Jean-Philippe Jehl

; Pan

Arnaud Voignier

; Nguyen

; Thierry Bastogne

Pablo Maureira

Franck Cleymand

Transverse isotropic modelling of left-ventricle passive filling: mechanical characterization for epicardial biomaterial manufacturing

Keywords: cardiac tissue, muscular fibers, transverse isotropic behavior, biomechanical modeling, finite element method

Biomaterials applied to the epicardium have been studied intensively in recent years for different therapeutic purposes. Their mechanical influence on the heart, however, has not been clearly identified. Most biomaterials for epicardial applications are manufactured as membranes or cardiac patches that have isotropic geometry, which is not well suited to myocardial wall motion. Myocardial wall motion during systole and diastole produces a complex force in different directions. Membrane or cardiac patches that cannot adapt to these specific directions will exert an inappropriate force on the heart, at the risk of overly restricting or dilating it. Accurately characterizing the mechanical properties of the myocardial wall is thus essential, through analysis of muscle orientation and elasticity. In this study, we investigated the Hertz contact theory for characterizing cardiac tissue, using nanoindentation measurements to distinguish different patterns in the local myocardium. We then evaluated the predictive accuracy of this model using Finite Element Analysis (FEA) to mimic the diastolic phase of the heart. Our results, extracted from instrumented nanoindentation experiments in a liquid environment using five pig hearts, revealed variations in elasticity according to the local orientation of the myocardial tissue. In addition, applying the Finite Element Method (FEM) in our model based on transverse isotropy and local tissue orientation proved able to accurately simulate the passive filling of a left ventricle (LV) in a representative 3D geometry. Our model enables improved understanding of the underlying mechanical properties of the LV wall and can serve as a guide for designing and manufacturing biomedical material better adapted to the local epicardial tissue.

Introduction

Biomedical materials for epicardial application have been extensively investigated over the past decades, with several different types of these materials having become clinically available [START_REF] Gaetani | Epicardial application of cardiac progenitor cells in a 3D-printed gelatin/hyaluronic acid patch preserves cardiac function after myocardial infarction[END_REF][START_REF] Pattar | Application of Bioengineered Materials in the Surgical Management of Heart Failure[END_REF]. Epicardial biomedical materials are usually designed as thin membranes containing diverse biological or mechanical properties and applied directly onto the target epicardial region. In general, these epicardial biomaterials can be used as hemostatic patches, creating an interface to prevent severe tissue adhesion following cardiac surgery, or as cardiac patches delivering cell therapy following myocardial infarction. However, research in this field has focused primarily on the biological or therapeutic behavior of these biomaterials, largely ignoring analysis of how they interact mechanically with the heart.

Once the biomedical material is adhered to the epicardium, however, it sustains the same cyclic strain and shear stress caused by the heart beating as the epicardium.

The muscle fiber structure also differs from one area to another, thus exerting mechanical force in different directions during heart circulation, as well as at different locations [START_REF] Bayer | A novel rule-based algorithm for assigning myocardial fiber orientation to computational heart models[END_REF][START_REF] H571 Lombaert | Human atlas of the cardiac fiber architecture: study on a healthy population[END_REF]. However, only a few biomaterials are designed considering the myofiber orientation and structural specificity of cardiac tissue [START_REF] Cui | 4D physiologically adaptable cardiac patch: A 4-month in vivo study for the treatment of myocardial infarction[END_REF]. Most epicardial biomaterials are manufactured as isotropic membranes, which cannot adapt to the specific muscle fiber structure of the heart, thus potentially applying inappropriate force to the epicardium, which could eventually cause a restriction or dilation effect on the heart.

Characterizing the mechanical properties of the heart wall, and particularly of the left ventricle, is thus of major importance for epicardial biomaterial design [START_REF] Weinberger | Engineering Cardiac Muscle Tissue: A Maturating Field of Research[END_REF]. The fibrous nature of the heart has long been known, and the spatial variation within the heart's fibers has already been described, with computational models established accordingly. It is also well known that the muscle fascicles of the myocardium are arranged in three main directions, forming three muscle layers within the ventricular wall from the epicardium to the endocardium [START_REF] Sánchez-Quintana | Spatial arrangement of the heart muscle fascicles and intramyocardial connective tissue in the Spanish fighting bull (Bos taurus)[END_REF]. The combined effect of these differently-oriented fibers on the ventricular wall can generate an average direction, and this direction varies from the apex to the aortic root [START_REF] Freeman | Relationship between myocardial fiber direction and segment shortening in the midwall of the canine left ventricle[END_REF].

An ideal epicardial biomaterial should, instead, expand in the same way as the local epicardium. Due to the complex wall motion in play here, epicardial biomaterials should closely match the target zone of the heart, which means offering a similar elasticity and fiber structure. Thus, understanding the mechanical performance of the diastolic ventricle can guide advances in the design and manufacturing of epicardial biomaterials. For this purpose, a heart model with mechanical characterization during diastole could serve as an invaluable tool.

Furthermore, heart simulation models are also of great importance in medical research and training. Given the complex composition of the heart on both macroscopic and microscopic scales, it is hard to establish a model that can perfectly simulate all aspects of the heart, including the mechanical movement, electric activity, and pump function. Studies from the literature have so far focused on only one aspect of the heart, primarily contributing to advances in cardiology [START_REF] Niederer | Computational models in cardiology[END_REF].

Woods was a pioneer in using models to understand cardiac physiology and mechanics. In his study, the stress in the heart wall was considered as a thin-walled spherical shell [START_REF] Woods | A Few Applications of a Physical Theorem to Membranes in the Human Body in a State of Tension[END_REF]. Modelling has since progressed to simulate in detail the anatomical and physiological complexities of the heart, and geometric models have been developed containing multiscale information of the heart [START_REF] Chabiniok | Multiphysics and multiscale modelling, data-model fusion and integration of organ physiology in the clinic: ventricular cardiac mechanics[END_REF].

It is now well known that cardiac muscle fibers run in parallel and form a 3D network enabling the heart wall's complex motion during the cardiac cycle. Thus, for a better understanding of heart function, the anatomical architecture of these cardiac fibers should first be described. Three-dimensional models of myocardial architecture have been built up from detailed histological studies in the 1990s [START_REF] Guccione | Finite element stress analysis of left ventricular mechanics in the beating dog heart[END_REF][START_REF] Legrice | Laminar structure of the heart: ventricular myocyte arrangement and connective tissue architecture in the dog[END_REF]. Since then, the development of invasive and non-invasive imaging techniques, such as CT and magnetic resonance imaging, has made it possible to construct patient-specific models of the beating heart to simulate its dynamics [START_REF] Gilbert | Visualization and quantification of whole rat heart laminar structure using high-spatial resolution contrast-enhanced MRI[END_REF][START_REF] Plank | Generation of histoanatomically representative models of the individual heart: tools and application[END_REF]. However, the lack of detailed tissue structure information in significant amounts of image data still constitutes a significant failing in computational models and could influence model results.

Various numerical frameworks of heart architecture have been described in previous studies, based on different modeling methods [START_REF] Chabiniok | Multiphysics and multiscale modelling, data-model fusion and integration of organ physiology in the clinic: ventricular cardiac mechanics[END_REF][START_REF] Niederer | Computational models in cardiology[END_REF]. Benefitting from 3-dimensional cardiac imaging techniques, many authors have been able to build 3D models of the heart illustrating detailed fiber structures [START_REF] Wang | 3D Printing, Computational Modeling, and Artificial Intelligence for Structural Heart Disease[END_REF]. Furthermore, powerful numerical tools now enable the construction and evaluation of models based on collected data. These numerical models are widely used in clinical and educational settings. For example, Finite Element Analysis (FEA) is a popular method for building and evaluating heart models with more detailed mechanical characterization [START_REF] Martonová | Towards the simulation of active cardiac mechanics using a smoothed finite element method[END_REF][START_REF] Morgan | Finite Element Modeling of Mitral Valve Repair[END_REF]. However, no study has yet presented the physical results of such simulations, such as overall local elasticity of the spatial arrangement of cardiac fibers. In this study, we evaluated the average fiber orientation and elasticity of the lateral part of the left ventricular wall in healthy pig hearts. We then built a numerical 3D model based on the obtained results, providing a simplified illustration of the complex fiber arrangement. We evaluated the method's accuracy by simulating the diastole phase of a left ventricle.

Materials and methods:

Pig cardiac tissue sample preparation:

The samples used in this study were extracted from five healthy pig hearts provided by the School of Surgery of the University of Lorraine. Ethical approval for the study was obtained from our university's ethics committee (committee number: 201922016556026) and then further validated by the French Ministry of Higher Education. The hearts were explanted during diastole for this study. One pig's heart was fully filled with 0.9% sodium chloride and sealed to mimic the end of passive filling during diastole. We then performed computed tomography (CT) and 3D reconstruction of the heart. To prevent the cardiac tissue from drying out, the samples were rapidly immersed in a protective medium (optimal cutting temperature compounds) and frozen at -80°𝐶. For each heart, the lateral region of the left ventricular wall was selected for obtaining reproductive data (Figure 1A) and a 0.5-cm wide slice was extracted from the long axis (Figure 1B). The extracted tissue was then cut into 16 cytological slices, horizontally from the base to the apex of the heart, in two different thicknesses (100 µm and 10 µm, eight slices each) using a cryomicrotome, and stored frozen. The thicker slices were used later for mechanical characterization while the thinner ones served for muscle fiber structure observation.

Microscopic observation of muscle fiber orientation

Heart samples cut to 10-µm thickness were stained with DAPI (D9542, Sigma-Aldrich), for the nuclei, and Phalloidin (P5282, Sigma-Aldrich), for the actin, as per manufacturer's instructions. Imaging was performed using fluorescent microscopy (Moticam 3000, Motic).

Indentation evaluation at different levels of the left ventricle:

The mechanical properties of the specimen were determined using a depth sensing indentation test. An ultra nanoindenter was used (ANTON-PAAR, Peseux, Switzerland), affording a penetration range of a few nanometers to 100 µm, using loads of 10 µN to 100 mN. The depth and load resolution were 0.003 nm and 0.01 μN, respectively. This tool is well suited to testing on biological materials in liquid medium, incorporating a sample holder adapted for biological tissue slices. This technique involves indenting the tissue using a spherical indenter of 100-μm radius (R).

Just before we commenced mechanical tests to determine the properties of the cardiac tissues, the specimens were thawed then soaked in physiological serum to avoid any dryness or premature destruction. To ensure that the tissue remained properly hydrated, the sample was kept in physiological serum during the entire depth-sensing procedure. The experiments were carried out at room temperature (21°𝐶). A 13x6 matrix of indentations was systematically performed on each specimen (78 measures).

Each indented site was identified and microscopically analyzed. The contact surface disc generated by indentations did not exceed a radius of 30 μm. The load and unload speeds were intentionally kept low so as to guarantee the elasticity behavior of the cardiac tissue. Our previous experimental protocol showed that indentation speed inferior or equal to 0.5mN/min allow a measurement of elasticity behavior other than viscoelasticity behavior. Furthermore, a 500-μm distance was maintained between each indentation to avoid any interference from neighboring indentations (Figure 1B).

Measurement of Young's modulus and sample fiber orientation

For the heart samples cut to 100-μm thickness, Young's modulus was calculated based on the Hertz theory formula outlined below. We designed a strategy enabling us to define the range of values on commencing the load for which the Hertz theory can be applied. As a brief reminder, this theory establishes the relationship between the force applied (𝐹), the relative approach distance of the two elements (ℎ), and the radius of the disc contact area (𝑎) [START_REF] Niederer | Computational models in cardiology[END_REF]. These formulae also involve the radius of the indenter's curve (𝑅 ! ) and the mechanical characteristics of the sample and indenter, i.e. their Young's moduli and Poisson ratios, using the reduced elasticity modulus, defined by Formula (3).

ℎ = 1 "•$ ! %&•' " •( * ! 2 % ) * (1)
with the bend radius 𝑅 ! defined as:

% ' " = % ' $ + % ' % (2)
and the reduced Young's modulus 𝐸 * given by:

% ( * = %,-! ( + %,-$ ! ( $ (3)
In these equations, 𝐸, 𝜈, 𝑅 . , 𝐸 / , 𝜈 / , and 𝑅 / are the Young's moduli, the Poisson ratios, and the bend radius of the sample and the indenter, respectively.

Given that all samples had a defined thickness, the variation in Young's modulus was caused by variations in the fiber orientation. According to the mechanism of cardiac muscle contraction, the Young's modulus is minimal when the fibers are orientated vertically and maximal when horizontally. Thus, the fiber orientation is calculated according to the measured Young's modulus.

With a spherical indenter radius Ri<<Rs (plane sample), the equation ( 2) became Rc=Ri. Moreover, the diamond indenter's Young's modulus was higher than that of the sample (Ei≫E). Thus, equation (3) became 𝐸 * = 𝐸/(1 -𝜈 0 ).

Given the liquid medium used and the uncertainties associated with measurement using very low loads, we developed a strategy for exploring the initial moments of The indenter output a continuous value of elasticity within the indentation depth, the initial point was determined once an elasticity behavior was detected. As too deep detection was influenced by the underlying glass support (F increased sharply while H was beyond 15µm), the indentation had to be optimized. In order to obtain the optimal detection parameter, the experimental indentation curve of every point of detection was crossmatched with the theoretical curve (applying Hertz theory) to determine the individual hmax (8 µm as indicated by the cross point, in the case of Figure 2). A regular limit of the deformation (h/R) 1/2 under 30% was observed.

Finite Element Analysis of left ventricle model

The 3D-reconstructed image of the heart from CT was transferred to Abaqus software.

In brief, the 3D image was decomposed into 8 stratums with a cylindrical landmark on each stratum. A local rotation landmark, the mean orientation angle of fiber arrangement were also input into each stratum in the radial axis. The isotropic matrix was thus output for each point of mesh, in which the axis z correspond to the mean direction of fiber orientation, axis x for radial direction of left ventricle, axis y for longitudinal direction of left ventricle. Based on the measured Young's modulus and average fiber orientation, FEA was applied to obtain the left ventricle (LV) model for the diastole simulation (LV passive phase). A tetrahedral quadratic mesh with 122170 nodes, of global size 4, and 83949 linear elements, was applied.

In order to test the feasibility of this numerical model's mechanical evaluation, a simplified model was also constructed according to the CT measurement: the left ventricle was represented by a hollow cylinder with internal and external radii equal to 20 mm and 40 mm, respectively. The tubular height was 110 mm. A tetrahedral quadratic mesh with 94433 nodes, of global size 4, and 66492 linear elements, was applied.

Mechanical evaluation of a transverse isotrope model by FEM

The volume in the left ventricle increases during diastole phase and is correlated with the internal pressure. This heart cycle is known as the pressure-volume loop. Using the two numerical left-ventricle models, we progressively increased the internal pressure until a level equivalent to the end of passive diastole filling in order to evaluate the change in volume. The diastolic movement of the left-ventricle wall was also recorded.

Results

Young's modulus and fiber orientation of left-ventricle lateral region

The Young's modulus detected in the samples revealed the minimum value was 1´10 4

Pa, and maximum value 2.5.´10 5 Pa. The fiber orientation was thus defined as vertical (90°) at the point of 1´10 4 Pa and horizontal (0°) at the point of 2.5´10 5 Pa.

Fiber variations caused variation in Young's modulus between 𝐸 2 , 𝐸 3 and Ei (El stands for longitudinal Young's modulus where fibers orientate parallelly to indenter, ET stands for transversal Young's modulus where fibers orientate perpendicularly to indenter and Ei is the measured Young's modulus which is related to the fibers orientation angle to be calculated). Where an ellipse can be considered representative of this evolution, Relation (5) can be determined and the local fiber orientation, 𝜃 / , estimated as follows:

The Young's modulus in the same sample was dependent of the location (Figure 3a).

These variations were the result of mixed muscle fiber orientation and were calculated according to the measurement of the local Young's modulus and based on the equation ( 5) (Figure 3b,c). tan 𝜃 ! = 𝐸 "

((𝐸 ! # -𝐸 " # ) . ((𝐸 $ # -𝐸 ! # ) 𝐸 $ (5) A B C
To confirm the accuracy of the calculated fiber orientation, fluorescent microscopic images were taken of the same level. At the basal level of the heart, the general value of Young's modulus was lower than the apex one. Accordingly, the calculated fiber orientation was more vertical at the basal (Figure 4A) than that found at the apex (Figure 4B). This calculated orientation was in accordance with the microscopic fluorescent observation. From the two-dimensional microscopic image, at the basal level, cell arrangement was predominantly in the "Y" direction, which was vertical to the indenter (Figure 4C). At the apex level, cell arrangement was in the "Z" direction, which was parallel to the indenter (Figure 4D).

Construction of whole left-ventricle model using Finite Element Method

In order to construct the whole left-ventricle model, we assumed that the entire ventricular wall expanded in the same manner as the lateral region. Consequently, the transverse isotropic matrix (5) and average fiber orientation detected (Figure 5A) on eight different levels were introduced as parameters into an FEA. Thus, we constructed a simplified cylindrical model (Figure 5B) and a CT-based model (Figure 5C). We defined the transversely isotropic matrix using five independent coefficients: the longitudinal and transverse Young's moduli, noted 𝐸 4 and 𝐸 3 , respectively; the Poisson ratio in the isotropic plane, 𝜈 33 , and transverse plane, 𝜈 43 ; a longitudinaltransverse shear modulus, 𝐺 43 (6).

𝐶 ,% = ⎝ ⎜ ⎜ ⎜ ⎜ ⎜ ⎛ % ( & - -&& ( & - -'& ( ' 0 0 0 - -&& ( & % ( & - -'& ( ' 0 0 0 - -&' ( & - -&' ( & % ( ' 0 0 0 0 0 0 0(%6-'& ) ( ' 0 0 0 0 0 0 𝐺 43 0 0 0 0 0 0 𝐺 43 ⎠ ⎟ ⎟ ⎟ ⎟ ⎟ ⎞ (6)
The symmetry of the stress tensors of the medium implies:

-

-'& ( ' = - -&' ( & (7)
The transverse strain could not be measured using nanoindentation. In this work, we assume 𝜈 43 = 𝜈 33 ≃ 0.49 to the deformability of the fibers. The shear modulus, 𝐺 43 , is determined by the following empirical expression, taken from Lekhnitskii (1981):

𝐺 43 = ( ' ( & ( ' (%60-'&)) ( & (8)
This formula was established for transversely isotropic rocks, also developed by Van Loocke for skeletal muscles [START_REF] Van Loocke | A validated model of passive muscle in compression[END_REF], and is applied here as a first approximation. All things considered equal, the elasticity matrix of the LV wall was defined as follows in Table 1:

C1111 C1122 C2222 C1133 C2233 C3333 C1212 C1313

Mechanical evaluation of the numerical model of the left ventricle

To evaluate the diastole phase of the numerical model, progressively increasing pressure was applied to the ventricular cavity. The simulated ventricular pressure was increased from 5.5 mmHg to 11 mmHg, while the ventricular volume was accordingly increased to 112 mL in the CT-based model and 113 mL in the cylindrical model. This pressure-volume change was compared to a known Pressure-Volume loop issued from a healthy pig heart [START_REF] Raake | Comprehensive cardiac phenotyping in large animals: comparison of pressurevolume analysis and cardiac magnetic resonance imaging in pig postmyocardial infarction systolic heart failure[END_REF]. The simulation demonstrated a linear change regression between pressure and volume, which was compatible with the detected P-V loop (Figure 7). This result indicated that the numerical model was capable of simulating the passive filling process of the left ventricle. During the increase in ventricular pressure, the wall motion was also recorded. In the cylindrical model, displacement was most significant in the basal and apex regions of the heart (3.5 mm). In the CT-based model, the most significant displacement was observed in the apex (4.9 mm), lateral free wall (5.11 mm), and septum (3.5 mm) of the heart. Due to the differently-arranged fibers from the base to the apex, the heart rotation could also be observed during the passive-filling phase, mimicking a real heart (Figure 8 and online video).

Discussion

In the study presented herein, we characterized the elasticity and fiber orientation of the lateral region of a healthy pig left ventricle. Based on this data and the scanning image of this heart, we constructed a model using FEM.

Cardiac muscle contraction was induced by sarcomeres, adapted according to this anatomic structure, with the indentation test demonstrating that the tissue was less stiff when the indentation tip was parallel to the fibers, meaning the muscle fiber was oriented vertically, at 90°. Since the cardiac muscle fibers are oriented differently from endocardium to epicardium, as well as from the base to the apex of the heart, it is difficult to obtain a complete map of the heart. Our results on eight different levels revealed the change in overall fiber orientation. They were aligned more toward the LV longitudinal axis at the base and apex of the heart than in the middle. This fiber arrangement was further confirmed by microscopy, and corresponded to findings in other studies [START_REF] Holzapfel | Constitutive modelling of passive myocardium: a structurally based framework for material characterization[END_REF][START_REF] H571 Lombaert | Human atlas of the cardiac fiber architecture: study on a healthy population[END_REF][START_REF] Sánchez-Quintana | Spatial arrangement of the heart muscle fascicles and intramyocardial connective tissue in the Spanish fighting bull (Bos taurus)[END_REF]. As a result, the formula that we proposed can adequately explain the relationship between fiber elasticity and overall fiber orientation. To the best of our knowledge, this is the first study to describe the relationship between fiber orientation and resulting elasticity.

While the fiber elasticity and orientation varies depending on measurement location, the wall motion direction is the result of average fiber orientation and the fibers' elasticity response to ventricular pressure [START_REF] Wong | Generating fiber orientation maps in human heart models using Poisson interpolation[END_REF]. Our results revealed similar average fiber orientation to that shown by [START_REF] H571 Lombaert | Human atlas of the cardiac fiber architecture: study on a healthy population[END_REF]. By using an average fiber orientation value, we were able to simplify the data input for the model construction and functional simulation. In this study, the measurements were taken on eight slices. Despite these measurements not containing all layers of cardiac tissue, the continuous fiber orientation change they revealed enabled our prediction of mechanical properties on locations between those histological cuts. Nevertheless, more slices would be needed if one sought to enrich the mechanical information in the model.

Our mechanical simulation based on measured fiber elasticity and orientation confirmed the accuracy of the model. By simulating the P-V loop, our results showed that the numerical model demonstrated a progressive increase in volume caused by internal pressure, which was compatible with a measured P-V loop [START_REF] Raake | Comprehensive cardiac phenotyping in large animals: comparison of pressurevolume analysis and cardiac magnetic resonance imaging in pig postmyocardial infarction systolic heart failure[END_REF].

Furthermore, changes in fiber angle distribution are known to alter fiber stress-strain distribution on the LV wall [START_REF] Palit | Computational modelling of left-ventricular diastolic mechanics: Effect of fibre orientation and right-ventricle topology[END_REF], and the simulation approach containing fiber angle distribution also revealed a rotation process, which is an important dynamic characteristic of the beating heart [START_REF] Nakatani | Left Ventricular Rotation and Twist: Why Should We Learn?[END_REF].

All these results together demonstrated that our computational model based on mechanical measurement and imaging data can represent the passive filling course of the left ventricle during diastole. By simulating the change in volume and wall displacement, it also enables detailed information about LV motion to be acquired. This detailed information is especially useful for the manufacturing of biomedical materials for epicardial applications.

The principal novelty of this study is that we found a simple method describing representative fiber orientation calculated within detected Young's modulus. In fact, the existing computational models describing fiber orientation are based on imaging observation (CT, RMI or histology), while the mechanical behavior detection was apart.

These two major characteristics were thus lack of relation. Furthermore, the structural characteristics of myocardium, such as the local orientation of the myo-and collagen fibers, are spatially heterogeneous and vary with position throughout the tissue from base to apex and from endocardium to epicardium. Therefore, the myocardium does not actually possess structural uniformity, which is essential to define a representative tissue element for an inhomogeneous specimen [START_REF] Avazmohammadi | A Contemporary Look at Biomechanical Models of Myocardium[END_REF].

Appling the overall fiber elasticity and calculated mean fiber orientation on different location of the specimen, we are thus able to construct a computation model that contain both the geometric and mechanical properties of myocardium, which were inherently related.

Study Limitations

First, the data used for this study was acquired from explanted hearts that were arrested during diastole. Thus, the model described solely the inactive diastole status.

Though the systolic phase was not investigated in this study, systolic wall motion is not the key factor influencing the mechanical performance of epicardial biomaterial.

Secondly, the cardiac tissue used in this study was from the lateral region of the LV, and mechanical testing was effectuated in eight slices from different levels. Even though numerous points were detected on each sample, any information from between slices was thus missed. More histological cuts are therefore needed to better represent the smooth variation of fiber orientation. Furthermore, we built the whole LV using the mechanical information obtained from the lateral region of the LV, and the authors are aware that the different regions of the LV vary in how they expand. Given this, every part of the LV should be measured individually to establish a complete numerical model.

Thirdly, an elasticity matrix was defined by instrumented indentation tests using a spherical tip, yet the Poisson ratio was obtained from the literature. In order to obtain it, other tests are needed. In this study, we consider a linear elastic model. Moreover, the fibers of the heart tissue have directional sensitivity and symmetry. We can thus consider them to be a material with transverse isotropic behavior.

In this study, the orientation of the fibers was defined as constant and an elasticity matrix was established for each layer of the left ventricle. The first simulation showed that this configuration seems to be a good candidate for simulating ventricular diastole.

This paves the way for a second study consisting in taking into account the variation in fiber density, viscoelastic behavior, and large deformations.

Conclusion

The mechanical performance of cardiac tissue is related to local fiber structure. The formula that we propose outlines, for the first time, a way to describe the elasticity of cardiac tissue and underlying fiber orientation. Building off CT imaging, we created a computational model that can accurately simulate the diastole phase of the LV. By modelling LV wall motion during passive diastole filling, our understanding of volume changes and the local deformation of the epicardium will be vastly improved, which will guide advances in the manufacturing of biomaterials for epicardial applications.

Figure 1 :

 1 Figure 1: A. A 0.5-cm wide slice was extracted from the lateral region of the left ventricle of each heart (green dash). B. Eight 100-µm and eight 10-µm slices were obtained from the longitudinal axis of the left ventricle, from the base to the apex. Slices of 100-µm thickness were used for indentation testing, 13x6 points were detected on each sample following the above planning and indentation parameters

Figure 2 .

 2 Figure 2. Example of optimization of indentation on one detected point. (A) Charging indentation curve obtained from detection. The initial point was determined once an elasticity behavior was detected. (B)Transformation of the experimental data of (A) into logarithmic curve (black), with a linear regression (red) obtained by applying Formula (4). (C) Reversal of the logarithmic curve issued from (B, red) into classical curved and crossmatch with experimental curve (black) to determine the optimized parameters

Figure 3 .

 3 Figure 3. (A) Young's modulus detected on eight heart samples cut into 100 µm; the value varied at different detection points. (B) Variation in fiber orientation between samples, according to Young's modulus. (C) Representative figure of fiber orientation on different levels of left-ventricle lateral region, result issued from one pig heart out of five, the color-scale represent the fibers orientation angle.

Figure 4 .

 4 Figure 4. Confirmation of calculated fiber orientation by microscopic fluorescent observation. Representative image of Young's modulus and individual fiber orientation at the basal (A) and apex (B) levels of the heart. Fluorescent microscopic images taken of the basal (C) and apex (D) levels demonstrated a vertical (C) and horizontal (D) arrangement of muscle fiber arrangement. Muscle cells were stained with DAPI for nuclei and with Phalloidin for actin visualization. Scale bar: 100 µm

Figure 5 .

 5 Figure 5. Construction of 3D transverse isotropic model of left ventricle. (A) Average fiber orientation calculated from eight different levels of detected cardiac tissue. (B) Simplified cylindrical model based on average fiber orientation and tissue elasticity. (C) CT-based model constructed with average fiber orientation, tissue elasticity, and 3D abaqus data transferred from CT imaging of the same heart

Figure 6 :

 6 Figure 6: In a detected Pressure-Volume loop (black curve), the left-ventricle volume increased progressively with the ventricular pressure caused by passive filling of blood from the left atrium. The simulated curve (red dot) demonstrated a similar Pressure-Volume relationship, which was a linear trend

Figure 7 .

 7 Figure 7. Left-ventricle wall motion during diastole simulation. Wall motion of cylindrical model (A-C) and CT-based model (D-F) during diastole revealed differing wall displacement. U1 represents wall motion in the X axis, U2 for the Y axis, and U3 for the Z axis

Table 1 :

 1 transversely isotropic stiffness tensor

	C2323

Acknowledgments

The authors wish to acknowledge the Nancy Lorraine School of Surgery, France, for their valuable collaboration.

Funding

This work was supported by the CARE & ASCATIM FEDER PROJECTS (University of Lorraine).


Eric Hermand
email: eric.hermand17@gmail.com

François J Lhuissier

Jean-Paul Richalet
email: richalet@univ-paris13.fr

Effect of dead space on breathing stability at exercise in hypoxia

Keywords: Control of ventilation, hypoxia, exercise, periodic breathing, breathing instability, dead space, alveolar ventilation NCT02201875

Recent studies have shown that normal subjects exhibit periodic breathing when submitted to concomitant environmental (hypoxia) and physiological (exercise) stresses. A mathematical model including mass balance equations confirmed the short period of ventilatory oscillations and pointed out an important role of dead space in the genesis of these phenomena. Ten healthy subjects performed mild exercise on a cycloergometer in different conditions: rest/exercise, normoxia/hypoxia and no added dead space / added dead space (aDS).

Ventilatory oscillations ( E peak power) were augmented by exercise, hypoxia and aDS (P<0.001, P<0.001 and P<0.01, respectively) whereas E period was only shortened by exercise (P<0.001), with an 11-second period. aDS also increased E (P<0.001), tidal volume (VT, P<0.001), and slightly augmented PETCO 2 (P<0.05) and the respiratory frequency (P<0.05). These results confirmed our previous model, showing an exacerbation of breathing instability by increasing dead space. This underlines opposite effects observed in heart failure patients and normal subjects, in which added dead space drastically reduced periodic breathing and sleep apneas. It also points out that alveolar ventilation remains very close to metabolic needs and is not affected by an added dead space. Clinical Trial reg.

Introduction

Since the 19 th century and its first description by Drs Cheyne and Stokes [START_REF] Naughton | Pathophysiology and treatment of Cheyne-Stokes respiration[END_REF], periodic breathing has been the center of numerous studies on ventilatory stability among normal subjects and patients. This dysfunction of respiration control is mainly observed in patients suffering from chronic heart failure (CHF) [START_REF] Javaheri | A mechanism of central sleep apnea in patients with heart failure[END_REF] or sleep apneas, from central [START_REF] Javaheri | Central sleep apnea[END_REF] (SACS), mixed or obstructive [START_REF] Pham | The pathogenesis of obstructive sleep apnea[END_REF] (SAOS) origin, but also in healthy subjects at high altitude, mostly in sleep state [START_REF] Ainslie | Breathing and sleep at high altitude[END_REF]. The pathophysiology of these manifestations involves a decreased cardiac output ( c) [START_REF] Agostoni | Acute Increase of Cardiac Output Reduces Central Sleep Apneas in Heart Failure Patients[END_REF] and/or a hypersensitivity of peripheral and central chemoreceptors to O 2 and CO 2 stimuli [START_REF] Chua | Relation between chemosensitivity and the ventilatory response to exercise in chronic heart failure[END_REF][START_REF] Francis | Quantitative general theory for periodic breathing in chronic heart failure and its clinical implications[END_REF][START_REF] Giannoni | Clinical significance of chemosensitivity in chronic heart failure: influence on neurohormonal derangement, Cheyne-Stokes respiration and arrhythmias[END_REF][START_REF] Ponikowski | Peripheral chemoreceptor hypersensitivity: an ominous sign in patients with chronic heart failure[END_REF][START_REF] Solin | Peripheral and central ventilatory responses in central sleep apnea with and without congestive heart failure[END_REF]. However, recent studies (Hermand et al., 2015b(Hermand et al., , 2015a;;[START_REF] Latshang | Acclimatization improves submaximal exercise economy at 5533 m[END_REF] have paradoxically underlined a similar phenomenon in normal subjects submitted to concomitant metabolic (exercise) and environmental (hypoxic) stresses. In these conditions, the amplitude of periodic breathing is positively related to both c and ventilation ( E), as opposed to the observations in CHF and SACS/SAOS patients whereas its period, much shorter (between 11 and 13 seconds), is inversely related to c and E.

Several methods to treat periodic breathing and sleep apneas are being used or experimented, with a variable efficiency: CPAP and oxygen therapy [START_REF] Pearse | Sleep-disordered breathing in heart failure[END_REF], acetazolamide [START_REF] Javaheri | Acetazolamide improves central sleep apnea in heart failure: a double-blind, prospective study[END_REF][START_REF] White | Central sleep apnea. Improvement with acetazolamide therapy[END_REF] and CO 2 inhalation [START_REF] Szollosi | Effect of CO2 inhalation on central sleep apnea and arousals from sleep[END_REF][START_REF] Wan | Dynamic CO₂ inhalation: a novel treatment for CSR-CSA associated with CHF[END_REF]. An alternative approach is the use of an additional external dead space, which has proven to be effective by drastically reducing periodic breathing during in patients [START_REF] Khayat | Cardiorespiratory Effects of Added Dead Space in Patients With Heart Failure and Central Sleep Apnea[END_REF][START_REF] Sharma | Sleep disordered breathing in patients with heart failure: pathophysiology and management[END_REF][START_REF] Xie | Effects of inhaled CO2 and added dead space on idiopathic central sleep apnea[END_REF] and in subjects at high altitude [START_REF] Lovis | Effect of added dead space on sleep disordered breathing at high altitude[END_REF][START_REF] Patz | Dead space mask eliminates central apnea at altitude[END_REF]. By maintaining a relatively high arterial partial pressure in CO 2 (PaCO 2 ) combined with a higher E, this device prevents its fall below the apnea threshold and the consequent genesis of a central apnea cycle. Augmented dead space also alters the breathing pattern when increasing E, as respiratory rate remains stable while tidal volume (VT) augments [START_REF] Agostoni | Mechanisms of periodic breathing during exercise in patients with chronic heart failure[END_REF][START_REF] Khayat | Cardiorespiratory Effects of Added Dead Space in Patients With Heart Failure and Central Sleep Apnea[END_REF][START_REF] Xie | Effects of inhaled CO2 and added dead space on idiopathic central sleep apnea[END_REF]. This underlines the additional contribution of low tidal volume in central sleep apneas in patients, besides cardiac output and chemosensitivity.

In exercise conditions, scarce studies highlight a similar inhibiting effect of added dead space on periodic breathing in CHF patients [START_REF] Agostoni | Mechanisms of periodic breathing during exercise in patients with chronic heart failure[END_REF].

However, in a previous work, we developed a model in order to evaluate the respective influence of various factors on breathing stability during moderate exercise in hypoxia. Our model predicted that a decrease in alveolar ventilation / minute ventilation ratio ( A/ E), therefore an increase in dead space, would increase breathing instability and ventilatory oscillations [START_REF] Hermand | Ventilatory oscillations at exercise in hypoxia: A mathematical model[END_REF], regardless of cardiac output and chemosensitivity. Therefore, we aimed to validate our mathematical model in normal subjects at moderate exercise in hypoxia, by adding dead space in the breathing circuit and we hypothesized that this intervention would promote breathing instability.

Subjects and methods

Subjects.

Ten healthy non-smoking male subjects volunteered for the study and were given complete information about the successive tests. All were in good physical condition, with a medium to high level of regular physical activity (from 2 to 10 hours per week). A preliminary medical examination showed no evidence of cardiovascular or pulmonary disease. Subjects' characteristics are presented in table 1. The protocol was approved by the Ile-de-France Ethics Committee (CPP-IDF2) and an individual written informed consent has been collected from all subjects. The study was registered as Clinical Trial reg. n°: NCT02201875.

Procedure.

All subjects were first asked to perform a standard ramp test protocol on a cycloergometer to be familiarized with calibrated breathing apparatus and determine their maximal aerobic power (MAP, Table 1): after a 3-minute warm-up at 60 watts, power output was increased by 30-watt steps every two minutes until exhaustion.

Four tests were then randomly conducted, in normoxia and hypoxia (fraction of inspired O 2 , FIO 2 = 14,5 %), in accordance with previous work (Hermand et al., 2015a), with and without a 500 mL added dead space (aDS), consisting in a cylindrical tube (diameter 5 cm) clipped on the mouthpiece. This volume was determined accordingly with our predictive model [START_REF] Hermand | Ventilatory oscillations at exercise in hypoxia: A mathematical model[END_REF] and with the existing literature [START_REF] Khayat | Cardiorespiratory Effects of Added Dead Space in Patients With Heart Failure and Central Sleep Apnea[END_REF][START_REF] Lovis | Effect of added dead space on sleep disordered breathing at high altitude[END_REF][START_REF] Patz | Dead space mask eliminates central apnea at altitude[END_REF].

After one minute rest for material habituation and cardiorespiratory parameters stabilization, subjects were first asked to keep a resting sitting position on the ergometer for 6 min, and then to pedal for 6 min at around 65 rpm pedaling cadence at an exercise intensity of E (L.min -1 ) and heart rate (HR, bpm) were measured through a metabograph (Vmax Encore, SensorMedics, Yorba Linda, CA). VT (L), O 2 consumption ( O 2 , L.min -1 ), CO 2 production ( CO 2 , L.min -1 ), total respiratory cycle time (Ttot, s) and inspiratory time (Ti, s) were derived from the ventilation signal. Pulse O 2 saturation (SpO 2 , %) was measured by transcutaneous oximetry (Nellcor N-595, Nellcor, Pleasanton, CA) on a pre-warmed ear lobe.

End tidal PCO 2 (PETCO 2 , mmHg) was measured by infrared thermopile (Vmax Encore, SensorMedics, Yorba Linda, CA). During the whole test, E, SpO 2 and PETCO 2 were recorded breath-by-breath (Fig. 1). Data were transferred to a computer for further variability analysis. A Fast Fourier Transform (FFT) was then applied to the breath-by-breath ventilation signal, extracted from the raw data, in sequences of 128 points (one point per second) of a steady state interval at the end of each phase of the test. This method allowed us to detect the presence of peaks in the frequency domain of the ventilation signal (Fig. 2) (Hermand et al., 2015b). Two main parameters were derived from the FFT: the frequency in hertz (or period in seconds) of the larger peak and its power estimated as the area under the peak at ± 0.02 Hz around the peak (in L 2 .min -2 for E spectrum). Thus, a high peak power translates into greater ventilatory oscillations. This method allowed us to precisely quantify the presence of oscillations in the signals that are not observable in a standard protocol routinely used where the signals are averaged every 20 seconds [START_REF] Bourdillon | Cerebral oxygenation during the Richalet hypoxia sensitivity test and cycling time-trial performance in severe hypoxia[END_REF][START_REF] Canouï-Poitrine | Risk prediction score for severe high altitude illness: a cohort study[END_REF][START_REF] Lhuissier | Ventilatory and cardiac responses to hypoxia at submaximal exercise are independent of altitude and exercise intensity[END_REF][START_REF] Richalet | Physiological risk factors for severe high-altitude illness: a prospective cohort study[END_REF]. Finally, alveolar ventilation was assessed from the values of end tidal CO 2 pressure, as a surrogate of alveolar CO 2 pressure (P A CO 2 ) and CO 2 production rate ( CO 2 ), which anatomical dead space (VD), alveolar / total ventilation ratio ( A/ E ) and dead space / tidal (VD/VT) are derived from [START_REF] Whipp | Determinants and control of breathing during muscular exercise[END_REF]

:
where K is the constant to adapt standard temperature and pressure dry (STPD) to body temperature pressure and saturation (BTPS) conditions;

where FR is the respiratory frequency (min -1 ) Statistical analysis. Results are presented as mean ± standard deviation. Regarding the expected difference in mean period (3 seconds), the standard deviation (2.4 seconds), a level of significance at 0.05% and a statistical power at 80%, the minimum number of subjects to be included was 7 for each protocol. Since spectral peak power showed a high standard deviation and a non-normal distribution, we performed a logarithmic transformation of raw data, and calculated a minimum number of subjects of 10 to include. Normality of data on each condition (rest/exercise, normoxia/hypoxia, without/with aDS) was verified by a Shapiro-Wilk normality test. Thus, a three-way analysis of variance (ANOVA) with repeated measures were done, including interactions between factors. A post-hoc paired Student's test was used when applicable. As exercise is associated with a concomitant variation of multiple variables, we performed a multivariate regression analysis in order to evaluate the independent influence of each cardiorespiratory variable on period and peak power of E spectrum. This approach, for example, will allow us to assess the specific influence of E and/or c on peak power and period of E.

Results

Values of measured cardiorespiratory variables and post-hoc tests in subgroups are presented in table 2 and in figures 3, 4, 5 and 6.

Effect of exercise vs rest

As expected, E, O 2 , CO 2 , PETCO 2 , VT, HR, A and A/ E increased with exercise (P < 0.001) whereas SpO 2 , Ttot and VD/VT decreased (P < 0.001). E peak power was greater (P < 0.001) and its period shorter (P < 0.001).

In hypoxia, O 2 desaturation was accentuated by exercise for both aDS condition (P < 0.01).

Effect of hypoxia vs normoxia

Hypoxia increased E (P < 0.01), HR, A (P < 0.001), A, A/ E (P < 0.05) and decreased SpO 2 and PETCO 2 (P < 0.001) and VD/VT (P < 0.05) whereas Ttot, VD and VT were not modified, except a trend for a rise in VT (P = 0.06). E peak power was augmented by hypoxia (P < 0.001) and period of E oscillations remained unchanged.

During exercise, E was not modified by hypoxia at aDS = 0 but significantly increased with a 500 mL aDS (P < 0.001).

Effect of added dead space

E, VT and O 2 increased with the aDS (P < 0.001) whereas Ttot was shortened (P < 0.05).

PETCO 2 was very slightly increased (+ 1.8%, P < 0.05). Added dead space had no effect on SpO 2 and A. However, it enhanced E peak power (P < 0.001), period remaining unchanged.

In most conditions, despite large increases in E due to aDS (+ 42 %, all values pooled, fig. 4, upper left), A remains stable and is not affected by aDS (Fig. 4, upper right).

In hypoxia, aDS increased A and E peak power during exercise in hypoxia (P < 0.05, P < 0.01 and respectively, fig. 4 and5).

Interactions between factors

The ANOVA showed that exercise accentuated, respectively, the effect of aDS on E, O 2 and on A/ E, the effect of hypoxia on O 2 desaturation, the effect of hypoxia on decreased PETCO 2 , the effect of aDS on increased E peak power.

Multivariate regression analysis: factors influencing E peak power and period

Among various cardiorespiratory parameters, E peak power was positively correlated to E and PETCO 2 (Fig. 6, P < 0.001), with a trend for A/ E (r = 0.67, P = 0.073). E period was strongly positively correlated to Ttot (Fig. 6, P < 0.001) and, in a lesser extent, negatively correlated to A/ E (P < 0.01).

Discussion

Two main conclusions might be drawn from these original data. First, this study confirms the mathematical simulations of the impact of added dead space on ventilatory instability in healthy subjects, during exercise in hypoxia (Fig. 1). Second, unlike the observations made in CHF/SAS patients and normal subjects during sleep at high altitude, an increased dead space promotes respiratory instability and ventilatory oscillations.

As observed in patients and normal subjects [START_REF] Ainslie | Breathing and sleep at high altitude[END_REF][START_REF] Khayat | Cardiorespiratory Effects of Added Dead Space in Patients With Heart Failure and Central Sleep Apnea[END_REF], the breathing pattern with aDS was mainly affected by VT swings (Fig. 3, lower panels). In addition, respiratory frequency was equally shortened by added dead space at rest and exercise (-8% and -7%, respectively): as the added dead space induces a higher alveolar PCO 2 , the ventilatory control system in a normal subject quickly adjusts E to eliminate CO 2 by augmenting both VT and respiratory rate, although in a lesser extent, as opposed to what is observed in CHF patients [START_REF] Khayat | Cardiorespiratory Effects of Added Dead Space in Patients With Heart Failure and Central Sleep Apnea[END_REF]. This illustrates a fully functional respiratory output in a normal subject. On a side note, the slight metabolic increase of O 2 with aDS (+9%, all conditions, fig. 5), along with a similar trend for CO 2 (P = 0.075), could be attributed to the additional workload of respiratory muscles [START_REF] Lorenzo | Oxygen cost of breathing and breathlessness during exercise in nonobese women and men[END_REF], due to a substantial increase of E, mainly through a large rise in VT. However, the increase of E did not modify SpO 2 as it does in patients and normal subjects at high altitude [START_REF] Khayat | Cardiorespiratory Effects of Added Dead Space in Patients With Heart Failure and Central Sleep Apnea[END_REF][START_REF] Lovis | Effect of added dead space on sleep disordered breathing at high altitude[END_REF][START_REF] Xie | Effects of inhaled CO2 and added dead space on idiopathic central sleep apnea[END_REF] (Fig. 3).

This study confirms that the ventilatory control is destabilized when the system is submitted to a double concomitant, physiological and environmental, stress, at exercise in hypoxia (Hermand et al., 2015b(Hermand et al., , 2015a)). Thus, amplitude of ventilatory oscillations are correlated to ventilation level and cardiac output (not shown) and their period, inferior to 11 seconds at exercise and therefore shorter than those observed in CHF and SAS patients [START_REF] Francis | Quantitative general theory for periodic breathing in chronic heart failure and its clinical implications[END_REF](Fig. 2), is strongly correlated to Ttot (Fig. 6).

This striking difference may have an origin in the regulatory system of arterial CO 2 pressure.

A well-known mechanism preventing a CHF/SAS patient from starting an apnea/hyperpnea cycle is to keep PaCO 2 above an apnea threshold [START_REF] Xie | Apnea-hypopnea threshold for CO2 in patients with congestive heart failure[END_REF] using CO 2 inhalation or external dead space device, even though the ventilation is augmented by the respiratory command via a central CO 2 chemoreflex activation. This explains why, in this context, the fall of apnea/hypopnea index (AHI) is systematically associated with a large increase in PaCO 2 and an inadequate response to hypercapnia due to an augmented ventilatory response to CO 2 , leading to successive CO 2 -threshold crossings and apnea cycles [START_REF] Khayat | Cardiorespiratory Effects of Added Dead Space in Patients With Heart Failure and Central Sleep Apnea[END_REF][START_REF] Xie | Effects of inhaled CO2 and added dead space on idiopathic central sleep apnea[END_REF]. The opposite phenomenon takes place in normal subjects: a slight change in arterial PCO 2 induces an immediate and appropriate ventilatory response to bring the system back to a homeostatic equilibrium. For instance, in CHF patients at rest, a ~15% rise in PETCO 2 , from 37 to 42 mmHg, elicits a ~50% increase in E, from 6.4 to 9.6 L.min -1 [START_REF] Khayat | Cardiorespiratory Effects of Added Dead Space in Patients With Heart Failure and Central Sleep Apnea[END_REF] whereas a mere 3% PETCO 2 gain, from 37.9 to 39.1 mmHg, in healthy subjects induces a 67% rise in E, from 11.1 to 18.5 L.min -1 (the E response is even greater at exercise). In the latter, a well-functioning CO 2 control system limits the aDS-induced CO 2 rise to a very low range, but nevertheless drastically augments the ventilation level which is associated to increased breathing instability at exercise (Hermand et al., 2015a(Hermand et al., , 2015b) (Fig. 5). In that perspective, the same remarkable mechanism was recently pointed out in obese patients with and without obstructive SAOS, in which progressive aDS-induced variations of PETCO 2 were kept within a 2 mmHg margin by rises of E [START_REF] Bernhardt | Short-term modulation of the ventilatory response to exercise is preserved in obstructive sleep apnea[END_REF].

It is interesting to note that the oscillatory pattern enhanced by adding dead space might be explained by the difference between the input and the output of the control system: the values of blood gases (PaO 2 and PaCO 2 ) are determined by alveolar ventilation ( A), while these blood gases act on total ventilation ( E) via the chemoreceptors and control centers. Thus, any difference between A and E will promote instability in blood gases and therefore in ventilation.

These systemic properties unveiled a second and noticeable mechanism: a stable A despite large swings of E in most conditions underlines a remarkable adaptation of ventilatory control system, in order to maintain the "effective" respiration, A, close to the metabolic needs of the organism, under environmental and physiological stresses, regarding the dead space status (VD, fig. 4, lower right). Assuming that the ratio ventilation-perfusion is optimal in healthy subjects at rest and at mild exercise [START_REF] Moinard | Pulmonary gas exchange during exercise in healthy subjects[END_REF], we suggest that the "extra" ventilation with aDS (Fig. 3 and4) is then attributed to the sole action of CO 2 chemoreflex, combined from peripheral and central chemoreceptors.

Central sleep apneas exhibited by normal subjects at high altitude are also greatly reduced by added dead space [START_REF] Lovis | Effect of added dead space on sleep disordered breathing at high altitude[END_REF][START_REF] Patz | Dead space mask eliminates central apnea at altitude[END_REF]. However, underlying mechanisms are different from patients. A broad consensus point out that an augmented activity of peripheral chemoreceptors in hypoxia is involved into the genesis of periodic breathing [START_REF] Ainslie | Breathing and sleep at high altitude[END_REF]Hermand et al., 2015b;[START_REF] Kumar | Peripheral chemoreceptors: Function and plasticity of the carotid body[END_REF][START_REF] Lahiri | Oxygen sensing in the body[END_REF], in a subtle interplay with central chemoreceptors through peripheral afferences into the nucleus tractus solitarii (NTS) [START_REF] Smith | Brainstem respiratory networks: building blocks and microcircuits[END_REF]. A higher E by aDS-induced central CO 2 stimulation will maintain a higher O 2 saturation [START_REF] Patz | Dead space mask eliminates central apnea at altitude[END_REF], lowering carotid bodies activity and its subsequent effect on periodic breathing. In the present work, aDS did not enhance SpO 2 in spite of a large increase in E especially in hypoxia, maintaining a higher peripheral sensitivity and therefore a greater tendency to develop periodic breathing. This may explain the oscillatory exacerbation observed in hypoxia, even more at exercise, during which O 2 desaturation is worsened. Furthermore, the prompt response of ventilatory control system to a higher aDS-induced PaCO 2 within a narrow range points out the role of CO 2 chemosensitivity, enhanced in hypoxia [START_REF] Masuyama | Periodic breathing at high altitude and ventilatory responses to O2 and CO2[END_REF], leading to greater ventilatory oscillations than those observed without added dead space. Whereas the latter points require further studies to quantify the involvement of central and peripheral chemoreceptors in this matter, other potential actors could come into play, such as the action of lung stretch receptors which could be activated by an augmented VT with aDS.

Lastly, we confirmed the tight relationship existing between E period and Ttot (Hermand et al., 2015a, 2015b) (Fig. 6, right), suggesting the existence of an intrinsic oscillator modulating the activity of the central pattern generator [START_REF] Forster | Contributions of the pre-Bötzinger complex and the Kölliker-fuse nuclei to respiratory rhythm and pattern generation in awake and sleeping goats[END_REF]. The theoretical limit of E period, when Ttot tends towards zero (i.e. respiratory frequency is infinite), is around 6 seconds.

In conclusion, these findings confirm the destabilizing role of added dead space in the ventilatory control system of normal subjects at exercise in hypoxia, as anticipated by a mathematical model. It also points out the discrepancy of the effect of CO 2 between healthy subjects on one hand, and CHF/SAS patients and normal subjects asleep in altitude on the other hand, counteracting or promoting breathing stability. This study, in an original manner, confirmed that total ventilation adapts to external constraints by maintaining adequate alveolar ventilation for metabolic needs of the organism. conditions: normoxia and hypoxia without added dead space (aDS), hypoxia with aDS (plain, dot and dashed lines, respectively). Peak power is higher when aDS is combined to both exercise and hypoxia. Exercise vs Rest: #, P < 0.05; ##, P < 0.01; ###, P < 0.001. Hypoxia vs normoxia: *, P < 0.05; **, P < 0.01; ***, P < 0.001. Exercise vs Rest: #, P < 0.05; ##, P < 0.01; ###, P < 0.001. Hypoxia vs normoxia: *, P < 0.05; **, P < 0.01; ***, P < 0.001. aDS 500 vs aDS 0: †, P < 0.05; † †, P < 0.01; † † †, P < 0.001

CAPTIONS

Figure 1 .

 1 Figure 1. Example of breath-by-breath ventilation recordings in hypoxia, without and with added dead space (respectively upper and lower panels). Ventilatory instability is noticeably increased with added dead space.

Figure 2 .

 2 Figure 2. Means of power spectral densities of the ventilation signal at exercise in 3

Figure 3 .

 3 Figure 3. Mean (± SD) values of O 2 saturation (SpO 2 ), end-tidal CO 2 pressure (PETCO 2 ), tidal volume (VT) and respiratory frequency. Exercise vs Rest: #, P < 0.05; ##, P < 0.01; ###, P < 0.001. Hypoxia vs normoxia: *, P < 0.05; **, P < 0.01; ***, P < 0.001. aDS 500 vs aDS 0: †, P < 0.05; † †, P < 0.01; † † †, P < 0.001

Figure 4 .Figure 5 .

 45 Figure 4. Mean (± SD) values of minute and alveolar ventilation ( E and A respectively),the A/ E ratio and the assessed total dead space (VD). Exercise vs Rest: #, P < 0.05; ##, P < 0.01; ###, P < 0.001. Hypoxia vs normoxia: *, P < 0.05; **, P < 0.01; ***, P < 0.001. aDS 500 vs aDS 0: †, P < 0.05; † †, P < 0.01; † † †, P < 0.001

Figure 6 .

 6 Figure 6. E peak power (left) and period (right) as a function of E and Ttot, respectively. Rest and exercise values have been pooled in all conditions.

Table 1 .

 1 Characteristics of the subjects

	n	Age (yrs)	Body weight (kg)	Height (cm)	Maximal Aerobic Power (MAP, W)
	Dead Space (DS) 10 29.0 ± 9.5	71.8 ± 9.1	175.1 ± 7.5	231.0 ± 31.1
	Mean ± SD.

Table 2 .

 2 Summary of three-way analysis of variance and interactions between factors. , P < 0.05; **, P < 0.01; ***, P < 0.001; ns, non-significant.

		Effect of Exer. vs. Rest	Effect of Hx vs. Nx	Effect of aDS	Interaction Rest / Exer. -Nx / Hx	Interaction Rest / Exer. -DS	Interaction Nx / Hx -DS
	E	***	**	***	ns	*	ns
	SpO 2	***	***	ns	**	ns	ns
	PETCO 2	***	***	*	**	ns	ns
	VT	***	P = 0.0629	***	ns	ns	ns
	Ttot	***	ns	*	ns	ns	ns
	HR	***	***	ns	P = 0.07	ns	ns
	A	***	***	ns	ns	ns	ns
	E peak power	***	***	**	ns	*	ns
	E period	***	ns	ns	ns	ns	ns

Nx: normoxia; Hx: hypoxia; Exer.: Exercise; aDS : added dead space ; E: minute ventilation; SpO 2 : pulse O 2 saturation; PETCO 2 : end-tidal PCO 2 ; VT: tidal volume; Ttot: total respiration cycle time; HR: heart rate; A: alveolar ventilation. *