Computational Anatomy As a Driver of Understanding Structural and Functional Cardiac Remodeling

Computational anatomy as a driver of understanding structural and functional cardiac remodeling.

Gabriel Bernardino

TESI DOCTORAL UPF / 2019

THESIS SUPERVISORS Bart Bijnens, Miguel Angel González Ballester and Mathieu De Craene

Department Engineering and Information and Communication Technologies Academic Coordination Unit

The cover artwork is a part of a photographic reproduction, available in Wikimedia, of a public domain domain painting: Anatomy of the heart by Enrique Simonet (1890), currently deposited in Museo de Málaga, Málaga, Spain.

III

Acknowledgements

This has been a long wandering, which I couldn’t have endured alone. All of this has been possible thanks to my supervisors: Bart, Miguel Angel and Mathieu. They helped me by putting order in chaos (and sometimes also chaos into order). Their constant guidance, advice and help have shaped this thesis. The quality of this work reflects their quality as supervisors. A very special thanks to my colleagues in UPF, partners in coffees, merendolas, beers, aperols and wine. They have made the hard moments easier to cope with, and our scientific discussions provided a lot of ideas and insights. I have to thank the people of Philips for their hospitality and the pauses gourmandes. I would like to thank the clinical collaborators, at the CHU Caen, Hospi- tal Clínic and Maternitat. Without them this thesis would be useless. Their patience explaining the most basic of the concepts of medicine and clinical cardiology has been crucial for this thesis. I also want to thank them for their time they took from their busy schedules to understand and discuss my results. A very special thanks to Eric and Amir of the CHU Caen who hosted me during a month. Finally, I want to thank my friend and family for all the support and understanding in the difficult times.

V VI Abstract

Cardiac structural and functional remodelling, induced by altered or adverse working conditions, has been extensively reported in the literature. The quantification and interpretation of such remodelling is still an ongoing research topic, and the mechanisms and lasting effects are not completely understood. A difficulty in understanding remodelling is that, even if, at cellular level, each cell acts independently, it is the organ-level aggregation that will ultimately determine the cardiac efficiency. Given that remodelling is driven by regional stimuli, it will not be homogeneous but will express as complex segmental patterns. The assessment through traditional methods is challenging due to the focus on global quantification of the current clinical measurements, as well as the large heterogeneity between the responses of individuals. We present a statistical shape analysis (SSA) framework to identify the expected appearance of regional shape remodelling. We use a pathological and control population to build a model that identifies populational differences in shape. This model consists of a dimensionality reduction step (PCA and PLS) and a classification step (logistic regression). Given the large natural shape variability present in the ventricles, that can create a confounding effect if there is an imbalance of the demographics, we applied and tested methods to account for that variability: adding the confounders as covariates in the classification model (adjustment) and building a model that predicts shape from the confounders, and analysing the regression residuals (confounder deflation). We show that these methods are able to correct for demographic imbalances. The previous methodology was applied to two distinct cardiac magnetic resonance imaging (MRI) datasets: one with triathletes and another one with small-for-gestational age (SGA) individuals, which were compared to a control population to obtain the remodelling. SGA is a syndrome occurring at foetal stage where the individual has an impaired growth during foetal development. It is hypothesized that it translates to a higher cardiovascular risk during seniority. Using our framework, we were able to identify that SGA presented a more curved base in the right ventricle (RV) compared with controls, especially in smokers and overweight SGA individuals. Athletes were also compared to controls in order to characterize endurance-activities-related remodelling. We identified a pattern that was comprised of the already known athlete’s remodelling: an increase of the left ventricular (LV) volume size and mass, but also an increase of RV volume localized in the outflow. The found quantification of the athletic remodelling was associated to a better cardiovascular response during a

VII maximal stress test. Finally, we explore alternatives to analyse regional shape of the RV that did rely on the point-to-point registration when the imaging modality is noisy and with low contrast, such as 3D echocardiography. We implemented a mesh independent volumetric parcellation of the RV in three parts: inlet, outﬂow and apex. The parcellation was deﬁned on the surface using the geodesic distances to the apex, tricuspid and pulmonary valve, and was propagated to the cavity using the Laplace equation. We tested the reproducibility of the parcellation and found an acceptable mean error ( 8%) in the intraobserver test, and a higher (>14%) for the interobserver. We validated the method in a synthetic-remodelling generated dataset and found that our method was accurate for capturing circumferential dilation but less suited for longitudinal elongations.

VIII IX Resumen

El remodelado cardiaco ha sido descrito extensivamente en la literatura. Este remodelado, que afecta tanto la estructura como la función, es inducido por una alteración de las condiciones de trabajo del corazón. Su cuantificación e interpretación es todavía un tema en investigación y sus mecanismos y efectos no han sido todavía completamente entendidos. Una dificultad para entender dicho remodelado es que, aunque a nivel celular cada célula actúa de manera independiente, es la agregación a nivel de órgano la que en ultima instancia determina la eficiencia cardíaca. Dado que el remodelado esta dirigido por estímulos regionales, éste no resultará en una reacción homogénea sino en complejos patrones seg- mentales. La evaluación con los métodos tradicionales es complicada ya que las medidas clínicas se centran en cuantificación de variables globa- les. Presentamos un sistema de análisis estadístico de forma (SSA) que permite identificar patrones esperados de remodelado estructural y regional. Usamos una población patológica y otra de control para construir un modelo que identifica diferencias de forma. Este modelo consiste en una reducción de dimensionalidad (PCA y PLS) seguida de una clasificación (regresión logística). Debido a la gran variabilidad estructural presente en los ventrículos, un desequilibrio en los demográficos de las poblaciones puede crear un factor de confusión, hemos aplicado y testeado dos méto- dos para ajustar por esa variabilidad: el primero añade los posibles factores de confusión como covariables en el modelo de clasificación (ajuste) y el segundo construye un modelo que predice la forma a partir de estos factores de confusión y analiza los residuos de regresión de dicho modelo (deflación de los factores de confusión). Mostramos que estos métodos son capaces de corregir desequilibrios en los demográficos. Aplicamos la metodología anterior a dos bases de datos de imagen por resonancia magnética: uno de triatletas y otro de individuos pequeños- para-su-edad-gestacional (SGA), a los que comparamos con una pobla- ción de controles para obtener el patrón de remodelado. SGA es un sín- drome que consiste en una restricción al crecimiento durante la etapa fetal. Se ha hipotetizado que los individuos con SGA tienen una mayor propensión a problemas cardiovascular durante la tercera edad. Usando nuestro sistema, encontramos que los SGA tienen una base del ventrícu- lo derecho (RV) más curvada, especialmente en SGA fumadores o con sobrepeso. Los atletas fueron también comparados con los controles para caracterizar el remodelado relacionado con la práctica de deportes de resistencia. Identificamos un remodelado concorde con la literatura: un in-

X cremento del ventrículo izquierdo (LV) tanto en tamaño como en masa, pero también un incremento del volumen del RV focalizado en el infun- díbulo. Asociamos la cuantificación de dicho remodelado con una mejor respuesta cardiovascular durante una prueba de ejercicio máxima. Finalmente, exploramos alternativas al análisis regional de forma del RV que no usasen el registro punto a punto para cuando la modalidad de imagen fuera ruidosa y con poco contraste, como es el caso de la ecocardiografía 3D. Implementamos un método de parcelación volumétri- ca independiente del mallado que divide el RV en 3 partes: apical, inlet y outflow. La parcelación fue definida usando las distancias geodésicas al apex, tricúspide y válvula pulmonar, y se propago a la cavidad usando la ecuación de Laplace. Probamos la reproducibilidad de la parcelación y encontramos un error medio intraobservador aceptable (8 %), pero mas error (>14 %) en el caso del interobservador. También validamos el méto- do usando una base de datos de remodelado generado sintéticamente y encontramos que nuestro método era exacto para analizar crecimientos circunferenciales, pero no para elongaciones longitudinales.

The only attitude worthy of a superior man is to persist in an activity he recognizes is useless, to observe a discipline he knows is sterile, and to apply certain norms of philosophical and metaphysical thought that he considers utterly inconsequential.

Fernando Pessoa, Livro do Desassossego.

XIII

Contents

List of ﬁgures XX

List of tables XXII

1. INTRODUCTION 1 1.1. Motivation ...... 1 1.2. Cardiac remodelling ...... 1 1.2.1. Morphological remodelling ...... 2 1.2.2. Functional remodelling ...... 3 1.3. Medical imaging ...... 5 1.4. Computational anatomy ...... 6 1.5. Thesis structure ...... 9

2. HANDLING CONFOUNDING VARIABLES IN STATISTICAL SHAPE ANALYSIS - APPLICATION TO CARDIAC REMODELLING 11 2.1. Introduction ...... 11 2.2. Methodology ...... 14 2.2.1. Atlas construction ...... 14 2.2.2. Confounding deflation ...... 15 2.2.3. Classification ...... 18 2.3. Experimental setup ...... 19 2.3.1. Clinical dataset ...... 19 2.3.2. Automatic measurements ...... 20 2.3.3. BMI-based downsampling ...... 21 2.4. Results ...... 22 2.4.1. Dimensionality reduction ...... 22 2.4.2. Athletic model ...... 23 2.4.3. BMI model ...... 26 2.4.4. Confounding adjustment ...... 28 2.4.5. Confounding deflation ...... 29 2.5. Discussion ...... 33

XV 2.6. Conclusion ...... 35

3. VOLUMETRIC PARCELLATION OF THE RIGHT VENTRICLE FOR REGIONAL GEOMETRIC AND FUNCTIONAL ASSESSMENT 37 3.1. Introduction ...... 37 3.2. Methodology ...... 40 3.2.1. Data acquisition ...... 40 3.2.2. Parcellation of the right ventricle ...... 40 3.2.3. Local and global anatomic frame of reference . . . . 43 3.2.4. Strain as a value to express local deformation . . . . 45 3.2.5. Synthetic regional remodeling patterns generation . 45 3.2.6. Global remodelling ...... 49 3.3. Validation ...... 49 3.3.1. Reproducibility of the 3D models ...... 49 3.3.2. Reproducibility of the parcellation method ...... 50 3.3.3. Validation of the parcellation method ...... 50 3.4. Results ...... 51 3.4.1. Reproducibility of the 3D models ...... 51 3.4.2. Reproducibility of the parcellation method ...... 55 3.4.3. Validation of the parcellation method ...... 56 3.5. Discussion ...... 59 3.6. Conclusion ...... 60

4. THREE-DIMENSIONAL REGIONAL BI-VENTRICULAR SHAPE REMODELLING IS ASSOCIATED WITH EXERCISE CAPACITY IN ENDURANCE ATHLETES 61 4.1. Introduction ...... 61 4.2. Methods ...... 62 4.2.1. Population ...... 62 4.2.2. Echocardiographic measurements ...... 63 4.2.3. Exercise Test ...... 63 4.2.4. MRI study ...... 64 4.2.5. Statistical shape analysis ...... 64 4.2.6. Statistical methods ...... 65 4.3. Results ...... 65 4.3.1. Population characteristics ...... 65 4.3.2. Athletic shape remodelling ...... 66 4.3.3. Exercise response ...... 71 4.3.4. Validation ...... 72 4.4. Discussion ...... 73 4.4.1. Limitations ...... 75 4.5. Conclusion ...... 75

XVI 5. REDUCED EXERCISE CAPACITY AND EXAGGERATED IMPACT OF CONVENTIONAL RISK FACTORS ON CARDIAC FUNCTION IN ADULTS BORN SMALL-FOR-GESTATIONAL AGE 77 5.1. Introduction ...... 77 5.2. Methods ...... 79 5.2.1. Study design ...... 79 5.2.2. Echocardiography ...... 79 5.2.3. Cardiovascular magnetic resonance ...... 80 5.2.4. Ventricular shapes ...... 81 5.2.5. Cardiopulmonary exercise testing ...... 81 5.2.6. Sample size calculation ...... 81 5.2.7. Statistical analysis ...... 82 5.3. Results ...... 83 5.3.1. Perinatal data and characteristics at recruitment . . 83 5.3.2. Baseline cardiac structure and function ...... 85 5.3.3. Exercise capacity ...... 90 5.3.4. Effect of smoking and overweight on cardiac remodelling among the study groups ...... 90 5.4. Discussion ...... 92 5.5. Conclusion ...... 98

6. CONCLUSION 99 6.1. Summary ...... 99 6.2. Methodological future work ...... 100 6.3. Clinical future work ...... 101

XVII

List of Figures

1.1. Concentric and eccentric remodelling ...... 3 1.2. Stroke volume, cardiac output and LV dimensions during exercise...... 4 1.3. Number of procedures in the different modalities at Chil- dren’s Hospital Boston...... 5 1.4. Segmented biventricular 3D model personalised from MRI .6 1.5. The heart as seen by different modalities...... 7

2.1. Schema of the SSA framework ...... 14 2.2. Comparison of different DR methods and confounding adjustment...... 24 2.3. Most discriminating shape patterns ...... 25 2.4. Effect of adjustment in the measurement response . . . . . 25 2.5. Close-up on the right ventricular free wall of the different models predicting the athletic remodelling shape pattern . . 26 2.6. Representative shapes of the BMI model ...... 27 2.7. Measurement response of the BMI-related shape changes. 28 2.8. Stability of adjustment in BMI-imbalanced datasets. . . . . 29 2.9. Measurement response of the models trained on the downsampled population ...... 30 2.10.Representative shapes of models trained on the downsampled population ...... 31 2.11.Stability analysis of the confounding deﬂation method trained with a non-downsampled population...... 32 2.12.Measurements response of the shape pattern found with the athlete-downsampled data...... 32 2.13.Effect of the population used to train the confounder deﬂa- tion model on the discriminative pattern stability...... 33 2.14.Distribution of the dummy variable and its dot product with the athletic remodelling shape pattern ...... 33

3.1. Steps to generate the volumetric partition...... 42

XIX 3.2. Circumferential and longitudinal directions deﬁned in each triangle of a sample RV mesh ...... 44 3.3. Local frames of reference and dihedral angles...... 46 3.4. Mean point-to-point registration error for each node on the interobserver and intraobserver reproducibility test...... 52 3.5. Mean point-to-surface distance for each node on the interobserver and intraobserver reproducibility test...... 53 3.6. The two generated 3D models on the test/retest experiment and their parcellations...... 54 3.7. Generated meshes with the local remodelling method . . . 57 3.8. Generated RV meshes for the global remodelling...... 58 3.9. Volume response to a global remodelling...... 58

4.1. Sample MRI segmentation of an athlete...... 68 4.2. Sample MRI segmentation of a control...... 69 4.3. Most discriminant shape mode that distinguishes the RV from athletes and controls...... 70 4.4. LOO-CV ROC of the model which considers shape and confounders, compared to a simple model that only considers the confounders...... 72 4.5. Quantiﬁcation of the athletic remodelling score for both male and female athletes...... 73

5.1. Baseline cardiac shape of the study populations (non-stressed) 86 5.2. Workload and peak VO2 and its relationship with LV mass and remodelling score in the study populations ...... 91 5.3. Left and right ventricular 3D meshes generated by CMR from control and SGA datasets among overweight and smoking populations respectively...... 93 5.4. Illustrative CMR examples in an over weighted and smoker control and SGA individuals...... 94 5.5. Regression lines showing an inverse relationship between the performance in the exercise test and ventricular remodelling score in smokers and overweight subpopulations. . . 94

XX List of Tables

2.1. Population demographics of the study participants. Athletes have a lower heart rate and weight than controls ...... 21 2.2. Results of DR model selection ...... 23 2.3. 10-fold CV log-loss results of different dimensionality reduction (DR) methods parameters, ...... 23

3.1. Intra and inter-observer variability of the segmentations and node positions...... 51 3.2. Intra- and inter-observer variability of the segmental and total end-diastolic volumes and EF ...... 55 3.3. Regional volumes resulting from two consecutive acquisitions of the same patient...... 55 3.4. Volume response to a global remodelling ...... 56

4.1. Demographics and echocardiographic functional measurements of the population...... 66 4.2. Comparison of the MRI- based measurements between athletes and controls...... 67 4.3. Values at rest, after exercise and percent ratio of function and geometry echocardiographic and ergospirometric measurements in athletes...... 67 4.4. MVR results between the shape remodelling score and different functional parameters during exercise...... 71 4.5. Results of the linear regression model predicting peak VO2 and the logistic model predicting athletes...... 73 4.6. Correlation coefﬁcient between the different classical indices used to quantify athletic morphological remodelling and our remodelling score...... 74

5.1. Perinatal and current baseline characteristics of the study population ...... 84

XXI 5.2. Perinatal characteristics and current laboratory results of the study population...... 85 5.3. Echocardiographic results of the left heart study populations 87 5.4. Echocardiographic results of the left heart study populations 88 5.5. Cardiovascular magnetic resonance results of the study populations...... 89 5.6. Results at peak exercise in the study populations...... 90

XXII Acronyms

AUC area under curve

BMI body mass index

BSA body surface area

CO cardiac output

CV cross validation

DR dimensionality reduction

ED end diastolic

EF ejection fraction

ES end systolic

HCM hypertrophic cardiomyopaty

HR heart rate

IUGR intrauterine growth restriction

LH left heart

LR logistic regression

LV left ventricle

LVGLS left ventricular global longitudinal strain

MAPSE mitral annular systolic excurse

MRI magnetic resonance imaging

MVR multivariate regression

PCA principal component analysis

PDM point distribution model

PER pulmonary extraction rate

PLS partial least squares

RA right atria

XXIII RH right heart

ROC receiver operating characteristic

RV right ventricle

RVOT right ventricular outﬂow tract

SA short axis

SGA small-for-gestational age

SSA statistical shape analysis

SV stroke volume

TAPSE tricuspid annular systolic excurse

VCO2 carbon dioxide production

VO2 oxygen uptake

XXIV Chapter 1

INTRODUCTION

1.1. Motivation

The aim of this thesis is to develop and apply computational tools to analyse, understand and quantify cardiac structural remodelling patterns. The heart experiences changes to adjust to altered loading conditions in both a chronic and acute manner. The adaptations occur to maintain a certain number of (functional) parameters within a physiological range, but, while beneﬁcial at some point, sometimes they have side effects that can become adverse in the long-term. The adaptation mechanisms show large heterogeneity: different individuals may remodel differently to the same stimulus. Understanding and quantifying the remodelling and its effects is relevant for diagnosis and prognosis, allowing to identify individuals at risk of having adverse remodelling. Despite the success of computational anatomy in the biomedical engineering community, analysis of remodelling in the clinic relies heavily on single-measurement based techniques, that are ill-suited to discriminate more subtle or complex regional patterns. In this thesis, we develop and use computational anatomy techniques to study subtle regional cardiac morphological remodelling and its association to functional changes.

1.2. Cardiac remodelling

As stated above, the heart is not the same through a whole life and has many compensatory mechanisms to respond to changes in the heart/body. These changes can be acute, like increasing heart rate to increase blood delivery during exercise, or can be chronic, like the thickening of the myocardium in the left ventricle (LV) of hypertensive patients. Overall, these

1 mechanisms try to maintain a sufﬁcient cardiac output (CO) to provide enough oxygen to the system, but also maintain the wall stress low so the cardiac myocytes don’t get damaged and die.

1.2.1. Morphological remodelling

In the past, morphological/structural remodelling has been simpliﬁed as a dilatation (or eccentric) remodelling reaction as a result of volume overload, and an increase of myocardial mass (concentric) induced by pressure overload (Grossman et al., 1975). However, this oversimpliﬁ- cation, often referring to the whole ventricle, does not match reality: the remodelling process at cellular level is a complex mechanism where each myocyte acts independently to the others, based on the local signalling re- ceived (Opie et al., 2006). The different cellular remodelling pathways are triggered not only by mechanical stress endured by the myocyte, but also by the presence of, for example, hormones. Hypertrophic growth of the cell has been associated to systolic stress, but myocyte elongation is more complex and is still under discussion. Therefore, the resulting remodelling is not homogeneous in the whole heart, but overall expresses as aggregation of all the individual cellular changes. These regional patterns are of diagnostic interest since they can allow to determine the cause of the remodelling, by inspecting the differences in remodelling magnitude among different areas, and the type of remodelling present. Even if the cellular reaction is depending only on the local stimulus, the relationship between ventricular pressure and wall stress is dependent of the local cardiac shape. Laplace’s Law describes the relationship between pressure and stress for thin-walled surfaces (Basford, 2002). The generalised Young-Laplace equation, where K notes the curvature tensor, the stress tensor, h the wall thickness and Tr the trace operator is:

P = T r(K)/(2h) (1.1)

As stated by Laplace’s Law, for the same pressure, wall stress decreases for more curved walls but increases for ﬂatter ones, and thicker walls are able to withstand pressure with lower stress. Therefore, remodelling to lower stress due to a pressure increase is a remodelling that does not only make the wall thicker but also goes towards more globular hearts (Ganau et al., 1992; Zhong et al., 2009). While differences in remodelling produce shape changes, differences in shape also trigger remodelling: the base of the LV is the ﬂattest, and therefore the one that undergoes bigger stresses when pressure is homogeneous, inducing potentially more remodelling (Baltaeva et al., 2007).

2 Figure 1.1: Concentric and eccentric remodelling. Reproduced from (Gjes- dal et al., 2011)

1.2.2. Functional remodelling

Not only the cardiac shape can change, but also the function can adapt. For instance, a common observation is the variation of heart rate (HR) and blood pressure to match alterations of systemic oxygen needs throughout the day. The capacity of the heart to acutely adapt to different situations is very important, and an indicator of early stages of disease: a patient can be asymptomatic at rest, but the heart is unable to adapt to changes. Usu- ally, this lack of adaptation capability will worsen over time, leading to heart failure. A good example is exercise: during exercise, the need of oxygen increases (Poole et al., 1997). How the heart acutely responds to exercise is very important and assessing this response can give information of the overall state of the heart (Sitges et al., 2017). An important mechanism of acute remodelling is the Frank-Starling law, which states that that contraction force of the cardiac myocites increases when the end diastolic (ED) volume increases (Katz, 2007). The increase of volume stretches the myosin in the sarcomeres and allows more of their heads to attach to the actin, resulting in more force development. However, when the sarcomeres are too stretched, the myosin heads separate from the actin and there is a loss of contractile force. This mechanism is very

3 Figure 1.2: Stroke volume, cardiac output and LV dimensions during exercise for controls and patients who underwent Fontan procedure. We can observe that, in controls, during maximal exercise, LV volume starts de- creasing (due to lack of ﬁlling) and so does SV. Data from Claessen et al., 2019

important during light/moderate exercise, because it increases ejected volume as a reaction to the increased venous return. When the exercise increases in intensity, the heart increases HR, thus shortening diastole. When diastole is too short, then stroke volume (SV) starts to decrease because the heart is not getting enough blood to ﬁll.

It is important to understand that geometry and function are not independent, but intimately related. Changes in function affect geometry, and geometry inﬂuences function. For instance, endurance athletes present dilated hearts to increase their SV. Since their CO demand at rest is maintained, they lower their resting HR, and often also muscle deformation, because they can. Understanding this interplay is crucial for assessment of the remodelling in order to determine whether it is adaptative or mal- adaptative.

4 Figure 1.3: Number of procedures in the different modalities at Children’s Hospital Boston. Echocardiography shows a steady increase and is currently the most common procedure. Data from Prakash et al., 2010

1.3. Medical imaging

In cardiology, the workhorse of imaging is echocardiography (>95% of the cardiac images generated are using this modality, Figure 1.3). 2D echocardiography allows assessment of both function and geometry. It is cheap (compared to other modalities), can be operated at the bedside and does not use ionising radiation. It has a good temporal resolution and short scanning times. Function can be assessed using B-mode and Doppler imaging to obtain blood or tissue velocities, or using speckle tracking on the walls to obtain strain. There are also derived indices, like ejection fraction (EF) or tricuspid annular systolic excurse (TAPSE)/mitral annular systolic excurse (MAPSE), that assess function by looking at the deformation of cardiac walls. The geometry of the LV can be reasonably assessed with simplified measurements, due to its symmetry, thicker walls and closer position to the chest. However, the RV has thin walls, is more trabeculated and cannot be easily imaged with 2D echocardiography due to its position in the chest (Figure 1.4). The RV asymmetric geometry also makes 2D- based assessment difficult, as the use of assumptions in the geometry introduces distortion. However, 2D echocardiography has many shortcomings: it is very dependent on the experience of the operator, and some patients have poor echocardiographic windows that produce images full of artefacts. Since it is 2D and the probe is positioned manually, it is difficult to acquire exactly the same images each time, resulting in a relatively low reproducibility of measurements (D’hooge et al., 2016). It has a low contrast to noise ratio, that increments with the distance from the transducer, hampering atrial assessment when viewed from the apical window. 3D technologies offer

5 Figure 1.4: Biventricular 3D model personalised from MRI. The RV is coloured in blue and the LV is coloured in red. We can see that while the LV resembles a prolate ellipsoid, the RV has a more triangular and biaxal shape. advantages, but at the expense of higher costs and lower temporal, as well as spatial, resolution. In this thesis, we have used 3D data acquired with MRI and 3D echocardiography. 3D techniques allow to improve reproducibility (Thavendiranathan et al., 2012), since they are less dependent on the acquisition plane, but this comes at a cost. Acquisition is longer: a 3D volume of the heart acquired by MRI requires several apneas, and 3D echo can be usually acquired in a single apnea of 4-6 cardiac cycles. This longer acquisition results in the need of using ECG gating and image compounding, and the generation of artefacts from the fusion of subvolumes. MRI cannot be operated at the bedside but needs the patient to be transported to the device. 3D echo has lower image quality than 2D echo. MRI has a relatively large pixel size but has a better contrast that allows for more easy automatic segmentation of the structures.

1.4. Computational anatomy

3D shapes are difficult to analyse by humans due to their high complexity and large data volume. As stated above, remodelling results in complex regional patterns that are difficult to express in a simplified quantitative manner. The use of computational techniques for its analysis allows to, not only quantify images, but also understanding them. These techniques allow to analyse data that is too big and tedious to be analysed by humans alone. Figure 1.4 shows an example of the shapes that are analysed in this thesis: the cardiac ventricles obtained from magnetic resonance imaging (MRI). We can see that the LV presents a regular, convex and symmetric shape. On the other hand the right ventricle (RV) resembles no simple

6 (a) B-mode echocardiography (b) Color Doppler echocardiography

Figure 1.5: The heart as seen by different modalities. geometric, thus requiring more sophisticated computational techniques for its analysis. Computational anatomy is the discipline that studies quantitatively the shape of organs. It intersects with other disciplines, such as medicine, mathematics and computer vision. Statistical shape analysis (SSA) is a subfield of computational anatomy that analyses organ shape variability(Dryden et al., 1998), learning it from a population(Cootes et al., 1995; Joshi et al., 2004). It has been extensively applied: as segmentation (O’Brien et al., 2009; Heimann et al., 2009), to recover complete organs from partial observations (Albrecht et al., 2013), or to compare populations (Zhang, Cowan, Bluemke, Finn, Fon- seca, Kadish, Lee, J. A. Lima, et al., 2014; Sarvari et al., 2017). In the latest years, SSA has been combined with machine learning techniques to build models that outperform, at least in the population used for training, traditional methods (Bernard et al., 2018; Gilbert et al., 2019; Bhuva et al., 2019). SSA allows to operate in the space of shapes directly, without being restricted to a few pre-specified measurements. It allows to identify and quantify complex shape patterns that would be otherwise difficult to find by simple observation. It is therefore a very potent tool to find remodelling patterns in an exploratory way, without imposing a hard constraint on which kind of patterns the researcher is trying to find.

7 SSA is a powerful tool, but it has shortcomings. The quality of the results often relies heavily on the quality of the point-to-point registration, which is an expensive and unstable process. The heart presents high shape variability and not many common anatomical landmarks that can be identified in the images. Therefore, point-to-point correspondence cannot be verified and registration uses pseudo-landmark defined through mathematical properties. Moreover, since it learns from populations, it is very dependent of the dataset that was used to construct the models. SSA can propagate biases existing in the datasets, which is very undesirable. Fi- nally, organ shapes are elements with a very high dimensionality, and most medical image datasets involve only sample sizes of the order of hundreds. There is a big risk of overfitting the model to the sample, instead of obtaining generalisable results. For the cases were SSA is not applicable, due to bad registration, or very few available samples, it is possible to generate shape features like volumes, curvatures or diameters. These measurements do not need to be only global since (meaningful) parcellations of the organ can be used. Knowledge on physiology and anatomy can be imposed to define problem- specific features based on educated guesses of what information is the most relevant. While this approach has been overlooked in recent years as opposed to more organ-agnostic approaches, like SSA, it is still useful and results in more interpretable models. It can also complement SSA, using SSA to identify and understand the remodelling, and developing more stable techniques to obtain remodelling image biomarkers that capture specific patterns.

8 1.5. Thesis structure

In this thesis, we present novel methods to identify and assess remodelling of the cardiac chambers in different, clinically challenging, settings. The applicability of our methods is in clinical research and diagnosis, and therefore we need them to be easily interpretable and reliable models. We have avoided addressing the steps of image acquisition and reconstruction, as well as most of the process of segmentation and 3D mesh reconstruction from medical images, where we used previously developed methods. The chapters (except the introduction and conclusion) are mostly self-contained and presented in the form of papers for academic journals.

2 In Chapter 2 we present a statistical shape analysis framework to robustly identify shape differences between two populations and validate it against demographic imbalances in the populations.

3 In Chapter 3 we use the previous framework to identify shape differences between endurance athletes and controls and link these resting shape differences to the cardiac performance in a maximal stress test.

4 In Chapter 4, we apply the SSA framework to analyse an adult population who had growth problems during their fetal gestation, comparing them to controls.

5 In Chapter 5, we propose a novel method for volumetric parcellation of the right ventricle in 3 regions (inlet, outﬂow and apex) based on geometric properties of the surface. This method allows to avoid the registration step and can work with small populations without enough samples to use the previous statistical techniques.

6 In the conclusion, we summarise the contributions and propose future directions of research to continue the lines of research present in this thesis.

Chapter 2

HANDLING CONFOUNDING VARIABLES IN STATISTICAL SHAPE ANALYSIS - APPLICATION TO CARDIAC REMODELLING

2.1. Introduction

Analysing the shapes of parts of biological organs and organisms has been the object of extensive study for over a century (Thompson, 1942). This interest in shape is also present in medicine: several studies have focused in the relationship between organ morphology and illness. For instance, cardiac shape remodels to improve cardiac pressure/volume output under abnormal working conditions, and it is used to assess the presence/evolution of illness (Arts et al., 1994; Grossman et al., 1975). In a nutshell, pressure overload produces concentric remodelling (thickening of the myocardium without dilation of the ventricle) to maintain wall stresses low, and volume overload dilates the ventricle without a myocardial mass thickening. This is an oversimplication, as a volume overload will also increase pressure, and the exact remodelling mechanisms and triggers at a cellular level are still under research and discussion. The classical way

This chapter is adapted from: Bernardino G, Benkarin O, Sanz de la Garza M., Prat-Gonzàlez S., Sepulveda A., Crispi F., Butakoff C., de Craene M., Sitges M., Bijens B., González Ballester M.A. "Handling confounding variables in statistical shape analysis - application to cardiac remodelling" [Under review]

11 of analysing shape in the clinical community consists in manually extract- ing hand-crafted features, and analysing these shape descriptors. These measurements are usually standardised and defined in guidelines (Lang et al., 2015), and usually refer to global characteristics of the shape that carry little regional information. Nowadays, it is possible to acquire 3D images in clinical routine. Fur- thermore, advances in computing permit to automatically segment the images and to generate personalised 3D models of the organs (González Ballester et al., 2000; Mitchell et al., 2002; Ecabert et al., 2006; Bernard et al., 2018). statistical shape analysis (SSA) is a set of techniques to represent both shapes and images and do the analysis directly with these ob- jects, not being limited to only analyse previously defined measurements. SSA is used in the medical imaging field, in order to identify and represent shape variability of those organs (Cerrolaza et al., 2015; Blanc et al., 2012; Rajamani et al., 2007; Sierra et al., 2006). This allows expressing and quantifying regional shape patterns in a robust and objective manner, instead of working with a small set of predefined measurements on the shapes (like volumes and diameters). SSA can be used together with statistical learning techniques to construct models that find regional differences in anatomy that are associated to pathologies (Zhang, Cowan, Bluemke, Finn, Fonseca, Kadish, Lee, J. A. Lima, et al., 2014; Singh et al., 2014; Varano, Gabriele, et al., 2017; Sarvari et al., 2017), based on a control and a pathological population. Roughly, the typical framework consists of first using SSA to construct an atlas of all shapes in the population, then use principal component analysis (PCA) or another dimensionality reduction (DR) technique to find a low-rank representation of the shape space, and finally use a classification algorithm on that space to train a model that predicts the control/pathologic status. Beyond pathological variability, the shape of an organ also exhibits variability due to other factors, like lifestyle, gender, ethnicity, or size. The framework described above uses the implicit hypothesis that differences in shape are only due to the pathology. In some cases the remodelling associated to the pathology is prominent and easily identifiable. However, in others, like subclinical or early-stage studies, differences can often be very subtle and less pronounced than demographic-related variability. In the latter case, an imbalance in the population demographics may result in wrong associations between shape differences caused by demographics and the illness. Even in cases where the pathological remodelling is significant, and the populations are similar in terms of demographics, demographic- related variability will add noise to the analysis.A number of authors have explored the usage of non-imaging information. For instance Singh et al.

12 proposed a procedure similar to partial correlation between shape and several clinical variables while correcting for confounding variables(Singh et al., 2014). Zhang et al adjusted by demographics in their studies of cardiac remodelling in myocardial infarction (Zhang, Cowan, Bluemke, Finn, Fonseca, Kadish, Lee, J. A. C. Lima, et al., 2014), and Zhang et al and Mauger at al explored the relationship between shape and classical clinical measurements (Zhang, Medrano-Gracia, et al., 2017; Zhang, Cowan, Bluemke, Finn, Fonseca, Kadish, Lee, J. A. C. Lima, et al., 2014; Mauger et al., 2019). However, not all authors include corrections for confounders, and their effect in shape analysis studies has not been yet quantitatively tested. In this chapter, we present a SSA framework to find differences between control and pathological populations that outputs the most discriminating shape pattern, that can be visualised for interpretability. We quantitatively and qualitatively show the effect an imbalance in the confounding variables has in the analysis, and propose techniques to reduce that effect. The proposed model consists of the following steps: (1) the construction of an atlas of the personalised 3D meshes automatically generated from images; (2) identification and removal of shape variability due to confounding variables; (3) dimensionality reduction and classification. To illustrate the framework, we use a dataset of cardiac magnetic resonance imaging (MRI) involving sedentary controls and triathlon athletes. This dataset was collected to study the remodelling due to the extended practice of endurance sport, which produces a volume overload to the heart. This volume overload triggers compensatory mechanisms to improve cardiac output and withstand the increased pressure during exercise. The whole of this remodelling is called the Athlete’s Heart and involves substantial changes in function and geometry at both rest and during exercise (D’Andrea et al., 2015; Schiros et al., 2013). Although the remodelling is not yet completely understood, researchers have established a strong relationship between cardiopulmonary performance during exercise and cardiac geometry at rest (La Gerche, Burns, et al., 2012; Scharhag et al., 2002).

13 2.2. Methodology

The full process to compute the confounder invariant most discriminating shape pattern between two populations is summarised in Figure 2.1. The presented framework consists of 3 main steps: 1. Compute the mean shape of the population, and register all shapes to this template.

2. Identify and remove shape variability attributable to confounding variables.

3. Train a classiﬁcation model to obtain the most discriminating shape pattern between both populations and generate a visual representation of the most discriminating shape pattern

Procrustes alignment Original images 3D reconstruction Text

Most discriminating shape pattern

Confounding Demographics deflation Classification Dimensionality reduction

Figure 2.1: Schema of the framework and its different components. The input are the short axis MRI, and the demographics of the population. From the image, we generate a personalised 3D mesh of the ventricles, and align them using Procrustes analysis. Afterwards, we remove confounding-related shape variability using confounding deflation. This is followed by a dimensionality reduction and a classification steps. The final step is to compute the most discriminative shape pattern from the classification model coefficients.

2.2.1. Atlas construction

From the short axis (SA) MRI sequence, we use a model-based automatic segmentation method to obtain personalised meshes with point- to-point correspondence (Ecabert et al., 2006). The method deforms a

14 full heart (4 chambers) template mesh using a polyafﬁne deformation to match the myocardial boundaries. The method includes slice correction to remove misalignment between consecutive slices. Since only the ventricles were visible in our images, we discarded the atria and big vessels from each segmented shape. Each resulting mesh has 4446 vertices (the left ventricle (LV) has 3052 vertices and the right ventricle (RV) has 1776 vertices, the right-most part of the septum belongs to both ventricles) in point-to-point correspondence, and 9004 triangles. Only the end diastolic (ED) frame is selected for the analysis. Since meshes are in point-to-point correspondence and share the same con- nectivity, they can be analysed using the point distribution model (PDM) (Cootes et al., 1995). In PDM, the shape of each patient j is associated to a vector with the concatenated position (x, y, z) of its nodes, giving a shape vector:

Xj = (x0, y0, z0, x1, y1, z1 . . . xN , yN , zN ) (2.1)

We chose PDM over other possible representations of shape due to its simplicity and ease of computation. We applied generalised Partial Pro- crustes Analysis (Dryden et al., 1998) to align the meshes thus removing the positioning and orientation variability. We maintained size during this step, but differences in size due to anthropometric variables will be iden- tiﬁed and removed in other steps of the framework. This algorithm is an iterative method, at each iteration computes an estimation of the mean shape X¯ j and then rigidly registers each shape to that estimated mean. This is repeated until convergence, in order to obtain an unbiased mean. Here we show a full iteration j of the algorithm:

n 1 X X¯ j = Xj (2.2) n i

j j ¯ j 2 ∀i : Ri , ti = arg min kR(Xi − t) − X k (2.3) R,t

j+1 j Xi = Ri (Xi − ti) (2.4)

2.2.2. Confounding deﬂation

To identify and remove the shape variability related to the confounding variables (M), and not to the studied condition, we use a procedure similar to partial correlation, as done in (Singh et al., 2014) for a regression problem. We assume that shape X can be decomposed in the sum of the population mean (µX ) and some deformation from that mean that

15 is composed of noise (), variability caused by the confounding variables (XM ) and variability from other sources (Xi). The last component includes remodelling due to pathology :

X = µX + XM + Xi + (2.5)

The first step consists in estimating XM by building a linear model (whose coefficients are wM ) that predicts the expected shape from the confounding variables M. The training data of this model is only one population (the controls), to avoid introducing possible inter-population differences in the model. This prediction will be our XM . Then, for the shape of each individual, we subtract the predicted shape from the actual shape obtaining the prediction residuals. Residuals represent the part of the shape variability that cannot be explained by the confounding variables. To maintain the residual vectors in the same range as the original shape vectors, we summate the original population shape mean. The final formula reads:

Xres = X − XM = (X − wc · M) + µX (2.6)

The regression model coefﬁcients wc are computed using partial least squares (PLS) with the shapes X and confounding variables M. PLS is a regression method that projects the input and output data to two low- dimension subspaces (called embeddings) that have maximal covariance (Wegelin, 2000). The confounding variables are standardised to have 1 standard deviation and 0 mean, but shapes are only standardised to have 0 mean. The full process is described below, and consists in an iterative process where at each iteration a new regression dimension of the low- dimensional spaces is computed. The predicted part is then removed from the input and output spaces, and the process is repeated until the desired number of iterations is reached. Several versions of PLS exist, and we used Wold’s version. All PLS versions agree in the ﬁrst iteration, but give different result for embedding spaces of more than one dimension. Here we show the algorithm for the r-th iteration of a PLS associating an input space X with some response Y , both being matrices. In our setting, and only for this part X will be the confounding variables(M in the rest of the chapter) and Y the shape vectors(X in the rest of the chapter). First, we compute the new dimensions of the embedding spaces by solving an eigenvector problem:

ur, vr = arg max u∗tXtY v∗ (2.7) ku∗k=1,kv∗k=1

We compute the rank one approximations (hat variables), and the re-

16 gression coefﬁcient wr; for OLS refers to the classical ordinary least squares.

r r r r r Xˆ = OLSprediction(X u ,Y v ) (Xrur)tY rvr wr = vr(ur)t (2.8) Xrur, r r r r r Yˆ = OLSprediction(Y u ,X v )

These rank one optimisations are used to update the input X and its output Y by removing the part that is already predicted.

Xr+1 = Xr − Xˆ r (2.9) Y r+1 = Y r − Yˆ r

The final result of the algorithm is the regression coefficients w from X to Y ; and it is obtained by summing all the one-rank approximation regression coefficients. X w = wr (2.10) r

The coefﬁcients wi of the prediction model, associated to confounder variable M i, of this model can also be visualised and interpreted. We can consider the partial determination coefﬁcient, and visualise the shape pattern most associated to a certain confounder, as if it were a discriminating shape (see subsection 2.2.3).

Dimensionality reduction

Given the high dimensionality of the shape vectors and low number of samples, we use a DR method to ﬁnd a subspace that contains the most relevant shape patterns. The general linear DR model reads:

Xorig = µX + KXred + (2.11)

Each shape Xorig is expressed as the population mean(µx) plus some shape-speciﬁc associated low-dimensionality vector Xred and a noise term . The embedding matrix K is constructed depending on the dimensionality reduction method, and contains the most interesting shape directions according to a certain metric. We use three different methods of linear DR: PCA, PLS and a combination of both. PCA and PLS have been reported to be used in conjunc- tion to classiﬁcation methods, and in particular logistic regression (Bastien, 2005). We have described the regression modality of PLS in subsection

17 2.2.2, but PLS also computes a DR space. The difference is that we dis- card the regression coefficients w and only use embedding vectors ur in equation 2.7 of the input space. These vectors define a vector subspace, but are not guaranteed to be orthogonal, so we use QR decomposition (Lord et al., 1999) to obtain an orthonormal base. The combined method is based on prefiltering the shape using PCA, keeping a high number of components (> 90% of the variance), to then use as input to a PLS. This decreases the computation time, and adds stability by denoising the data. Contrary to the typical procedure in machine learning, we chose not to standardise the PCA modes by variance before applying PLS, as the variance of each PCA mode carries important information of the signal-to- noise-ratio.

2.2.3. Classiﬁcation

In this section, we present the method used to train the classiﬁer model and use the model coefﬁcients to obtain the most discriminating shape. The shape features obtained from the DR are combined with the confounding variables in a logistic regression model. We choose logistic regression because we expect not to have a complete separation between both populations, and we want the model to be simple and interpretable. The logistic model gives a probability that an individual j with shape Xj and confounding variables Mj belongs to the pathological or control populations.

P r(yj = control |Xj,Mj) = logit(hXj, wX i + hMjwM i + b) (2.12)

Logit refers to the logistic function x 7→ 1/(1 + exp(−x)). wX and wM are the logistic regression coefﬁcients for the shape and confounding variables respectively, and are chosen to minimize the log-loss of the probability of the training data X. The log-loss is the logarithm of the probability that the model is inconsistent with the observed data:

n 1 X log (|y − P r(y = 1|X ,M )|) (2.13) n j j j j

The logistic regression coefficients associated to the shape wX , can be mapped from the reduced shape space to the full space by using the pseudoinverse of the dimensionality reduction matrix. Let wXred be the coefficients associated to the reduced shape models, and KPCA and KP LS the projection matrices of PCA and PLS respectively. Then the coefficients associated with the full shape are:

t t wX = KPCAKP LSwXred (2.14)

18 Then, we can visualise and interpret the shape pattern. Analogously to multivariate regression, where the coefﬁcients are indexed by the standard deviation to allow comparison among them, we need to adjust for differences in variance of the different coordinates. Since node coordinates carry no meaning on their own, we treat shape as an object itself and do PCA whitening of the shape, as is typically done with other multi- dimensional signals (Kessy et al., 2018). Since we are only interested in the remodelling direction, we normalise the vector to be unitary in the L2 norm. With these corrections, all the shape features are correctly scaled by their importance in prediction. The full process to ﬁnd the standardised shape pattern wˆ reads:

Σ1/2w wˆ = X (2.15) 1/2 kΣ wX k Where Σ is the covariance matrix estimated using PCA. For visualisation, we can generate shapes that are representative of that shape pattern by adding the remodelling shape pattern, scaled with a parameter λ, to the mean shape. To keep the shapes within the original range, we impose that λ has to be within 3 standard deviations of the variance associated to the shape pattern.

Xrepr(λ) = µX + λwˆ (2.16) We can quantify the presence of remodelling in each shape, obtaining a scalar score for each individual, by computing the dot product of the shape vectors with the raw logistic regression coefﬁcients associated to the shape only. The previous PCA whitening is only done for visualisation and comparison of modes. If the shape pattern needs to be quantiﬁed in a population, the original one without standardization needs to be used.

scorei = hwX ,Xi − µX i (2.17)

The shape patterns can be compared using the L2 dot product between standardised shape vectors, which coincides with the correlation of the scores associated to each pattern.

2.3. Experimental setup

2.3.1. Clinical dataset

The study comprises 77 controls and 89 athletes that underwent a MRI, to study the cardiac remodelling triggered by the practice of endurance

19 sport. The study was approved by a local ethical board, and all participants gave written informed consent for the handling of their data. Re- cruited athletes had been training an endurance sport, triathlon, over 10h a week during the last 5 years. None of the study participants had previous cardiovascular illnesses, nor any were detected during the study. Table 2.1 shows the demographics of both populations. The controls and athletes come from different studies, and the demographics of both populations did not match exactly in age, but roughly represent the same general population in age and gender. The study protocol and radiologist were the same for both cases. Age is statistically different between athletes and controls, but the difference is very small (2 years). We do not expect big differences due to this imbalance, since both athletes and controls are middle-aged. There are also statistically significant differences in both weight and body surface area (BSA), but these correspond to physiological remodelling since endurance athletes are obviously fitter than the general population. We used as possible confounders age, BSA and gender, the typical adjustment variables in cardiology studies. The MRI acquisition was ECG-gated from the R-peak during breath- hold. The MRI machines were Siemens Aereo and Siemens Magnetom, with an in-plane spatial resolution ranging from 0.5mm to 1mm. The spac- ing between slices range between 8mm and 10.4mm, and the slice thickness was 8mm. MRI sequences were acquired with 25 frames per cardiac cycle. The ventricular contours (epicardium and endocardium in the case of the LV, and only epicardium of the RV ) were automatically segmented from the MRI SA using the automatic procedure described in the methodology. The quality of the automatic segmentations was assessed by one of our experts, but no manual refinement was performed in order to preserve point-wise correspondences. Cases where errors could not be considered to be small were discarded: two individuals (both of them athletes) were discarded because the segmentation was inconsistent with the image. The segmentation and registration errors are handled as noise in our study. The meshes were very uniform and we found no self-intersecting artefacts. As a consequence of the thick slices, the apex was not correctly imaged and presented much more noise than the basal part of the ventricles.

2.3.2. Automatic measurements

We computed automatic measurements of the 3D shapes that are analogous to the classical clinical measurements, using the point-to-point correspondence and labelling coming from the model-based registration

20 Table 2.1: Population demographics of the study participants. Athletes have a lower heart rate and weight than controls. The age is signiﬁcantly different, but both cohorts are middle-aged and we do not expect major age-related differences. The p-values are obtained using a Mann-Whitney test.

Athletes Controls p-value Age [y] 35.4(6.1) 33.4(3.8) 0.013 BSA [m2] 1.78(0.19) 1.86(0.20) 0.005 Weight [kg] 66.8(11.3) 73.5(15.1) 0.001 Height [m] 1.71(0.09) 1.73(0.08) 0.151 Women [%] 0.48 0.44 0.938 Resting HR [bpm] 57.2(8.4) 65.8(10.6) <0.001 and segmentation. This allowed to get a better understanding of the discriminative shape patterns by assessing how these measurements vary in response to the remodelling score λ on the synthetically generated meshes according to equation 2.16. We computed the ED volumes of both ventricles, as well as the myocardial mass of the LV.

2.3.3. BMI-based downsampling

Obesity (defined as body mass index (BMI) > 30) and overweight (defined as BMI > 25) have been reported as risk factors to cardiovascular illnesses in the literature and have a clear influence in cardiac shape and function (Alpert et al., 2018). Surprisingly, overweight and athletic remodelling share similarities. Even if one might expect them to be opposite, as endurance athletes and overweight body fat are in the opposite sides of the spectrum, both remodellings are triggered by an increase of the heart’s loading. In the case of the athletes, it is the increase of cardiac output (CO) during exercise that produces a volume overload, and in the obese it is a mix of increased CO needs at rest to account for the bigger body size (Lavie et al., 2007) and a ventricular pressure overload due to an increase of arterial pressure (Messerli et al., 1982). To study the effect of an imbalance in a shape-affecting variable between the control and case populations, we biased our population to increase the BMI of the controls, as overweight has a well known effect on the heart. To generate the imbalance, the control class was downsampled to maintain only 25% of its controls, favouring keeping the ones with higher BMI. The individuals to remove were selected randomly among the

21 controls, with a probability of being kept proportional to the rank of its BMI in the control population. Athletes were not downsampled. This procedure was repeated with 100 different seeds to obtain different imbalanced datasets and add robustness to the results. We analysed how this imbalance affected the found remodelling pattern, and to which extent could confounding adjustment and confounding deflation correct this effect. To study the stability of the shape pattern, we computed the L2 product between the discriminative shape patterns obtained with the downsampled datasets and the results obtained with the full dataset, that serves as groundtruth. This was performed for the different DR methods. We also tested the L2 product of the discriminative patterns with the BMI-shape pattern, obtained with an adaptation of our framework to the regression problem. Additionally, we compared qualitatively the automatic measurement response to the remodelling score of both the downsampled and original dataset. We tested both the covariate adjustment, and the confounding deflation. For the confounding deflation, we also evaluated how different choices during the training of the shape prediction model affected the obtained most discriminative shape pattern.

2.4. Results

2.4.1. Dimensionality reduction

To choose the best configuration of parameters for the DR method, we used 10-fold cross validation (CV) and computed the mean log-loss of all the validation set, defined in equation 2.13, over a wide combination of parameters. In table 2.2 we find the log-loss of the best parameter choice for the 3 different DR methods (PCA, PLS and PCA + PLS). They correspond to a PCA with 5 modes, a PLS with 3 and the PCA + PLS with 20 PCA modes and 3 PLS modes. Table 2.3 shows the results of all the combinations tested. This experiment also provided an overview of how the use of demographics affected the classification metrics: there is a considerable improvement in terms of log-loss when the confounding variables are used in the model, and a minor improvement when using PLS instead of PCA. When using PCA + PLS, the metric is very similar to PLS. Confounding deflation gave a worse result than the raw (non-deflated) shapes when adjustment is used. However, confounding deflation improved the resulting classification metric with respect to the raw when confounders are not added to the logistic regression model.

22 Table 2.2: 10-fold CV log-loss scores of the best choice for each DR method.

No deﬂation No deﬂation Method No adj. Confounders adj. No adj. Confounders adj.

PCA5 0.58 0.46 0.48 0.46 PLS3 0.59 0.44 0.52 0.48 PCA20 + PLS3 0.59 0.43 0.50 0.46

Table 2.3: 10-fold CV log-loss results of different DR methods parameters,

No deﬂation Confounder deﬂation No adj. Conf. adj. No adj. Conf. adj. Method

PCA3 0.61 0.45 0.49 0.45 PCA5 0.58 0.46 0.48 0.46 PCA10 0.62 0.49 0.52 0.48 PCA15 0.65 0.55 0.53 0.54 P LS2 0.60 0.44 0.49 0.45 P LS3 0.59 0.44 0.52 0.48 P LS4 0.66 0.48 0.51 0.50 PCA10 + P LS2 0.60 0.44 0.49 0.45 PCA10 + P LS3 0.59 0.43 0.49 0.45 PCA10 + P LS4 0.60 0.45 0.50 0.47 PCA15 + P LS2 0.60 0.44 0.48 0.45 PCA15 + P LS3 0.59 0.43 0.50 0.46 PCA15 + P LS4 0.62 0.46 0.49 0.47 PCA20 + P LS2 0.60 0.44 0.48 0.45 PCA20 + P LS3 0.59 0.43 0.50 0.46 PCA20 + P LS4 0.63 0.46 0.49 0.47

2.4.2. Athletic model

We applied our framework to identify the athletic remodelling in our dataset, and compared the effect of using the different DR method and confounding-bias correction methods (confounding deﬂation and adjustment). We used the DR parameters found in the previous section via CV. Figure 2.2 shows the L2 product between all combinations of DR methods and the adjustment or not by confounding variables. For the original (no confounding deﬂated) shapes (left), we found big differences due the inclu-

23 ouei h dutdmdli oepoone hni h unadjusted the in than pronounced more is model. model adjusted the ventricular prone the of of more in increase is base the volume adjusted it Finally, the so the thickening. stress, apex: myocardial mechanical of the bigger compensatory mass to in to exposed lower of is and and increase flatter base is The the LV in mass. concentrated is LV the model of in model increase difference unadjusted the large no while a found dilation, ventricular observed to we similar mass adjustment, myocardial re- confounder and different shape After base gave found inlet models the the sults. models however, than Both mass, more myocardial RV. dilated Regarding region and outflow apex. LV the ventricular both RV: the the for Both in of same changes adjust- increase the response. without an is measurement found and that models asociated with volumes unadjusted model their and PCA shows adjusted the 2.4 the by Figure obtained STD, ment. 2 + mean as did and redundant shape. became resulting adjustment the confounding influence the not (Figure of applied was use the deflation the of confounding minor the 2.2b), modes only When discriminating gave similar. most choice very resulting were DR the DR The dataset: variables. this confounding in the differences of not or sion after deflation. disappear confounding adjusment using to corrected subfig- due are In differences shapes the deflated. the that not were see are can method shapes we DR 2.2b, the the ure when to adjustment due model. differences the logistic that to the see secondary in can adjustment we confounding 2.2a, subfigure the In not or tech- using DR and of combinations niques different using obtained scores) between relation L 2.2: Figure 2 PCAPLS -Noconfounders rdc ewe h otdsrmntv hp onie ihtecor- the with coincides shape discriminative most the between product PCA -Noconfounders PLS -Noconfounders iue23dpcstems iciiaiesaepten,expressed patterns, shape discriminative most the depicts 2.3 Figure PCAPLS -Adjusted PCA -Adjusted PLS -Adjusted a rgnlshapes. Original (a)

L PCA - No confounders 2 PCAPLS - No confounders rdc ewe h otdsrmntv hp pattern(the shape discriminative most the between product L2 product PLS - No confounders

PCA - Adjusted

PCAPLS - Adjusted

PLS - Adjusted 0.75 0.80 0.85 0.90 0.95 1.00 PCAPLS -Noconfounders b ofudn deﬂation. Confounding (b) PCA -Noconfounders PLS -Noconfounders PCAPLS -Adjusted PCA -Adjusted PLS -Adjusted 24

PCA - No confounders

PCAPLS - No confounders L2 product PLS - No confounders

PCA - Adjusted

PCAPLS - Adjusted

PLS - Adjusted 0.75 0.80 0.85 0.90 0.95 1.00 Figure 2.3: The picture shows the mean shape of the population (right), and that mean shape after applying 2STD of the athletic remodelling obtained after adjusting by confounding (left) and the same remodelling without the adjustment (center). Both remodelling patterns show a dilation of the ventricles, with a bigger dilation of the RV outlet, but the one adjusted by confounders has a more pronounced dilation, and also a clear increase of the basal LV wall thickness. The different rows correspond to two different views: the top row depicts a longitudinal view of the anterior wall of both ventricles and the bottom corresponds to a short axis view of the base, with the observer located in the atria.

Confounder adjustment No confounder adjustment

1.6 LV EDV LV Myocardial Mass RV EDV 1.4

1.2

1.0 Increase factor Increase factor

0.8

0.6 2.0 1.5 1.0 0.5 0.0 0.5 1.0 1.5 2.0 2.0 1.5 1.0 0.5 0.0 0.5 1.0 1.5 2.0 Remodeling score Remodeling score

Figure 2.4: The plot shows the measurement response to the remodelling: for each of the synthetic meshes generated by adding the shape remodelling pattern to the mean shape with different magnitude, we compute classical measurements and show the variation ratio with respect to the mean shape.

25 Figure 2.5: Close-up on the right ventricular free wall of the different models predicting the athletic remodelling shape pattern. The red-blue color map encodes the regional amount of remodelling: red means big differences compared to the control population, and blue small/ no remodelling. We can see that PCA remodelling is smoothly distributed through the whole ventricle, while the results obtained with PLS and PCA + PLS present a more localized remodelling with a sharper red-blue transition: the remodelling is concentrated in the outﬂow.

The adjustment or not by confounders resulted in big differences between the found remodelling patterns. On the other hand, differences due to DR were smaller, yet noteworthy. Figure 2.5 shows the remodelling patterns found for the different DR techniques, with a colormap showing the local amount of remodelling: reed indicates substantial changes and blue no remodelling. The ﬁgure shows a view of the RV free wall, which is the region that experienced more shape changes. All 3 shape patterns were similar and followed the same global trends, but they presented regional differences. We observed that both PLS and PCA + PLS found a remodelling that was localised in the RV outlet and , at a lower degree, in the apex, while PCA showed a more spatially distributed remodelling that also affected the base and had a smoother transition between the affected and unaffected areas.

2.4.3. BMI model

To have a better understanding of the effect of an elevated BMI in the ventricles, we constructed a regression model that predicts BMI from the cardiac shape. As athletes and controls had different ranges of BMI, and to avoid ﬁnding any interference with the remodelling due to endurance sport, we only use the controls to build the BMI model. Also, since BMI

26 Figure 2.6: Synthetic representative shapes of a patient with BMI of 17.5 and another with BMI 30 according to the BMI predicting model. The remodelling consisted of an increase of volume (specially in the axial directions) and LV myocardial mass. and body size are related, we did not use the confounding variables in this model. The model was built using a PLS in its original regression mode, using 3 dimensions. To evaluate the model prediction capability, we computed the determination coefﬁcient R2 using 5-fold CV, which was 0.44. Similar to classiﬁcation, we obtained synthetic representative shapes (xˆb) associated with certain BMI value b. The synthetic mesh associated with a certain BMI was the one having minimal-distance to the mean shape (using the Mahalanobis distance), constrained to having the required predicted BMI. The representative shapes associated to BMI values of 17.5 and 30, which are very extreme values, can be seen in Figure 2.6, and Figure 2.7 shows the measurement response of the remodelling. The BMI- associated remodelling consists of a moderate increase of ventricular size and a bigger increment of the myocardial mass.

27 LV EDV 1.3 LV Myocardial Mass RV EDV 1.2

1.1

1.0

0.9 Relative increment 0.8

0.7

17.5 20.0 22.5 25.0 27.5 30.0 32.5 BMI shape score

Figure 2.7: Measurement response of the BMI-related shape changes. As seen in the visual representation of the shapes, its main component is an increase of the myocardial mass, complemented with a smaller increase of volumes.

2.4.4. Confounding adjustment

Figure 2.8a depicts the L2 products between the athletic remodelling shape pattern (normalised to be a unitary vector) derived from the full population, and the shape pattern derived from the BMI-imbalanced populations. We found that without adjustment the imbalance confused the method, and it mixed the differences due to BMI with the ones related to endurance training. The adjustment by confounding variables resulted in a better agreement between the downsampled-derived remodelling patterns and the full-population pattern than the unadjusted model, as can be seen in Figure 2.9a. Figure 2.8b shows the dot product between the most discriminating shape pattern obtained with the downsampled (boxplot) and full (thick solid lines) datasets, and also the shape pattern associated to BMI, computed as described in section 2.4.3. There, we can see that in the downsampled datasets, the BMI-associated remodelling and the athletic one had lower correlation. This drop of correlation was larger for the models unadjusted by confounder variables. Figure 2.9a shows the measurement response to the athletic remodelling of several models trained with a downsampled population. It shows different DR methods with confounding adjustment (upper row) and without confounding adjustment (lower row). We can see that when no confounding correction is used, the found remodelling is associated with lower myocardial mass, contrary to what is observed with the full dataset ex-

28 Stability analysis Stability analysis 1.00 0.6

0.95 0.4

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0.4 0.75 Confounding adjustment Confounding adjustment No confounding adjustment 0.6 No confounding adjustment 0.70 PCA PCAPLS PLS PCA PCAPLS PLS

(a) Stability to imbalance (b) Dot product with BMI model.

Figure 2.8: Effect of using confounding adjustment in model stability from the imbalanced datasets for the 3 different DR methods. a) agreement of the model trained on downsampled data with the one on full data, measured via its dot product. b) The thick solid lines correspond to the dot product between the BMI shape remodelling , and the athletic shape remodelling derived from the full population. The boxplots show the dot product between the downsampled derived shape and the BMI shape remodelling. When adjustment is used, the athletic and BMI mode have a positive relation (ie, they have remodelling partially in the same direction), due to both partially responding to an increase of pressure; however, that relation can become negative after downsampling, since controls become more overweight. periment in which myocardial mass was maintained. When the shape is adjusted by confounders, athletic remodelling was again associated with an increase of myocardial mass, consistent with the full population model. Figure 2.10 shows the discriminating shape patterns for a randomly selected downsampled dataset. There, we can observe that the model associates athletic remodelling with a decrease of the wall thickness in the septum and apical regions of the LV when confounders are not considered. Resulting shape patterns were affected by the DR methods, PLS was more unstable than PCA and PCA + PLS, who had a better correlation to their full-population discriminating shape. In Figure 2.9a, we can see that PLS was not able to recover the increase of myocardial mass, and its mode presented no variation in the myocardial mass while both PCA and PCA + PLS could.

2.4.5. Confounding deﬂation

In this subsection we analyze the effect of the confounding deﬂation. As stated above, the shape prediction model of the confounding deﬂation

29 PCA + PLS PLS PCA

LV EDV 1.6 LV Myocardial Mass RV EDV 1.4

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0.6 2.0 1.5 1.0 0.5 0.0 0.5 1.0 1.5 2.0 2.0 1.5 1.0 0.5 0.0 0.5 1.0 1.5 2.0 2.0 1.5 1.0 0.5 0.0 0.5 1.0 1.5 2.0 Remodeling score Remodeling score Remodeling score (a) Measurement response with confounder adjustment.

PCA + PLS PLS PCA 1.3 LV EDV LV Myocardial Mass 1.2 RV EDV

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2.0 1.5 1.0 0.5 0.0 0.5 1.0 1.5 2.0 2.0 1.5 1.0 0.5 0.0 0.5 1.0 1.5 2.0 2.0 1.5 1.0 0.5 0.0 0.5 1.0 1.5 2.0 Remodeling score Remodeling score Remodeling score (b) Measurement response without confounder adjustment.

Figure 2.9: Measurement response of the downsampled population with and without adjustment. We can see that the unadjusted methods find a negative relationship between athletic remodelling and LV mass, but the adjusted methods find a positive relationship. Figure 2.4 shows the equivalent plots for the models trained with the full population, which we use as groundtruth. The adjusted models are more similar to the groundtruth than the unadjusted. was trained using only the controls. We tested two possible scenarios: the case in which the athletes population was downsampled, and therefore the building of the shape residual model was not affected; and when the controls were downsampled (as in the previous subsection). The former was the most appropriate situation to apply confounding deflation, since there would not be extra unstability/bias introduced during the confounding deflation step, while the latter could introduce the bias in the dataset during the confounding deflation process. Finally, we show the potential danger of training the residual model using both populations and how the confounding deflation could even increment bias. When controls were not downsampled, the population used to train the shape prediction model was relatively unbiased, as is shown in Figure 2.11. Instead of downsampling the controls, we downsampled the athletes, removing athletes with high BMI analogously to the procedure used to downsample the controls. Figure 2.11a and 2.11b depict the same experiments as in the previous section: the dot product between the most discriminating shape obtained with the downsampled data and the remodelling obtained considering the whole population, and also the dot product with the BMI mode. Results showed a considerable decrease in variabil-

30 Figure 2.10: Mean shape (right), and mean shape + 2STD of the athletic shape remodelling pattern(left), derived from a BMI-imbalanced population. The pattern in the center column was obtained without adjustment, while the one on the right was adjusted. We can that the unadjusted model finds a decrease of myocardial mass in the apical and septal walls, while the adjusted finds an increase of mass ity and a higher correlation with the full-dataset-derived remodelling than the confounder adjustment experiments (Figure 2.8a). Adding confounder adjustment on top of confounding deflation did not produce an increase of accuracy. Figure 2.13a shows the results when the population in which the residual is trained is downsampled. We downsampled the controls based on their BMI. Results were much worse than when athletes were downsampled, and even worse than a simple confounder adjustment. Adding confounding adjustment on top of confounding deflation had a beneficial effect. Figure 2.13b shows the effect of using both athletes and controls in the training of the shape-prediction model for confounding deflation: there was a drop in stability compared to the use of a single population when PLS and PCA + PLS were used (Figure 2.8a). Strangely there was an improvement compared to the baseline (where confounders are completely ignored). Therefore we observed that using both populations in the training of the shape prediction model during the confounding deflation step resulted in worse results. We explored the reason why using both populations can

31 Stability analysis Stability analysis 1.00 0.8

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0.0 0.75 Confounding adjustment Confounding adjustment No confounding adjustment No confounding adjustment 0.70 PCA PCAPLS PLS PCA PCAPLS PLS

(a) Dot product with full data (b) Dot product to BMI model for model. residual.

Figure 2.11: Stability analysis of the confounding deﬂation method when the athletes (that are not used in the construction of the residual model) are downsampled.

Full population Downsampled + Conf Downsampled + No Conf 1.6 LV EDV LV Myocardial Mass RV EDV 1.4

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Figure 2.12: Measurements response of the shape pattern found with the athlete-downsampled data. There were very small differences between the different DR methods, and all methods were able to recover the original shape pattern. create a confounding effect, associating an imbalance in a variable to the inter-class shape differences. This can happen even when the variable is not associated to any shape remodelling. To illustrate this effect, we created a dummy synthetic variable which is just the athlete label plus Gaus- sian noise. Obviously, by generation we knew that this variable did not have any direct relationship to shape. To evaluate this effect, we computed the L2 dot product with the most discriminating shape between athletes and controls and the shape pattern associated to the dummy variable in the shape-prediction model. We repeated this full variable generation and L2 products computation process 100 times to remove randomness of the analysis. Figure 2.14 (left) shows the distribution of this dummy variable for a certain seed. We constructed two residual models one only with the controls, and the other with both populations. Figure 2.14 (right) shows the distribution of the dot product of the shape prediction model coefﬁ- cients associated to the dummy variable when both populations are used, and when only the controls are used. The shape associated to the dummy

32 variable is independent to the athletic remodelling when only one population is used, but becomes very similar to the control-athlete difference when both populations are used in training due to confounding effect.

Stability analysis Stability analysis 1.00 1.00

0.95 0.95

0.90 0.90

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0.75 0.75 Confounding adjustment Confounding adjustment No confounding adjustment No confounding adjustment 0.70 0.70 PCA PCAPLS PLS PCA PCAPLS PLS

(a) Confounder deﬂation trained (b) Confounder deﬂation trained on controls only. on both classes.

Figure 2.13: Effect of the population used to train the confounder deflation model on the discriminative pattern stability, assessed via its L2 product with the result obtained using the full population. Subfigure a) shows when the training of the shape prediction model in the confounder deflation step is trained using the downsampled class, and subfigure b) shows when both controls and athletes are used for training.

Figure 2.14: This ﬁgure shows the distribution of the dummy variable used as a confounder, and the dot product between the regression coefﬁcients associated to the dummy variable in the residual model and the athletic remodelling shape pattern.

2.5. Discussion

The shape models corresponding to the athletic and overweight remodelling corroborated the current clinical literature. The BMI remodelling consisted in mostly a concentric remodelling, both the LV mass and LV EDV increased, increasing more the mass than the volume: this coincides with the hypothesis that remodelling is concentric to cope with elevated

33 pressure (increase of myocardial mass) and CO demands (increase of volume). Another hint that the remodelling was mostly pressure driven is that the septum of the mesh representing a high BMI individual presents a bulge below the aorta, that has been described as an early indicator of elevated pressure (Baltaeva et al., 2007; Gaudron et al., 2016). The athletic remodelling consisted of a predominant increase of volume, and if confounder adjustment was performed, an increase of myocardial mass. There is some controversy if endurance athletes remodelling is more eccentric ( they increase their volume more than their mass) or concentric (they increase their mass more than their volume), but there is a consensus that there is both an increase of mass and volume (Scharhag et al., 2002), and therefore we considered the adjusted model more accurate. The increase of ventricular volume in the confounder adjusted model is considerably larger than the unadjusted. These differences between the adjusted and not adjusted models can be explained because the variability in size and myocardial mass can come also from the patients morphometrics: big persons have big hearts. Without considering this extra non- imaging information, it is not possible to discern when the size of the heart is due to the patient being big, or the heart had a dilation as a remodelling reaction to exercise. The artificially generated imbalanced sets allowed us to validate our hypothesis: without any correction, the athletic remodelling presented a reduction in LV myocardial mass. This is obviously false, since all studies have found that endurance exercise provokes an increase of myocardial mass. The downsampled control population had a high percentage of overweight, who had a concentric remodelling and causing the previous association with control and higher myocardial mass was done. The stability analysis, also showed a bigger match between the downsampled- derived remodelling and the full-dataset one when confounding adjustment was used. We also studied another strategy: confounding deflation. Confound- ing deflation consists of generating a model that predicts shape from the confounders, and working with the residual of that prediction. Our results showed that this strategy worked well when there was access to a good population to train the shape prediction model: otherwise it can actually increase bias. This was shown when training on the downsampled population, or when both the case and control were used simultaneously. Finally, we compared different linear methods for DR: PCA and PLS. In the original dataset, we obtained a better classification accuracy using PLS. We also showed that PLS was able to capture more localised remodelling than PCA, that was limited to smooth and global remodelling.

34 However, PCA overperformed PLS in stability tested during the downsampling analysis. Both models could be combined by using a coarse PCA, that only removes the modes encoding very little variance, with a PLS. With this method we were able to capture both localised remodelling and have high stability to imbalances.

2.6. Conclusion

We have presented a SSA framework to find regional shape differences between two populations, taking special care to correct for any potential bias related to demographics parameters. The framework is fully linear: it used a PCA sequentially combined with a PLS as dimensionality reduction of the shapes, followed by a logistic regression model. The linearity allows to easily interpret and visualise the model and build synthetic representative shapes of the model. To correct for confounding effects, it incorporates adjustment, where the confounding variables are added to the logistic model and confounding deflation, which consists of building a regression model that predicts shape from confounding variables, and we used it to remove the shape variability associated to these variables. We applied our framework to a real dataset consisting of athletes and controls to find the remodelling due to the practice of endurance exercise. Our results confirmed the current literature on endurance-sport remodelling in the LV: ventricular dilation and increment of myocardial mass, specially in the basal area. In the RV, we found that the volume increase was not homogeneous but concentrated in the outflow. In the controls, we used an adaptation of our classification framework to regression to explore obesity remodelling and found it to be mainly an increase of myocardial mass. In this population, we analysed the effect of confounders in a semi- synthetic dataset obtained by downsampling the control population non- uniformly, keeping individuals with high BMI. Even if athletic remodelling is very prominent, we were able to bias the model to output that athletes have lower myocardial mass than controls. This was corrected when adjustment was used. However, we found that we could only use confounding deflation when the control population was relatively big and balanced, and if that is not the case using confounding deflation can actually increment bias. In our work we have tested only linear SSA methods, but this confounder- related problems might appear even more with the use of more complex frameworks, able to capture non-linear shape patterns to capture subtler morphology differences in populations that are almost indistinguishable from controls and differences cannot be found through traditional means.

Chapter 3

VOLUMETRIC PARCELLATION OF THE RIGHT VENTRICLE FOR REGIONAL GEOMETRIC AND FUNCTIONAL ASSESSMENT

3.1. Introduction

When altered stimuli (such as pressure or volume loading) are present, cardiac morphological remodelling is induced through the ability of the individual cardiac myocytes to change size and shape (Arts et al., 1994; Grossman et al., 1975; Opie et al., 2006). This remodelling can either be adaptive, in which it helps the heart to compensate for the changes and keep pumping enough blood to satisfy the system oxygen demands while at the same time maintaining pressure within physiological range. Or, it can be maladaptive in which case the changes are not compensated thus provoking a maladjustment that starts damaging the heart or makes it unable to satisfy the systemic oxygen demands and fail. In clinical practice, remodelling of a ventricle is often simpliﬁed to global changes. These are categorised as either wall thickening with inward motion of the inner wall (thus reducing cavity size and wall stress) as a reaction to pressure loading - often referred to as concentric remodelling, or This chapter is adapted from: Bernardino G, Hodzic A, Langet H, González Ballester M.A., De Craene M., Saloux S.,Bijnens B.. "Volumetric parcellation of the right ventricle for regional geometric and functional assessment." [In preparation]

37 dilatation of the cavity to cope with volume overload so that, without changing the wall deformation during contraction, more stroke volume is ejected with each beat - often referred to as eccentric remodelling. An example of a maladaptive remodelling would be the hypertrophic cardiomyopaty (HCM) (Olivotto et al., 2012), where the concentric remodelling thickens the myocardial walls so much that the filling volumes are reduced, leading to diastolic heart failure, and the outflow tract can become obstructed. Maladaptive remodelling can get the heart into a vicious circle in which it tries to maintain blood flow by contracting harder, increasing even more the pressure, thus triggering more concentric remodelling. Therefore, it is clinically very important to assess the induced changes and interpret them to distinguish different types of remodelling patterns. The underlying mechanism of remodelling is the adaption of individual myocytes as response to very local stimuli. Additionally, the cardiac chambers are no spheres and the muscle is highly anisotropic with internally changing myocardial fiber orientations depending on the position within the wall. Therefor, changes induced by alterations in loading conditions do not have the same effect in all regions of the heart but show specific local trends, such as for instance the presence of a basal septal bulge induced by hypertension (Baltaeva et al., 2007) or a base-to-apex gradient in deformation in deposition diseases as amyloidosis (Cikes et al., 2010) or thalassemia (HAMDY, 2007). However, in clinical practice, these regional patterns are often ignored and the quantitative assessment of morphological remodelling is performed by interpreting only global measurements, namely ventricular volumes and myocardial mass (particularly in the case of the left ventricle (LV)). There have been some efforts and advances towards the quantification of regional patterns although these mostly involve segmental motion assessment (particularly in coronary artery disease) rather than local geometry. For the LV, a standardised partition in 17 wall segments has been proposed (Cerqueira et al., 2002), which recently also has been used to quantitatively assess regional strain patterns. However, these wall segments are by definition equal in size and thus of limited utility to assess changes in morphology. Compared to the LV, the right ventricle (RV) has a complex and ir- regular shape, with more variability (Haddad, Doyle, et al., 2008) so that regional analysis of the RV is even more difficult than of the LV. While there have been studies referring to a regional analysis of the RV (Adde- tia, Maffessanti, Yamat, et al., 2016; Addetia, Maffessanti, Muraru, et al., 2018; Moceri et al., 2018), these are limited to the epicardium, and mostly focus on assessing wall curvature. While local curvature is an important

38 component of the wall stress generated by pressure and thus very important in pressure-overload remodelling, an analysis in terms of regional dilatation/volume is needed to correctly assess remodelling from volume- overload. Therefor, there is a need for quantitative approaches that can assess regional shape as well as volume remodelling in a clinically relevant and physiological plausible way. To address this, in medical image analysis, the typical method to assess regional morphology is through the creation of an atlas, which is a template shape representative of a population, and registering each patient-specific shape to this atlas. This has shown useful to describe inter-individual variations overall morphology in populations, but is more challenging when following subtle regional remodelling within an individual over time. Additionally, this approach has the drawback that it requires registration (deforming the atlas to match the individual) (Joshi et al., 2004). This is an unstable and computationally expensive process. Especially since there are few and separated landmarks for the ventricles, this registration is based on image intensity/shape patterns, and has no guarantee of the correctness of the point-to-point correspondence. Thus, when using computational meshes to represent the heart through image segmentation, after atlas registration, an important part of the mesh nodes’ positions do not correspond to identifiable anatomic landmarks among different individuals so that point-to-point correspondence cannot be used anymore to assess physiological remodelling. To avoid explicit registration, some authors have proposed parametri- sation methods to create anatomical maps of organs(Nuñez-Garcia et al., 2019; Vera et al., 2013; Paun et al., 2017) by finding smooth bijective maps 2 3 from each surface/volume to a common domain, a subset of R or R respectively. The parametrisations of individual anatomies can subsequently be used to obtain a point-to-point correspondence. The mapping is typically obtained through a minimisation of some kind of distortion metric. The most common is trying to force it to be as conformal as possible, ie that locally maintains angles. This is typically enforced by the minimisation of a Laplacian energy (resp. Laplace-Beltrami), but it is not the only pos- sibility: there are other approaches that try to maintain, for instance, local distances (Sorkine et al., 2007). In this chapter we develop this further for a clinical application, using images of suboptimal quality, to propose an automatic method for mesh- independent volumetric parcellation of the RV based on the geodesic distance to three easily identifiable landmarks: tricuspid valve, pulmonary valve and apex. To assess the method, to identify clinically relevant and

39 physiologically plausible regional remodelling, we validated is using a synthetic dataset created through regional induction of circumferential and longitudinal elongation and analyse the sensitivity of the parcellation to both global and regional. To assess the performance, and robustness to noise, in a real setting, we also do an inter- and intraobserver reproducibility analysis, as well as a test/retest comparison of two sequential acquisitions, on the same patient. This technique enables both a regional analysis of anatomy, using the end diastolic (ED) volumes, as well as function, via regional ejection fraction (EF).

3.2. Methodology

3.2.1. Data acquisition

3D echocardiographic images of 5 competitive american style football players were acquired using a modified apical 4 chambers view using an EPIQ7 ultrasound system (Philips Medical Systems, Andover, MA) equipped with a 1 to 5 MHz transthoracic matrix array transducer (X5-1). For each patient, 4-6 different ECG-gated subvolumes where acquired in a single breath-hold to be compounded into the full 3D+t images of 2 complete cardiac cycles. A written informed consent form was obtained from all study participants. A control was imaged in two consecutive acquisitions by different operators to obtain an estimate on the variability due to the imaging process. The image loops were processed using a clinically validated software (4D RV-FUNCTION Tomtec-Arena TTA2, Tomtec Imaging Systems GmbH, Unterschleissheim, Germany (Niemann et al., 2007)) to segment the RV and obtain a 3D-model for each patient. These models were exportable in ucd, a standard file format. All 3D models had the same topology: a triangular watertight mesh with 938 nodes and 1872 faces. The points were in approximate point-to-point correspondence. The segmentation pipeline consisted of: the clinician segments the RV endocardium contour of the frame corresponding to the R peak using the semiautomatic tool, and the result is tracked during a full cycle. Afterwards, the clinician can adjust the end systolic (ES) and ED (defined as the peak of the R wave in the ECG) segmentation iteratively until visually satisfied with the resulting contours.

3.2.2. Parcellation of the right ventricle

Compared to the LV, which resembles a prolate ellipsoid, the RV has a more complex shape and partially surrounds the LV. Its anatomy is most

40 commonly described biaxial: one axis goes from tricuspid valve to the apex, and the other from the apex to the pulmonary valve. The RV can be grossly separated in 3 main anatomically and functionally different parts: the outflow infundibulum, the smooth inlet and the trabeculated apex (Had- dad, Doyle, et al., 2008; Haddad, Hunt, et al., 2008). However, there is no consensus on the exact border between these parts, and different experts can draw different partition boundaries over the sames images. Given that the partition is crucial to described volume and shape changes over time when doing follow-up in individuals, we propose an automatic method for volumetric parcellation of the RV, based only on geometric properties. This partition has the advantage of being fully automatic and therefore completely reproducible under the same image and segmentation, however it still depends on image and segmentation quality. To avoid errors due to a bad point-to-point correspondence, our parcellation only uses the geodesic distances from anatomic landmarks that can be clearly identified in 3D echocardiography: the apex, tricuspid and pulmonary valve. The method is independent of the exact triangulation of the ventricular surface. We applied our method to the analysis of 3D echocardiography images of the RV processed with Tomtec software, but it can easily be adapted to other processing platforms and imaging modalities. Figure 3.1 shows the full process used to parcellate the RV. The first step of our parcellation is the identification of the valves and apex using the provided point-to-point correspondence in the surface mesh (given that these are stable anatomical landmarks in the mesh). Next, for each node of the mesh, we compute the geodesic distances to the apex, pulmonary valve and tricuspid valve. The geodesic distances between two points are computed on the surface with an exact algorithm (Surazhsky et al., 2005) that computes the length of the minimal on-surface path between two points. The distance between a point and an anatomical substructure is defined as the minimum distance from the point to any point that belongs that anatomical substructure:

dt(x) = min{dgeo(x, y)|y ∈ tricuspid valve} dp(x) = min{dgeo(x, y)|y ∈ pulmonary valve} (3.1) da(x) = min{dgeo(x, y)|y ∈ apex}

Figure 3.1.a shows the geodesic path from a sample point to the different landmarks, and Figure 3.1.b shows distance from every point of the surface to the apex represented as a heatmap: the points furthest to the apex are coloured in red and the closest in blue. After this distance is computed for every point of the surface, the interior of the triangular surface

41 (a) (b) (c)

(d) (e) (f)

Figure 3.1: Steps to generate the volumetric partition. a) For each point, the geodesic distances to the apex/tricuspid and pulmonary valve are computed. b) The geodesic distances to each of the landmarks deﬁne a scalar map over the surface mesh. c) This distance map from the surface to the cavity by tetrahedralising the mesh, and the Laplace equation is used to interpolate values to the interior. d) The ventricle is split in the regions by assigning each point of the cavity to the closest landmark. e-f) Visualisa- tion of the RV parcellation over slices of the original 3D images.

42 mesh is tetrahedralissed using a publicly available software (TetGen version 1.5.1, (Si, 2015)) (Figure 3.1.c). The distance defined on the surface of the mesh is propagated to the interior of the ventricle using Laplace’s equation. This equation is discretized using finite elements with a publicly available software (Sfepy (Cimrman et al., 2019)). The equation uses the tetrahedralized mesh as domain and Dirichlet boundary conditions specified by the surface-defined distance maps. Formally, this interpolation step is defined as follows, where M ∈ {apical, inlet, outflow}, Ω refers to the volumetric domain and ∂Ω to its boundary (the surface mesh):

∆u = 0 for x ∈ ˚Ω M (3.2) uM (x) = dM (x) for x ∈ ∂Ω

This process is repeated to compute and extend to the interior of the cavity of the 3 distances. Once the distances are defined in the volumetric mesh, we partition the ventricle, assigning each point of the mesh to the "closest" landmark, using the interpolated distances. Minlet,Mapical and Moutlet respectively are the partition corresponding to the inlet, apex and outflow. Each point is assigned to the region whose representing landmark is "closer", using the interpolated dzs, as shown in Figure 3.1.d. The partition does not follow the mesh vertices and edges, but new elements are generated during the partition. We used linear interpolation to define the distance values inside each tetrahedron. A formal definition of the segments is:

Minlet = {x|dtricuspid (x) < dpulmonary (x) , dtricuspid (x) < dapex (x)}(3.3)

Moutlet = {x|dpulmonary (x) < dtricuspid (x) , dpulmonary (x) < dapex (x) (3.4)

Mapical = {x|dapex (x) < dtricuspid (x) , dapex (x) < dpulmonary (x)(3.5)

This partition can be propagated from the ED-surface to ES-surface using the point-to-point correspondence between surfaces belonging to the same individual, that are obtained via tracking the initial surface, and then extended to the interior cavity via the same Laplacian interpolation. With this procedure, we can compute regional ES volumes and ejection fractions, allowing for regional functional assessment of the acRV.

3.2.3. Local and global anatomic frame of reference

To clinically interpret local geometric changes, it is better to work in an anatomical frame of reference, with longitudinal and circumferential directions, instead of the Cartesian system of coordinates. At each point of the

43 Figure 3.2: Circumferential (right) and longitudinal (left) directions defined in each triangle of a sample RV mesh. The tricuspid valve is shown in green and the pulmonary in blue. Since valve are not part of the myocardium, the definition of the anatomical direction there has no meaning. mesh, circumferential and longitudinal directions are defined locally using the method proposed by Doste et al., 2019. We defined the longitudinal direction using the stationary heat flow in surfaces, with a cold source in the apex, and two hot sources at the same temperature in the two valves. The heat flow is solved using the Laplace-Beltrami linear differential equation on a surface. The Laplace-Beltrami operator (∆) is discretized using the cotangent formulation (Pinkall et al., 1993):

  ∆u = 0 u(apex) = 0 (3.6)  u(valves) = 0

The longitudinal direction (l) at each point is the result of normalising the resulting temperature gradient. The circumferential (c) is chosen to be orthogonal to both the longitudinal and the surface normal at that point (n), so that (l,c) form a base of the tangent space at the given point:

∇u l = (3.7) kuk c = l × n (3.8)

Figure 3.2 shows the local circumferential and longitudinal directions. A global longitudinal direction is computed by averaging all the local ones, and the circumferential directions are deﬁned as orthogonal to the longitudinal.

44 3.2.4. Strain as a value to express local deformation

For two meshes, a reference and a deformed mesh, in point-to-point correspondence, we can compute the strain associated to the deformation. This strain fully characterises the deformation, modulo rigid body deformations. To interpret this strain, it is more natural to work in the previously deﬁned local anatomical reference frame. For each triangle, we can express each of its edges as a combination of the local anatomical direc- m tions (l, c). We note Et the concatenated vectors corresponding to the edges of triangle t and mesh m. With this, we can compute the local linear transformation Ft at triangle t. In a continuous setting, this Ft corresponds to the Jacobian matrix of the deformation.

mdef mref −1 Ft = Et Et (3.9)

From this transformation, we can compute the Cauchy strain tensor for small displacements = (F t + F )/2, and extract the strain in the longitudinal (ll) and circumferential (cc) directions. Note that longitudinal and circumferential directions are not necessarily aligned to the principal strain directions, which are the eigenvectors of the strain tensor.

3.2.5. Synthetic regional remodeling patterns generation

For the localised remodelling, we used a modification of a linear surface construction method (Wang et al., 2012) that generates 3D meshes from a local description. The generated mesh has a fixed topology, that cannot contain a non-manifold edge. The local description consists of the edge lengths and the dihedral angle associated to every edge (the angle formed by the normals of the adjacent triangles). Obviously, not all combinations of lengths and angles define a valid surface, but we can formulate the reconstruction in a minimisation setting so we obtain the possible surface satisfying as much as possible the local description.

Variables deﬁnition

We describe a local frame of reference for each triangle of the mesh from the input data. This frame is arbitrary but uniquely defined, assuming a unique ordering of the nodes inside each triangle. It uses the first node of the triangle as origin, the direction of the first edge as x-axis, the normal as the z-axis and then completes the base to be orthonormal. We will t call ai the coordinates of the i-th point of the triangle expressed in local t frame. By convention, a0 = (0, 0, 0), the third coordinate is always 0 for

45 Figure 3.3: Two adjacent triangles Ti and Tj, with their respective local systems of references. dij is the dihedral angle, which is the angle formed between the two normals. It is represented in the midpoint of the common edge. fi and fj are the orthogonal frame of reference associated to each triangle.

t all points (since they are coplanar), and a1 = (x, 0, 0) . Note that by basic trigonometry we can compute the local coordinates in that of the triangle nodes given the 3 lengths, using the constraints that the ﬁrst node is in 0, and the second one lies in the x-axis. The method unknown variables are the 3D coordinates xi for each mesh point i, and a reference frame ft associated to each triangle t, that corresponds to the mapping from the triangle coordinates a to the 3D space. Figure 3.3 shows two adjacent triangles, with their dihedral angle and the associated frames of reference. For two adjacent triangles i and j, we can obtain the rotation Rij from frame fj to fi: T Rij = fj fi (3.10)

We can express Rij using only elements of the local descriptor: the θ triangle coordinates and the dihedral angles dij. We call φv to the rotation of angle θ around the axis of rotation v. Let e be the common edge between triangles Ti and Tj, we can compute the angle θ between edge e and the 0 ﬁrst edge of Ti, and θ is the respective angle for Tj. Then, we can express Rij as the composition of 3 rotations:

θ dij θ Rij = φzφx φz (3.11)

Linear reconstruction

The reconstruction method is an inverse problem of the computation of the local triangle coordinates as and transition matrices Rs. We operate

46 the previous equations to obtain an equivalent form linear on xs and fs, and use their quadratic residual as energy, thus formulating an optimisation problem with the world position of the nodes x and the frames f as variables. To easily solve this problem, we do not enforces that matrices fs are rotations, but general matrices. By multiplying by fj equation 3.10 and rearranging terms, we obtain the following equivalent equation:

fi − fjRij = 0 (3.12)

For every edge eij in every triangle t, where the nodes have in-triangle indices i’ and j’ respectively, we can use that ft to transform from triangle coordinates to world coordinate: xi − xj = ft ati0 − atj0 (3.13)

After moving all terms to the LHS, we obtain:

xi − xj − ft ati0 − atj0 = 0 (3.14) Thus, we have obtained equations for computing x and f from the Rs and as. We create an energy by minimising the squared L2 error of the sum over all edges of equations 3.12 and 3.14. For the matrices we use the Frobenius norm, which is simply the sum of squares of all the elements. We can add weights to each term of the equation (the one that solves for the frames, and the one that solves for the node position) to control their relative contribution to the global solution. This energy is quadratic and sparse, so it can be efﬁciently solved with linear methods via its normal equations. Its ﬁnal form reads:

X X 2 EI (x, f) = kxi − xj − ft(ati0 − atj0 )k (3.15) ij∈E| t ij X 2 EII (f) = kfi − Rijfjk (3.16) ij∈E|

E = λ1EI + λ2EII (3.17)

Log-domain reconstruction

In the previous formulation, it is not imposed that the frames fs are really orthonormal matrices. This can lead to artefacts where the fs have a determinant < 1 and shrinking of the mesh. To avoid this situation, a

47 solution to that is to enforce that matrices fs are rotations by parametrising them on another domain. Any scalar function that can be expressed by a Taylor series can be converted to a matricial function, by using the matrix product instead of the scalar to compute the powers of the variable. The matrix exponential is defined as: X Xn exp (X) = (3.18) n! n A well known result is that the matrix exponential of a matrix A is a rotation if and only if A is antisymmetric, so, we can make fi = exp(wi), where wi is an antisymmetric matrix. An antisymmetric matrix can be parametrised by its 3 lower triangular components. We define [v]× as the mapping from the reduced parameters v to the associated antisymmetric 3 matrix, where v ∈ R :   0 −v3 v2 [v]× =  v3 0 −v1 (3.19) −v2 v1 0 This parametrization disrupts the linearity of the previous energy (Eq 3.15), but we are still able of computing the derivatives. Usually matrix functions are very cumbersome to differentiate, but for the particular case of the matrix exponential of a 3D antisymmetric matrix, there exists a closed formula (Gallego et al., 2015). Specifically, when applied to a fixed vector, and using the notation f = exp([v]), where v is the reduced parameters of an antisymmetric matrix :

∂f(v)u vvt + (f t − Id)[v] = −f[u] × (3.20) ∂v × kvk2 Using the derivative formula of the matrix exponential, and typical matrix calculus we find the derivatives of the previous expressions. We use the trick that, for any orthonormal base (e0, e1, e2) and any matrices A, B ∈ 3x3 R : X hA, BiF = hAek, Beki (3.21) k The first dot product is the Frobenius product between matrices, and the second is the usual dot product between vectors. With this trick, we can compute the derivatives for each rotation defined over a face fi, and ∂f(v)u each node position xi. We note as D(v)[u] the derivative ∂v to avoid a cumbersone notation. After some trivial computations and reordering, we obtain:

48 fi = exp(vi) (3.22) X X ∇fi EI (v, x) = 2 ti tjD(f)[ek](fiek − Rijfjek) (3.23) k X 0 0 0 0 ∇fi EI I(v, x) = 2 D(f)[au − av](xu − xv − f(au − av) (3.24) e=(u,v)∈ti X X 0 0 ∇xi EI (v, x) = 2 hxi − xj − ft(ai − aj)i (3.25) t e=(i,j) i

∇xi EI (v, x) = 0 (3.26)

Since we can analytically compute the gradient, we can use a ﬁrst order method optimisation method. We use the L-BFGS quasi-newton algorithm (Dennis et al., 1977; Nocedal, 1980).

3.2.6. Global remodelling

Global remodelling involves large changes that correspond to overall size rather than the local shape remodelling. It correspond to the variability due to for instance the individual’s height and weight. The global longitudinal direction lglob is determined similar to the mean local longitudinal direction. The longitudinal and circumferential remodelling transformations are modelled as linear function for each t ∈ R, which is the factor of stretch- ing in the desired direction. The longitudinal transformation√ is deﬁned as (Id + t ∗ lglob ⊗ lglob), and the circumferential as (Id + t ∗ (Id − lglob ⊗ lglob), where Id is the 3x3 identity matrix and t the scaling parameter.

3.3. Validation

3.3.1. Reproducibility of the 3D models

We use the re-analysed individuals to assess the stability of the segmentation, the generated 3D models and the point-to-point correspondence. For each pair of re-analysed surfaces derived from the same images, we computed the difference of global volumes and the Dice coef- ﬁcient of the different segmentations, a standard measure for comparing two different segmentations (noted as S1 and S2) and deﬁned as:

2|S1 ∩ S2| Dice(S1,S2) = (3.27) |S1| + |S2|

49 As a measure of the mesh node stability, we computed for each node the registration error as the euclidean difference between nodes with the same indices from different analyses as well as the point-to-surface distance (distance from a point to the closest point on the mesh, that might lie inside a face) for every node. For visualisation, we show the mean point-to-point (resp point-to-surface) error map, averaged over the different individuals. This map was plotted over a template mesh, which was the population mean shape computed via Generalised Partial Procrustes Analysis. Since the test/retest segmentations come from different images, we cannot use the previous metrics that depends on image coordinates. There- fore, we assessed the resulting 3D models only qualitatively.

3.3.2. Reproducibility of the parcellation method

The RV parcellation provided by our method is dependent on the RV segmentation. Therefore, even if the method is automatic and 100% reproducible under the same image and segmentation, we need to evaluate the robustness of the method to the segmentation variability that is present in a normal clinical setting. We used the re-analyzed dataset to test the reproducibility of the regional volumes and EF in the inter- and intraobserver tests. We report the mean and percent absolute difference in volumes and EF. For the data obtained in the test-retest setting, we report the regional volumes for both acquisitions, as well as the absolute and percent differences.

3.3.3. Validation of the parcellation method

To validate our method, given the lack of a clinical ground truth, we remodelled a template shapes synthetically, both locally and globally. Since we imposed the remodelling, we know the specific areas as well as the exact amount. We also compute the global difference in volume between the template and the remodeled meshes. For each RV segment (apical, inlet, outflow), we generate two localised remodelling patterns: one elongating in the longitudinal direction, and the other in the circumferential. The localisation of the remodelling is achieved by imposing a decay on the desired strain magnitude: the strain at each triangle decays proportional to a Gaussian function of the distance from the center of the triangle to the anatomical landmark defining the segment (apex, tricuspid, pulmonary valve). The circumferential and longitudinal

50 strains are defined as follows: d (x)2 (x) = v exp M (3.28) v max ω2 Where v ∈ {longitudinal, circumferential}, and M ∈ {tricuspid, pulmonary, apical}. The maximal strain Vmax is chosen to satisfy a predefined total volume increment of 5 ml. The valves’ annuli are composed of fibrous tissue and do not show much remodelling in most cases, but they can passively stretch in severe volume overload. Since this localized model is primarily aimed to assess short-term remodelling only, the strain is set at 0 in the triangles corresponding to a valve. Shear strain is currently not included in our work. The global remodelling was generated by applying the linear transformation corresponding to a scaling range that increases from 0% to 10% the global volume. We applied our parcellation method to the template mesh and the remodelled meshes. Afterwards, we compute the differences in regional volumes from the template, and assess our method’s accuracy. The global remodelling homogeneously affects all regions: the volume percentages of each region have to be preserved. The local remodelling only affects one region, and therefore only the deformed region must increase its volume.

3.4. Results

3.4.1. Reproducibility of the 3D models

Here we present the inter and intra-observer results regarding the reproducibility of the ED shapes, as acquired from 3D echocardiography.

Table 3.1: Intra and inter-observer variability (in ml and percent) of the segmentations and node positions.

Interobserver Intraobserver Volume difference 13ml (9%) 6ml (4%) Dice coefﬁcient 0.64 0.89 Mean node error 7.6mm ± 2.3mm 6.2 ± 1.5 Mean point-to-surface error 1.8mm ± 1.0mm 1.3mm ±.5mm

Table 3.1 shows the mean error of the different metrics to assess shape differences: total volume difference, Dice coefﬁcient and mean point-to- point and point-to-surface distances. As expected, interobserver reproducibility was lower than intraobserver. The total volume error was below

51 10% for both inter- and intra-observer, but the other metrics, that evaluated local differences, indicated lower stability. In particular, the interobserver Dice coefﬁcient(0.64) was considerably lower than the intraobserver one (0.89). Figure 3.4 shows the regional mean inter- and intra-observer point-to- point distance. We can see that the anterior insertion points, specially near the right ventricular outﬂow tract (RVOT), presents a higher level of instability with mean distances above 1cm. Instability is not only present in the anterior wall, but also affects the septum. Figure 3.5 shows the mean error using the point-to-surface distance instead of the point-to-point, thus

(a) Intraobserver reproducibility

(b) Interobserver reproducibility

Figure 3.4: Mean point-to-point registration error for each node on the interobserver and intraobserver reproducibility test. We can see that the biggest errors are concentrated near the outﬂow tract, and in the anterior wall. The posterior wall and apical regions are more stable.

52 assessing the stability of the contours independently of the node place- ment. The mean error is lower compared to the point-to-point case and contained to the outﬂow.

(a) Intraobserver reproducibility

(b) Interobserver reproducibility

Figure 3.5: Mean point-to-surface distance for each node on the interobserver and intraobserver reproducibility test. The errors are much lower than the point-to-point case, and concentrated in the boundaries, specially the outﬂow tract, and a fragment of the posterior wall near the apex that is usually cut in the images.

Figure 3.6 shows the test/retest experiment. Both meshes have the same total volume, but differ in shape: acquisition #2 has a higher tricuspid valve and in acquisition #1 the pulmonary valve is further. Also, acquisition #1 presents a displaced anterior insertion "line" . Acquisition #2 segmentation has a wider septum, that extends further in the anterior

53 segment. Acquisition #2 has a more spherical apex and a ﬂatter posterior wall.

Figure 3.6: The two generated 3D models and their parcellations. Even if they have the same approximate size, they have signiﬁcant differences especially in the anterior wall. We can see that the biggest parcellation differences are in the center of the septum and free wall.

54 3.4.2. Reproducibility of the parcellation method

In this section we report the stability of the measurements obtained proposed parcellation method. Reproducibility was estimated using the meshes obtained from the data used for the inter- and intra-observer reproducibility test. Table 3.2 shows the mean intra- and inter-observer errors and the mean value of the variables for the regional and global ED volumes and EF. We can observe big errors in the interobserver case (>12%), but lower for the intraobserver case ( 6 − 8%). The outﬂow segmented had the biggest error for volume(11%), and regarding function, the apical EF has the biggest error.

Table 3.2: Intra- and inter-observer variability of the segmental and total end-diastolic volumes and EF, expressed as the mean error and mean percent error (in parenthesis).

Interobserver error Intraobserver error Mean value RV EDV 12.7ml (9%) 6.2ml (4%) 144ml Outﬂow EDV 5.1ml (14%) 3.9ml (11%) 36ml Inlet EDV 9.3ml (13%) 4.2ml (6%) 68ml Apex EDV 4.7ml (14%) 3.0ml (8%) 39 RV EF 6% (12%) 3% (6%) 50% Outﬂow EF 6% (14%) 4% (8%) 42 % Inlet EF 8% (16%) 3% (8%) 50% Apex EF 9% (15%) 6% (10%) 61%

We used the test/retest acquisition to verify whether the level of noise is higher in that situation. The 2 generated 3D models can be found in Figure 3.6, and we can see clear differences in shape. Table 3.3 shows the quantitative analysis of the regional volume differences. The errors found in the test/retest experiment corresponded to the ones observed in the intraobserver reproducibility test.

Table 3.3: Regional volumes resulting from two consecutive acquisitions of the same patient.

Outﬂow (ml) Inlet (ml) Apex (ml) Acquisition #1 20.81 50.82 18.64 Acquisition #2 22.45 47.51 20.0 Absolute error 1.64 3.25 1.40 Relative error 7.5% 6.8% 7.3%

55 3.4.3. Validation of the parcellation method

We used the synthetic remodelling method to generate different types of localised and global affecting remodelling in the longitudinal and circumferential directions. As template we used the mean shape of our control population, obtained using the Partial Generalised Procrustes Analysis. The local remodelling scaling parameters are set to obtain a total volume increase of 5ml, with all combinations of affected part (apical, inlet or out- ﬂow) and direction (longitudinal or circumferential). Figure 3.7 shows the locally deformed meshes. Several meshes were generated for the global remodelling, its volume increase ranging from 0% to 10%. An example of the generated meshes using this method can be seen in Figure 3.8. Figure 3.9 shows the regional dilatation (%) response to a global circumferential and longitudinal scaling, together with the total volume scaling, which is the identity line. We can see that global remodelling dis- tributes quite homogeneously for both longitudinal and circumferential remodelling (with a 90% accuracy), with circumferential scaling presenting a much lower noise than longitudinal scaling. Note that, by construction, the result of a pure scaling maintains exactly the volume proportions. Among the different regions, the outﬂow presents bigger variability. The changes of regional volumes after applying the local synthetic remodelling are shown in Table 3.4. We see that circumferential remodelling is mostly associated to the correct segment (80 – 90% ) in the apex and inlet, while the method is less suited to capture local longitudinal elongations.

Table 3.4: Regional volume differences between the synthetically remodelled mesh and the reference RV. The remodelling consists of an increment of 5ml in a certain region only. We can see that the method is able to capture between 90% and 80% o the circumferential remodelling, but has difﬁculties when there is a longitudinal scaling.

∆ Outflow ∆ Inlet ∆ Apical ∆ Total Apical circ. -0.46 2.27 4.55 5ml Apical long. 0.37 9.11 4.48 5ml Outflow circ. 3.94 0.65 0.42 5ml Outflow long. 0.25 4.28 0.48 5ml Inlet circ. 0.57 3.91 0.70 5ml Inlet long. 0.35 2.90 1.75 5ml

56 Figure 3.7: Generated meshes with the local synthetic remodelling method.The colour map shows the longitudinal / circumferential strain with respect to the template, which is showed in the right column. 57 Figure 3.8: Generated RV meshes for the global synthetic remodelling, corresponding to a 10% dilation in both the longitudinal and circumferential. The colour map shows the strain of the deformation from the template.

Figure 3.9: Volume response to a global remodelling. The red and grey coloured regions mark the 90% and 80% deviance from an homogeneous scaling. As with local remodelling, we found that the outﬂow is the most unstable region, and that circumferential remodelling is easier to recover than longitudinal.

58 3.5. Discussion

In this chapter we proposed a mesh-independent method to volumet- rically parcellate the RV in 3 clinically relevant regions: inlet, outlet and apex, with the aim to quantify inter- or intra-individual remodelling in regional morphology. For validation, we additionally presented a method to synthetically remodel meshes in a localised and global manner, thus generating a synthetic dataset resembling closely monitoring clinical remodelling. From these, we found that the parcellation had a good sensitivity to circumferential or global remodelling, able to attribute it to the correct segment (80/90% of the volume was assigned to the correct segment). However, our method is less accurate when analysing local longitudinal localised remodelling. However, this is not a major problem given that in many clinical scenarios, regional volume and shape remodelling is often in the circumferential direction (D’Ascenzi et al., 2016). The interobserver reproducibility test of meshes resulting from the segmentation of 3D echocardiography, show that, even if the mean volume difference was under 10%, the Dice coefficient was very low (0.64). This implies that RV shapes segmented by different operators cannot be directly compared and pooled together in an analysis. On the other hand, the intraobserver reproducibility was much higher using the same image (Dice coefficient = 0.89). A test/retest experiment presented significant visual differences. Moreover, the point-to-point (6.2mm) error was much higher than the point-to-surface (1.3mm): the interior nodes of the mesh do not correspond to any anatomical landmark but are equally distributed, thus their correct position does not depend only on the correct segmentation of the RV contour in their position, but on the whole segmentation. Consequently, regional volumes and EF also present a high error (>10%) in the interobserver reproducibility test. On the other hand, the intraobserver reproducibility presented a more reasonable error: in volumes only the outflow had a variability >10%, while inlet and apex were below (6% and 8%) respectively. The outflow is complicated to segment given the images there often have lower quality. A qualitative analysis of the partitions showed big differences in the middle of the RV since this is the furthest from all landmarks and the method has no information to make the exact parcellation. The inclussion of anatomical landmarks in that area could improve the reproducibility of the method. Regarding the EF, the most unstable was the apical part. This is likely caused by the presence of trabeculations introducing variability in the segmentation as well as the nearfield effect playing are role there and making the full visualisation of the apex

59 challenging.

3.6. Conclusion

We proposed a geometry processing method to parcellate the RV in 3 regions: inlet, inflow and apical for analysing regional morphology of the RV without depending on point-to-point correspondence of image-based segmented meshes. This parcellation also allowed to assess function via regional EF. We assessed the reproducibility of the regional measurements, and found it below 8% in both apex and inlet segments for the intraobserver, but above 12% in the interobserver case and outflow. Given that most of the instability comes from segmentation errors in the outflow portion, the addition of extra landmarks (like for example in the middle of the septum) would allow to improve reproducibility. We also proposed and used a novel method to generate localised remodelling patterns. We used it to generate synthetic remodelling surfaces to validate our parcellation method and showed that it captures global scaling of the ventricles as well as localised remodelling in the circumferential directions, but has difficul- ties in local longitudinal elongations.

60 Chapter 4

THREE-DIMENSIONAL REGIONAL BI-VENTRICULAR SHAPE REMODELLING IS ASSOCIATED WITH EXERCISE CAPACITY IN ENDURANCE ATHLETES

4.1. Introduction

As reported in the literature, extensive periods of physical exercise result in chronic exposure to volume and pressure overload, inducing cardiac remodelling (La Gerche, Baggish, et al., 2013; Schmied et al., 2014). This cardiac remodelling includes a set of morphological and functional changes to better cope with the cardiovascular response to exercise. Known examples of such remodelling are left ventricle (LV) hypertrophy and dilatation, dilated right ventricle (RV) and right atria (RA), decreased resting heart rate (HR) and a slight decrease in myocardial deformation at rest. These changes vary importantly among individuals, but remodelling is consistently stronger in the right heart (RH) (Rhodes et al., 1990; La Gerche,

This chapter is adapted from: Bernardino G, Sanz de la Garza M., Domenech-Ximenos B., Prat-Gonzàlez S., Perea RJ, Blanco I„ Burgos F., Sepulveda-Martinez A., Rodriguez-Lopez M., Crispi F., Butakoff C. González Ballester MA., De Craene M., Sitges M.; Bijnens B.; "Three-dimensional regional bi-ventricular shape remodeling is associated with exercise capacity in endurance athletes." [Under review]

61 Burns, et al., 2012; D’Andrea et al., 2015), which is exposed to a bigger relative pressure increase during exercise in comparison to baseline than the left heart (LH). Exercise-induced remodelling is known to be in- fluenced by lifestyle parameters such as sport discipline, training load and individual-specific parameters such as age, gender, ethnicity (Sanz-de la Garza et al., 2017; Sitges et al., 2017). However, the details and spectrum of physiological adaptation to sport is not yet completely understood. Geometric assessment of cardiac structures in the clinical community is still predominantly focusing on sparse length/volumes measurements rather than 3D shape patterns. These measurements are insuffi- cient to analyse regional differences, and especially cannot account for the RV shape complexity and variability. Statistical shape analysis (SSA) denotes a set of techniques that compute a reference shape for a population and subsequently describe each individual shape with the transformation from the template to this individual (Dryden et al., 1998). These techniques have been applied to find regional morphology and deformation differences between two different populations (Varela et al., 2017; Zhang, Cowan, Bluemke, Finn, Fonseca, Kadish, Lee, J. A. Lima, et al., 2014; Varano, Piras, et al., 2018; De Craene et al., 2012). This chapter uses SSA methods to find regional differences between bi-ventricular shapes, as retrieved from magnetic resonance imaging (MRI), of endurance athletes and non-athletes and relate these to exercise response and classical imaging parameters. Given that the RH plays a crucial role during exercise, and that its complex shape is difficult to assess using traditional clinical image-based measurements, the proposed approach is particularly suited to study exercise-induced shape alteration in the RH.

4.2. Methods

4.2.1. Population

A cohort of healthy 89 triathlon athletes and 77 controls was recruited at Hospital Clínic, Barcelona, according to an internal research protocol validated by the internal ethical committee, and written informed consent was obtained for each of the participants. The triathlete inclusion criteria implied that they exercised a mean of at least 10 hours weekly during the last 5 years, evaluated via a physical activity questionnaire (Ainsworth et al., 2011). Controls were randomly selected from the birth registry between years 1975 and 1985. All patients included in this study were asymptomatic with no previous known cardiovascular illnesses and no car-

62 diac disease detected on echocardiography.

4.2.2. Echocardiographic measurements

Echocardiographic images for athletes were acquired with a commercially available ultrasound system (Vivid Q; GE Medical; Milwaukee, USA) with a 2.5 MHz (M5S) and an active matrix 4-dimensional volume phased array transducer in the case of the controls. Images were acquired from the parasternal (long- and short-axis) and apical (RV-focused 4-, 4-, 3- and 2-chamber) views. Three consecutive cardiac cycles for each acquisition were digitally stored in a cine loop format for off-line analysis with commercially available software (EchoPac GE, Vingmed). Cardiac chamber dimensions were measured according to the standards of the European Society of Echocardiography and indexed for body surface area according to the DuBois formula (Du Bois et al., 1916). RV end-diastolic area and end-systolic area were estimated by tracing the endocardium from a RV-focused apical 4-chamber view. LV volumes and LV ejection fraction were derived using the biplane Simpson method. Myocardial deformation of both ventricles was evaluated by 2D-STE (2Dstrain, Echo Pac, version 202.41.0, General Electric Healthcare, Milwaukee, WI, USA). Global RV peak systolic strain (RVGLS) was measured as an average of all six RV segments (3 RV-FW and 3 inter-ventricular septum). Left ventricular global longitudinal strains was calculated as an average of LV systolic strain in 2-, 3- and 4- chamber apical views (Lang et al., 2015).

4.2.3. Exercise Test

All patients performed an standard incremental cardiopulmonary exercise testing in an up-right position on an electrically braked cycle ergometer (range 6-999 watts) using an Ergoselected 100 (Ergoline, Bitz, Germany). Over the course, of this test, they performed an increasingly demanding exercise until exhaustion, while their gas exchange parameters and HR were being monitored using a breath-by-breath and a 12 lead ECG. From this, the peak and basal oxygen uptake, as well as the HR were measured using the ExpAir software (Medisoft, Sorinnes, Belgium). All measurements were performed according to international guidelines (Ross et al., 2003; Albert et al., 2008). Athletes were subjected to a post-exercise echocardiographic exam. Immediately after the end of the exercise test, they were moved to a bed next to the ergometer and were scanned to assess function and geometry changes occurring during exercise.

63 4.2.4. MRI study

Cardiac MRI studies were performed using a 3T (72 athletes and 77 controls) or 1,5T (17 athletes) scanner (Magnetom Trio Tim and Magneton Aera respectively, Siemens Medical Solutions, Erlangen, Germany) in all subjects involved in this protocol. Images were acquired during apnea. A cine sequence in short axis (SA) view was acquired with 8mm slice thickness, an interslice gap ranging from 0 to 2.4mm, and a pixel size ranging between 0.8 to 1.5 mm. For each individual in our population, we generated a 3D surface by ﬁtting a whole-heart deformable template, for all time instances, to the SA MRI, using the algorithm described and validated in (Ecabert et al., 2006; Peters et al., 2010). From this, we extracted the LV end diastolic (ED) frame and selected the LV epicardial and endocardial surfaces as well as the RV endocardium. All contour points were in one-to-one correspondence due to the model-based segmentation. An expert visually checked all automatic segmentations in the SA, and 2 individuals were discarded for inadequate tracing of the ventricular contour.

4.2.5. Statistical shape analysis

We represented the surfaces/shapes by a point distribution model (PDM) (Cootes et al., 1995), and we used Partial Procrustes Analysis to generate a population mean shape, and rigidly align each individual with that mean. We used principal component analysis (PCA) and partial least squares (PLS) to build a dimensionality reduction that encoded most of the shape variability that correlated with the athlete label. First, we used PCA to obtain a dimensionality reduction that kept 95% of the shape variability, serving as a denoising step. Then, we used PLS to further reduce the shape space to 4 modes that maximiwed covariance with the athlete label. Finally, we used logistic regression (LR) to find an optimal separation between athletes and controls in that reduced space, using BSA, age and gender as covariates. This LR corresponded to a certain shape pattern, the athletic remodelling, that subsequently could be quantified for each individual and expressed as a remodelling score. To verify the model invariance to age and gender, we used the same SSA method as described above to obtain the athletic remodelling shape pattern, after gender-stratifying the population, as well as with age-equalized subpopulation. We computed Pearson’s correlation coefficient between remodelling scores obtained with the restricted datasets and the remodelling scores derived from the full dataset.

64 4.2.6. Statistical methods

We tested the difference of scalar variables using the Mann-Whitney U-test, and the Chi-Square test for categorical variables. We used multivariate regression (MVR) to assess the relationship between the athletic remodelling score and the scalar measurements, independently of the confounding variables that are introduced as covariates in the model. To assess the results of the MVR, we used the Fisher F-test, comparing with a model with only the confounding variables as predictors. The logistic model was evaluated using the area under curve (AUC) of the receiver operating characteristic (ROC). We evaluated the models using leave one out cross validation (LOOCV) to split the data in a derivation and validation cohorts without loss of sample size. We compared the SSA model with a simple LR using the confounding variables via a DeLong test (DeLong et al., 1988). We implemented the analysis in Python 2.7.14 (En- thought Inc, Austin USA), with the following packages: numpy (v1.13.0), scikit-learn(v0.18.1) and scipy(v0.19.0) and RStudio 1.1.423 (RStudio Inc, Boston MA) with package pROC (Robin et al., 2011). We set a threshold of 0.05 to determine statistical signiﬁcance.

4.3. Results

4.3.1. Population characteristics

The population demographics and functional echocardiographic-based parameters are reported in Table 4.1. Athletes had a lower deformation, body surface area (BSA) and resting heart rate (HR), which is consistent with chronic exercise, but were also 2 years older than controls. Their cardiac output (CO) indexed by BSA is maintained. In appendix S2, we tested the inﬂuence of this age imbalance in the analysis and found it to be neg- ligible. Table 4.2 shows the comparison geometric MRI-based measurements between athletes and controls. We found an overall increase of the ventricular size. Table 4.3 shows the difference between resting state and after maximal exercise in athletes. Figure 4.1 and 4.2 show respectively the segmentation contours of a randomly selected control and athletes su- perposed to SA, 4-chambers, 3-chambers and 2-chambers MRI.

4.3.2. Athletic shape remodelling

We built a model that captures the differences in 3D shape between athletes and non-athletes using our SSA technique described in the method-

65 Table 4.1: Demographics and echocardiographic functional measurements of the population, in the format of mean (STD).

Athletes Controls p-value Age [y] 35.4(6.1) 33.4(3.8) 0.013 BSA [m2] 1.78(0.19) 1.86(0.20) 0.005 Weight [kg] 66.8(11.3) 73.5(15.1) 0.001 Height [m] 1.71(0.09) 1.73(0.08) 0.151 Women [%] 42(48%) 32(44%) 0.938 HR - echo [bpm] 57.2(8.4) 65.8(10.6) <0.001 LV EF [%] 54.6(4.4) 62.6(5.6) <0.001 SV [ml/m2] 47.5(9.5) 40.2(8.6) <0.001 CO [l/min/m2] 2.7(0.6) 2.6(0.5) 0.302 RV FAC [%] 45.2(5.2) 45.6(8.7) 0.767 TAPSE [mm] 25.9(2.9) 25.3(3.4) 0.197 VO2 peak [l/min/m2] 1.63(0.28) 1.11(0.28) <0.001 BSA: body surface area, HR: heart rate, LV EF: left ventricular ejection fraction, SV: stroke volume, CO: Cardiac output, RV FAC: right ventricular fractional area change, TAPSE: tricuspid annular plane systolic excursion, VO2 max: Maximal oxygen uptake ology. The model output is a shape pattern that best discriminates between athletes and controls and is therefore the remodelling acquired due to the practice of sport. To visualise that remodelling, in Figure 4.3 we show the mean shape computed from the controls only, as well as the shape obtained by adding the remodelling with 3 STD of the found athletic shape pattern, thus representing the shape of an extreme athlete. A qualitative assessment of the figure shows that shape remodelling is concentrated in the RV: the outflow and RV apex of the extreme athlete are considerably dilated and more spherical than the mean control. Finally, for each athlete, we quantified how much of this athletic remodelling was present in their individual cardiac shape, to study the relation to acute exercise response. We normalised such score to have 0 mean and 1 STD in the controls.

66 Table 4.2: Comparison of the MRI- based measurements between athletes and controls.

Athletes Controls p-value LV EDV [mL/m2] 101.7(17.4) 82.9(12.1) <0.001 LV Mass [mg/m2] 83.7(14.0) 71.7(11.4) <0.001 LV LA[mm/ m2] 53.9(4.2) 49.4(4.2) <0.001 LV OT [mm/ m2] 14.6(1.0) 13.4(0.9) <0.001 RV EDV [mL/m2] 108.3(22.6) 86.4(15.7) <0.001 RV EDA [cm2/m2] 18.0(2.6) 15.7(2.2) <0.001 RV LA [mm/m2] 51.8(3.8) 47.2(3.9) <0.001 RV Basal Dimension [mm/m2] 28.1(2.5) 25.8(2.4) <0.001 RV OT [mm/m2m2 16.6(1.4) 15.0(1.1) <0.001 LV EDV: left ventricular end-diastolic volume, LV LA: left ventricular long axis, LV OT: left ventricular outﬂow tract, RV EDV: right ventricular end-diastolic volume, RV EDA: right ventricular end-diastolic area RV LA: right ventricular long axis, RV OT: right ventricular outﬂow tract

Table 4.3: Values at rest, after exercise and percent ratio of function and geometry echocardiographic and ergospirometric measurements in athletes.

Baseline Exercise Increment ratio [%] LV EDV [mL/m2] 67.2(11.7) 64.8(12.5) 97(8) RV EDA [cm2/m2] 12.7(1.9) 12.3(1.7) 97(9) SV [ml/m2] 47.5(9.5) 55.5(9.61) 118(15) CO [l/min/m2] 2.7(0.6) 5.5(1.0) 118(012) LV GLS [%] 21.1(1.7) 23.94(2.0) 114(8) EF[%] 55.1(4.4) 60.0(5.0) 111(11) RV GLS [%] 24.8(2.7) 28.4(3.00) 115(11) RV FAC [%] 45.5(5.2) 52.0(5.1) 115(16) VO2 [L/min/m2] 0.19(0.06) 1.63(0.27) 955(358) HR (CPET) [bpm] 62.2(10.3) 169.5(10.6) 279(45) HR (RV GLS) [bpm] 57.2(7.8) 104.4(9.7) 185(23) EDV: end-diastolic volume, EDA: end-diastolic area, SV: Stroke Volume GLS: Global Longitudinal Strain, EF: Ejection Fraction, FAC: Fractional Area Change, VO2: Oxygen uptake

67 Figure 4.1: Example of the segmentation of an athlete. The top row corresponds to 3 SA slices near the apex, papillary muscles and base respectively, that were used by the segmentation. The bottom row corresponds to a frame in the 2CV, 3CV and 4CV sequences respectively, that were not used for the segmentation.

68 Figure 4.2: Example segmentation of a control. The top row corresponds to 3 SA slices near the apex, papillary muscles and base respectively, that were used by the segmentation. The bottom row corresponds to a frame in the 2CV, 3CV and 4CV sequences respectively.

69 Figure 4.3: Most discriminant shape mode that distinguishes the RV from athletes and controls. The upper row corresponds to a representative extreme athlete (population mean + 3STD of athletic remodelling), and the lower one to the mean shape of the non-athletes. The three views correspond to: a view of the base from the atria (left), a longitudinal view of the inferior RV and LV walls (center), and a longitudinal view of the LV free wall (center). The red-blue colour map indicates in red the regions that present more remodelling, and the purple lines the observed differences. Both ventricles are very different from the controls, but while the LV mostly scale, more regional shape changes occur in the RV, especially in the out- ﬂow.

70 4.3.3. Exercise response

Using MVR, we investigated in the athletes how different degrees of athletic shape remodelling corresponded to cardiovascular performance in the stress test. Table 4.4 shows the standardised regression coefﬁcients of the remodelling score with p-values. All models used the confounding variables as covariates. Table 4.4: Results of the MVR to check the relationship between shape remodelling score to different functional parameters during exercise. Only athletes are included in this analysis. The p-values were obtained by comparing the regression model involving the athletic remodelling score and the confounders with a model that uses only confounders with a Fisher F-test.

Standardized coefﬁcient R2 P-value Resting HR -0.18 0.08 0.03 Maximal HR -0.17 0.19 0.08 Baseline VO2 -0.10 0.09 0.50 Maximal VO2 0.20 0.49 <0.01 Maximal Oxygen Pulse 0.26 0.51 <0.001 Baseline RV GLS -0.17 0.29 0.11 Post-exercise RV GLS 0.04 0.41 0.69 RVGLS reserve 0.22 0.20 0.03 Resting LV GLS 0.02 0.31 0.84 Post-exercise LV GLS 0.11 0.30 0.23 Resting LV EDV 0.67 0.73 <0.001 LV Myocardial Volume 0.50 0.72 <0.001 LV EDV increase ratio 0.02 0.01 0.70 Resting RV EDV 0.61 0.69 <0.001 RV EDA increase ratio -0.10 0.05 0.24 VO2: oxygen uptake, RV GLS: right ventricular global longitudinal strain, LV GLS: left ventricular global longitudinal strain, LV EDV: left ventricular end- diastolic volume, RV EDV: right ventricle end-diastolic volume

We found a negative association of athletic shape remodelling to both resting and maximal HR (p=0.03, R2=0.08; p=0.08, R2=0.19 respectively). Resting VO2 was unassociated to athletic remodelling, but maximal VO2 and maximal oxygen pulse were (p<0.01, R2=0.49; p<0.001, R2=0.51). There was an association between athletic remodelling and greater RVGLS reserve (p=0.04, R2=0.21). Neither resting nor post-exercise LVGLS were associated to shape remodelling. While the athletic remodelling score was associated with larger cavities at rest, we found no association with acute

71 Figure 4.4: LOO-CV ROC of the model which considers shape and confounders (orange), compared to a simple model that only considers the confounders (blue).

RV/LV dilation during the maximal stress test.

4.3.4. Validation

We compared the AUC of the shape’s model (AUC = 0.91) and that of a LR that only takes confounding variables into account (AUC = 0.71). The improvement due to the inclusion of shape was statistically significant according to the DeLong test (p<1e-6). Figure 4.4 shows the ROC of both models. We checked the influence of gender and age in the found remodelling pattern. The gender stratified models presented a very strong correlation with the pooled model (ρ = 0.92 for the female model, and ρ = 0.93 for the male model). While we observed no gender differences in the most discriminative shape pattern, men presented a higher quantity of remodelling than women, as can be seen in Figure 4.5. The age equalised model (using only athletes with age ≤ 40y) presented an almost perfect with the pooled model (ρ = 0.98 ). LV mass and ventricular size has been used as an indicator of cardiovascular output during exercise. Here, we compare the value of shape to the classical indices to predict 1) VO2 max using a linear model and 2) athletic model using a logistic model. To obtain accurate estimators, we use LOO CV for both the VO2 and athletic model, and also use the classical confounding variables (age, gender and BSA) as covariates. Both the dimensionality reduction and classifier of the shape model were subject to cross-validation. Table 4.5 shows the results. There is no big difference between them, with the remodelling score a bit better at discriminating athletes and LV mass slightly better at predicting VO2 max. This similar

72 Figure 4.5: Quantiﬁcation of the athletic remodelling score for both male and female athletes. We can see that male athletes present more remodelling and lower variability.

Table 4.5: Results of the linear regression model predicting peak VO2 and the logistic model predicting athletes. All results are obtained using CV on a linear /logistic model.

2 Predictors VO2 R Athletic predictor AUC Confounders 0.37 0.71 Confounders + score 0.41 0.91 Confounders + LVMass 0.42 0.88 Confounders + LV EDV 0.40 0.88 Confounders + RV EDV 0.39 0.87 behaviour is not surprising, given that both the classical geometric descriptors and our remodelling are very correlated (Table 4.6).

4.4. Discussion

Complementary to the well-known differences in size and mass, we found strongly significant statistical differences in resting ventricular regional shape between athletes and controls. Within athletes, those differences are positively associated with better performance in an exercise test, as measured by VO2 uptake. There was a small, yet significant (p=0.04), positive relation with RVGLS reserve. We found a negative, non- significant, association with maximal and resting HR and no association with baseline VO2 uptake or CO. The identified athletic LV remodelling corresponds to a dilation and increased myocardial mass compared to the control LV, resulting in a more spherical LV. The ventricular dilation is an adaptation to increase the stroke

73 Table 4.6: Correlation coefﬁcient between the different classical indices used to quantify athletic morphological remodelling and our remodelling score. We can observe that all have a strong correlation.

LVM LV EDV RV EDV Rem. score LVM 1.00 0.83 0.85 0.83 LV EDV 0.83 1.00 0.94 0.92 RV EDV 0.85 0.94 1.00 0.90 Rem. score 0.83 0.92 0.90 1.00 volume, and the increased ventricular wall thickness, help to maintain wall stress limited when the pressure increases during exercise. The RV presents a different type of remodelling: the global effect is an increase in volume, but that increase is not homogeneous and is more prominent in the outflow. RV shape becomes more elongated in the inlet, and there is a shift of volume from inlet to outflow, that is dilated and more spherical. In conclusion, the RV remodelling corresponds more to a change in shape rather than in size while the LV mostly dilates homogenously. The different behaviour of the RV and LV can be explained from its intrinsic different morphological characteristics, as well as the changes in loading conditions induced by exercise. The RV is more compliant and elastic than the LV since LV cavity has not been observed to increase acutely in size during extended submaximal exercise, while RV size can increase up to 10% during moderate exercise (Claesen et al., 2014). Thus, the RV can change shape acutely. The pulmonary artery and aorta also have very different behavior and characteristics with the pulmonary artery being more compliant than the aorta (Slife et al., 1990; Marcus et al., 1994). Additionally, the pressure increases proportionally more in the pulmonary artery during exercise, which translates to RV loading (La Gerche, Rakhit, et al., 2017; Kovacs et al., 2009). This is consistent with the observed remodelling in the RV outflow. Another contributing factor, which could not be assessed using the currently available data, might be the induced hypertrophy in the trabeculated RV apex, thus effectively reducing the potential apical stroke volume and forcing the base to remodel accord- ingly. Our data show that athletic remodelling at rest has a clear relationship with exercise response: athletes with more remodelling can reach bigger VO2 max and O2 pulse. Via Fick’s Principle, O2 uptake can be used to obtain an estimate of the CO during exercise, even when the pulmonary extraction rate (PER) is not known (Stringer et al., 1997). In (La Gerche, MacIsaac, et al., 2010), La Gerche et al. reported that the PER interindi-

74 vidual variability was independent of physical training, so we can conclude that the differences in VO2 max and O2 pulse were due to differences in CO and SV respectively. Since we found no correlation of athletic remodelling and acute changes of ventricular geometry during exercise, we suggest that the higher SV might be caused by increased deformation during exercise, explained by the weak link between athletic remodelling and RV GLS reserve. The long-term consequences of this remodelling are unknown, as follow- up is not available, but remodelling seems positive, given that it is correlated with a better cardiovascular response.

4.4.1. Limitations

The SA MRI images had lower quality in the apical part due to the low resolution in the axial direction, and the presence of trabeculations making distinguishing between cavity and myocardium difficult. Therefore, while standard practice, using only MRI SA to construct the 3D model is not ideal to evaluate the apical region and apical differences between the populations might have stayed undetected due to this. Additionally, we did not manually correct the automatic segmentations contours in the images, to better maintain the point-to-point correspondence. We treated these segmentation errors as measurement error in the analysis. Finally, the atria were not included in the image and therefore we could not evaluate them using SSA. The echocardiographic assessment was done only pre- and post-exercise, and given the rapid recovery of athletes can affect the post- exercise analysis. Assessing shape during exercise would allow to better understand the acute changes occurring during exercise, and characterise the relationship between athletic shape remodelling and cardiovascular response to exercise. As stated, there is no follow-up data to confirm the positive effect of this remodelling. It must be studied if this remodelling, that dilates the RV outflow, has any relationship with arrhythmogenic right ventricle outflow in the long term.

4.5. Conclusion

This work uses SSA to identify chronic resting shape remodelling induced by endurance sport in both ventricles, using MRI. This remodelling consists of an LV increase in size and myocardial mass, and a shape change in the RV: a shift of the volume distribution from the inlet towards the outﬂow. Since RV remodelling is concentrated in the outﬂow, it adds more evidence to the importance of the pulmonary circulation in athletes.

75 After quantifying the remodelling in all athletes we found that, during acute exercise, it is associated to maximal O2 consumption, O2 pulse and, weakly, to RV GLS reserve: athletes with more athletic remodelling showed better acute exercise performance. As future work, SSA could be used to ﬁnd regional shape differences induced by pathological remodelling (hypertrophic cardiomyopaties, arrhythmogenic right ventricle) that might have an overlapping remodelling with the athlete’s heart, and where current clinical measurements are not well discriminating.

76 Chapter 5

REDUCED EXERCISE CAPACITY AND EXAGGERATED IMPACT OF CONVENTIONAL RISK FACTORS ON CARDIAC FUNCTION IN ADULTS BORN SMALL-FOR-GESTATIONAL AGE

5.1. Introduction

Small-for-gestational age (SGA), deﬁned as being born with a birth weight below the 10th percentile, affects 6-10% of pregnancies and predominantly includes growth-restricted fetuses. For over 30 years, epidemiological studies (Barker, Osmond, Golding, et al., 1989; Rich-Edwards et al., 1997; Leon et al., 1998; Syddall et al., 2005; Lawlor et al., 2005) have

This chapter is adapted from: Crispi F., Rodríguez-López M., Bernardino G., Sepúlveda-Martínez A., Prat-Gonzalez S., Pajuelo C., Perea R. J., Caralt M.T., Casu G., Vellvé K., Crovetto F.,Burgos F., De Craene M. , Butakoff C., Gonzalez Ballester M.A., Blanco I., Sitges M., Bijnens B., Gratacós E. "Reduced exercise capacity and exaggerated impact of conventional risk factors on cardiac function in adults born small-for-gestational age" [Under review]

77 shown a consistent association between SGA and cardiovascular mortality. While the precise mechanisms underlying this association are not fully clarified, fetal cardiac remodelling and dysfunction are proposed as main contributors. SGA is associated with cardiac remodelling and dysfunction in fetuses(Girsen2007; Hecher et al., 1995; Crispi, Hernandez-Andrade, et al., 2008; Rodríguez-López et al., 2017), children(Sehgal et al., 2014; Cruz-Lemini et al., 2016; Crispi, Bijnens, Figueras, et al., 2010) and preadolescents(Sarvari et al., 2017). However, the persistence of the cardiac effects of SGA into adulthood is unclear. A Swedish cohort of 19 young adults (aged 22-25 years) born extremely small described slightly smaller ventricular and vascular dimensions with normal function(Bjarnegård et al., 2013). A follow-up of the Young Finns Study, including 157 adults (34-49 years of age) born SGA, showed subtle increase in heart size with preserved systolic and diastolic function(Arnott et al., 2015). The Enigma study, a long-term follow-up study of 882 young adults in UK, reported a small increase in systolic blood pressure in those born SGA, but this association disappeared after adjustment for body size(Miles et al., 2011). Overall, these studies suggest some statistically significant but clinically subtle changes in cardiac structure and function in adults born SGA. All the above studies evaluated baseline changes, but no tests to challenge the heart were conducted. Evaluating the effect of stress could be relevant to reveal the long term effects of in utero adverse conditions, particularly in young patients. For instance, Scherrer et al. showed that children conceived by assisted reproductive technologies had similar baseline measures but remarkable differences in pulmonary pressure when exposed to low environmental oxygen(Scherrer et al., 2012). Likewise, Huckstep et al. showed similar baseline values between young adults born preterm and controls, but a marked reduction of ejection fraction under exercise(Huckstep et al., 2018). On the other hand, cardiac remodelling induced in early stages of life might be at- tenuated or boosted by postnatal lifestyle. Overweight after SGA further increases the risk of coronary events, insulin resistance and raised blood pressure(Huxley et al., 2000; Eriksson, T. Forsén, et al., 2001; Barker, Os- mond, T. J. Forsén, et al., 2005). A detrimental effect of tobacco smoking on pulmonary function of SGA individuals has also been suggested (C. E. Stein et al., 1997). The effect of prevalent risk factors such as smoking or overweight in cardiac remodelling and function of SGA adults has not been investigated. We postulated that adults born SGA might show permanent cardiac remodelling and could have increased cardiac susceptibility to external stressors. To evaluate this hypothesis, we identified young adults born

78 SGA and controls from a perinatal cohort. We performed echocardiography, cardiac magnetic resonance imaging (MRI) and cardiopulmonary exercise testing. In addition, interaction analyses were conducted to assess the potential synergistic effect of overweight and tobacco smoking on cardiac remodelling and function.

5.2. Methods

5.2.1. Study design

Ambispective cohort study including young adults (20-40 y old), 245 born with SGA and 251 with normal intrauterine growth (controls). Sub- jects were randomly identified within a perinatal registry of 32,490 deliv- eries taking place from 1975 to 1995 in a tertiary university hospital in Barcelona (Hospital Sant Joan de Déu), Spain. From 870 adults con- tacted, 287 refused to participate and 87 were excluded due to current pregnancy (n=25), twin pregnancy (n=17), neonatal macrosomia (n=16), major mental disorder (n=11), congenital malformations (n=10), genetic syndromes (n=5) or professional sport practice (n=3), leading to a final sample size of 245 SGA and 251 controls. SGA was defined as a birth weight below the 10th centile for gestational age, according to the strictest definition from contemporary(Jiménez et al., 1982) and current(Figueras et al., 2008) local standards. SGA was defined as being below the 10th centile for both references curves. Controls were defined as birth weight above 10th centile for the two standards used. Young adults recruited for the study were evaluated with a medical history and physical examination, blood pressure, carotid intima-media thickness by ultrasound(J. H. Stein et al., 2008), questionnaires for physical activity(Craig et al., 2003), smoking(Becoña et al., 1998) and glucose and lipid profile tests. Overweight was defined as body mass index above 25. Echocardiography was performed in all subjects (n=496), and cardiovascular magnetic resonance (n=158) and cardiopulmonary exercise testing (n=127) were conducted in randomly selected subgroups. The study protocol was approved by the local Ethics Committee and written consent was obtained for a study participants.

5.2.2. Echocardiography

Each individual underwent a comprehensive echocardiogram using a Vivid E9 (General Electric Healthcare) with a 2.5 MHz (M5S) phased array transducer. Standard echocardiographic views were obtained and images

79 were analyzed offline with commercially available software (EchoPac, version 108.1.6; General Electric Healthcare, Milwaukee, WI). Cardiac dimensions were measured according to the current recommendations(Lang et al., 2015) and indexed by body surface area (BSA). Ventricular sphericity indices were calculated as the ratio base-to-apex length/basal diameters. Relative wall thickness was calculate as (posterior left ventricular (LV) wall thickness*2)/end-diastolic LV cavity diameter. Systolic function was assessed by LV ejection fraction (by biplane method of disks, modified Simpson’s rule) and cardiac output and measured by conventional 2D echocardiogram. LV global longitudinal strain was obtained from 2D speckle-tracking offline analysis (2D strain, EchoPac; General Electric Healthcare). Right ventricular (RV) end-diastolic and end-systolic areas were calculated by planimetry from 2D 4-chamber view in order to estimate fractional area change. Mitral and tricuspid annular plane systolic excursion were assessed by M-mode and systolic annular peak velocities (s’) by real-time tissue Doppler from an apical 4-chamber view. Diastolic function was assessed by mitral and tricuspid peak early (E) and late diastolic (A) filling ratios, tissue Doppler early diastolic (e’) peak annular velocities, and LV isovolumic relaxation time. RV outflow tract (RVOT) acceleration time was also measured as an indirect parameter of pulmonary hypertension.

5.2.3. Cardiovascular magnetic resonance

A total of 77 controls and 81 SGA adults underwent MRI performed on a 3T scanner (MAGNETOM R Trio TimTM, Siemens Healthiners, Er- langen, Germany) using retrospective ECG gating an a dedicated 32- element phased-array receiver coil. Contiguous short-axis cine images covering both ventricles from base to apex were acquired using a standard steady-state free-precession sequence (slice thickness 8 mm, 2 mm interslice gap) during breath hold. Also, long-axis cine images of 4-, 3- and 2-chamber views were acquired. Flow imaging was performed per- pendicular to the main pulmonary artery and of the ascending aorta with a velocity-encoded gradient echo sequence. Forty phases were acquired and encoded velocities were adjusted to the limit range without aliasing. Finally, delayed enhancement imaging was performed 15 minutes after the administration of 0.15 mmol/Kg of gadobutrol (Gadovist R , Bayer His- pania), using a standard inversion-recovery fast gradient-echo sequence matching short axis cine sequence. All images were stored on a digital archive for post processing. LV and RV function analysis were performed with dedicated software (Argus (Siemens, Argus, Siemens Medical Solutions, Germany) and Segment R

80 (Medviso AB, Lund, Sweden)(Heiberg et al., 2010)). Epicardial and endocardial borders were traced in each cine image to obtain LV end-diastolic volume, LV end-systolic volume, LV ejection fraction, and end-diastolic mass. In order to calculate the parameters corresponding to the RV, the endocardial contours of it were drawn at the end of diastole and systole. Right and left atrial areas were planimetered in the cine 4- chamber view. For ventricular sphericity and wall thickness indices by MRI were calculated as described for echocardiography. All parameters were indexed by BSA.

5.2.4. Ventricular shapes

A 3D model of the whole heart was constructed with a in-house customized software using a deformable template to ﬁt the MRI short axis, using a previously described algorithm(Ecabert et al., 2006; Peters et al., 2010). From this model, the endocardial surface of the RV and both the endocardium and epicardium of the LV in end-diastole were extracted. Those 3D surfaces were scaled by BSA, and positioning variability was removed using Procustes Algorithm(Dryden et al., 1998). Shape analysis was done using point distribution model (PDM), which associates each shape with a vector concatenating all the coordinates of the shape vertices.

5.2.5. Cardiopulmonary exercise testing

All subjects completed standard incremental cardiopulmonary exercise testing on a cycloergometer (rage 6-999 watts) using an Ergoselected 100 (Ergoline, Bitz, Germany) with an automatic blood pressure measurement. All measurements were made in a breath-by-breathrespiratory gas exchange system (Medisoft, Sorinnes, Belgium) with peak exercise measurements as follows: workload, minute ventilation, oxygen uptake (VO2), carbon dioxide production (VCO2), oxygen saturation and heart rate. Oxy- gen pulse was calculated as VO2 divided by heart rate. Calculation of the incremental ramp was carried out in a personalised way using the formula described by Hansen et al.(Hansen et al., 1984) All measurements were performed according to the international recommendations and reference values.(Jones et al., 1985)

5.2.6. Sample size calculation

Sample sizes were calculated assuming an unknown but equal variance (previous studies suggest that variances among SGA and controls

81 are similar), 80% power, 5% alpha-error, 1:1 allocation index. A sample of 225 per group was estimated to identify 3% difference between groups in LV ejection fraction by echocardiography assuming a mean of 64 and a standard deviation of 6.5 and a standardised difference of 0.3(Lang et al., 2015). We also calculated the sample size for assuming a standardised mean difference of 0.25 which is an acceptable value to max- imis sample size (standardized mean difference quantiﬁes the between group differences, independently of the units of measurement)(Whitley et al., 2002), estimating 250 individuals per group for echocardiography. For magnetic resonance studies, a sample of 80 individuals per group was estimated to identify 3% difference between groups in ejection fraction by MRI and assuming a standard deviation of 4.5(Lewandowski, Augustine, et al., 2013) and a standardised difference of 0.43. The reduction in sample size needed to detect differences by MRI has been described to be lower than echocardiography due to the high accuracy and low variability of MRI(Bellenger et al., 2000). For cardiopulmonary exercise testing, a sample of 55 individuals per group was estimated to detect a 15% difference in indexed VO2 (Kaminsky et al., 2015).

5.2.7. Statistical analysis

Stata IC version 14.0 (StataCorp. LP, College Station, TX) and Python 2.7 (Enthought INC, Austin TX) were used for statistical analysis. Study groups were described using mean ± SD, median (interquartile range) or frequencies and compared by Student’s t-test, Wilcoxon-Mann Whitney, chi-square or Fisher exact tests as appropriate. Multivariate linear or robust regressions were ﬁtted to adjust for age, gender, asthma, obesity, university education, smoking habit, mean blood pressure, gestational age at delivery, breastfeeding and gestational hypertension. All reported p-values are 2-sided.

Ventricular shape statistical analysis

Ventricular shape variability between the groups was assessed by principal component analysis (PCA) applied to the end-diastolic surfaces obtained from MRI. Ten components were kept, so that 95% of the shape variability was kept in the model.Partial least squares (PLS) - Logistic Re- gression(Bastien, 2005) was performed in that compact representation of the shape space to ﬁnd the three most discriminative shape patterns between controls and SGA, that were combined using a logistic regression model. Age, gender and BSA were added as covariates in this logistic

82 model to correct for potential bias. Statistical signiﬁcance was established by comparing the cross-validated receiver operating characteristic (ROC) of a model that considers shape and confounders to a simpler one that only considers the confounders(DeLong et al., 1988).

Interaction analyses

Smoking habit and overweight were selected for interaction analyses as previous evidence suggested a synergistic effect with SGA(Huxley et al., 2000; Eriksson, T. Forsén, et al., 2001; Barker, Osmond, T. J. Forsén, et al., 2005; C. E. Stein et al., 1997) and they were expected to be relatively highly prevalent cardiovascular risk factors in the population under study. On the contrary, other risk factors such as hypertension or diabetes were not selected due to the expected low prevalence in 20-40 years old adults. To analyse the MRI ventricular shape variability among subpopulations (non-smokers vs smokers and non-overweight vs overweight controls and SGA), we compared the discriminative power of the logistic model applied to the subpopulation with different randomly-generated subpopulations satisfying the same proportion of the outcome class. The p-value was obtained with a Mann Whitney U-test. The association between VO2 and ventricular remodelling score and LV mass were calculated in the overall populations and in the subpopulations of smokers and over weighted subjects using Spearman’s correlation.

5.3. Results

5.3.1. Perinatal data and characteristics at recruitment

Perinatal and adult characteristics are shown in Table 5.1. By design, SGA subjects showed lower birth weight and birth weight centile with similar gestational age at delivery as compared to controls. At baseline assessment, SGA cases showed lower height, weight and BSA, with similar body mass index and rate of sedentary activities as compared to control subjects. Smoking habit was more prevalent in SGA cases as compared to controls. There were no cases of pulmonary hypertension or chronic ob- structive pulmonary diseases. Both groups presented similar rates of overweight, chronic hypertension and diabetes mellitus. Plasmatic concen- trations of glucose, cholesterol and triglyceride were also similar among groups (Table 5.2).

83 Table 5.1: Perinatal and current baseline characteristics of the study population

Controls SGA N 251 245 Perinatal characteristics Birthweight (g) 3400 (3180-3550) 2600 (2400-2700)* Gestational age at delivery (weeks) 40 (39-41) 40 (39-41) Birthweight centile 51 (36-65) 3 (1-5)* Current characteristics Age (years) 30.99 (26.83-35.07) 30.19 (25.93-34.82) Female 120 (47.81) 137 (55.92) White ethnicity 251 (100) 243 (99.18) Height (m2) 1.72 (1.65-1.78) 1.64 (1.58-1.71)* Weight (kg) 71.60 (60.42-81.91) 63.51 (53.81-75)* Body mass index (kg/m2) 24.19 (21.34-26.74) 23.52 (20.79-26.26) Body surface area (m2) 1.84 (1.67-1.98) 1.70 (1.55-1.86)* Previous familiar history of MI 7.57 (19) 8.57 (21) University education 149 (59.6) 99 (40.41)* Smoking habit 65 (25.89) 81 (33.06)* Overweight 98 (39.04) 81 (33.06) Sedentary hours 90 (74.1-105) 87 (71.25-105) Diabetes mellitus 0 (0) 3 (1.22) Chronic hypertension 3 (1.2) 4 (1.63) Systolic blood pressure (mmHg) 116.98 ± 12.39 117.21 ± 13 Diastolic blood pressure (mmHg) 71.91 ± 9.73 71.33 ± 9.8 Carotid intima-media thickness (mm) 0.50 ± 0.07 0.50 ± 0.07 Data are median (interquartile range) or n (percentage). *P<0.05 as compared to controls. MI, myocardial infarction; SGA, small-for-gestational age. Body mass index calculated as the weight in kilograms divided by the square of the height in meters. Body surface area was calculated by the Haycock formula. Overweight deﬁned as body mass index above 25 kg/m2. Blood pressure was obtained at the beginning of the medical evaluation by a trained nurse while the individual was seated after having rested for 5 to 10 minutes. Carotid intima-media thickness was performed ofﬂine based on a trace method with the assistance of a computerised program (EchoPAC, General Electric Healthcare, version 108.1.x) from ultrasonographic images.

84 Table 5.2: Perinatal characteristics and current laboratory results of the study population.

Controls SGA N 251 245 Perinatal characteristics Prematurity 11 (4.18) 6 (2.3) Gestational hypertension 7 (2.79) 17 (6.94)* Breastfeeding 40 (16.33) 68 (28.45)* Current laboratory results Glucose (mg/dL) 89.62 ±11.82 88.61 ±14.26 Cholesterol LDL (mg/dL) 113.18± 27.83 114.57± 27.65 Cholesterol HDL (mg/dL) 47.74 ±14.36 48.54 ±12.76 Triglyceride (mg/dL) 106.08± 60.31 106.52± 58.71 Data are median (interquartile range) or n (percentage). *P<0.05 as compared to controls. SGA indicates small-for-gestational age; LDL, low-density lipoprotein; and HDL high-density lipoprotein.

5.3.2. Baseline cardiac structure and function

Echocardiographic and MRI results of the overall study populations are shown in Tables 5.3, 5.4 and 5.5 and Figure 5.1. Indexed biventricular and RVOT dimensions were slightly increased in SGA as compared to controls, with similar ventricular sphericity, mass and relative wall thickness. Atrial and LVOT dimensions were similar among groups. Cardiac function was mainly preserved, with a slight decrease in LV ejection fraction, mitral e’, tricuspid annular plane systolic excursion and RVOT acceleration time in SGA as compared to controls. No delayed enhancement patterns were seen in MRI of any individual of both groups. Statistical shape analysis was subsequently applied to find the most discriminating shape pattern between SGA and controls. Figure 5.1 illustrates the resulting pattern, which corresponds to subtle changes mainly in the RV with SGA displaying slight flattening of the basal septum and enlargement of the basal portion of RV, which increases the basal curvature. Delong test was used to compare the cross-validated area under de ROC curve of the statistical shape analysis model with a simple one that only considered confounders, establishing statistical significance with a p-value of 0.02.

85 (a) (b)

Figure 5.1: Baseline cardiac shape of the study populations (non- stressed). 5.1a) Individual cardiac magnetic resonance (CMR) images in a control subject and a small for gestational age (SGA) case subject. Four- chamber (top) and three-chamber left ventricular (LV) outﬂow tract (bottom) views at end-diastole illustrating a ﬂattening of the basal septum and enlargement of the basal portion of RV, that increases the basal RV curvature (red arrows) in SGA. 5.1b) Population-derived representative synthetic meshes depicting a mean control and an extreme SGA. The reddish colour map shows the places with more differences of SGA as compared to the control, that are concentrated in the RV, mostly an increase of the RV curvature at the lateral- posterior base and infundibulum

86 Table 5.3: Echocardiographic results of the left heart study populations

Controls SGA N 251 245 Left morphometry LV base-to-apex length (mm/m2) 45.53 (42.31-48.38) 47.49 (43.44-50.49)* LV basal diameter (mm/m2) 24.81 (23.47-26.23) 25.74 (24.14-27.12)* LV sphericity index 1.84 ± 0.18 1.85 ± 0.20 Relative wall thickness 0.30 (0.27-0.34) 0.30 (0.26-0.33) Left atrial area (mm2/m2) 8.91 (7.74-9.89) 8.97 (7.93-10.14) LVOT diameter (mm/m2) 11.82 (10.88-12.56) 11.96 (11.29-12.89) LV function LV ejection fraction (%) 64 (59-67) 62 (58-66)* LV stroke volume (L/m2) 39.64 (34.54-45.67) 39.08 (34.23-45.43) LV cardiac index (L/min/m2) 2.66 (2.26-3.07) 2.75 (2.33-3.20) Heart rate (bpm) 67 (60-75) 69 (62-80) MAPSE (mm/m2) 9.65 (8.67-10.70) 9.82 (8.57-11.30) LV isovolumic relaxation time (ms) 69.26 ± 16.40 70.01 ± 16.68 Mitral E/A 1.62 ± 0.41 1.67 ± 0.50 Mitral s’ (cm/s/m2) 6.17 ± 1.29 6.41 ± 1.38 Mitral e’ (cm/s/m2) 9.64 (7.33-9.98) 9.45 (7.77-10.96)* LV global strain (%) -18.27 ± 3.75 -18.46 ± 2.71 Data are mean±SD or median (interquartile range). Cardiac dimensions, volumes, output and motion were indexed for body surface area. *P-value <0.05 as compared to controls adjusted by age, gender, asthma, obesity, university education, smoking habit, mean blood pressure, gestational age at delivery, breastfeeding and gestational hypertension. SGA indicates small-for-gestational age; LV, left ventricle; LVOT, left ventricular outﬂow tract; ; MAPSE, mitral annular plane systolic excursion; E, early diastole; A, atrial contraction; s’, systolic annular peak velocity; e’, early diastolic annular peak velocity; .

87 Table 5.4: Echocardiographic results of the left heart study populations

Controls SGA N 251 245 Right morphometry RV base-to-apex length (mm/m2) 37.98 (34.73-41.13) 39.14 (36.27-42.47)* RV basal diameter (mm/m2) 20.09 ± 2.88 20.31 ± 2.96 RV sphericity index 1.92 ± 0.28 1.96 ± 0.27 Right atrial area (mm2/m2) 7.43 ± 1.43 7.18 ± 1.29 RVOT diameter (mm/m2) 11.81 ± 1.66 12.20 ± 1.57* RV function Fractional area change (%) 0.44 ± 0.08 0.46 ± 0.09 TAPSE (mm/m2) 13.64 (12.16-15.25) 14.46 (12.61-16.11)* Tricuspid s’ (cm/s/m2) 7.53 ± 1.53 7.75 ± 1.45 Tricuspid e’ (cm/s/m2) 8.44 (7.15-10.15) 8.66 (7.08-10.78) RVOT acceleration time (ms) 150 (135-160) 147 (132-159)* Data are mean±SD or median (interquartile range). Cardiac dimensions, volumes, output and motion were indexed for body surface area. *P-value <0.05 as compared to controls adjusted by age, gender, asthma, obesity, university education, smoking habit, mean blood pressure, gestational age at delivery, breastfeeding and gestational hypertension. SGA indicates small-for-gestational age; RV, right ventricle; RVOT, right ventricular outﬂow tract; s’, systolic annular peak velocity; e’, early diastolic annular peak velocity; TAPSE, tricuspid annular plane systolic excursion .

88 Table 5.5: Cardiovascular magnetic resonance results of the study populations.

Controls SGA N 77 81 Left morphometry LVEDV (mL/m2) 86.65 ± 12.76 83.39 ± 12.19 LVESV (mL/m2) 34.46 ± 7.21 34.33 ± 6.53 LV base-to-apex length (mm/m2) 4.99 (4.67-5.30) 5.03 (4.67-5.53)* LV basal diameter (mm/m2) 25.6 (23.8-27) 25.9 (24.1-27.1)* LV sphericity index 0.40 ± 0.08 0.41 ± 0.10 Relative wall thickness 2.28 (2.03-2.45) 2.19 (1.93-2.58) LV mass (g/m2) 47.75 ± 11.93 45.45 ± 8.85 Left atrial area (mm2/m2) 12.59 (11.74-13.69) 12.32 (10.86-14.26) Aortic area (mm2/m2) 3.58 ± 0.60 3.67 ± 0.72 Right morphometry RVEDV (mL/m2) 78.84 ± 15.10 74.13 ± 13.76 RVESV (mL/m2) 34.42 (28.33-42.91) 32.06 (26.89-36.85) Right atrial area (mm2/m2) 11.37 ± 2.11 10.34 ± 1.98 Pulmonary artery area (mm2/m2) 3.91 (3.4-4.29) 3.7 (3.3-4.34) LV function LV ejection fraction (%) 60.25 (58.83-63.64) 59.2 (55.68-61.84)* LV cardiac index (mL/min/m2) 2.34 (2.99-3.72) 3.16 (2.91-3.66) RV function Right ejection fraction (%) 54.97 (51.57-58.47) 56.12 (52.94-60.67) RV cardiac index (mL/min/m2) 2.78 ± 0.54 2.77 ± 0.51 Data are mean±SD or median (interquartile range). Cardiac dimensions, volumes, mass and output were indexed for body surface area. *P-value <0.05 as compared to controls adjusted by age, gender, asthma, obesity, university education, smoking habit, mean blood pressure, gestational age at delivery, breastfeeding and gestational hypertension. SGA indicates small-for-gestational age; LV, left ventricle; RV, right ventricle; EDV, end-diastolic volume; ESV, end-systolic volume.

89 5.3.3. Exercise capacity

Results of cardiopulmonary exercise testing are shown in Table 5.6 and Figure 5.2. Adults born SGA achieved lower maximal workload and showed less oxygen consumption at peak exercise with similar saturation as compared to controls.

Table 5.6: Results at peak exercise in the study populations.

Controls SGA N 66 61 Maximal workload (watts) 214 ± 60 180 ± 62* Ventilation (%) 91.1 (71.2-109.7) 76.9 (60.6-90.9)* VO2 (mL/min/kg) 29.5 (24-36) 26 (21.5-33.5)* VCO2 (mL/min/kg) 44.37 (38.24-50.09) 39.18 (33.03-48.93) O2 saturation (%) 97.69 ± 1.52 97.56 ± 1.55 Heart rate (bpm) 176 (168-185) 176 (165-184) Pulse pressure (mmHg) 90 (75-108) 75 (56-90)* Oxygen pulse (mL/beat/min) 12.67 ± 3.93 10.64 ± 3.43* Data are mean ± SD or median (interquartile range). *P-value <0.05 as compared to controls adjusted by age, gender, asthma, obesity, university education, smoking habit, mean blood pressure, gestational age at delivery, breastfeeding and gestational hypertension. Pulse pressure calculated as systolic blood pressure divided by diastolic blood pressure. Oxygen pulse calculated as VO2 divided by heart rate. SGA indicates small-for-gestational age; O2, oxygen; VO2, oxygen consumption; and VCO2, carbon dioxide production.

Exercise capacity signiﬁcantly correlated to LV mass (Rho=0.7934, P<0.001) and biventricular shape index (Rho=-0.2549, P=0.0094) in the overall population (Figures 5.2b and 5.2d). SGA adults presented a different regression line and had signiﬁcantly less exercise capacity per unit of cardiac mass than controls (interaction p=0.04) (5.2c).

5.3.4. Effect of smoking and overweight on cardiac remodelling among the study groups

Interaction analysis on MRI shape revealed a differential effect of smoking on RV remodelling in SGA vs controls (Figure 5.3) with no differen-

90 (a) (b)

Figure 5.2: Workload and oxygen consumption (VO2) at peak exercise and its relationship with left ventricular (LV) mass and remodelling score in the study populations: 5.2a) Bar graphs showing decreased maximal workload, VO2 and VO2 per unit of LV mass in SGA as compared to controls. Bars are mean values and lines SD. *denotes P-value < 0.05 as compared to controls. 5.2b) Regression line for VO2 by workload for SGA in red and controls in blue (left), and the plot of all regression lines for each patient (right) illustrating the reduced maximal workload of SGA; 5.2c) Re- gression line showing a positive relationship between the peak VO2 and the indexed LV mass (Rho 0.7934, P<0.001). SGA adults in red presented a different regression line and had signiﬁcantly less exercise capacity per unit of LV mass than controls in blue (interaction p=0.04) 5.2d) Regres- sion line showing an inverse relationship between the peak VO2 and the quantity of biventricular ventricular remodelling score by 3D shape analysis (ρ = −0.25, P = 0.01).

91 tial impact on LV shape. As anticipated, the control group showed larger RV dimensions in response to smoking. Remarkably, SGA individuals showed a greater RV remodelling in response to smoking with wider RV base and RVOT (p = 0.04) (Figure 5.4 and 5.3 ). A significant correlation between biventricular remodelling score and oxygen consumption at maximum exercise could be observed in the subpopulation of smokers (ρ = 0.45 p=0.02) (Figure 5.5). Interaction analysis on MRI shape was also used to assess the impact of overweight on cardiac structure in the study groups, revealing a differential pattern of LV remodelling in SGA vs controls (p=0.04) (Figures 5.4, 5.3 and 5.5) with no differential impact on RV shape. Overweight SGA had shorter and more spherical LV than overweight controls. Overweight SGA had also signs compatible with basal septal hypertrophy, with more flat- tened septum and septal bulge [the septal surface in the RV side is more flatten, and there appears to be a bulge in the LV part]. A significant negative correlation between LV remodelling score and oxygen consumption at maximum exercise could be observed in the subpopulation of overweight (Rho 0.459 p=0.0037) and also in overweight SGA (Rho 0.610 p=0.0032, as shown in (Figure 5.5.

5.4. Discussion

This study reveals less exercise capacity and exaggerated cardiac susceptibility to stress in adults who were born SGA. Risk factors such as smoking or overweight were associated with distinct changes in cardiac structure and function that correlated with reduced exercise capacity in SGA individuals. Thus, we provide evidence that SGA is a modifier exag- gerating the impact of traditional cardiovascular risk factors which could be one of the contributing factors of the well-documented increase in cardiovascular mortality in this population. We found subtle cardiac structural and functional changes in SGA adults in basal conditions. At rest, adults born SGA showed slightly increased ventricular and outflow indexed dimensions, with similar mass and relative wall thickness. Ventricular shape analysis also confirmed subtle changes with slight flattening of the basal septum and enlargement of the RV basal portion. Cardiac function was mainly preserved with a slight decrease in LV ejection fraction and pulmonary acceleration time. These data are con- cordant with previous studies evaluating SGA in adulthood(Cruz-Lemini et al., 2016; Cunha et al., 2015) suggesting that postnatal lifestyle partly compensates for the cardiac remodelling observed in SGA fetuses and children (Becoña et al., 1998; Bellenger et al., 2000; Bellinger et al., 2006;

92 Figure 5.3: Left and right ventricular 3D meshes generated by CMR from control and SGA datasets among overweight and smoking populations respectively. The left column shows the mean control. The center column the effect of the stress within the controls, where the colour map in green highlights the most signiﬁcant differences between unstressed and stressed controls. Finally, the right column shows the extreme stressed SGA, where the color map in red depicts differences between stressed controls and stressed SGA. It illustrates a more intense RV remodelling in SGA smokers, and a different pattern of LV remodelling (more spherical apex and septal bulge) in overweighted SGA.

93 Figure 5.4: Illustrative CMR examples in an over weighted and smoker control and SGA individuals. Control individuals (central column) respond to smoking by right ventricular (RV) dilation, and to overweight by increasing left ventricular (LV) myocardial wall thickness and mass (pointed out by red arrows). SGA individuals (right column) presented a more exaggerated response to smoking with wider RV base and RVOT, and different response to overweight with milder increase of LV mass (mainly focused in the basal septum) and more spherical LV shape (pointed out by red arrows).

Figure 5.5: Regression lines showing an inverse relationship between the performance in the exercise test (VO2 at maximum exercise) and ventricular remodelling score by 3D shape analysis in smokers (right) and overweight (left) subpopulations.

94 Bjarnegård et al., 2013). Fetal cardiac remodelling and dysfunction is thought to reﬂect the effects of chronic pressure overload from a smaller, more resistant, placental vascular system, together with chronic volume overload due to fetal hemodynamic redistribution to cope with restriction of nutrients and oxygen(Bellinger et al., 2006). Growth restricted fetuses present larger, globular and hypertrophic ventricles with reduced longitudinal motion and impaired relaxation.(Bellinger et al., 2006; Bjarnegård et al., 2013) Sixty percent have also a post systolic shortening in the basal segment of the septal ventricular wall(Crispi, Bijnens, Sepulveda-Swatson, et al., 2014). Most of these features persist in infancy(Sehgal et al., 2014; Cruz-Lemini et al., 2016), childhood(Crispi, Bijnens, Figueras, et al., 2010) and pre-adolescence(Sarvari et al., 2017). The subtle nature of the cardiac changes observed in adulthood might be partially explained by the inclusion of milder cases of fetal growth restriction in adult cohorts. In addition, multiple inﬂuences during lifetime contribute to attenuate or boost the effects of fetal programming changes, as discussed below.

Our results demonstrated a reduced exercise capacity in SGA adults with average reductions of 16% in maximal workload and 12% in oxygen consumption at peak exercise. Such differences are noteworthy considering that the study subjects were healthy and 30 year-old on average. To our knowledge, this is the first study evaluating cardiopulmonary performance in response to an incremental exercise test in a cohort of SGA. Previous studies had evaluated the association between exercise capacity and SGA indirectly with conflicting findings. While some data suggest lower levels of leisure-time physical activity and increased levels of sedentary behaviour in SGA individuals(Eriksson, Ylihärsilä, et al., 2004; Rogers, 2005; Ander- sen et al., 2009; Martin et al., 2009; Kajantie et al., 2010; Fernandes et al., 2010; Bonsdorff et al., 2011), other studies could not demonstrate any association of SGA with physical activity (Mattocks et al., 2008; Salonen et al., 2011; Ridgway et al., 2011) or even less sedentary time(Hildebrand et al., 2015). The interpretation of previous studies is hampered by the use of definitions of SGA based purely on birth weight, which likely includes variable proportions of individuals with low birth weight due to prematurity(Rogers, 2005; Kajantie et al., 2010). Furthermore, previous studies did not apply cardiopulmonary exercise workouts but surrogates of physical activity such as questionnaires, accelerometer or dynamometer. We established strict criteria and used centiles for gestational age to select a group of well-defined SGA predominantly resulting from fetal growth restriction. Likewise, the use of a standardised incremental cardiopulmonary exercise test allowed to measure precisely cardiopulmonary performance. Our results are also consistent with experimental data showing that off-

95 spring from food-restricted pregnant rats present a lower physical activity at adult age(Vickers et al., 2003; Cunha et al., 2015; Bellinger et al., 2006). In addition, the results showed that exercise capacity significantly correlated with LV mass and biventricular remodelling score. Interestingly, SGA showed less exercise capacity for the same amount of LV mass as compared to controls suggesting altered intrinsic myocardia tissue properties (contractility, compliance,...) or cardio-pulmonary maladaptation to exercise. This finding is in line with animal studies demonstrating a reduced cardiac performance and increased cardiac superoxide generation in response to exercise in male SGA rats(Reyes et al., 2015). These data indicate that the poorer exercise capacity might be–at least partially- ex- plained by the cardiac changes observed in SGA, and deserve further investigation in experimental and clinical studies. We provide evidence that SGA adults develop a different cardiac response to smoking and overweight. SGA who smoke showed more marked RV changes as compared to controls, with wider RV base and RVOT. Like- wise, overweight SGA showed signs of basal septal hypertrophy together with shorter and more spherical LV as compared to overweight controls. The results are consistent with experimental evidence. In SGA rats, a postnatal high-fat diet triggered decreased aerobic cardiac performance and increased myocardial susceptibility to ischemia(Rueda-Clausen et al., 2012; Shah et al., 2017). This study provides first evidence in humans suggesting an augmented effect of cardiac risk factors in SGA adults. Together with previous studies, the findings support the hypothesis that SGA could operate as a first hit leading to latent susceptibility, which combined with risk factors could accelerate progression to cardiac disease. This notion is indirectly supported by previous epidemiologic and experimental studies. Postnatal excessive weight gain after SGA further increases the risk of coronary events, insulin resistance and raised blood pressure(Huxley et al., 2000; Eriksson, T. Forsén, et al., 2001; Barker, Osmond, T. J. Forsén, et al., 2005). Likewise, it negatively affects childhood aerobic and neuro- muscular fitness(Deutekom et al., 2015) and physical functioning in older age(Bonsdorff et al., 2011). A detrimental effect of tobacco smoking on pulmonary function of SGA individuals has also been suggested(C. E. Stein et al., 1997). Conversely, breastfeeding and healthy-fat dietary intake seem to improve cardiovascular outcomes in individuals born SGA or preterm (Rodriguez-Lopez et al., 2016; Lewandowski, Lamata, et al., 2016). This study has some strengths and limitations that merit comment. This constitutes a large cohort study of well-characterised cases selected from delivery and assessed in adulthood. The use of birth weight centiles

96 by two standards(Jiménez et al., 1982; Figueras et al., 2008) ensured a fair identification of true SGA cases most likely reflecting true fetal growth restriction. We acknowledge that prenatal ultrasonographic information could have helped to improve the selection, but routine ultrasound was only implemented in late 80s and therefore the data were either not available or not reliable. The study comprised a comprehensive cardiovascular assessment including cardiopulmonary exercise testing and ventricular shape analysis. We chose smoking habit and overweight because previous evidence suggested a synergistic effect with SGA(Huxley et al., 2000; Eriksson, T. Forsén, et al., 2001; Barker, Osmond, T. J. Forsén, et al., 2005) and they are prevalent and modifiable cardiovascular risk factors. Future studies are warranted to study the impact of other risk factors such as diabetes, metabolic syndrome or coronary events. A sub analysis according to gender could not find sex-specific differences in cardiac results (data not shown), however our sample size might not be powered enough to demonstrate gender differences. All cardiovascular results were adjusted by several potential confounders such as age, gender, asthma, obesity, university education, smoking habit, mean blood pressure, gestational age at delivery, breastfeeding and gestational hypertension. However, we acknowledge that our study was not designed to assess the effect of other prenatal, neonatal, and postnatal factors on cardiac structure or function. In addition, we acknowledge that the changes reported here are subclinical with most baseline cardiovascular measurements lying within normal ranges. The use of a young adult cohort avoided the interference of other co morbidities -such as hypertension, diabetes, coronary disease, heart valve disease, stroke or heart failure- but it prevented confirming whether the risk factors evaluated in SGA subjects are truly associated with increased cardiovascular disease later in life. Despite the differences here reported, their longer-term persistence and association with cardiovascular disease remains to be proven.

For more than 20 years, epidemiological studies have consistently demonstrated that low birth weight is associated with increased adult cardiovascular mortality. However, the mechanisms underlying this association are still unclear. Here, we provide strong evidence to support increased cardiac susceptibility to stress, indicating a second hit mechanism for the higher cardiovascular risk of SGA adults. If conﬁrmed, these ﬁndings open new opportunities for prevention of cardiovascular disease. The implications for public health are important as growth-restricted SGA affects 6- 10% of the population and overweight ranges 20-50% in the developed world. SGA can be easily picked up in a routine clinical history and labelling SGA as a high-risk population could allow personalized interven-

97 tion strategies in this subgroup. The impact of reducing morbidity in only a fraction of these patients could be remarkable. Although it is likely that, as a whole, the effects of SGA on adult cardiovascular mortality rate are not huge (ranging 1-25%), a conservative estimate of 5% attributed risk and 30% improvement would result in reductions of 12,000 deaths/yearly in the US.

5.5. Conclusion

In conclusion, this study reveals for the first time that young adults born SGA have reduced exercise capacity and increased cardiac susceptibility to risk factors. Our results support that the in utero cardiac effects of fetal growth restriction persist into adulthood predominantly in the form of cardiac susceptibility. Studies with larger sample sizes and including older subjects are required to confirm and better characterise these observations. These results support that SGA should be considered a cardiovascular risk factor that might benefit from preventive strategies. Given the high prevalence of SGA, targeting lifestyle policies in this group could have a high impact from a public health perspective.

98 Chapter 6

CONCLUSION

6.1. Summary

In this thesis, we have proposed computational methods to analyse cardiac regional shape remodelling based on information extracted from 3D imaging modalities: magnetic resonance imaging (MRI) and 3D-echo. These techniques have been applied to identify and quantify the presence of subtle cardiac regional shape remodelling in individuals. These techniques are particularly interesting for the right ventricle (RV) assessment, which has a high morphological complexity that hampers its analysis through traditional means. To explore the function-geometry interplay, we used traditional statistical methods to find relationships between our shape remodelling patterns and functional parameters, as retrieved from 2D and 3D echocardiography, MRI as well as compared them to cardiorespiratory parameters during a maximal exercise test. The first method developed during this thesis was a statistical shape analysis (SSA) framework that identified shape differences between two populations while taking into account the shape variability due to certain demographic variables (age, gender and body surface area (BSA)). We studied the effect of a demographics imbalance, and how our framework was able to correct for this imbalance allowing us to recover unbiased shape remodelling patterns when the input populations where unbalanced. This method was used to obtain insights in the functional and shape remodelling of athletes and small-for-gestational age (SGA) individuals. We were able to identify particular shape patterns, specially affecting the RV, that were associated to the specific conditions of athletes and SGA. Fur- thermore, for the first time, we showed that in the case of SGA, the presence of remodelling was associated to external risk factors like smoking and overweight. We also discovered that the found RV athletic remodelling

99 was associated to a better cardiopulmonary performance during exercise testing. The second method consisted of a geometry processing method that parcellated the RV in 3 meaningful regions: apex, inlet and outflow. This method was more specific and less exploratory than the previous one, particularly suited for when the image quality is too low to establish point- to-point registration. The parcellation of the RV in 3 regions intended to re- produce and formalise the typical biaxial structure of the RV: one from the apex to the tricuspid and the other from the apex to the pulmonary valve. We tested the reproducibility and validated our method: we found that our method intraobserver reproducibility coefficient was below < 10%, and a validation with a synthetically remodelled RVs showed that the method was able to identify circumferential remodelling but less longitudinal ones.

6.2. Methodological future work

The proposed SSA pipeline was currently used to answer research questions where traditional methods failed to detect relevant remodelling and thus to obtain novel insights. However, with more elaborate validation, it could also be deployed in clinical practice. The derived remodelling indices can assess and discriminate adverse and benign remodelling. The confounder correction used a relatively small control population (77), a further improvement of the framework would be to use a larger datasets in the determination of the normality models, such as for example the UK BioBank. In this thesis, the analysis of cardiac function was based on clinically- derived indices. A next step is to develop computational tools to analyse cardiac function analogously to the ones developed for the anatomy. This would allow for example for a better assessment of the pulmonary circulation: our analysis suggested its importance, but its evaluation is still very difﬁcult using non-invasive imaging. A computational model-based analysis of the cardiac function, that incorporates both bio-physical modelling and physiology/anatomy knowledge, may give further insights in the relation between changes of morphology and function. A second step in that direction would be to couple the functional and anatomical model in a full representation of the heart. Finally, another line of research is to incorporate uncertainty in our models. So far we have only considered one modality and one acquisition for each patient, while in reality there are several acquisitions in each study. This data inconsistency can be addressed through the development of a model that explicitly integrates these multiple sources of information

100 and outputs a probability distribution over the different parameter, taking into account noise and variability.

6.3. Clinical future work

This thesis contributed and applied statistical analysis tools for helping to better understand heart remodelling. Even if we have made progress towards answering some question, many more follow-up questions and research directions were raised. Even if the morphological remodelling at rest has been well characterised, the trigger of some specific pathologies, such as an arrythmogenic right ventricular outflow tract, has yet to be discovered. Understanding such complex relationship will likely require the framework to accommo- date for longitudinal data. Also, since the incidence of this disease is very low, an alternative might be to use biophysical modelling to explore the relationship between shape and the propensity of arrhythmia’s. Another research direction is to assess the physiological changes of shape occurring in acute and chronic heart failure. Novel protocols also allow MRI acquisition during exercise, and would allow to identify the acute shape response to exercise and compare it to the chronic changes. The objective of the analysis of the SGA cohort was to see how intrauterine growth restriction (IUGR) influences the heart in the long term. However, in the current study, IUGR could not be diagnosed directly and had to be observed through its proxy, weight at birth. Given the small magnitude of the cardiac differences, it is important to verify in a more con- trolled population that the found differences correspond indeed to IUGR and not an external factor. Our results have found clear differences in the RV as well as a lower oxygen capacity during exercise: it now has to be further investigated if the problem is originating from the heart or the lungs. Finally, the technique proposed for volumetric parcellation of the RV can be used to assess regional remodelling in clinical 3D echocardiographic datasets involving volume overload of the RV. This might help to better differentiating pathologies that with current measurements have overlapping syndromes.

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Publications

Conference papers

1. Bernardino G., Butakoff C., Nuñez-Garcia M., Sarvari S., Rodriguez- Lopez M., Crispi F., González Ballester M. A., De Craene M., Bijnens B., "Estimating 3D Ventricular Shape From 2D Echocardiography: Feasibility and Effect of Noise". In: Pop M., Wright G. (eds) Func- tional Imaging and Modelling of the Heart 2017. Lecture Notes in Computer Science, vol 10263. Springer

2. Doste R., Soto-Iglesias D., Bernardino G., Sebastian R., Giffard- Roisin S., Cabrera-Lozoya R., Sermesant M., Berruezo A., Sánchez- Quintana D., Camara O., "A Rule-Based Method to Model Myocar- dial Fiber Orientation for Simulating Ventricular Outﬂow Tract Arrhyth- mias." In: Pop M., Wright G. (eds) Functional Imaging and Modelling of the Heart. FIMH 2017. Lecture Notes in Computer Science, vol 10263. Springer In: Pop M., Wright G. (eds) Functional Imaging and Modelling of the Heart. FIMH 2017. Lecture Notes in Computer Sci- ence, vol 10263. Springer

3. Giménez Mínguez P, Bijnens B, Bernardino G, Lluch E, Soveral I, Gómez O, Garcia-Canadilla P. "Assessment of haemodynamic remodeling in fetal aortic coarctation using a lumped model of the circulation. "

4. Nuñez-Garcia M, Bernardino G, Doste R, Zhao J, Camara O, Bu- takoff C. "Standard quasi-conformal ﬂattening of the right and left atria". In: Coudière Y, Ozenne V, Vigmond E, Zemzemi M (eds). Functional Imaging and Modeling of the Heart 2019; Lecture Notes in Computer Science, vol 11504. Springer

121 Journal papers

1. Doste, R, Soto-Iglesias, D, Bernardino, G, Alcaine A., Sebastian R., Giffard-Roisin S., Sermesant M., Berruezo A., Sanchez-Quintana D., Camara O. "A rule-based method to model myocardial ﬁber orientation in cardiac biventricular geometries with outﬂow tracts." Int J Numer Meth Biomed Engng. 2019

2. Nuñez-Garcia, M., Bernardino, G., Camara, O., and Butakoff, C., 2018. "Fast quasi-conformal regional ﬂattening of the left atrium." [Under review].

3. Bernardino G, Sanz de la Garza M., Domenech-Ximenos B., Prat- Gonzàlez S., Perea RJ, Blanco I„ Burgos F., Sepulveda-Martinez A., Rodriguez-Lopez M., Crispi F., Butakoff C. González Ballester MA., De Craene M., Sitges M.; Bijnens B.; "Three-dimensional regional bi-ventricular shape remodeling is associated with exercise capacity in endurance athletes." [Under review]

4. Bernardino G, Benkarin O, Sanz de la Garza M., Prat-Gonzàlez S., Sepulveda A., Crispi F., Butakoff C., de Craene M., Sitges M., Bijens B., González Ballester M.A. "Handling confounding variables in statistical shape analysis - application to cardiac remodelling" [Under review]

5. Crispi F., Rodríguez-López M., Bernardino G., Sepúlveda-Martínez A., Prat-Gonzalez S., Pajuelo C., Perea R. J., Caralt M.T., Casu G., Vellvé K., Crovetto F.,Burgos F., De Craene M. , Butakoff C., Gon- zalez Ballester M.A., Blanco I., Sitges M., Bijnens B., Gratacós E. "Reduced exercise capacity and exaggerated impact of conventional risk factors on cardiac function in adults born small-for-gestational age" [Under review]

6. Balagurunathan Y., Beers A., McNitt-Gray M., Hadjiiski L., Napel S., Goldgof D., Perez G., Arbelaez P., Mehrtash A., Kapur T., Yang E., Yi CA., Bernardino G, Delgado-Gonzalo R., Mehdi Farhang M., Amini A., Ni R., Xue Feng X., Bagaria A., Vaidhyaa K., Veasey B., Safta W., Frigui H., Enguehard J., Gholipour A., Silvana Castillo L., Arbelaez P., Farahani K., Kalpathy-Cramer J. "Lung Nodule Malignancy Pre- diction in Sequential CT Scans: Summary of ISBI 2018 Challenge" [Under review]

7. Bernardino G, Hodzic A, Langet H, González Ballester M.A., De Craene M., Saloux S.,Bijnens B.. "Volumetric parcellation of the

122 right ventricle for regional geometric and functional assessment." [In preparation]

8. Hodzic A, Bernardino G, Damien L, Patrick G , Langet H, González Ballester M.A., De Craene M., Milliez P., Normand H., Bijnens B., Saloux S., Tournoux F. "Regional right ventricular remodelling during the preseason in american-style-football university athletes: a 3D echocardiography study." [In preparation]

123

Funding information

This work was supported by:

European Union Horizon 2020 research and innovation programme under grant agreement 642676 (Cardiofunxion)

The Spanish Ministry of Economy and Competitiveness (grant TIN2014- 52923-R; Maria de Maeztu Units of Excellence Programme - MDM- 2015-0502)

125