Claude Descorme
email: claude.descorme@univ-poitiers.fr

Rachid Taha

Najat Mouaddib-Moral

Daniel Duprez

Oxygen storage capacity measurements of three-way catalysts under transient conditions

Keywords: Oxygen storage, Transient conditions, Stationary conditions, Palladium, Platinum, Rhodium, Catalyst, Alumina, Ceria-alumina

Oxygen storage capacity (OSC) measurements at 450 • C were carried out on 10 different alumina and ceria-alumina supported Pd, Pt, Rh, PdRh and PtRh catalysts. Experiments were performed under both transient (0.5 and 1 Hz) and stationary reaction conditions using a mass spectrometer for the gas phase analysis every 100 ms. OSC was shown to be strongly dependent on the metal nature -oxidized or reduced. Rh appeared to be the best OSC promoter. Furthermore, ceria addition to the alumina support strongly enhances the OSC. In fact looking at the OSC values, a factor of 3 was evidenced between Pt/Al 2 O 3 and Rh/Al 2 O 3 and an additional factor of about 12 between Rh/Al 2 O 3 and Rh/CeO 2 -Al 2 O 3 . The metal oxides relative stability as well as the metal electronic configuration were shown to be strongly influent on the overall reactivity of the catalyst. Additional kinetic studies showed that the oxide reduction rate under CO is slower than the oxide oxidation rate under O 2 . Finally a general scheme for the oxygen storage process is proposed and discussed.

Introduction

In the field of three-way catalysis (TWC), oxygen storage is a crucial point. As a result, lots of studies have been devoted to oxygen storage capacity (OSC) measurements [1][2][3][4][5][6][7][8][9]. The performances of automotive pollution control catalysts have been shown to somehow correlates with the OSC of these solids. In fact, the OSC measurement has been considered as a potential indication of the catalyst state -active or inactive -for on-board diagnostic (OBD) applications [10][11][12][START_REF] Sideris | Methods for Monitoring and Diagnosing the Efficiency of Catalytic Converters. A Patent-oriented Survey[END_REF][14]. However, up to now, OSC measurements have been carried out under ideal conditions, in a continuous mode [1,7]. Such measurement conditions are far from real post-combustion operating conditions, when the exhaust gas composition rapidly oscillates between hydrocarbon-rich and hydrocarbon-poor mixtures.

This paper deals with the development of a new OSC measurement technique. OSC could be measured in a transient regime by injection of alternate CO or O 2 pulses every 1 or 2 s (F = 1 or 0.5 Hz). Such measurements conditions were shown to be appropriate to simulate the fluctuations in the real exhaust gas composition.

This technique was applied to the study of two series of Pt-, Rh-and Pd-based model three-way catalysts. Our study will concentrate on both the effect of ceria on the OSC and the influence of the nature of the noble metal on the CO oxidation catalytic reaction. 1

Experimental

Catalysts preparation

Alumina support (A) was obtained from ␥-alumina (100 m 2 g -1 ) directly supplied by Institut Français du Pétrole (IFP, France). After treatment at 900 • C, the ␦-Al 2 O 3 phase is predominant.

A 12% CeO 2 -Al 2 O 3 support (CA) was prepared by impregnation of the alumina support with an aqueous solution of an ammonium and cerium nitrate (Ce(NH 4 ) 2 (NO 3 ) 6 ). After evaporation and drying, the CeO 2 -Al 2 O 3 support is calcined at 450 • C for 5 h.

Monometallic catalysts were prepared by incipient wetness impregnation of the support either with an aqueous solution of diaminodinitro platinum(II) (Pt(NH 3 ) 2 (NO 2 ) 2 ) or with a solution of palladium(II) diacetylacetonate (Pd(C 5 H 7 O 2 ) 2 ) in acetone. Bimetallic catalysts were subsequently prepared by impregnation of the pre-reduced monometallic catalyst with an aqueous solution of Rh 3+ (Rh(NO 3 ) 3 ). Every metal precursor was chlorine-free. In fact, chlorine was found to decrease both oxygen mobility at the oxides surface and the OSC [15][16][17][18]. Such an effect of chlorine could result in an inhibition of the oxygen storage.

After impregnation Pt-based (series 1) and Pd-based (series 2) catalysts were dried and further calcined at 350 • C [19]. Every catalyst was further aged under 10% H 2 O + 1% O 2 at 900 • C for 2 h [20]. In fact, fresh catalysts were too active so that oxygen storage kinetics could not be accessed.

The composition of the catalysts is, respectively, given in Tables 1 and2 for series 1 and 2 samples. The composition of the metallic phase was adjusted so that every catalyst contains about 50 mol of metal atoms per gram of catalyst.

Experimental setup

The apparatus used for this set of experiments is dedicated to the study of reactions -CO + O 2 in our case -carried out under transient conditions at any given frequency lower than 1 Hz. This system consists in two parts: the gas manifold and the mass spectrometer.

Reactants (CO and O 2 ) flows are regulated using mass flow controllers. Before the reactor entrance, reactants are mixed with a 1% Ar in He carrier gas (100 cm 3 min -1 ). Any kind of CO/(1% Ar + He) and O 2 /(1% Ar + He) mixtures could be obtained. For this study, 2% CO and 1% O 2 mixtures were used. Reactant injections were controlled using automated injection valves. Alternate CO and O 2 injections may take place at a frequency as high as 1 Hz. To optimize the response time, the dead volume was reduce to less than 2.5 cm 3 , including the whole reaction circuit from the automated valve up to the capillary tube before the mass spectrometer.

A 2 mg sample, diluted in 18 mg cordierite, is placed in a straight Pyrex reactor and pretreated under pure helium at 450 • C (ramp rate: 2 • C min -1 ) for 15 min. Reactions are carried out at 450 • C. Despite of the low sample weight, reproducibility was checked to be better than 5%.

The experiment consists in five different steps, as presented in Fig. 1 -( The evolution of the gas phase composition is followed by mass spectrometry. Masses m/e = 4 (He), 28 (CO), 32 (O 2 ), 44 (CO 2 ) and 40 (Ar) are monitored every 0.1 s. The global experimental setup used for both OSC measurements is schematized in Fig. 2.

All the results presented below will be expressed per gram of solid. Every sample consisted of 2 mg catalyst plus 18 mg cordierite for a total of 20 mg of solid.

Results and discussion

CO and O 2 steps -stationary regime

Data deduced from the second part of the OSC measurement being necessary for the interpretation of the results obtained in the first part, the results drawn from the second part of the experiment will be described first for a better readability of our manuscript.

In that second part of the experiment, OSC measurements are carried out at 450 • C under "stationary" conditions. All samples are subsequently submitted to a 2 min long 2% CO step (step (iii), see Fig. 1) and a 2 min long 1% O 2 step (step (v), see Fig. 1) with intermediate outgassing under pure He for 10 min. Evolutions of the unconverted CO and the produced CO 2 during step (iii) (see Fig. 1) and the unconverted O 2 during step (v) (see Fig. 1) are monitored as a function of time. Examples are given in Figs. 3 and4 for Pd-based (series 2) and Pt-based (series 1) catalysts, respectively. The amounts of CO and O 2 or CO 2 , respectively, consumed or produced were expressed as differential amounts of molecules consumed or produced per gram of solid and per unit time (mol g -1 t -1 ). Differential calculations were performed using 0.1 s time increments. Every points on the curves correspond to the amount of CO, CO 2 or O 2 consumed or produced during the last 0.1 s. Cumulated amounts of CO and O 2 consumption and CO 2 production could be derived from the integration of these CO, CO 2 and O 2 curves. An example is given in Fig. 5 for Pt-based catalysts (series 1).

Table 3 summarizes the amounts of CO consumed and CO 2 produced during CO step and the amounts of O 2 consumed during O 2 step at time t equals 0.5, 1, 5 and 40 s for all 10 catalysts under study. A close look to this table shows that alumina-supported catalysts have a very low OSC. On the opposite, ceria-containing catalysts have the highest activity towards oxygen storage. These catalysts may be classified in descending order as follows:

Rh/CeO 2 -Al 2 O 3 (RhCA)>PtRh/CeO 2 -Al 2 O 3 (PtRhCA)>PdRh/CeO 2 -Al 2 O 3 (PdRhCA)> Pd/CeO 2 -Al 2 O 3 (PdCA)>Pt/CeO 2 -Al 2 O 3 (PtCA)> Rh/Al 2 O 3 (RhA) ∼ = PtRh/Al 2 O 3 (PtRhA)>PdRh/ Al 2 O 3 (PdRhA)>Pt/Al 2 O 3 (PtA) ∼ = Pd/Al 2 O 3 (PdA)
. Differences in OSC among these "aged" catalysts could be explained by the different sintering modes for Rh, Pt and Pd [21][22][23]. Furthermore, this reactivity ordering may be explained by the presence of both Rh and ceria. Rhodium strongly enhance the reducibility of ceria so that the OSC is greatly improved.

Furthermore, one can see that PtRh/CeO 2 -Al 2 O 3 (PtRhCA) behaves like a pure rhodium catalyst. This would indicate that (i) either Pt and Rh particles are distinct and Rh particles are in direct Finally, initial rates for CO consumption and CO 2 formation upon CO step and for O 2 consumption upon O 2 step are reported in Fig. 6 for both alumina (A) and ceria-alumina (CA) supported catalysts. Initial rates were deduced from the slopes, extrapolated at zero time, of the plots presented in Fig. 5. One may immediately conclude that reoxidation of the catalysts by molecular oxygen is much faster than the reduction under CO.

High frequency alternate CO and O 2 pulses -transient regime

As stated in Section 2, every experiment starts with the OSC measurement at 450 • C under transient a Cumulative amounts "Q t "(mol g -1 ) consumed or produced between zero time and time t (s) on Pt, Pd, Rh, PtRh-and PdRhbased alumina (A) and ceria-alumina (CA) supported catalysts.

b CO consumed or CO 2 formed (mol g -1 ) after the CO step. c O 2 consumed (mol O atoms g -1 ) after the O 2 step. conditions. Alternate 2% CO or 1% O 2 pulses are injected on the catalyst at a frequency of 1 or 0.5 Hz for 10 min (step (i), see Fig. 1). To understand what follows, one must keep in mind that, at every gas change, both gases (CO and O 2 ) coexist in the gas phase for a fraction of a second. In those conditions, CO catalytic oxidation with gaseous oxygen may occur (CO 2ox ).

Looking at CO 2 formation, one will have to make the difference between CO 2 originating from the CO catalytic oxidation using gaseous oxygen (CO 2ox ) and CO 2 coming from the reverse oxygen storage reaction (CO 2 OSC ). In all cases, CO 2 formation occurs after every gas change. One CO 2 formation peak (CO 2 (1)) appears going from O 2 to CO (peak 1, see Fig. 7). In this case the catalyst is partially oxidized before the introduction of CO. This CO 2 formation peak includes CO 2 coming from both the catalytic oxidation of CO in the presence of gaseous oxygen (CO 2ox (1) ) and the oxygen storage reverse reaction (CO 2 (1) = CO 2ox(1) + CO 2 OSC ). The second CO 2 formation peak (CO 2 (2)) forms when CO is replaced by O 2 in the gas feed (peak 2, see Fig. 7). In that case, the catalyst is partially reduced. Here, the only reaction responsible for the formation of CO 2 is the catalytic oxidation of CO (CO 2 (2) = CO 2ox(2) ): upon step change from 0 to 1% O 2 (step (v), see Fig. 1) practically no CO 2 evolution was observed. These observations indicate that CO oxidation kinetics are governed by the catalyst state: oxidized or reduced. In fact, CO 2 formation related a Bimetallic PtRh-based alumina (A) and ceria-alumina (CA) supported catalysts. b Expressed either in mol CO g -1 or in m o lOg -1 or in mol CO 2 g -1 .

c Determined from stationary regime measurements: OSC step = Q 0.5 (see Table 3). d Determined from the integration of peak 1. e Determined from the integration of peak 2. f CO 2 catalytic = (CO 2 (1) -OSC step ) + CO 2 (2). g Peaks could not be differentiated.

to the oxygen storage process (CO 2 OSC ) only occurs on the oxidized catalyst when O 2 is replaced by CO (peak 1). In the course of a switch from CO to O 2 , oxygen storage occurs: an oxygen uptake is observed b u tn oC O 2 forms. Furthermore, we may see from Tables 4-7 that CO 2ox(1) = CO 2ox (2) .

Examples are given in Fig. 7 for PtRh/CeO 2 -Al 2 O 3 (PtRhCA) and PdRh/CeO 2 -Al 2 O 3 (PdRhCA). The evolution of the gas phase composition (CO, O 2 and CO 2 ) at the reactor outlet is presented as a function of time. One can see that an increase of the alternating frequency does not modify the qualitative results. The resolution between peak 1 (CO 2 (1)) and peak 2 (CO 2 (2)) is just harder in some cases, when the reactivity of the catalyst is high. For comparison, the evolution of CO 2 formation as a function of time is presented in Fig. 8 for Pd-based catalysts (series 2) and in Fig. 9 for Pt-based catalysts (series 1).

Quantitative information may be obtained from the integration of the CO, O 2 and CO 2 profiles. In the case of CO 2 formation, the so-called peaks 1 and 2 were integrated separately. To calculate the total amount of CO 2 produced from the CO catalytic oxidation (CO 2 catalytic ), the amount of CO 2 originating from the reverse oxygen storage reaction must be subtracted from peak 1 (CO 2 (1)). For that purpose, OSC values (OSC step ) were estimated from the data acquired in the course of step (iii) (see Fig. 1) in the second part of the experiment (CO step). To compare values after the same contact time, OSC step was taken to be c Determined from stationary regime measurements: OSC step = Q 1 (see Table 3). d Determined from the integration of peak 1.

e Determined from the integration of peak 2. c Determined from stationary regime measurements: OSC step = Q 0.5 (see Table 3). d Determined from the integration of peak 1. e Determined from the integration of peak 2. f CO 2 catalytic = (CO 2 (1) -OSC step ) + CO 2 (2). c Determined from stationary regime measurements: OSC step = Q 1 (see Table 3). d Determined from the integration of peak 1. e Determined from the integration of peak 2. f CO 2 catalytic = (CO 2 (1) -OSC step ) + CO 2 (2). equal to the cumulated amount of CO 2 produced after half a period of time. For example, in the case of experiments performed at 0.5 Hz, OSC step is given by the integrated amount of CO 2 produced after 1 s. The average value of the calculated amounts of CO and O 2 consumed and CO 2 produced during one period of time (1 or 2 s) are displayed in Tables 4 and5 for Pt, Rh and PtRh catalysts (series 1) and in Tables 6 and7 for Pd-based catalysts (series 2). From all those results we could conclude that (i) mass balance is complete and no carbon is left over the surface and (ii) oxygen storage is more sensitive to the catalyst state than the catalytic CO oxidation reaction. In fact, OSC depends on both the number and the nature of the active sites. In that case, the nature of the metal (Pt, Pd or Rh) as well as the support (alumina or ceria-alumina) are important factors. On the opposite, in the case of the CO + O 2 catalytic reaction, oxygen essentially comes from the gas phase. Thus, even if the catalyst has a low OSC, it will be, however, continuously fed with oxygen and the reaction may still proceed. At 450 • C this reaction is fast. Moreover, the activation energy for the catalytic CO oxidation reaction was found to vary between 80 and 130 kJ mol -1 [24,25]. Nevertheless, the activity stays high even for strongly aged catalysts.

f CO 2 catalytic = (CO 2 (1) -OSC step ) + CO 2 (2).
Looking at OSC values (OSC step ), catalysts may be classified in descending order as follows: Rh/CeO Relative reactivities could be explained both by the introduction of ceria on the alumina support or by the substitution of Rh particles to Pt or Pd particles. The presence of ceria would induce a new reaction pathway through a bifunctional mechanism. CO 2 formation would derive from the reaction between an adsorbed CO molecule on the metal surface and an oxygen atom coming from the ceria surface in the vicinity of the metal particles. As a result, cerium oxide would reduce deactivation effects related to metal sintering.

Furthermore, at 450 • C, Rh-based catalysts are more active than Pt-and Pd-based catalysts. The activity of the aged Rh-based catalysts would derive from both a high stability of Rh 2 O 3 particles towards sintering compared to PtO 2 and PdO [8] and a better oxygen transfer from CeO 2 to Rh [7,26].

Additionally, a comparison between the amounts of CO 2 produced on Pt/Al 2 O 3 (PtA) and Pt/CeO 2 -Al 2 O 3 (PtCA) catalysts in the course of step (i) (see Fig. 1), going from O 2 to CO (peak 1) and vice versa (peak 2), shows that CO 2 (2) is slightly larger than CO 2 (1) (Tables 4 and 5). This observation confirms that the OSC of these two catalysts must be very low. In fact, if the OSC were high, CO 2 (1) would be much larger than CO 2 (2). In these two cases, CO 2 essentially originates from the CO oxidation catalytic reaction. Moreover, considering that CO 2 (2) is slightly larger than CO 2 (1), one can conclude that CO catalytic oxidation is faster on a reduced catalyst than on a partially pre-oxidized catalyst. These two different behaviors could be related to the electronic configuration of Pt. Electronic configuration of reduced platinum may be written [Xe] f 14 5d 9 6s 1 . Both d and s orbitals are not fully occupied and electronic transfers may occur. Platinum oxide (PtO) has a [Xe] f 14 5d 10 6s 2 electronic configuration. The d and s orbitals are fully occupied and electronic transfer may hardly take place. This would explain the better activity of reduced catalysts compared to oxidized catalysts.

In the case of the bimetallic PtRh-based catalysts (series 1), OSC is much higher. CO 2 (1) is then larger than CO 2 (2) and the whole amount of CO 2 produced mainly originates from the oxygen storage reverse reaction. If the contribution of the OSC to peak 1 is subtracted, peak 2 becomes larger than peak 1. This situation is the same as for Pt catalysts. For Pd catalysts, the opposite is observed. Oxidized Pd catalysts are slightly more active than the reduced ones.

This difference between CO 2 (1) and CO 2 (2) is even more pronounced when experiments are carried out at F = 0.5 Hz. At F = 0.5 Hz, CO or O 2 injections length are too short and the catalyst does not fully reduce or oxidize.

Finally, looking at the global catalytic activity of these catalysts, one can conclude that Pt catalysts are less sensitive to frequency than Pd catalysts. It is clear from Tables 6 and7 that Pd-based catalysts (series 2) are more active in the CO catalytic oxidation when experiments are carried out at a lower frequency. This observation could indicate that Pt-based catalysts (series 1) would be more reactive, with faster response time.

Conclusions

Our experimental setup was shown to be appropriate for the measurement of both the OSC under transient conditions and the reactivity in the CO catalytic oxidation reaction of any catalyst. For the first time, OSC could be measured under dynamic conditions with alternate CO and O 2 pulses at frequency up to 1 Hz.

This study showed that CO 2 formation occurs after every modification in the gas phase composition. CO 2 may form on a pre-oxidized catalyst when O 2 is replaced by CO. In that case, both OSC and CO catalytic oxidation participate to CO 2 formation. Second, CO 2 is also produced on a pre-reduced catalysts when O 2 replaces CO. In that case, CO 2 exclusively originates from CO catalytic oxidation.

At 450 • C, catalysts reactivity in the catalytic oxidation of CO was shown to slightly depend on the metal nature. On the opposite, OSC strongly depends on the catalysts state -oxidized or reduced. Considering the OSC value, a combination of Rh and ceria appeared to be the optimum among the catalysts under study. Relative activities were analyzed on the basis of the metal oxides relative stability and the metals electronic configuration.

Furthermore, in all cases, catalysts reduction rates under CO were shown to be smaller than the reoxidation rates under O 2 . An optimized catalyst would have to have an enhance reducibility. Finally, based on all these observations, a general scheme of the oxygen storage process is presented in Fig. 10. CO would be activated on the metal surface and react with oxygen atoms coming from the oxide support. Oxygen transfer from the support to the metal surface would depend on both oxygen mobility at the surface (2) and in the bulk of the oxide (3) and on the metal/support interface. CO direct oxidation on the support is assumed to be very low.

Fig. 1 .

 1 Fig. 1. One typical experiment. General scheme for the measurement progression.

Fig. 2 .

 2 Fig. 2. Flow-sheet of the homemade apparatus used for OSC measurements.

  interaction with ceria or (ii) Rh segregates at the surface of PtRh bimetallic particles. On the opposite, PdRh/CeO 2 -Al 2 O 3 (PdRhCA) reacts as pure Pd and we concluded that (i) either Pd and Rh particles are distinct and Rh particles do not interact with ceria or (ii) Pd segregates at the surface of PdRh bimetallic particles. In one case almost pure rhodium is the active surface and OSC is high, in the second case almost pure palladium is the active surface and OSC is low.

Fig. 3 .

 3 Fig. 3. CO and O 2 step changes on pre-oxidized on bimetallic PdRh-based alumina (A) and ceria-alumina (CA) supported catalysts at 450 • C: (a) differential CO consumption during CO step; (b) differential CO 2 formation during CO step; (c) differential O 2 consumption during O 2 step expressed in mol g -1 t -1 ( t = 0.1 s).

Fig. 4 .

 4 Fig. 4. CO and O 2 step changes on pre-oxidized on bimetallic PtRh-based alumina (A) and ceria-alumina (CA) supported catalysts at 450 • C: (a) differential CO consumption during CO step; (b) differential CO 2 formation during CO step; (c) differential O 2 consumption during O 2 step expressed in mol g -1 t -1 ( t = 0.1 s).

Fig. 5 .

 5 Fig. 5. Cumulative curves for CO consumption and CO 2 formation during CO step and for O 2 consumption during O 2 step on bimetallic PtRh-based alumina (A) and ceria-alumina (CA) supported catalysts at 450 • C. Curves were built from points acquired every 0.1 s. For sake of clarity, only a few experimental points are displayed.

Fig. 6 .Fig. 7 .

 67 Fig. 6. Comparison of the initial rates for CO consumption and CO 2 formation during CO step and for O 2 consumption during O 2 step on alumina (A) and ceria-alumina (CA) supported catalysts at 450 • C.

Fig. 8 .

 8 Fig. 8. Evolution of CO 2 produced under transient conditions (F = 0.5 and 1 Hz) upon reaction at 450 • C on Pd-based alumina (A) and ceria-alumina (CA) supported catalysts.

Fig. 9 .

 9 Fig. 9. Evolution of CO 2 produced under transient conditions (F = 0.5 and 1 Hz) upon reaction at 450 • C on Pt-based alumina (A) and ceria-alumina (CA) supported catalysts.

  2 -Al 2 O 3 (RhCA)>PtRh/CeO 2 -Al 2 O 3 (PtRhCA)> PdRh/CeO 2 -Al 2 O 3 (PdRhCA)>Pd/CeO 2 -Al 2 O 3 (PdCA)>Pt/CeO 2 -Al 2 O 3 (PtCA)>Rh/Al 2 O 3 (RhA) ∼ = PtRh/Al 2 O 3 (PtRhA)>PdRh/Al 2 O 3 (PdRhA)>Pt/Al 2 O 3 (PtA) ∼ = Pd/Al 2 O 3 (PdA).

Fig. 10 .

 10 Fig. 10. Schematic representation of all processes potentially involved during OSC measurements.

Table 1

 1

	Metal loading for the different bimetallic PtRh-based alumina (A)
	and ceria-alumina (CA) supported catalysts (series 1)
	Catalyst	wt.%		mol of metal atoms
		Pt	Rh	per gram of catalyst
	PtA	1.17	0.00	60
	PtCA	1.00	0.00	51.3
	PtRhA a	0.70	0.21	55.3
	PtRhCA a	0.60	0.21	51.2
	RhA	0.00	0.50	49.5
	RhCA	0.00	0.53	51.4

a The metallic phase consist in 35% Rh and 65% Pt or Pd.

Table 2

 2 Metal loading for the different bimetallic PdRh-based alumina (A) and ceria-alumina (CA) supported catalysts (series 2)

	Catalyst	wt.%		mol of metal atoms
		Pd	Rh	per gram of catalyst
	PdA	0.50	0.00	47
	PdCA	0.50	0.00	47
	PdRhA a	0.33	0.17	47
	PdRhCA a	0.33	0.17	47
	RhA	0.00	0.50	49.5
	RhCA	0.00	0.53	51.4

a The metallic phase consist in 35% Rh and 65% Pt or Pd.

Table 3

 3 CO and O 2 steps a

				Q 0.5	Q 1	Q 5	Q 40
	PdA
	CO b		0.2	0.3	0.7	3.9
	CO 2	b	0.2	0.3	0.7	3.2
	O 2	c		0.4	0.9	2.7	4.4
	PtA
	CO b		0.1	0.3	0.3	7
	CO 2	b	0.1	0.2	0.6	3
	O 2	c		0.2	0.4	1.7	13
	RhA
	CO b		0.4	0.9	3.0	8
	CO 2	b	0.3	0.6	2.0	7
	O 2	c		2.4	4.2	9.1	9
	PdRhA
	CO b		0.2	0.4	1.1	6.6
	CO 2	b	0.2	0.4	1.3	6.1
	O 2	c		0.4	1.3	4.8	6.5
	PtRhA
	CO b		0.4	0.7	4.0	20
	CO 2	b	0.3	0.6	2.0	14
	O 2	c		0.8	1.5	4.2	14
	PdCA
	CO b		0.8	2.0	6.7	15.3
	CO 2	b	0.8	1.7	6.2	15.2
	O 2	c		1.3	2.9	8.7	20.1
	PtCA
	CO b		0.5	0.8	4.5	23
	CO 2	b	0.3	0.7	3.1	19
	O 2	c		5.3	6.6	14.3	22
	RhCA
	CO b		4.9	7.8	17.2	58
	CO 2	b	3.5	7.9	17.2	55
	O 2	c		5.4	8.7	19.7	81
	PdRhCA
	CO b		1.3	2.7	6.4	11.9
	CO 2	b	1.1	2.6	6.2	11.9
	O 2	c		1.2	2.8	6.5	13.4
	PtRhCA
	CO b		3.1	5.4	12.0	54
	CO 2	b	2.4	5.2	12.3	52
	O 2	c		7.2	8.6	15.9	64

Table 4

 4 Determination of the different contributions to the CO 2 formation (CO 2 (1), CO 2 (2) and CO 2 catalytic ) from the total amount CO and O 2 consumed (CO and O 2 ) and the total amount of CO 2 formed (CO 2 ) during one period of time (1 s) under transient conditions at 450 • C for series 1 samples a

	Catalyst	CO b	O 2	b	CO 2	b	OSC step	c	CO 2 (1) d	CO 2 (2) e	CO 2 catalytic	f
	PtA	16.5	15.8	15.3		0.1		7.5	7.9	15.3
	RhA	17.2	16.6	16.7		0.3		8.6	8.1	16.4
	PtRhA	19.1	18		17.4		0.3		8.4	9.0	17.1
	PtCA	16.8	15.8	15.4		0.3		7.3	8.1	15.1
	PtRhCA	17.8	17.6	16.7		2.4		9.2	7.6	14.4
	RhCA	24.8	24.8	23.9		3.5		-g	-g	20.4

Table 5

 5 Determination of the different contributions to the CO 2 formation (CO 2 (1), CO 2 (2) and CO 2 catalytic ) from the total amount of CO and O 2 consumed (CO and O 2 ) and the total amount of CO 2 formed (CO 2 ) during one period of time (2 s) under transient conditions at 450 • C for series 1 samples a Expressed either in mol CO g -1 or in m o lOg -1 or in mol CO 2 g -1 .

	Catalyst	CO b	O 2	b	CO 2	b	OSC step	c	CO 2 (1) d	CO 2 (2) e	CO 2 catalytic	f
	PtA	16.1	16.4	15.6		0.2		6.6	9.1	15.5
	RhA	19.3	18.8	18.3		0.6		9.7	8.5	17.6
	PtRhA	19.1	24.2	19.1		0.6		8.4	10.7	18.5
	PtCA	19.6	20.0	19.0		0.7		8.3	10.7	18.3
	PtRhCA	20.0	19.8	19.4		5.2		9.8	9.5	14.1
	RhCA	25.9	26.2	25.3		7.9		13.6	11.7	17.4
	a Bimetallic PtRh-based alumina (A) and ceria-alumina (CA) supported catalysts.

b

Table 6

 6 Determination of the different contributions to the CO 2 formation (CO 2 (1), CO 2 (2) and CO 2 catalytic ) from the total amount CO and O 2 consumed (CO and O 2 ) and the total amount of CO 2 formed (CO 2 ) during one period of time (1 s) under transient conditions at 450 • C for series 2 samples a

	Catalyst	CO b	O 2	b	CO 2	b	OSC step	c	CO 2 (1) d	CO 2 (2) e	CO 2 catalytic	f
	PdA	14.0	14.2	13.7		0.2		7.3	6.4	13.5
	PdCA	14.4	13.9	13.7		0.8		7.4	6.3	12.9
	PdRhA	14.7	14.2	14.0		0.2		8.4	5.6	13.8
	PdRhCA	16.6	17.0	16.6		1.1		9.6	7.0	15.5

a Bimetallic PdRh-based alumina (A) and ceria-alumina (CA) supported catalysts. b Expressed either in mol CO g -1 or in m o lOg -1 or in mol CO 2 g -1 .

Table 7

 7 Determination of the different contributions to the CO 2 formation (CO 2 (1), CO 2 (2) and CO 2 catalytic ) from the total amount of CO and O 2 consumed (CO and O 2 ) and the total amount of CO 2 formed (CO 2 ) during one period of time (2 s) under transient conditions at 450 • C for series 2 samples a Expressed either in mol CO g -1 or in m o lOg -1 or in mol CO 2 g -1 .

	Catalyst	CO b	O 2	b	CO 2	b	OSC step	c	CO 2 (1) d	CO 2 (2) e	CO 2 catalytic	f
	PdA	15.5	16.2	15.4		0.3		8.4	7.0	15.1
	PdCA	18.1	18.6	17.8		1.7		10.1	7.9	16.3
	PdRhA	15.6	15.6	15.4		0.4		8.9	6.6	15.1
	PdRhCA	20.0	20.0	19.8		2.6		10.9	8.9	17.2
	a Bimetallic PdRh-based alumina (A) and ceria-alumina (CA) supported catalysts.

b


Yingyu Yang

Maxime Sermesant

Shape Constraints in Deep Learning for Robust 2D Echocardiography Analysis

Keywords: Segmentation, Deep Learning, Deformation, Echocardiography

Echocardiography is a popular and cost-efficient tool for cardiac dysfunction diagnosis. Automatic solutions that could effectively and efficiently analyse cardiac functions are highly desired in clinical situations. Segmentation and motion tracking are two important techniques to extract useful cardiac indexes, such as left ventricle ejection fraction (LVEF), global longitudinal strain (GLS), etc. However, these tasks are non-trivial since ultrasound images usually suffer from poor signal-to-noise ratio, boundary ambiguity and out of view problem. In this paper, we explore how to introduce shape constraints from global, regional and pixel level into a baseline U-Net model for better segmentation and landmark tracking. Our experiments show that all the three propositions perform similarly as the baseline model in terms of geometrical scores, while our pixel-level model, which uses a multi-class contour loss, reduces segmentation outliers and improves the tracking accuracy of 3 landmarks used for GLS computation. With appropriate augmentation techniques, our models also show a good generalisation performance when testing on a larger unseen cohort.

Introduction

Echocardiography, a non-invasive and cost-efficient imaging technique, is widely used by cardiologists to evaluate the cardiac function. Segmentation and motion tracking are two essential tasks that can help cardiologists in clinical decisionmaking. Segmentation offers information of shape and volume while motion tracking provides knowledge of deformation and function.

Deep learning based methods have shown very good performance for medical segmentation and registration. As for segmentation, the U-Net architecture has proved its overwhelming power in large cohort echocardiography segmentation [START_REF] Leclerc | Deep learning for segmentation using an open large-scale dataset in 2d echocardiography[END_REF]. With appropriate adaptation of U-Net model and data augmentation, the U-Net architecture also demonstrated good generalisation ability in segmenting cardiac magnetic resonance images (CMRI) [START_REF] Chen | Improving the generalizability of convolutional neural network-based segmentation on cmr images[END_REF]. However, echocardiography segmentation is still difficult since it usually encounters the problem of out of view, poor signal-to-noise ratio etc, especially for myocardium segmentation.

In the field of cardiac motion tracking, unsupervised deep learning are very popular and these schemes reach similar performance or even outperform traditional registration methods. Krebs et al. proposed a conditional variational autoencoder which learned a diffeomorphic transformation from pairwise CMRI in an unsupervised way [START_REF] Krebs | Learning a Probabilistic Model for Diffeomorphic Registration[END_REF]. Shawn et al [START_REF] Ahn | Unsupervised motion tracking of left ventricle in echocardiography[END_REF] designed a U-Net like network for unsupervised pairwise echocardiography motion tracking. However, the displacement field can be unrealistic without relevant regularisation.

Numerous studies have shown that global longitudinal strain (GLS) is more sensitive than left ventricular ejection fraction (LVEF) as a measure of systolic function and has potential in identifying left ventricle dysfunction in clinical [9][7]. This value can be approximated by measuring the left ventricle length change [START_REF] Støylen | Left ventricular global strains by linear measurements in three dimensions: Interrelations and relations to age, gender and body size in the HUNT Study[END_REF]. Therefore, estimating a dense displacement may not be necessary.

U-Net like deep learning models depend largely on pixel-level classification, which can generate artefacts which are irregular with the organ shape. Researchers are seeking to combine shape constraints with deep learning methods [START_REF] Bohlender | A survey on shape-constraint deep learning for medical image segmentation[END_REF]. With the same intention to improve the segmentation consistency with anatomical shapes in 2D echocardiography, in our work, we explore to introduce shape constraints from global, regional and pixel level into a baseline U-Net model. From the segmentation results, useful information such as ejection fraction, landmark based GLS can be extracted. The detailed model architecture will be explained in section 2. We then present the implementation and experiment results for segmentation and landmark detection in section 3.

Methods

We use a U-Net model as our baseline model. Its encoder consists of 5 downsampling (MaxPool + Conv) blocks with ReLU activation after the 3x3 convolution. The corresponding decoder has 5 up-sampling (UpSample + Conv) blocks and is skip-connected with the encoder. Based on this model, we consider to incorporate shape constraints from three levels:

-Global-level: estimate a triangle like landmark map in parallel with segmentation (SEG-LM) -Regional-level: add a poly-affine myocardium reconstruction network to constrain the shape of myocardium mask (SEG-AFFINE) -Pixel-level: use a multi-class contour-loss to finely classify the boundary pixel (SEG-CONTOUR)

We will explain the three methods in detail in the following subsections.

SEG-LM: Parallel segmentation and landmark detection

We adapt the baseline U-Net model for simultaneous segmentation and landmark prediction by adding a separate branch of decoder for landmark map estimation. The two decoders process the encoder information in parallel. The final layer of segmentation branch and landmark detection have SoftMax activation, Sigmoid activation respectively. In particular, we consider the two end points of mitral valve (basal points) and the apex along the endocardial contour. The basal points are identified as the two end-points of adjacent boundary of both left ventricle and left atrium. The endo-apex point is then calculated as the furthest point to the mid-basal point along the endocardium. The output of landmark detection network is a heatmap of the corresponding target point. From the output heatmap, we extract the landmark position by finding the location of maximum or computing the centroid.

As we have different labels in the ground-truth data (myocardium, blood pool, atrium), a multi-class dice L dice is used as the segmentation loss. As for landmark detection, we first penalise on the squared error of landmark heat-map (L2 loss: L l2 ). In order to avoid landmark overlapping on different output layers, we regularise the centre distance loss L CD of different landmark heat-maps as proposed in [START_REF] Wang | Joint segmentation and landmark localization of fetal femur in ultrasound volumes[END_REF]:

L CD = 1 2 3 i=1,j =i 1/(C(H i ) -C(H j )) 2 (1)
with C the operation to obtain the centre position and H i the landmark heatmap. Finally, a mean squared distance loss between the predicted heatmap centre and the ground truth point L point is also applied. Thus we have a total loss L total for optimisation:

L total = L dice + αL l2 + βL CD + γL point (2)

SEG-AFFINE: Poly-affine Regulariser for Myocardium

With the intention to constrain the regularity of predicted myocardium mask, we propose to model the myocardium mask as a combination of 6 AHA regions [START_REF] Cerqueira | Standardized myocardial segmentation and nomenclature for tomographic imaging of the heart: A statement for healthcare professionals from the Cardiac Imaging Committee of the Council on Clinical Cardiology of the American Heart Association[END_REF].

We first choose a reference myocardium mask R from the training set. All the N training myocardium masks (M i ) N i=1 are aligned to the reference mask by an affine transform (T i ) N i=1 estimated from the three landmarks (left basal, right basal and endo-apex). Then all aligned masks are averaged to a mean mask R. The mean mask R is threshold-ed ( Rf ) and split into 6 AHA regions ( Īj ) 6 j=1 . For every myocardium mask M i , we aim to first find 1 affine matrix A g that globally transform the reference mask to Mi g . The corresponding reference regions become ( Īg j ) 6 j=1 = A g Īj . We then find 6 affine matrices (A ij ) 6 j=1 , that transform the transformed (globally) mean AHA regions ( Īg j ) 6 j=1 into Mi = 6 j=1 A ij Īg j that best reconstructs the target mask M i , i.e. Mi ≈ M i . For better fusion of the transformed 6 regions, we use the spatially weighted regions (multi-variate Gaussian) Ĩw j instead of Īj , s.t.

j=1

Ĩw j = Rf . We use a CNN to estimate the affine parameters and reconstruct the given mask. The proposed network has two sub-networks. The first one seeks to estimate global affine parameters for global alignment which consists of two hidden convolutional layers with down-sampling. The second sub-network is to find the 6 regional affine matrix. It begins with an encoder for high level feature extraction. The extracted features are passed through fully connected layers for affine matrix estimation Âij . By affine transform, we could reconstruct M 0 from the 6 mean regions M 0 = 6 j=1 Âij Ĩwg j . Two Conv layers are followed to refine the fusion mask M 0 and thus we obtain the final output M f (detailed information in fig. 2).

In order to regularise the value of the affine parameters, we approach the affine parameter estimation problem using Maximum A Posteriori (MAP) with prior probabilities on the parameter values P (A). The MAP aims to optimise: arg max[P (A|M )] ∝ P (M |A)P (A), i.e. arg min[-log P (M |A) -log P (A)] We use Gaussian distributions for conditional likelihood and priors. For

P (M |A) ∝ exp(-1 2 (M -M (A)) T Σ -1 (M -M (A))
), the variance is identity. For P (A) ∼ Fig. 2: Architecture of Proposed Poly-affine Regulariser N (μ, Σ), μ and Σ are the maximum likelihood estimate (here we only consider diagonal covariance matrices) from the aligned transformation parameters (T i ) N i=1 . The regularisation for affine parameters is L af f ine = αL l2 + βL prior , where L l2 is the mean square error between the reconstructed image and the input and

L prior = K k=1 6 j=1 δ j (A k j -μj ) 2 Σjj ( 3
)
where K = 1 for global affine parameter and K = 6 for regional affine parameters.

Thus the total loss for the poly-affine reconstruction network is:

L total = L dice ( M g ) + β g L g prior global sub-net +L dice ( M 0 ) + L dice ( M f ) + αL l2 + β r L r prior regional sub-net (4)
Once the poly-affine regulariser network is trained, the 6+36 affine parameters serve as explicit hidden variables to regularise the shape of myocardium prediction. We train a U-Net model (same as baseline model) which seeks for the best overlapping of mask as well as the minimum distance between the corresponding affine parameters of predicted myocardium and that of ground truth myocardium. The loss function for this method is

loss = dice + αM SE(P A(P ) -P A(M )) (5)
, where MSE is the mean squared error, P A is poly-affine regulariser that outputs the 42 affine parameters.

SEG-CONTOUR: multi-class contour-loss

In order to increase the classification accuracy on the boundary, we choose to use an adapted multi-class contour loss [START_REF] Jia | Automatically Segmenting the Left Atrium from Cardiac Images Using Successive 3D U-Nets and a Contour Loss[END_REF]. Firstly, a distance map D(M ) is calculated from ground truth mask and it illustrates the shortest euclidean distance of each pixel to the closest border. Then the contour loss is calculated as

loss contour = (D(M ) • contour(B(P ))) (6)
where • performs element-wise multiplication. P is the prediction output after SoftMax activation of U-Net for a certain class. B(P ) represents a differentiable thresholded Sigmoid for binarisation

B(P ) = 1 1 + exp -γ(P -T ) (7)
where γ = 20 and T = 0.5. The contour of the binarised mask is obtained by applying a 2D Sobel filter

contour(P ) = |G x * P | + |G y * P | (8)
where * denotes 2D convolution and G x , G y are 2D Sobel kernel in x-,y-dimension:

G x =   1 0 -1 2 0 -2 1 0 -1   , G y =   1 2 1 0 0 0 -1 -2 -1   .
3 Experiments and Results

Datasets

In this work, we work on two public data sets: CAMUS1 and ECHONET2 . CA-MUS dataset consist of publicly accessible 2D echocardiographies and the corresponding annotations of 450 patients. For each patient, 2D apical 4-chambers (A4C) and 2-chambers (A2C) view sequences are available. Manual annotation of cardiac structures (left endocardium, left epicardium and left atrium) were acquired by expert cardiologists for each patient in each view, at end-diastole (ED) and end-systole (ES) [START_REF] Leclerc | Deep learning for segmentation using an open large-scale dataset in 2d echocardiography[END_REF]. Along with the image and annotation data, we also have the following information: image quality (good/medium/poor), left ventricle end-diastole volume (LVedv), left ventricle end-systole volume (LVesv) and left ventricle ejection fraction(LVef). ECHONET dataset contains 10 030 apical 4-chambers echocardiography videos as part of routine clinical care at Stanford University Hospital [START_REF] Ouyang | Video-based AI for beat-to-beat assessment of cardiac function[END_REF]. Segmentation measurements (left endocardium) at end-diastole and end-systole are available for all videos. The corresponding LVedv, LVesv, LVef are also provided for each video.

Experiments

We trained the baseline UNet, SEG-LM, SEG-AFFINE, SEG-CONTOUR models on the CAMUS dataset (both 2-chamber and 4 chamber ED/ES frames) using 10-fold cross validation. The 450 patients are randomly split-ed into 10 (c-d) GLS calculation illustration (background is one echo image from CAMUS). We calculate the GLS from the LV length change by following the approximation method in [START_REF] Støylen | Left ventricular global strains by linear measurements in three dimensions: Interrelations and relations to age, gender and body size in the HUNT Study[END_REF].

folds, with each fold has similar distribution of image quality and LVef distribution. Every turn we use 8 fold data for training, 1 fold for validation (for model selection) and 1 fold for testing.

From the segmentation result, we first find the largest connected component for each class and applied a closing operation to fill the potential hole that could exist inside the predicted mask. We then extract the basal and apex landmark points following protocol described in section 2.1 for the four models except SEG-LM whose landmark is extracted from the landmark branch. The direction of mid-basal to apex will be regarded as grand axe of left ventricle and is used for left ventricle volume estimation by using modified Simpson's rule [START_REF] Folland | Assessment of left ventricular ejection fraction and volumes by real-time, two-dimensional echocardiography. A comparison of cineangiographic and radionuclide techniques[END_REF], thus the calculation of ejection fraction. The distance from mid-basal to apex forms the ventricle length and serves for global longitudinal strain calculation [START_REF] Støylen | Left ventricular global strains by linear measurements in three dimensions: Interrelations and relations to age, gender and body size in the HUNT Study[END_REF]. Because of the dataset limitation, we don't have the all the 3 apical views for left ventricle, so the GLS estimation will not be very accurate. However, we still calculate the GLS from 2 views (CAMUS) and 1 view (ECHONET) as reference to test the landmark detection accuracy.

All the segmentation models are implemented with Pytorch with a batch size of 8 and input image resized to 256 × 256. In order to avoid over-fitting and improve generalisation performance, we apply random data augmentation at training phase for all the networks. A stack of rotation, random cropping, brightness adjustment, contrast change, sharpening, blurring and speckle noise addition is conducted with each a probability of 0.5 for every input image. CA-MUS dataset does not contain the ground truth of desired landmarks. We generated the 'ground truth' landmark position from ground truth segmentation masks. The Gaussian heatmap of ground-truth landmarks is computed with σ = 4.

The baseline U-Net is trained with a multi-class dice loss. An Adam optimiser is applied with a learning rate of 1 e-3 . The training is early stopped when the dice loss on validation data shows no increase for more than 5 epochs. For SEG-LM model, we set α = 0.05, β = 0.5, γ = 0.5 in eq.2. An Adam optimiser is applied (lr= 10 -4 ). The output heatmap of landmarks is first processed to keep only one point cluster per layer and then the landmark location is extracted as the centroid. The poly-affine regulariser network is first trained with the myocardium ground truth for reconstruction. We set α = 0.005, β r = β g = 0.01, σ 6 i=1 = 1 and learning rate at 1e-4. We then train a baseline U-Net with the polyaffine regulariser using loss function (eq.5) with α = 10. The parameter for global prior is calculated from the training-specific (T i ) N i=1 . The parameter for regional prior is set as µ 1...6 = [1, 0, 0, 0, 1, 0] and [Σ 6 i=1 ] = 0.1. As for SEG-CONTOUR model, contour loss is optimised along with the dice loss. The contour loss is easy to fall into a local minimum of 0 so we set a weight of 100, 1e-4 for dice loss and contour loss respectively.

Evaluation metrics

For segmentation results, apart from the most used geometrical metrics: Dice coefficient, Hausdorff distance (HD) and Mean Surface Distance (MSD), we also use two anatomical metrics: Convexity(Cx) and Simplicity(Sp) [START_REF] Leclerc | Ru-net: A refining segmentation network for 2d echocardiography[END_REF].

Convexity(Cx) = Area(P ) Area(ConvexHull(P ) (9)
Simplicity(Sp) = 4π * Area(P ) P erimeter(P ) [START_REF] Krebs | Learning a Probabilistic Model for Diffeomorphic Registration[END_REF] Based on these metrics, we calculate the number of outliers for algorithm/model robustness evaluation. The outlier of segmentation prediction for CAMUS dataset is established from the inter-variability tests with the upper limit values for HD and MSD, and lower limit values for the simplicity and convexity [START_REF] Leclerc | Ru-net: A refining segmentation network for 2d echocardiography[END_REF]. A prediction mask is considered as a geometrical outlier if its HD > 3.5mm or M SD > 8.2mm at ED, if HD > 4mm or M SD > 8.8mm at ES. The corresponding limit for anatomical outlier is if Cx < 0.529 or Sp < 0.741 for endocardium, if Cx < 0.694 or Sp < 0.960 for epicardium [START_REF] Leclerc | Ru-net: A refining segmentation network for 2d echocardiography[END_REF].

Results

We show the evaluation results in Tables 1 and2 SEG-CONTOUR reduces the classification error along the boundary area thus less outlier predictions. This is consistent with the observations that a good Dice score does not always guarantee a good HD [START_REF] Bernard | Deep learning techniques for automatic mri cardiac multi-structures segmentation and diagnosis: Is the problem solved[END_REF] and in our case, not always leads to anatomically-plausible segmentation. The SEG-CONTOUR model is also capable of tracking more precisely the boundary especially the landmarks (table .2) thus a smaller bias of GLS prediction. In terms of EF calculation, the baseline U-Net model shows smaller mean absolute error but a larger bias than the SEG-CONTOUR loss. We show three CAMUS test examples (fig. 4) where each row has a good/medium/bad performance in terms of HD score respectively. Comparing with the the rest 3 models, SEG-CONTOUR has a more fluent border similar as the ground truth annotation.

The evaluation results of applying the trained model on a totally different dataset ECHONET (the same test fold of 1277 patients as in [START_REF] Ouyang | Video-based AI for beat-to-beat assessment of cardiac function[END_REF]) show the same trend of performance of our 4 methods. The SEG-CONTOUR method demonstrates a good performance on tasks related to boundary information, for example, lower HD and MSD, better GLS estimation. It's less accurate on area based task, i.e. volume estimation thus ejection fraction prediction. It is noticeable that all of the four models demonstrate a nice Dice coefficient on this different dataset (the Dice coefficient of models trained on ECHONET data is 0.92% [START_REF] Ouyang | Video-based AI for beat-to-beat assessment of cardiac function[END_REF]), which proves the importance of appropriate image augmentation techniques.

Conclusion

In this paper, we explored methods to introduce shape constraints into 2D Echocardiography segmentation models from three levels: global-level (SEG-LM), regional-level (SEG-AFFINE), pixel-level (SEG-CONTOUR). From the evaluation results on CAMUS dataset and its generalisation result on a unseen dataset ECHONET, it is more efficient to introduce pixel-level shape con- straint than global or regional level constraints for U-Net based models. With a multi-class contour loss, SEG-CONTOUR model achieves better classification on the boundary pixels with a reduced a Hausdorff distance and more accurate landmark detection result. Our experiments showed the good potential of SEG-CONTOUR for a more robust segmentation and deformation analysis.

Fig. 1 :

 1 Fig. 1: Detailed information of the 4 explored methods.

Fig. 3 :

 3 Fig. 3: (a)An example of segmentation ground truth of CAMUS dataset. The two basal and apex landmarks are extracted following the procedures described in section 2.1. (b) An example of annotation provided by ECHONET dataset. We generate the ground truth mask of LV by linearly connecting the border points. The grand axe (in red) is considered as the line connecting the apex and mid-basal point. The length of grand axe is considered as the LV length.(c-d) GLS calculation illustration (background is one echo image from CAMUS). We calculate the GLS from the LV length change by following the approximation method in[START_REF] Støylen | Left ventricular global strains by linear measurements in three dimensions: Interrelations and relations to age, gender and body size in the HUNT Study[END_REF].

Fig. 4 :

 4 Fig. 4: 3 CAMUS segmentation examples (good/medium/bad in terms of HD). The 4 four columns represent the baseline model, SEG-LM, SEG-AFFINE, SEG-CONTOUR respectively from left to right. The red, green, cyan lines represent the predicted segmentation contours of epicardium, endocardium and left atrium. The transparent green, blue and yellow regions are the ground truth masks of myocardium, left ventricle blood pool and left atrium respectively.

Fig. 5 :

 5 Fig. 5: The baseline U-Net model is trained with only one of the mentioned augmentation methods on CAMUS dataset and then is evaluated on the same test fold of ECHONET segmentation model, whose dice coefficient is 0.92. Contrast adjustment contributes most to the improvement of generalisation result while with all the techniques, we obtain the best Dice score and less variation. No-aug-5: trained model of 5 th epoch without augmentation, No-aug-30: trained model of 30 th epoch without augmentation. At 30 th epoch, the model has already overfitted the CAMUS data.

  , computed from 450 patients of CAMUS dataset using 10 fold cross-validation for the four methods detailed in Section 2. Compared with the baseline model, the SEG-LM, SEG-AFFINE models demonstrate only a slight decrease in terms of segmentation metric, ejection fraction (EF) prediction accuracy and landmark detection accuracy. The SEG-CONTOUR model shows a similar performance with baseline model in Dice score (table.1), but reduces greatly the number of geometrical and anatomical outliers (table.1). It's quite reasonable that with a smaller HD and MSD, the

			Endo			Epi		Outlier
	Method	Dice	HD (mm)	MSD (mm)	Dice	HD (mm)	MSD (mm)	Geo. Ana. Both
	Baseline	0.931 ± 0.040	5.04 ± 3.00	1.51 ± 0.83	0.951 ± 0.025	5.75 ± 3.61	1.71 ± 0.91	15% 2.8% 2.5%
	SEG-LM	0.928 ± 0.042	5.47 ± 3.04	1.59 ± 0.84	0.950 ± 0.025	6.22 ± 3.74	1.79 ± 0.93	20% 7.6% 5.3%
	SEG-AFFINE	0.930 ± 0.042	5.14 ± 3.00	1.53 ± 0.88	0.951 ± 0.027	5.84 ± 3.75	1.72 ± 0.95	14.3% 5.1% 3.7%
	SEG-CONTOUR	0.931 ± 0.041	4.99 ± 2.95	1.50 ± 0.73	0.952 ± 0.026	5.63 ± 3.32	1.67 ± 0.87	13.8% 1.5% 1.2%

Table 1 :

 1 CAMUS Segmentation Metric. Endo.: endocardium, Epi: epicardium, HD: Hausdorff distance, MSD: mean surface distance, Geo.: Geometrical outlier, Ana.: Anatomical outlier. Values in bold represent the best score.

		Basal1 Basal2 Apex		GLS(%)		EF(%)
	Method	MAE (mm)	MAE (mm)	MAE (mm)	MAE (%)	Corr.	Bias(%) ± std	MAE (%)	Corr.	Bias(%) ± std
	Baseline	2.36 3.06 4.06 3.97 0.74	-0.73 ± 5.20	4.76 0.86	0.93 ± 7.07
	SEG-LM	2.82 3.45 4.48 4.51 0.70	-1.74 ± 5.27	5.26 0.84	2.51 ± 8.04
	SEG-AFFINE	2.35 2.97 4.22 4.03 0.74	-0.9 ± 5.15	4.96 0.85	1.16 ± 7.31
	SEG-CONTOUR 2.25 2.80 3.97 3.96 0.75	-0.36 ± 5.34	5.06 0.84	0.7 ± 7.50

Table 2 :

 2 CAMUS Landmark/GLS and EF Prediction. Basal1: the left mitral valve end point, Basal2: the right mitral valve end point, EF: ejection fraction, GLS: global longitudinal strain. Values in bold represent the best score.

Table 3 :

 3 ECHONET Prediction

		Endo-cardium (LV)		EF			GLS
	Method	Dice	HD (pxls)	MSD (pxls)	MAE (%)	R2 Corr.	Bias(%) ± std	MAE (%)	R2 Corr.	Bias(%) ± std
	Baseline	0.892 ± 0.069	12.99 ± 7.96	3.74 ± 3.42	7.97 0.11 0.69	4.46 ± 12.80	4.96 -1.2 0.38	0.36 ± 7.94
	SEG-LM	0.886 ± 0.063	13.54 ± 6.86	3.87 ± 2.63	8.79 0.02 0.72	6.21 ± 13.39	5.61 -1.49 0.36	-1.9 ± 7.07
	SEG-AFFINE	0.887 ± 0.068	13.12 ± 7.25	3.87 ± 2.97	9.35 -0.14 0.67	7.11 ± 14.41	5.88 -2.44 0.29	-0.75 ± 9.29
	SEG-CONTOUR	0.895 ± 0.057	12.56 ± 6.34	3.58 ± 2.16	8.39 0.07 0.69	5.03 ± 13.21	4.39 -0.43 0.51	0.59 ± 6.52

https://www.creatis.insa-lyon.fr/Challenge/camus/databases.html

https://echonet.github.io/dynamic/)

Acknowledgments

This work has been supported by the French government through the National Research Agency (ANR) Investments in the Future with 3IA Côte d'Azur (ANR-19-P3IA-0002) and by Inria PhD funding.