from multiple tomographic views. In this work, we leverage on two idealized mathematical models of the left ventricle — a truncated prolate spheroid (TPS) and a paraboloid geometric model to characterize the LV shape according to the range of possible dimensions gathered from our patient-specific multi-plane US imaging data. The objective of this work is to reveal the necessity of calculating LVEFs based on volumes by showing that LVEF estimated using area changes underestimate the LVEF computed using volume changes. Additionally, we present a method to reconstruct the LV volume from 2D blood pool representations identified in the multi-plane 2D US images and use the reconstructed 3D volume throughout the cardiac cycle to estimate the LVEF. Our preliminary results show that the area-based LVEF significantly underestimates the true volume-based LVEF across both the theoretical simulations using idealized geometric models of the LV shape, as well as the patient-specific US imaging data. Specifically, both the TPS and paraboloid model showed an area-based LVEF of 41.3 ± 4.7% and a volume-based LVEF of 55.4 ± 5.7%, while the US image data showed an area-based LVEF of 34.7 ± 11.9% and a volume-based LVEF of 48.0 ± 14.0%. In summary, the area-based LVEF estimations using both the idealized TPS and paraboloid models was 14.1% lower than volume- based LVEF calculations using corresponding models. Furthermore, the area-based LVEF based on reconstructed LV volumes...

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Section: Methodsmentioning

confidence: 99%

Left ventricular ejection fraction assessment: unraveling the bias between area- and volume-based estimates

Liu

Peck

Dangi

et al. 2019

Medical Imaging 2019: Ultrasonic Imaging and Tomography

View full text Add to dashboard Cite

show abstract

“…We first used mathematical models of the idealized LV geometry to study the difference between area- and volume- based estimations of LVEF. Researchers previously proposed several mathematical approximations of the LV geometry: cylindrical [5], truncated prolate spheroid (TPS) [6], and paraboloid [7] models. Of these, the TPS and paraboloid models matched more closely to the LV shapes observed in our US imaging data, so they were used for geometric simulations to characterize and describe the LV.…”

Section: Methodsmentioning

confidence: 99%

Left Ventricular Ejection Fraction: Comparison Between True Volume-Based Measurements and Area-Based Estimates

Liu

Peck

Dangi

et al. 2018

2018 IEEE Western New York Image and Signal Processing Workshop (WNYISPW)

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Left ventricular ejection fraction (LVEF) is a critical measure of cardiac health commonly acquired in clinical practice, which serves as the basis for cardiovascular therapeutic treatment. Ultrasound (US) imaging of the heart is the most common, least expensive, reliable and non-invasive modality to assess LVEF. Cardiologists, in practice, persistently use 2D US images to provide visual estimates of LVEF, which are based on 2D information embedded in the US images by examining the area changes in LV blood pool between diastole and systole. There has been some anecdotal evidence that visual estimation of the LVEF based on the area changes of the LV blood pool significantly underestimate true LVEF. True LVEF should be calculated based on changes in LV volumes between diastole and systole. In this project, we utilized both idealized models of the LV geometry — a truncated prolate spheroid (TPS) and a paraboloid model — to represent the LV anatomy. Cross-sectional areas and volumes of simulated LV shapes using both models were calculated to compare the LVEF. Further, a LV reconstruction algorithm was employed to build the LV blood pool volume in both systole and diastole from multi-plane 2D US imaging data. Our mathematical models yielded an area-based LVEF of 41 4.7% and a volume-based LVEF of 55 ±5.7%, while the 3D recon-struction model showed an area-based LVEF of 35 11.9% and a volume-based LVEF of 48.0 ± 14.0%. In summary, the area-based LVEF using all three models ±underestimate the volume-based LVEF using corresponding models by 13% to 14%. This preliminary study confirms both mathematically and empirically that area-based LVEF estimates indeed underestimate the true volume-based LVEF measurements and suggests that true volumetric measurements of the LV blood pool must be computed to correctly assess cardiac LVEF.

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“…Left ventricles can have innumerable shapes that pose challenges for developing a comprehensive model to encompass the variations in their geometries. A few geometric models such as cylindrical [4], truncated prolate spheroid [3], and paraboloid [15] were published to mathematically describe an LV shape, but they are not sufficiently accurate to represent patient-specific anatomy. Statistical shape models (SSMs) have been employed by several researchers in the field of cardiology to capture the characteristics of LV shapes and endocardial wall motion from a population of subjects.…”

Section: Introductionmentioning

confidence: 99%

A Statistical Shape Model Approach for Computing Left Ventricle Volume and Ejection Fraction Using Multi-plane Ultrasound Images

et al. 2019

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Assessing the left ventricular ejection fraction (LVEF) accurately requires 3D volumetric data of the LV. Cardiologists either have no access to 3D ultrasound (US) systems or prefer to visually estimate LVEF based on 2D US images. To facilitate the consistent estimation of the end-diastolic and end-systolic blood pool volume and LVEF based on 3D data without extensive complicated manual input, we propose a statistical shape model (SSM) based on 13 key anchor points-the LV apex (1), mitral valve hinges (6), and the midpoints of the endocardial contours (6)-identified from the LV endocardial contour of the tri-plane 2D US images. We use principal component analysis (PCA) to identify the principle modes of variation needed to represent the LV shapes, which enables us to estimate an incoming LV as a linear combination of the principle components (PC). For a new, incoming patient image, its 13 anchor points are projected onto the PC space; its shape is compared to each LV shape in the SSM based on Mahalanobis distance, which is normalized with respect to the LV size, as well as direct vector distance (i.e., PCA distance), without any size normalization. These distances are used to determine the weight each training shape in the SSM contributes to the description of the new patient LV shape. Finally, the new patient's LV systolic and diastolic volumes are estimated as the weighted average of the training volumes in the SSM. To assess our proposed method, we compared the SSM-based estimates of diastolic, systolic, stroke volumes, and LVEF with those computed directly from 16 tri-plane 2D US imaging datasets using the GE Echo-Pac PC clinical platform. The estimated LVEF based on Mahalanobis distance and PCA distance were within 6.8% and 1.7% of the reference LVEF computed using the GE Echo-Pac PC clinical platform.

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New Mathematical Model for the Surface Area of the Left Ventricle by the Truncated Prolate Spheroid

Cited by 8 publications

References 19 publications

Left ventricular ejection fraction assessment: unraveling the bias between area- and volume-based estimates

Left ventricular ejection fraction assessment: unraveling the bias between area- and volume-based estimates

Left Ventricular Ejection Fraction: Comparison Between True Volume-Based Measurements and Area-Based Estimates

A Statistical Shape Model Approach for Computing Left Ventricle Volume and Ejection Fraction Using Multi-plane Ultrasound Images

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