Mathilde Yverneau

Stephanie Leroux

Apolline Imbard

Florian Gleich

Alina Arion

Caroline Moreau

Marie-Cecile Nassogne

Marie Szymanowski

Marine Tardieu

Guy Touati

Stéphanie Leroux

Marie-Cécile Nassogne

María Bueno

Kimberly A Chapman

Yin-Hsiu Chien

Martina Huemer

Pavel Ješina

Mirian Ch Janssen

Stefan Kölker

Viktor Kožich

Christian Lavigne

Allan Meldgaard Lund

Fanny Mochel

Mónica Andrew Morris

Mónica Ruiz Pons

Gloria Liliana Porras-Hurtado

Jean-François Benoist

Léna Damaj

Manuel Schiff

E-Hod Consortium

E-Hod Registry Alina Arion

Marie-Cécile Nassogne

Ruiz Pons

Ana Maria Martins

Javier Blasco Alonso

Brigitte Chabrol

Ellen Crushell

Carlo Dionisi-Vici

Stephanie Grünewald

Karine Mention

Helen Mundy

Pilar Elaine Murphy

Quijada Fraile

Carlos José Ruiz

Maria Ángeles

Ruiz Gómez

Saikat Santra

Thomas Scherer

Collette Stainforth

Karolina M Stepien

Gere Sunder-Plassmann

Johan L K Van Hove

Pilar Quijada Fraile

Maria Ángeles Ruiz Gómez

Influence of early identification and therapy on long-term outcomes in early-onset MTHFR deficiency

Keywords: Homocystinuria, remethylation defects, MTHFR deficiency, neurodevelopmental outcome, newborn screening, patient registry

niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

This article has been accepted for publication and undergone full peer review but has not been through the copyediting, typesetting, pagination and proofreading process which may lead to differences between this version and the Version of Record. Please cite this article as doi: 10.1002/jimd.12504 The enzyme MTHFR catalyses the reduction of 5,10 -methylenetetrahydrofolate (5,10-MTHF) to 5 -methyltetrahydrofolate (5-MTHF), that acts as a methyl donor for the remethylation of homocysteine into methionine [START_REF] Schiff | Treatment of Inherited Homocystinurias[END_REF][START_REF] Matthews | Methylenetetrahydrofolate reductase and methionine synthase: biochemistry and molecular biology[END_REF][START_REF] Huemer | The clinical presentation of cobalamin-related disorders: From acquired deficiencies to inborn errors of absorption and intracellular pathways[END_REF] . Consequently, MTHFR deficiency leads to hyperhomocysteinemia and low methionine due to the dysfunction of the remethylation pathway.

Pathogenesis of MTHFR deficiency is complex. On the one hand, the accumulating homocysteine is a well-known multisystem toxic agent [START_REF] Castro | Homocysteine metabolism, hyperhomocysteinaemia and vascular disease: An overview[END_REF] . Homocysteine toxicity induces central nervous system (CNS) damages, either directly through endothelial toxicity [START_REF] Castro | Homocysteine metabolism, hyperhomocysteinaemia and vascular disease: An overview[END_REF] and neuronal cell death [START_REF] Mattson | Folate and homocysteine metabolism in neural plasticity and neurodegenerative disorders[END_REF][START_REF] Kishi | Effect of betaine onS-adenosylmethionine levels in the cerebrospinal fluid in a patient with methylenetetrahydrofolate reductase deficiency and peripheral neuropathy[END_REF][START_REF] Strauss | Prevention of brain disease from severe 5,10-methylenetetrahydrofolate reductase deficiency[END_REF][START_REF] Surtees | Association of demyelination with deficiency of cerebrospinal-fluid S-adenosylmethionine in inborn errors of methyl-transfer pathway[END_REF][START_REF] D'aco | Severe 5,10-Methylenetetrahydrofolate Reductase Deficiency and Two MTHFR Variants in an Adolescent With Progressive Myoclonic Epilepsy[END_REF][START_REF] Wang | Reversal of homocysteineinduced neurotoxicity in rat hippocampal neurons by astaxanthin: evidences for mitochondrial dysfunction and signaling crosstalk[END_REF] , or indirectly via its conversion to S -adenosylhomocysteine (SAH), a potent inhibitor of methyltransferases [START_REF] Schiff | Treatment of Inherited Homocystinurias[END_REF][START_REF] Schatz | Decreased Transmethylation of Biogenic Amines After In Vivo Elevation of Brain S-Adenosyl-l-Homocysteine[END_REF] . On the other hand, MTHFR deficiency causes a secondary impairment of methionine synthase with subsequent methionine and Sadenosylmethionine (SAM) depletion. The latter causes an additional reduction of cellular methylation capacity in the CNS [START_REF] Schiff | Treatment of Inherited Homocystinurias[END_REF][START_REF] Surtees | Demyelination and inborn errors of the single carbon transfer pathway[END_REF] . CNS methylation reactions are critical for myelination and brain development [START_REF] Kishi | Effect of betaine onS-adenosylmethionine levels in the cerebrospinal fluid in a patient with methylenetetrahydrofolate reductase deficiency and peripheral neuropathy[END_REF][START_REF] Chiang | S-Adenosylmetliionine and methylation[END_REF] .

Remethylation of homocysteine into methionine can also proceed via an alternate pathway [START_REF] Schiff | Treatment of Inherited Homocystinurias[END_REF] using betaine as methyl donor and catalysed by betaine-homocysteine methyltransferase (BHMT), mainly expressed in liver and kidney. BHMT converts a significant part of tHcy (total homocysteine) formed in the body, however not in the brain due to its limited expression in this tissue. Betaine is thus a central drug and the cornerstone of the treatment for MTHFR deficiency, which general therapeutic goal is to bypass the remethylation defect, in order to normalize plasma methionine and SAM levels [START_REF] Surtees | Association of demyelination with deficiency of cerebrospinal-fluid S-adenosylmethionine in inborn errors of methyl-transfer pathway[END_REF] and reduce plasma tHcy accumulation [START_REF] Schiff | Treatment of Inherited Homocystinurias[END_REF][START_REF] Schiff | Isolated remethylation disorders: do our treatments benefit patients?[END_REF][START_REF] Ogier De Baulny | Remethylation defects: guidelines for clinical diagnosis and treatment[END_REF][START_REF] Holme | Betaine for treatment of homocystinuria caused by methylenetetrahydrofolate reductase deficiency[END_REF] . Other, less validated therapeutic means include folate supplementation either as methylfolate [START_REF] Knowles | Erratum to: Treatment with Mefolinate (5-Methyltetrahydrofolate), but Not Folic Acid or Folinic Acid, Leads to Measurable 5-Methyltetrahydrofolate in Cerebrospinal Fluid in Methylenetetrahydrofolate Reductase Deficiency[END_REF] or folinic acid and L-methionine.

MTHFR deficiency can present at any age. The clinical course varies according to the age of onset: the early-onset presentations (neonatal period and early infancy [≤ 3 months]) and the late-onset presentations (late infancy or early childhood [from 3 months to 10 years] and adolescence or adulthood [> 10 years]) [START_REF] Ogier De Baulny | Remethylation defects: guidelines for clinical diagnosis and treatment[END_REF] . Early-onset patients mostly exhibit a lifethreatening acute neurologic deterioration frequently with apnoea following a free interval after birth that can be short (a few weeks). Data on initial phenotype and long-term outcomes of these early-onset patients are scarce, predominantly derived from case reports or small case series [START_REF] Schiff | Isolated remethylation disorders: do our treatments benefit patients?[END_REF][START_REF] Huemer | Clinical pattern, mutations and in vitro residual activity in 33 patients with severe 5, 10 methylenetetrahydrofolate reductase (MTHFR) deficiency[END_REF][START_REF] Diekman | Survival and Psychomotor Development With Early Betaine Treatment in Patients With Severe Methylenetetrahydrofolate Reductase Deficiency[END_REF][START_REF] Tawari | An early onset form of methylenetetrahydrofolate reductase deficiency: a report of a family from Kuwait[END_REF][START_REF] Balasubramaniam | A case of severe methylenetetrahydrofolate reductase deficiency presenting as neonatal encephalopathy, seizures, microcephaly and central hypoventilation[END_REF][START_REF] Watkins | Update and new concepts in vitamin responsive disorders of folate transport and metabolism[END_REF] . Several authors suggested that early initiation of treatment prevents mortality and allows better neurodevelopmental outcomes [START_REF] Schiff | Treatment of Inherited Homocystinurias[END_REF][START_REF] Diekman | Survival and Psychomotor Development With Early Betaine Treatment in Patients With Severe Methylenetetrahydrofolate Reductase Deficiency[END_REF][START_REF] Huemer | Phenotype, treatment practice and outcome in the cobalamin-dependent remethylation disorders and MTHFR deficiency: Data from the E-HOD registry[END_REF] . More specifically, a pivotal metaanalysis demonstrated that early betaine treatment prevented mortality and allowed normal psychomotor development in 36 patients with severe MTHFR deficiency [START_REF] Diekman | Survival and Psychomotor Development With Early Betaine Treatment in Patients With Severe Methylenetetrahydrofolate Reductase Deficiency[END_REF] . The majority of patients are diagnosed during late infancy and early childhood, with progressive neurologic deterioration [START_REF] Schiff | Treatment of Inherited Homocystinurias[END_REF] , delayed or arrested development and acquired microcephaly [START_REF] Schiff | Treatment of Inherited Homocystinurias[END_REF][START_REF] Prasad | Methylenetetrahydrofolate reductase (MTHFR) deficiency and infantile epilepsy[END_REF] . Adolescent or adult patients exhibit, after a period of normal development or mild developmental delay, a neurologic and/or psychiatric deterioration [START_REF] Schiff | Treatment of Inherited Homocystinurias[END_REF] .

The aims of this study were 1) to retrospectively study clinical and laboratory parameters of patients with early-onset MTHFR deficiency (≤ 3 months of age) at time of diagnosis and at last follow-up visit and 2) to identify predictive factors of severe neurodevelopmental outcomes in a broader set of patients with MTHFR deficiency without restriction of age at disease presentation (early and non-early-onset forms).

Patients and Methods

Study design and setting

A retrospective multicentric cohort study was conducted on 62 patients from the E-HOD registry and 10 separately recruited French patients with MTHFR deficiency. for data analysis, we ensured that there was full interoperability of the data models between the E-HOD registry and this French survey.

Subjects, ethical issues and E-HOD registry

Data collection included patients' socio-demographic characteristics, medical history, clinical and laboratory data at disease onset and at the last follow-up visit, brain magnetic resonance imaging (MRI), electroencephalogram (EEG) results and treatment modalities.

"Early-onset" and "non-early-onset" disease were defined as " ≤ 3 months of age" and " > 3 months of age" at time of diagnosis, respectively, in accordance with literature [START_REF] Ogier De Baulny | Remethylation defects: guidelines for clinical diagnosis and treatment[END_REF] data.

Outcomes were categorized as mild or severe. Severe neurodevelopmental outcome was defined in patient with motor disability ranging from need of assistance to walk to impossibility to walk or to sit alone and/or behavioral problems and/or special educational needs at the time of the last follow-up visit or who died during their follow-up, in accordance with previous studies evaluating neurodevelopmental outcomes [START_REF] Duncan | Neurodevelopmental Outcomes in Early Childhood[END_REF] . Mild patients were those whose phenotype did not fall into the "severe" category.

Among the whole cohort of 72 patients with MTHFR deficiency, eight were excluded because of incomplete or missing outcome information.

Statistical analysis

First, early-onset MTHFR patients were described at time of diagnosis and at the last followup visit. Continuous variables were presented as median and range (minimum, maximum).

Categorical variables were presented as number and/or percentage of the total number of patients with available data. Results were presented as "n/N (%)" where n and N are the concerned patients and the total number of patients with available data respectively. Continuous variables were compared using the Student's t-test. Normality of the distribution and homogeneity of variances were previously verified.

Second, all MTHFR-deficient patients (early-and late-onset) were analyzed in terms of clinical outcomes. A logistic regression analysis was performed to assess the relation between patients' characteristics at the time of disease diagnosis and the risk of severe neurodevelopmental outcomes evaluated at the last follow-up visit. Only variables with less than 10% of missing data were included in this analysis. The variables that were not included in the logistic regression model due to missing data >10% were the following: microcephaly at birth, disturbance of consciousness, age at first symptoms, delay of diagnosis, EEG and MRI parameters, plasma total homocysteine concentration at first and last visit, plasma methionine concentration at last visit. Continuous variables were examined for their linearity in relation to the logit of the outcome. In case of non-linearity, a categorization was applied (based on graphical inspection). Factors associated with a risk of severe neurodevelopmental outcome were first identified by univariate analysis. This was followed by a manual backward multivariate logistic regression analysis of variables with p value less than 0.25 in the univariate analysis [START_REF] Zhang | Model building strategy for logistic regression: purposeful selection[END_REF] . These variables were examined in multiple clinically relevant 2×2 analyses to assess first-order interactions. The odds ratio, with its 95% confidence interval (CI), was computed for each identified factor. The model's goodness of fit was assessed using the Hosmer-Lemeshow test: the p value of 1 indicated that there was no significant difference between observed and predicted values. Statistical tests were performed using R software (version 3.6.1).

Results

MTHFR

Presentation of the 32 patients with early-onset MTHFR deficiency

The population of patients with early-onset MTHFR deficiency included 17 females and 15 males, born between 1985 and 2019.

Pregnancy and birth data

Initial patients' characteristics are detailed in Table 1 and Supplemental Table 1. Pregnancy was uneventful in most cases. Nonspecific complications were reported during 5 out of 27 pregnancies (gestational diabetes, folate deficiency, gastroenteritis). The adaptation to extrauterine life was optimal for all patients (N=10/10). Among patients with early-onset MTHFR deficiency, 28/29 (97%) were term newborns (one individual was born at 36 weeks gestation), 26/27 (96%) had appropriate birth weight for gestational age (GA) and 5/19 (26%) had neonatal microcephaly (i.e. head circumference below the third percentile matched for gestational age and sex). Consanguinity was reported in 7/10 (70%) of patients.

Presentation at time of diagnosis

Four of the 32 patients were pre-symptomatically diagnosed thanks to positive family history.

The median age at diagnosis was 32 days (range: 6-90 days) for the 28 clinically diagnosed patients. The median diagnosis delay, defined as the time between first symptoms and diagnosis, was 4 days (range: 0-65 days). Major symptoms at diagnosis were feeding difficulties (21/28, 75%) and neurologic symptoms (23/28, 82%) including hypotonia (17/28, 61%), microcephaly (9/28, 32%), and seizures (6/28, 21%). Respiratory failure (including respiratory distress and/or apnoea) was reported in 30% (9/28) of patients. Poor or absent eye contact was reported in 38% (10/26) of patients. Other main symptoms included hypothermia (5/10, 50%), drowsiness and impaired level of consciousness (3/10, 30%), haemodynamic failure (3/10, 30%). Cardiac, kidney, liver diseases and thromboembolic events were rare (2/28 (7%), 0/28 (0%), 2/28 (7%) and 2/28 (7%) of patients respectively. Initial brain MRI reports were available for nine patients: all were abnormal. Main abnormalities included ventricle dilatation (6/9, 67%), cortical atrophy (5/9, 56%), external CSF spaces dilatation (5/9, 56%) and myelination delay (4/9, 44%) (Table 1

, Supplemental Table 2).

Seven out of the eight available initial EEGs were abnormal (Table 1, Supplemental Table 2).

Among the 22 patients with available data, the median initial plasma tHcy concentration (laboratory reference levels: <10 µmol/L) was 202.8 µmol/L (range: 45-353 µmol/L) (Table 1). Median initial methionine concentration (laboratory reference levels: 17-43 µmol/L) was 6 µmol/L (range: 4-18 µmol/L). Additional metabolic data are provided in Figure 1.

Treatment modalities and outcome at time of the last follow-up visit

Table 2 presents patients' characteristics at the last follow-up visit. One out of the 32 patients died during the follow-up period. This patient was diagnosed at 13 days of life with seizures and feeding problems. He died at 39 months of age from cardiomyopathy that had not been 2).

At the last follow-up visit, all patients received betaine with a median daily dose of 157 mg/kg/day (range: 52-350 mg/kg/day). Vitamin B9 (folic or folinic acid) and vitamin B12 (hydroxocobalamin -by intramuscular or oral route -or cyanocobalamin) were administered to 24/29 (83%) and 23/29 (79%) of the patients respectively. Other treatments were inconsistently given: pyridoxine (vitamin B6), riboflavin (vitamin B2), L-methionine, Lcarnitine, 5-MTHF were administered to 11/29 (38%), 10/29 (34%), 7/29 (24%), 4/29 (14%) and 2/29 (7%) of the patients respectively. The combinations of (betaine+B12+B9) and (betaine+B12+B9+B6) were the two most frequent combinations used (31% of patients for both -N=29) (Table 2).

At the last follow-up visit, 7/23 (30%) of patients had microcephaly. Among them, 17% had had a normal head circumference at birth (acquired microcephaly). Neurologic examination was abnormal in 19/29 (65%) of the patients. The most frequent abnormality was pyramidal syndrome (14/28, 50%) mainly characterized by hyperactive patellar reflexes (10/27, 37%), hypertonia (9/27, 33%), spasticity (9/27, 32%), and abnormal motion range (6/26, 23%). Gait abnormalities (ataxia and/or abnormal balance) were observed in 9/27 (33%) of patients and hypotonia (abnormal head control and/or hypotonia muscle tone) in 9/28 (32%) of patients.

Global abnormal muscle strength concerned 7/24 (29%) of patients. One patient (early-onset) exhibited hydrocephalus.

Seventy-six percent (22/29) of early-onset patients exhibited severe neurodevelopmental outcomes at the last follow-up visit. Gross motor was abnormal in 14/28 (50%) of the patients, with 21% of mild disability, 18% of moderate disability and 11% of severe disability. Fine motor evaluation was abnormal in 14/26 (54%) of patients. Behavioural problems were reported in 13/27 (48%) of patients. Language difficulties (absence of speech development or speech delay) were reported in 7/9 (78%) of patients. Special educational needs were retrieved for 12/20 (60%) of patients. Feeding problems were reported in only two patients; both had a G-tube (2/23, 9%). Forty-eight percent of patients (14/29) exhibited eye issues (mainly nystagmus and strabismus; and more rarely uncoordinated eye movements, optic nerve atrophy, cataract). Treatment significantly reduced the frequency of feeding problems (p<0.001). There were no other affected organ systems. Between time of diagnosis and last follow-up visit, "general state and overall well-being" were considered stable over time for 14/21 (67%) and were improved for 4/21 (19%) of patients (Table 2).

Among the patients with abnormal initial brain MRI, 6/9 (67%) had severe neurodevelopmental outcomes at the last follow-up visit. EEG was abnormal for 14/17 (82%) of patients. Clinical epilepsy was reported in 3/10 (30%) of patients and was easily managed with one antiepileptic drug.

As shown in Figure 1, plasma tHcy concentrations significantly decreased under treatment for all patients (on average decreased by 1.8 times p<0.001), but remained higher than the reference levels for 26/28 (93%) of them. Plasma tHcy decreased below 70 µmol/L for 2/28 (7%) of patients. Methionine plasma concentrations significantly increased under treatment (on average increased by more than 3 times p<0.001) and were in the laboratory reference range for all patients with available data (N=24) at the last follow-up visit (Figure 1). Plasma tHcy concentrations were not significantly different in patients with severe vs non-severe outcome at the initial evaluation (p=0.35) and at the last follow-up visit (p=0.93).

Predictors of severe neurodevelopmental outcomes in 64 patients with early and non-earlyonset MTHFR deficiency Among the whole cohort of 72 patients with MTHFR deficiency, eight were excluded because of incomplete or missing outcome information. Among the remaining 64 patients, 30 and 34 patients had early-onset and late-onset disease manifestation, respectively. The median follow-up time was 8.2 years (range: 94 days-37.4 years). Factor(s) associated with a risk of severe neurodevelopmental outcome are shown in Table 3 (univariate analysis) and Table 4 (multivariate analysis). Four factors were introduced in the multivariate regression analysis because of p-values less than 0.25 in the univariate analysis: age at diagnosis (with 53% of patients with early-onset disease in the severe outcome group vs 33% in the other group), Caucasian ethnic background (with 77% in the severe outcome group vs 62%), respiratory failure at time of diagnosis (with 28% of patients presenting respiratory failure in the severe outcome group vs 14%), and pre-symptomatic disease diagnosis (with 2% of presymptomatically diagnosed patients in the severe outcome group vs 38% in the non-severe group). Follow-up time was also added to the multivariate analysis because of a potential clinically confounding effect. Pre-symptomatic disease diagnosis was the only independent factor associated with outcome in multivariate analysis. Pre-symptomatically diagnosed patients (see next paragraph) were significantly less likely to exhibit severe neurodevelopmental outcomes (aOR 0.04, [95% CI, 0.002-0.232], p=0.003). We did not identify any significant interaction between pre-symptomatic diagnosis and early-/late-onset disease. The goodness of fit of the model was assessed using the Hosmer-Lemeshow test: the p value of 1 indicated that there was no significant difference between observed and predicted values.

Focus on the pre-symptomatically diagnosed patients (n=9)

As pre-symptomatic diagnosis was identified as an independent protective factor for severe neurodevelopmental outcome, the following information focused on this subset of patients (Supplemental Tables 1 and3). These nine patients were pre-symptomatically diagnosed and treated because of a symptomatic sibling. Nine out of nine patients exhibited normal cognitive outcome. Eight of nine patients did not exhibit any symptom during the follow-up period. One patient required special educational needs due to severe visual problems and therefore potentially arbitrarily fell into the severe group. Regardless, he exhibited a normal neurologic examination and a normal neurodevelopment. The neurologic examination was normal for 9/9 patients at the last follow-up visit (range: 3 months old -52 years old). For two pre-symptomatic patients, information were available on the outcomes of their late treated sibling showing unequivocally a much poorer outcome in the late treated than in the pre-symptomatic ones. Initial plasma tHcy concentrations did not significantly differ from clinically diagnosed patients (p=0.17) (Supplemental Figure 1). Plasma tHcy decreased from diagnosis to the last follow-up visit in all cases. Plasma tHcy at the last follow-up visit did not significantly differ from clinically diagnosed patients (p=0.89). In keeping with this, we analysed treatment data in these nine pre-symptomatic patients. In terms of treatment either at initial management or for long-term therapy, no major differences was observed among patients (Supplemental Table 3): all of the patients for whom data were available (5/5) were treated with betaine at a median dose of 174.5 mg/kg/d (range 44-284). Remaining therapies were variable and included, folic or folinic acid, L-Methionine and vitamin B12.

Discussion

Though previous studies already reported clinical data on MTHFR-deficient patients, these studies either included late-onset MTHFR deficiency or did not focus on neurodevelopmental outcomes [START_REF] Huemer | Phenotype, treatment practice and outcome in the cobalamin-dependent remethylation disorders and MTHFR deficiency: Data from the E-HOD registry[END_REF][START_REF] Marelli | Clinical and molecular characterization of adult patients with late-onset MTHFR deficiency[END_REF] . Huemer et al analysed the clinical presentation of 50 MTHFR-deficient patients [START_REF] Huemer | Phenotype, treatment practice and outcome in the cobalamin-dependent remethylation disorders and MTHFR deficiency: Data from the E-HOD registry[END_REF] . Forty-three of these previously reported patients (including two with presymptomatic diagnosis) were included into our study, which, in contrast to the earlier publication focused on early-onset presentation and neurodevelopmental outcomes of MTHFR-deficient patients. [START_REF] Huemer | Phenotype, treatment practice and outcome in the cobalamin-dependent remethylation disorders and MTHFR deficiency: Data from the E-HOD registry[END_REF] We reported in detail clinical and laboratory parameters of 32 patients with an age of less than 3 months at time of diagnosis. Seventy six % of these patients exhibited severe neurodevelopmental outcomes at the last follow-up visit. The median follow-up period was 8 years for these early-onset patients. Using multivariate analysis, factors associated with severe neurodevelopmental outcomes were assessed in 64 patients with early and late-onset MTHFR deficiency. Our data emphasizes that pre-symptomatic diagnosis and subsequent treatment are associated with a significantly better outcome.

Similar to literature data [START_REF] Ogier De Baulny | Remethylation defects: guidelines for clinical diagnosis and treatment[END_REF][START_REF] Huemer | Clinical pattern, mutations and in vitro residual activity in 33 patients with severe 5, 10 methylenetetrahydrofolate reductase (MTHFR) deficiency[END_REF] , our patients with early-onset MTHFR deficiency were born after uneventful pregnancy, delivery and perinatal adaptation. Among the 32 patients with early-onset MTHFR deficiency, more than 70% exhibited feeding difficulties and neurologic symptoms (mainly muscular hypotonia) at time of diagnosis. In brain, remethylation of homocysteine into methionine is exclusively dependent on 5-MTHF [START_REF] Huemer | Clinical pattern, mutations and in vitro residual activity in 33 patients with severe 5, 10 methylenetetrahydrofolate reductase (MTHFR) deficiency[END_REF] since BHMT is not expressed in this tissue [START_REF] Mckeever | Betaine-homocysteine methyltransferase: organ distribution in man, pig and rat and subcellular distribution in the rat[END_REF] . This could explain the particular vulnerability of the CNS in MTHFR deficiency.

Six out of 32 patients exhibited central apnoea at time of diagnosis as reported elsewhere [START_REF] Schiff | Treatment of Inherited Homocystinurias[END_REF][START_REF] Surtees | Association of demyelination with deficiency of cerebrospinal-fluid S-adenosylmethionine in inborn errors of methyl-transfer pathway[END_REF][START_REF] Huemer | Clinical pattern, mutations and in vitro residual activity in 33 patients with severe 5, 10 methylenetetrahydrofolate reductase (MTHFR) deficiency[END_REF][START_REF] Fattal-Valevski | Methylenetetrahydrofolate Reductase Deficiency: Importance of Early Diagnosis[END_REF] .

Detailed analysis of initial brain MRI showed abnormalities in all patients with available data.

Ventricle dilatation, cortex atrophy and myelination delay were among the most frequent MRI abnormalities, similar to previous case series [START_REF] Ogier De Baulny | Remethylation defects: guidelines for clinical diagnosis and treatment[END_REF][START_REF] Engelbrecht | MR and Proton MR Spectroscopy of the Brain in Hyperhomocysteinemia Caused by Methylenetetrahydrofolate Reductase Deficiency[END_REF] . Low methionine levels and concomitant SAM deficiency characterizing the disease were shown to be associated with demyelination [START_REF] Surtees | Association of demyelination with deficiency of cerebrospinal-fluid S-adenosylmethionine in inborn errors of methyl-transfer pathway[END_REF][START_REF] Hyland | Demyelination and decreased S-adenosylmethionine in 5,10-methylenetetrahydrofolate reductase deficiency[END_REF] , as well as accumulation of SAH that would also contribute to hypomyelination [START_REF] Schatz | Decreased Transmethylation of Biogenic Amines After In Vivo Elevation of Brain S-Adenosyl-l-Homocysteine[END_REF] . Of note, one patient of the early-onset disease cohort needed a ventriculoperitoneal shunt during follow-up. This complication was previously reported in a few case reports and points to a malformation of the neural tube in mid-gestation at the origin of hydrocephalus [START_REF] Holme | Betaine for treatment of homocystinuria caused by methylenetetrahydrofolate reductase deficiency[END_REF][START_REF] Baethmann | Hydrocephalus Internus in Two Patients with 5,10-Methylenetetrahydrofolate Reductase Deficiency[END_REF] .

Deficiency of methionine and SAM, affecting protein synthesis and all methylation dependent activities, possibly provides the basis for epileptogenesis [START_REF] Prasad | Methylenetetrahydrofolate reductase (MTHFR) deficiency and infantile epilepsy[END_REF] . A wide variation in seizure phenotypes was documented in previous case reports [START_REF] Surtees | Association of demyelination with deficiency of cerebrospinal-fluid S-adenosylmethionine in inborn errors of methyl-transfer pathway[END_REF][START_REF] Holme | Betaine for treatment of homocystinuria caused by methylenetetrahydrofolate reductase deficiency[END_REF][START_REF] Baethmann | Hydrocephalus Internus in Two Patients with 5,10-Methylenetetrahydrofolate Reductase Deficiency[END_REF] . Unfortunately, it was not possible to precisely describe epilepsy in the present retrospective study apart from its occurrence in 30% of the patients. Similarly, data on psychometric tests were missing.

Ophthalmologic manifestations were frequent (38%) in the present cohort, with a wide heterogeneity of clinical damages. Patients mainly exhibited strabismus and nystagmus, but a variety of symptoms were also inconsistently observed such as uncoordinated eye movements, optic nerve atrophy, and secondary cataract. Frequency of ophthalmologic issues is variable in the literature [START_REF] Huemer | Clinical pattern, mutations and in vitro residual activity in 33 patients with severe 5, 10 methylenetetrahydrofolate reductase (MTHFR) deficiency[END_REF][START_REF] Huemer | Phenotype, treatment practice and outcome in the cobalamin-dependent remethylation disorders and MTHFR deficiency: Data from the E-HOD registry[END_REF][START_REF] Ronge | Long term treatment with betaine in methylenetetrahydrofolate reductase deficiency[END_REF] . The precise pathomechanism has not yet been elucidated, and multiple factors have been considered to be involved [START_REF] Huemer | Phenotype, treatment practice and outcome in the cobalamin-dependent remethylation disorders and MTHFR deficiency: Data from the E-HOD registry[END_REF] . Studies on human and mouse models mainly suggest the role of hyper-homocysteinemia in inducing retinal degeneration and/or impairing retinal function [START_REF] Tsina | Maculopathy and retinal degeneration in cobalamin C methylmalonic aciduria and homocystinuria[END_REF][START_REF] Lahey | Hypercoagulable states and central retinal vein occlusion[END_REF][START_REF] Lawrance | Complete deficiency of methylenetetrahydrofolate reductase in mice is associated with impaired retinal function and variable mortality, hematological profiles, and reproductive outcomes[END_REF] . MTHFR deficiency in mice was suggested to induce eye disease [START_REF] Lawrance | Complete deficiency of methylenetetrahydrofolate reductase in mice is associated with impaired retinal function and variable mortality, hematological profiles, and reproductive outcomes[END_REF] . More importantly, impaired vision might be due to visual cortex damage, even though no related MRI lesion was identified [START_REF] Ronge | Long term treatment with betaine in methylenetetrahydrofolate reductase deficiency[END_REF] . Given our results, we recommend a frequent eye follow-up for early-onset MTHFR-deficient patients. As compromised remethylation processes play an important role in the poor removal of retinal homocysteine, decrease of plasma tHcy levels might improve retinal damage [START_REF] Kowluru | Faulty homocysteine recycling in diabetic retinopathy[END_REF] . Frequency of eye issues was not significantly improved under treatment in line with recent literature data [START_REF] Huemer | Phenotype, treatment practice and outcome in the cobalamin-dependent remethylation disorders and MTHFR deficiency: Data from the E-HOD registry[END_REF] .

In our cohort, "general state and overall well-being" were considered stable in 14/21 patients and improved in only 4/21 patients with early-onset MTHFR deficiency. Despite the short diagnosis delay (median of 4 days), a total of 76% of treated patients exhibited severe neurodevelopmental outcomes as reported in the literature [START_REF] Huemer | Phenotype, treatment practice and outcome in the cobalamin-dependent remethylation disorders and MTHFR deficiency: Data from the E-HOD registry[END_REF] . Irreversible brain damage caused by severe demyelination may explain this finding [START_REF] Ronge | Long term treatment with betaine in methylenetetrahydrofolate reductase deficiency[END_REF] . Plasma tHcy levels significantly decreased under treatment but were not normalized at the last follow-up visit, in line with previous findings [START_REF] Schiff | Treatment of Inherited Homocystinurias[END_REF] . There is no clear explanation for that.

It was previously argued that decreasing plasma tHcy to 50 to 70 µmol/L was a reasonable goal of treatment in patients with remethylation disorders 1 but it could be achieved for a small number of patients only. In contrast to plasma tHcy concentrations, plasma methionine concentrations were normalized at the time of last follow-up in all of the patients with earlyonset MTHFR deficiency as previously reported [START_REF] Strauss | Prevention of brain disease from severe 5,10-methylenetetrahydrofolate reductase deficiency[END_REF][START_REF] Surtees | Association of demyelination with deficiency of cerebrospinal-fluid S-adenosylmethionine in inborn errors of methyl-transfer pathway[END_REF][START_REF] Hyland | Demyelination and decreased S-adenosylmethionine in 5,10-methylenetetrahydrofolate reductase deficiency[END_REF] . Of note, normalization of CSF SAM level was reported to be associated with improved remyelination under betaine treatment [START_REF] Surtees | Association of demyelination with deficiency of cerebrospinal-fluid S-adenosylmethionine in inborn errors of methyl-transfer pathway[END_REF] . Therefore, one could hypothesize that pre-symptomatic treatment would be beneficial because of normalization of methionine and SAM with correction of the remethylation defect in spite of persisting high tHcy concentrations.

The multivariate analysis on 64 patients with early and late-onset MTHFR deficiency highlighted that pre-symptomatic diagnosis was an independent protective factor for severe neurodevelopmental outcome. This significantly better neurodevelopmental outcome of presymptomatically diagnosed patients highlights the need for timely diagnosis through newborn screening (NBS). Indeed, NBS is indicated if early intervention is effective with a better outcome in a severe disease generally not detectable early in life on a clinical basis, with sensitive and specific biochemical markers [START_REF] Wilson | Principles and Practice of Screening for Disease[END_REF] . A prospective study of pre-symptomatically diagnosed and treated patients preferably identified through NBS would be warranted to further confirm this benefit. MTHFR deficiency is currently detected by very few NBS programs using methionine concentration and methionine-to-phenylalanine ratio in dried blood spots (DBS) and DBS tHcy concentrations as a second tier test [START_REF] Huemer | Newborn screening for homocystinurias and methylation disorders: systematic review and proposed guidelines[END_REF][START_REF] Gramer | Newborn screening for remethylation disorders and vitamin B12 deficiency-evaluation of new strategies in cohorts from Qatar and Germany[END_REF][START_REF] Tortorelli | Two-Tier Approach to the Newborn Screening of Methylenetetrahydrofolate Reductase Deficiency and Other Remethylation Disorders with Tandem Mass Spectrometry[END_REF][START_REF] Keller | Newborn screening for homocystinurias: Recent recommendations versus current practice[END_REF] . The yield of methionine or methionine/phenylalanine ratios seem however imperfect and the cost of tHcy determination on DBS high therefore questioning the practical feasibility of NBS for MTHFR deficiency. Regardless, an argument for NBS is the availability of a generally effective therapy for MTHFR deficiency i.e. betaine. This would however require confirmation by a prospective study.

Despite the previously suggested different clinical patterns between early and non-early-onset forms of the disease [START_REF] Schiff | Treatment of Inherited Homocystinurias[END_REF][START_REF] Huemer | Phenotype, treatment practice and outcome in the cobalamin-dependent remethylation disorders and MTHFR deficiency: Data from the E-HOD registry[END_REF] , our results did not show any significant impact of age at diagnosis on the risk of severe neurodevelopmental outcomes among clinically-diagnosed patients (p=0.13). The limited number of patients can explain this result.

The limitations of this study are inherent with the retrospective methodology. The E-HOD registry includes data from several countries with different health care systems and standards of care. Treatment regimens varied by site, and there was a high inter-patient variability regarding schedules of follow-up visits. Thus, the main result regarding neurodevelopmental outcomes should be adjusted on this potentially confounding variable. Second, the problem of a relatively high proportion of missing data needs to be highlighted. For the same reason, it was not possible to integrate microcephaly, median diagnosis delay, initial plasma tHcy concentrations and initial brain MRI abnormalities, in the prognosis model. Importantly microcephaly at birth was not associated with a more severe outcome (not shown). Due to the high proportion of missing data regarding speech difficulties, it was not possible to include this item in our composite criteria of severe neurodevelopmental outcome. All these criteria should be assessed in further larger studies.

Conclusions

Paediatricians need to be aware of MTHFR deficiency as a rare and severe but potentially treatable inborn error of metabolism. Treatment should be initiated as early as possible, prior to irreversible brain damage. As previously alluded by a seminal meta-analysis [START_REF] Diekman | Survival and Psychomotor Development With Early Betaine Treatment in Patients With Severe Methylenetetrahydrofolate Reductase Deficiency[END_REF] , this study provides clear evidence for a benefit of pre-symptomatic diagnosis and subsequent therapeutic management, highlighting the need for newborn screening for MTHFR deficiency and pre-symptomatic treatment that may improve outcomes.

Introduction 5 , 10 -

 510 Methylenetetrahydrofolate reductase (MTHFR) (MIM #607093) deficiency is a severe autosomal recessive inborn error of metabolism. Though rare, MTHFR deficiency is the most prevalent inborn error of folate metabolism.

  The E-HOD (European Network and Registry for Homocystinurias and Methylation Defects) registry was first approved by the Ethics Committee of University Hospital in Heidelberg (N° S-525/2010; 14.3.2013). All participating centres received approval from their local ethics committees before enrolling patients and all patients provided written informed consent before pseudonymized data were entered into the registry. The E-HOD registry documents natural history (symptoms by organs), biochemical and treatment data. It records intelligence and developmental scores (IQ, DQ) from age-appropriate standardized instruments. Standardized self-and proxy report questionnaires inform about neuropsychological development and behaviour. In 2019, participating centres were asked for permission to use the data of the MTHFR-deficient patients for analysis and publication, and the project was approved by the E-HOD Steering Committee. Analysis of data and publication of results was approved by the Ethics Committee of all E-HOD centres and for patients not included in the E-HOD registry (n=7). Regarding the additional survey, informed written consent was obtained from parents for all of the patients regarding reporting patient data. Each of the local ethics committees provided approval for patient data collection. and at regular follow-up visits using standardized forms. The additional French survey aimed at identifying a French cohort of children with MTHFR deficiency. For this purpose, a data collection sheet was developed on the basis of relevant literature on the disease and expert discussions. Physicians shared the totality of anonymized medical reports. These reports were used to fill in the questionnaire for each patient of the French cohort. Three of the French patients were already included in E-HOD and data were not duplicated. Of note, forty-three of previously reported patients by Huemer et al. were included into our study. As a pre-requisite

  deficiency was suspected based on clinical signs and symptoms except for the patients diagnosed at the pre-symptomatic stage (either prenatally or at birth) associated with equivocal biochemical findings and later on confirmed by the presence of two pathogenic/likely pathogenic variants in the MTHFR gene and/or MTHFR enzyme activity in fibroblasts (data not shown). The study cohort consisted of 32 and 40 patients with early and late-onset MTHFR deficiency, respectively: 62 from the E-HOD registry and 10 from the French survey. Patients were followed by 32 European and North American metabolic centers (25 E-HOD partner sites and 7 additional French centers).

  identified at time of diagnosis. The median follow-up time of the 31 other patients was 8.1 years (range: 7.2 months-34.1 years). Median age of patients at the last follow-up visit was 8.6 years (range: 7.5 months-34.3 years) (Table

Figures legendsFigure 1 .

 1 Figures legends

Table 4 .

 4 Independent factors predictive of severe neurodevelopmental outcomes a outcome is defined as patients with moderate or severe gross motor disability and/or behavioral problems and/or special educational needs at time of the last follow-up visit or who died during their follow-up; CI, confidence interval; b aOR, adjusted odds ratio; ns, not significant

Table 1 . Initial presentation of 32 patients with early-onset MTHFR deficiencyTable 2 . Presentation of 32 patients with early-onset MTHFR deficiency, at their last follow-up visitTable 3 . Factors predictive of severe neurodevelopmental outcomesTable 4 . Independent factors predictive of severe neurodevelopmental outcomes in multivariate analysis in univariate analysisTable 1 . Initial presentation of 32 patients with early-onset MTHFR deficiency

 12341 M agnetic Resonance Imaging; c Electroencephalogram; d reference laboratory level <10 µmol/L; e reference laboratory level 17-43 µmol/L; f [25 th percentile; 75 th percentile]

	Total number of	Number M edian (range)
	patients with
	available data (N)

b

Table 2 . Presentation of 32 patients with early-onset MTHFR deficiency, at their last follow-up visit

 2

	Total number of patients	Number M edian (range)
	with available data (N)

a daily oral dose in mg/kg/day; b intramuscular dose in mg/kg/day; c reference laboratory level <10 µmol/L; d reference laboratory level 17-43 µmol/L

Table 3 . Factors predictive of severe neurodevelopmental outcomes a in univariate analysis

 3 severe neurodevelopmental outcome is defined as patients with moderate or severe gross motor disability and/or behavioral problems and/or special educational needs at time of the last follow-up visit or who died during their follow-up; b CI, confidence interval; OR, odds ratio

		Patients, n (%)
		Severe outcome	Non-severe outcome	OR (95% CI) b	P value
		(N=43)	(N=21)
	Characteristics at time of diagnosis
	Age ≤ 3 months (early-onset disease)	23 (53.4)	7 (33.3)	2.3 (0.8-7.2)	0.13
	Sex male	21 (48.9)	12 (57.1)	0.7 (0.2-2.0)	0.53
	Caucasian ethnic background	33 (76.7)	13 (61.9)	2.0 (0.6-6.3)	0.22
	Pre-symptomatic diagnosis	1 (2.3)	8 (38.1)	0.039 (0.002-0.238)	0.003
	Seizures	13 (30.2)	4 (19.0)	1.8 (0.6-7.3)	0.34
	Respiratory failure	12 (27.9)	3 (14.3)	2.3 (0.6-11.2)	0.23
	Follow-up time > 11 years	22 (51.1)	13 (61.9)	0.6 (0.2-1.8)	0.42

a

Acknowledgements

The authors would like to thank patients and data managers for providing data for the registry. Several authors of this publication are members of the European Reference Network for Rare Hereditary Metabolic Disorders (MetabERN) -Project ID No 739543. The European network and registry for homocystinurias and methylation defects (EHOD) project has been established with funding from the European Union in the framework of the Health Program (Chafea grant N°. 2012 12 02). From the end of the EU-project phase, the E-HOD project has received ongoing support from SOBI, Recordati Rare Disease Foundation, Vitaflo, Aeglea, and Nutricia Metabolics, Germany. E-HOD was initially funded by the European Union in the

Data collection

Data were extracted from two sources: the web-based E-HOD registry database URL: https://www.ehod-registry.org/about-ehod) and via an additional French survey especially designed for this study. Physicians entered the data in this multinational registry at enrolment

Competing interest statement

All of the authors declare that they have no conflict of interest.

Details of funding

The European network and registry for homocystinurias and methylation defects (E-HOD) project has been established with funding from the European Union in the framework of the Health Program (Chafea grant N°. 2012 12 02). From the end of the EU project phase, the E-HOD project has received ongoing support from SOBI, Recordati Rare Disease Foundation, Vitaflo, Aeglea Bio Therapeutics, and Nutricia Metabolics Germany. The authors confirm independence from the sponsors; the content of the article has not been influenced by the sponsors.

Details of ethics approval


O Duport

V Le Rolle

E Galli

D Danan

E Darrigrand

E Donal

A I Hernández

Model-based analysis of myocardial contraction patterns in ischemic heart disease ⋆

Keywords:

Objectives: The objective of the current study is to assess the feasibility of using a left ventricle (LV) model in order to reproduce myocardial strains in the case of ischemic heart disease (IHD).

Materials and Methods:

The proposed integrated LV model couples a finite element method (FEM) sub-model of the cardiac electrical activity, representing the propagation of the transmembrane potential through the LV, a FEM sub-model of the cardiac mechanical activity, and a lumped-parameter model of the circulatory system that improves the physiological definition of appropriate boundary conditions. Simulations were compared to myocardial strain data obtained from echocardiography, performed on two healthy subjects and two patients diagnosed with chronic IHD. Results: Results show the model ability to simulate jointly the hemodynamic variables (Systolic and diastolic pressures respectively equal to 110 and 60 mmHg) and myocardial strain curves during each phase of the cardiac cycle. A close match is observed between minimum strains obtained from simulations and clinical data from healthy subjects and IHD patient, with a root mean square error around 2, 81% and 2, 63% respectively. The modifications of regional LV systolic strains observed from IHD patients with respect to healthy cases were partially explained by a decrease of regional cardiac stress.

Conclusion:

This paper provides a description of a new coupling algorithm between FEM and lumped-parameter models. Results are promising for the analysis of cardiac strains in the context of IHD.

Introduction

Ischemic heart diseases (IHD), also known as coronary artery disease, usually occurs when coronary arteries, which supply heart with blood, oxygen and nutrients, become damaged or diseased. The imbalance between oxygen demand and supply results in an impairment of contractile function [START_REF] Henn | Quantifying "normalized" regional left ventricular contractile function in ischemic coronary artery disease[END_REF]. Assessing the impact of IHD on the cardiac mechanical function may be performed by echocardiography, by evaluating regional myocardial kinetics and deformation (strain) [START_REF] Hoit | Strain and strain rate echocardiography and coronary artery disease[END_REF]. These alterations of LV mechanics can be due to changes in contractility, loading conditions, and LV geometry [START_REF] Mada | Tissue Doppler, strain and strain rate in ischemic heart disease how I do it[END_REF]. However, echocardiography imaging could not be used to assess ventricular pressure or myocardial stress and is, thus, not able to take into account loading conditions. In this context, modeling of cardiac activity could be useful in order to provide a better understanding of myocardial deformations observed in IHD.

Modeling cardiac mechanics is a challenging task, mainly because of the lack of observability and the complexity of the mechanical properties of myocardial tissues. A variety of cardiac electro-mechanical modeling methods have been proposed in the literature, at many different levels of detail Niederer SA (2019). Most models are based on the Finite Element Method (FEM) to simulated time-varying cardiac mechanics Ponnaluri AVS (2019), Gsell (2018) Crozier, Blazevic, Lamata, Plank, Ginks, Duckett, Sohal, Shetty, Rinaldi, Razavi andet al. (2016) [START_REF] Constantino | A computational approach to understanding the cardiac electromechanical activation sequence in the normal and failing heart, with translation to the clinical practice of crt[END_REF]. Simulations and personalization of these models usually require high computational resources. Some alternative solutions have been proposed to overcome this computational cost for the analysis of myocardial strains [START_REF] Walmsley | Septal flash and septal rebound stretch have different underlying mechanisms[END_REF] [START_REF] Lumens | Mechanistic evaluation of echocardiographic dyssynchrony indices patient data combined with multiscale computer simulations[END_REF] Everdingen, W.M.; [START_REF] Everdingen | Echocardiographic prediction of cardiac resynchronization therapy response requires analysis of both mechanical dyssynchrony and right ventricular function: A combined analysis of patient data and computer simulations[END_REF]. Our team has also proposed a patient-specific model-based analysis of myocardial strains Le Rolle, Hernandez, Richard, [START_REF] Le Rolle | Model-based analysis of myocardial strain data acquired by tissue Doppler imaging[END_REF], which has been recently adapted to analyse desynchronization strain patterns and contractility in left bundle branch block through computer model simulation [START_REF] Owashi | Desynchronization strain patterns and contractility in left bundle branch block through computer model simulation[END_REF]. However, these alternative approaches are based on simplified electromechanical laws and patient anatomy. As a consequence, some complementary approaches should be developed in order to propose tissue-level LV models that preserve computational costs, while integrating mechanical properties of myocardial tissues.

The aim of the current study was to assess the feasibility of using a relative low-resolution FEM LV model in order to evaluate regional contractility and to reproduce regional myocardial deformations in the case of IHD. One of the main challenge was to take into account loading conditions while preserving computational costs. The preload description should notably include the pulsatile behaviour of the left atria. Based on a preliminary version Le Rolle, Galli, [START_REF] Le Rolle | Sensitivity Analysis of a Left Ventricle Model in the Context of Intraventricular Dyssynchrony[END_REF], a 3D FEM model of LV electro-mechanical activity was proposed and coupled to a lumped-parameter model of preload and afterload. The document is organised as follows: in Section 2, the experimental data and an exhaustive description of the LV model, from the geometry to the multi-physics modelling and including the coupling procedures, are presented. Next in Section 3 and 4, the results of applying the described methods are presented and discussed.

Method

The proposed methodology is based on a model-based interpretation of LV contraction patterns observed in myocardial scarring. Two-dimensional transthoracic echocardiography was used to obtain deformation patterns in two healthy subjects and two patients with myocardial scar. A 3D FEM model of LV electro-mechanical activity was proposed and coupled to a lumped-parameter model of preload and afterload. Model parameters were evaluated manually to reproduce patient-derived strain curves obtained from echocardiography (figure 1).

Cardiac Magnetic Resonance Imaging

cMRI was performed using a 3-T clinical magnetic resonance system (Ingenia, Philips Medical Systems, Best, The Netherlands) with a 32-channel cardiovascular array coil. LGE images were acquired 10-15 min after intravenous administration of 0.2 mmol/kg of gadolinium (Gadoterate meglumine, Dotarem, Guerbet, Aulnay-sous-Bois, France), using 2D breath-hold inversion-recovery and phase-sensitive inversion-recovery sequences in the short-axis plane (spoiled gradient-echo, slice thickness 8 mm, repetition time 6.1 ms, echo time 2.9 ms, flip angle 25 • , inversion time adjusted to null normal myocardium, typical breath-hold 11 s). The presence and localization of myocardial scar were assessed by a trained radiologist on a 16-segment LV model and the regional LGE extent was determined qualitatively and assessed on a per-segment basis.

Echocardiography

All patients underwent a standard TransThoracic Echocardiography (TTE) using a Vivid E9 ultrasound system (General Electric Healthcare, Horten, Norway). Images were recorded on a remote station for off-line analysis by dedicated software (EchoPAC PC, version BT 13, General Electric Healthcare, Horten, Norway) and segmental strain signals were obtained from standard apical 4-chamber, 3-chamber, and 2-chamber views.

Model of the left ventricle 2.2.1. Geometry

The left ventricle was approximated by a truncated ellipsoid Ω, whose parametrization in the undeformed configuration is given below

= ⎛ ⎜ ⎜ ⎝ ⎞ ⎟ ⎟ ⎠ = ⎛ ⎜ ⎜ ⎝ sin cos sin sin cos ⎞ ⎟ ⎟ ⎠ (1)
The undeformed geometry is defined by the volume between:

• the endocardial surface Γ , , , ∈ [-, -arccos ℎ ], ∈ [-, ],

• the epicardial surface Γ , , , ∈ [-, -arccos ℎ ], ∈ [-, ],

• the base plane height ℎ which is implicitly defined by the ranges for .

Parameters , and ℎ were evaluated specifically by fitting the truncated ellipsoid to the LV knot positions obtained from the semi-automatic segmentation of the endocardial wall, extracted from echocardiographic apical 4 and 2 chamber-views. Parameters , were computed by assuming the uniformity the left ventricular wall thickness. A 3D mesh was generated from this truncated ellipsoid by gmsh (http://gmsh.info/) [START_REF] Geuzaine | Gmsh: a three-dimensional finite element mesh generator with built-in pre-and post-processing facilities[END_REF]. The mesh size is composed of about 10000 tetrahedrons with an average volume of 6 mm.

Electrical problem

The propagation of the transmembrane potential through the ventricle, under the equal anisotropy ratio assumption, was described as follows:

Problem . Find a transmembrane potential ∶ Ω × [0, ] → ℝ and a ionic variable ∶ Ω × [0, ] → ℝ such that ( ∇ ) = ( + ( , )) in Ω, (2) = ( , ) in Ω, (3)
-( ∇ ). = ( ) if < 0 else on , ( 4
)
with = ( -1 + -1 ) -1 and, moreover,

(0) = 0 in Ω, ( 5
) (0) = 0 in Ω. (6)
where , , are respectively the extracellular, intracellular and equivalent electrical conductivities, is the membrane surface capacitance, is the rate of cellular membrane surface per volume unit and is the unit outward normal vector. Here, ( 4) is a Neumann condition; a point of the domain Ω is electrically stimulated with a value for a preset time . The functions and are described by the FitzHugh-Nagumo model [START_REF] Fitzhugh | Impulses and Physiological States in Theoretical Models of Nerve Membrane[END_REF]:

( , ) = 1 ( -)( - - )(1 - - ) + 2 ( -) (7) ( , ) = ( - - -). (8)
where , , 1 , 2 , , , , and are region specific parameters Sovilj S (2013); El Houari and Hernandez (2017).

Problem  was solved with the finite element method (FEM) and the peak depolarization instants ( ) were detected for each node during simulation.

Electrical-mechanical coupling

In order to represent, in a simplified manner, the complex processes involved in the electro-mechanical coupling at the tissue-level (e.g. calcium dynamics of each cell composing the tissue, effect of the heterogeneous mechanical activation of each cell, etc.), the choice was made in this work to represent the active constraint as an electro-mechanical activation function Le [START_REF] Le Rolle | Model-based analysis of myocardial strain data acquired by tissue Doppler imaging[END_REF][START_REF] Le Rolle | A tissue-level electromechanical model of the left ventricle: application to the analysis of intraventricular pressure[END_REF]. In order to take into account the asymmetry between the contraction and relaxation phases, a three-steps continuous Gaussian function was considered:

( ) = ⎧ ⎪ ⎨ ⎪ ⎩ 0 -1 ( -) 2 if ≤ ( 0 -1 ) -2 ( -) 2 + 1 if < ≤ (( 0 -1 ) -2 ( -) 2 + 1 ) -3 ( -) 2 otherwise (9)
where 0 is the amplitude of the active constraint signal, 1 is a growth parameter associated to the contraction phase, 2 and 3 are growth parameters associated to the relaxation phase.

is the time of maximum active constraint, and is the time of contraction of the left atrium.

Mechanical problem

Passive myocardial properties can be described through hyperelastic mechanical constitutive laws [START_REF] Land | Verification of cardiac mechanics software: benchmark problems and solutions for testing active and passive material behaviour[END_REF]. Although this kind of formulation allows a rather detailed description of the myocardium dynamics, it also requires higher computational resources [START_REF] Danan | Validation of a Finite Element Method framework for cardiac mechanics applications[END_REF]. In this paper, linear elasticity was assumed in order to describe the ventricle motion:

Problem . Find a displacement field ∶ Ω × [0, ] → ℝ and a constraint field ∶ Ω × [0, ] → such that = + in Ω × [0, ], (10)
div ( ) = in Ω × [0, ], (11)
( ) = Γ 1 on Γ × [0, ], (12)
( ) = ( ) on Γ × [0, ], (13)
( ) = 0 on Γ × [0, ], (14)
The Cauchy stress is composed of a passive component and an active component (9). Relation (11) is the equilibrium equation. The displacement in the base to the apex direction is set to zero, the circumferential motion in the basis endocardium is prevented (only radial motion is allowed), that is the so-called Dirichlet condition in (12), and the apex is free. Furthermore, the pressure is prescribed at the endocardium (13) and epicardium ( 14). Here, the passive material behaviour is modeled by a Hooke's law, meaning

( ) = + 2 (15)
where we denote by and , the Lame coefficients, by the Kronecker symbol and with

( ) = 1 2 + (16) and = (1 + )(1 -2 ) , = 2(1 + ) ,
where is the displacement vector, the Young modulus, and the Poisson's ratio.

Circulatory model

The description of the volumes, pressures and flows through a cardiac cycle are given by a lumped-parameter model of the circulation. Left atria and ventricle were represented by elastance-based models, which offer a good compromise between complexity and number of parameters Smith, Andreassen, Shaw, Jensen, Rees and Chase (2007); Ugalde, Ojeda, Le Rolle, Andreu, Guiraud, Bonnet, Henry, Karam, Hagege, Mabo, Carrault and Hernandez (2016); Calvo, Le Rolle, Romero, Behar, Gomis, Mabo and Hernandez (2018a,b).

Problem . Find the volume scalar fields , and such that

( ) = -( -- ) 2 (17) =( ( )( - ) + )( - ) (18)
( ) = -( -- ) 2 (19) = ( ) ( - ) + (1 -( )) 0 ( ( -0 ) -1) (20) = ∕ (21) = ∕ (22) _ = ( -)∕ _ if < 0 else. ( 23
) _ = ( - )∕ _ if > 0 else. (24) =( 0 -)∕ (25) ̇ = _ - _ (26) ̇ = - (27) ̇ = _ - (28)
where , and are associated with pressure, volume and flux cavities, whereas subscribes , and respectively stand for aorta, left atria and ventricle. Mitral and aortic valves are represented as diodes, which simulate the one-way direction of blood. Afterload pressure was calculated as a linear relationship between volume and vascular compliance (21) and flows between chambers was obtained by considering vascular resistance ( 22). ( ) and ( ) are driver functions that controls time-variant elastance Ojeda, Rolle, Koon, Thebault, Donal and Hernández (2013); Calvo et al. (2018a). To account for the mechanical function of the atria, the atrial pressure is represented as a linear function of its instantaneous volume , whose slope represents the elastic properties of the atrial wall (18). Regarding the left ventricle, its pressure is represented by a combination of the end-systolic and end-diastolic pressure-volume relationships (20), associated with parameters , , 0 , , 0 .

Coupling procedure between circulation and the mechanical problem

In order to take into account the influence of loading conditions on myocardial strains, the electro-mechanical problem should be coupled to the circulatory model. Although some couplings have been already used to associate 3D cardiac model to lumped-parameter models of the circulation Bovendeerd, Borsje, Arts and [START_REF] Bovendeerd | Dependence of intramyocardial pressure and coronary flow on ventricular loading and contractility: a model study[END_REF], the coupling algorithm is rarely described precisely. Briefly, it consists in estimating the volume predicted by the circulatory and electromechanical models through the left ventricular pressure, as long as the difference between these volumes is not less than a predefined accuracy (Fig. 2). The index stand for the time step in a numerical simulation, the index of the step of the pressure-generating algorithm presented in this section (initialized at 0), refers to the electromechanical coupled problem solved with the finite element method and refers to the hemodynamic problem derived from Problem .

• Step 1: Estimation of the left ventricular pressure

At the beginning of each time step, each first estimate of ventricular pressure is based on a fourth order Adams-Bashfort explicit scheme [START_REF] Kreyszig | Advanced Engineering Mathematics[END_REF]; it uses previous pressures to extrapolate and estimate the new initial pressure 0 , +1 = ( , , , -1 , , -2 , , -3 );

(29) except at the very first time step, where an initial value is considered.

•

Step 2: Volume estimation with the finite element model The pressure , +1 is applied to the endocardium surface, just as described in equation ( 13), and a new volume

,
for the left ventricle is returned by solving the resulting electromechanical problem.

•

Step 3: Volume estimation based on the flows arising from the pressure Volumes ( 26)-( 28) and flows ( 22)-( 25) are calculated using a mid-point scheme. Then, and are updated with ( 18) and ( 21), respectively along with , = , +1 .

•

4: Volumes comparison and next estimation

We compute the relative difference

= | , -, |
, between these two volumes -If the criteria < is satisfied, where is an arbitrarily small parameter, hemodynamic coupling is achieved.

-Else, a next estimation of pressure +1 , +1 is calculated using a conjugate gradient method and we go back to Step 2.

The proposed algorithm allows the integration of electro-mechanical problem and the circulatory model. Cardiac valves states are determined by hemodynamic model and each cardiac cycle phase depends on the coupling between the two models.

Extraction of myocardial strains

In order to perform comparisons between simulations and clinical data, left ventricle was divided into 16 segment according to the standardized segmentation of the AHA Cerqueira, Weissman, Dilsizian, Jacobs, Kaul, Laskey, Pennell, Rumberger, [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]. The left ventricle is divided into equal thirds perpendicular to the long axis of the heart: basal, mid-cavity, and apical:

• Six segments of 60°each are used for the basal slice: BasAnt, BasAntSept, BasInfSept, BasInf, BasInfLat, and BasAntLat.

• The mid part is also divided into six 60°segments: MidAnt, MidAntSept, MidInfSept, MidInf, MidInfLat, and MidAntLat.

• Four segments of 90°each are used for the apex: ApiAnt, ApiSept, ApiInf, and ApiLat.

16 couples of points were considered, each of them belonging to a different segment of the left ventricle (Fig. 1).

Let

,1 ( ), ,2 ( ) be the position of 2 points of interest at a given time and let ,1 , ,2 be the position of the same points in the reference configuration, then the strain ( ) is defined by Reference configuration corresponds to the instant when the LV enters depolarization, during the first cycle of the fully coupled numerical simulation, at the end of the diastole. In this work, the parameter estimation was performed manually by varying the mechanical parameters in order to obtained simulated systolic and diastolic strain values similar to the observed clinical data. The different physical problems and numerical methods have been implemented in a code which is based on a finite element library in C++ under the GNU Public license: GEneric Tools for Finite Elements Methods (GETFEM++) (https://savannah.nongnu.org/projects/getfem).

( ) = ‖ ,1 ( ) - ,2 ( )‖ ‖ ,1 - ,2 ‖ -1 × 100 (30) Time step n Estimation i of pressure p i lv,n+1 Solve electro- mechanical problem, return V i lv,F E Solve hemo- dynamical problem, return V i lv,S |V i lv,S -V i lv,F E | V i lv,S < n = n + 1 i = i + 1 yes no

Results

Hemodynamic simulations and myocardial strains in a healthy case

Fig. 3 presents the simulation of hemodynamic variables: ventricular pressure and volume for a cardiac cycle in healthy case. The systolic LV pressure is equal to 110 mmHg, and the aortic pressure varies between 60 and 105 mmHg. Ventricular volume is equal to 95 ml at the end of diastole and 45 ml at the end of diastole. For each cardiac cycle, myocardial strains were simulated jointly to hemodynamic variables. Pressure-volume loop illustrate the model ability to reproduce the four basic phases of the cardiac cycle: i) the isovolumic contraction phase; ii) the systole; iii) the isovolumic relaxation; iv) the diastole.

Analysis of myocardial strains

Figure 4 shows strain curves obtained at each location of the standardised AHA segmentation for two healthy subjects. The strain morphology corresponds globally to the clinical data. In fact, root mean square error (RMSE), calculated at minimum strain value, are respectively equal to 3.56% and 2.06% for the first and second subjects. During systole, strain values decrease with a negative peak around the aortic valve closure, representing the maximal longitudinal myocardial shortening during contraction. In diastole, strain values increase towards zero, which mean that the length of the analysed myocardial segment returns to its original length at the beginning of the cardiac cycle. The diastole period can be divided into three periods: the first one corresponding to a rapid filling phase due to an aspiration of blood inside the ventricle, a slower filling period and the late diastolic filling phase, corresponding to the atrial systole. Bull-eye plots, which are accepted analysis tools in cardiac diagnosis, were generated to depict minimum strains associated with each AHA segment. Bull-eyes on figure 4 show a close match between the minimum values of strains obtained from the simulated and experimental data. Figure 5 illustrates simulated and experimental strains within scarred segments on the anterior (first column) and inferior (second column) walls. Since the shade is directly scaled with respect to the minimal value of the strain for the associated segment, bull-eye plots show some extent closeness between the simulation and the data. The RMSE calculated at minimum strain value was respectively equal to 2.41% and 2.84% for the anterior IHD and the inferior IHD subjects. Concerning the anterior ischemia case, a global increase of minimum strain values was observed for the anterior region, with maximum values equal to -5.8% and -6.2% for the MidAnt simulated and data strain. Similar increases of minimum strain values were observed for the inferior ischemia, which reach -6.5% and -3.4% for the BasInf segment.

Bull-eyes of figure 6 illustrate the maximum myocardial stresses associated with 2 healthy subjects and 2 chronic IHD patients. The two healthy cases show homogeneous stress values, whereas IHD patients presents low stress values on segments with diagnosed LV scar. On the anterior ischemia case, the global increase of minimum strain of the anterior region is associated with a decrease of maximum stress values for the concerned segments. Similarly, concerning the inferior IHD, minimum strains of inferior regions (especially BasInf and BasInfLat) increase in association with a diminution of stress values.

Discussion

In this paper, a model-based approach was proposed in order to analyse LV contraction patterns observed by echocardiography and to replicate the intrinsic electromechanical properties of the myocardium observed in two healthy subjects and two real-life patients with previous myocardial infarction (chronic IHD). The proposed model was able to reproduce local alteration that corresponds to the areas of myocardial scar observed with cMRI.

Model-based approach

Simulated strains illustrated the model ability to simulate jointly the hemodynamic variables and myocardial deformations. Strain curves notably reflected typical characteristics associated with each phase of the cardiac cycle. The LV model was also used to reproduce regional myocardial deformations in the case of IHD. We have observed a close match between minimum strains obtained from simulations and clinical data from chronic IHD patients. Our results show that the overall dynamics of strain curves in the LV scarred region could be partially explained by the regional decrease in cardiac stress. The proposed model-based approach thus provide a better understanding of strain curves observed with ischemic myocardial abnormalities. Although previous models [START_REF] Albatat | Multisite pacing and myocardial scars: a computational study[END_REF]Connolly and Bishop (2016)) already proposed computational representations of myocardial infarct scars, our approach provides interesting points. Our approach requires low computational resources due to the level of detail of the model, which is consistent with a translation to clinical practice. In fact, the electrical model is based on the adapted monodomain formalism together with the FitzHugh-Nagumo representation and the mechanical part is represented by a simplified linear law. Although the model was defined from simplified assumptions, this approach has been already used in [START_REF] Sovilj | A simplified 3D model of whole heart electrical activity and 12-lead ECG generation[END_REF], [START_REF] Dokos | Computational model of atrial electrical activation and propagation[END_REF], [START_REF] Kunisch | On the one-dimensional nonlinear monodomain equations with moving controls[END_REF]) and have showed significant reduction of: (i) the computational costs and (ii) the number of parameters that need to be tuned. One major contribution of this paper is the description of the coupling algorithm between a 3D model of LV and a lumped-parameter of the circulation. This coupling is essential to take into account preload and afterload influence on patterns of LV contraction.

The results, illustrating similarities between simulations and clinical data, show potential applications in personalized therapy and the global approach is an important step toward the proposition of personalized models since it allows low computational costs and realistic boundary conditions.

Healthy subject 1 Healthy subject 2

Anterior IHD Inferior IHD

Strain Patterns and Scar Localization

In IHD, modifications of myocardial strains are mainly characterized by i) regional inhomogeneities, ii) reduction of systolic strain within the ischemic segments, and iii) alteration in the onset and duration of fibre contraction, which leads to a characteristic shortening or thickening of the myocardium after aortic valve closure [START_REF] Mada | Tissue Doppler, strain and strain rate in ischemic heart disease how I do it[END_REF]. Reduction in systolic strain is related to significant modifications of regional cardiac function. IHD is usually caused by a reduction of blood flow in the coronary vessels, which results in a lack of oxygen consumption and a decrease of force production [START_REF] Allen | Myocardial contractile function during ischemia and hypoxia[END_REF]. The regional differences of myocardial contractility also induce some regional inhomogeneities of cardiac strains [START_REF] Mada | Tissue Doppler, strain and strain rate in ischemic heart disease how I do it[END_REF]. In fact, all segments that are associated with reduced contractility do not bring an effective contribution to blood ejection and could affect the contraction of neighboring segments. In clinical practice, the area of reduced contractility in ischemic patients is usually assessed visually, which might lead to poor reproducibility because the visual identification of these contraction patterns is largely influenced by the experience of the clinician. The proposed computational model was able to disclose the characteristics of the LV deformation patterns observed in patients of both ischemic and non-ischemic etiology. In fact, results show that segments with increased systolic strains are associated with important reductions in myocardial stress, which reflect the alteration of cardiac function due to local scar [START_REF] Lee | Mechanisms of acute ischemic contractile failure of the heart. Role of intracellular calcium[END_REF].

Limitations

Nevertheless, some limitations should be mentioned. First, the strain curve dynamics is not completely reproduced with the LV model. Previous work have shown that the strain curves obtained in ischemic segments are characterized by a reduced strain peak, which occurs after the aortic valve closure [START_REF] Voigt | Strain-rate imaging during dobutamine stress echocardiography provides objective evidence of inducible ischemia[END_REF]. This morphology, also referred as "post-systolic shortening" is only partially explained by the regional decrease in cardiac stress. The reciprocal interaction between neighbour segments, between LV scarred segments and normal LV segments, as far as sub-clinical LV conduction disturbances and changes in the overall LV geometry, might contribute to the typical strain pattern observed in IHD [START_REF] Voigt | Strain-rate imaging during dobutamine stress echocardiography provides objective evidence of inducible ischemia[END_REF]; [START_REF] Asanuma | Myocardial ischaemia and post-systolic shortening[END_REF]. Improvements concerning the electro-mechanical function will be proposed and the possibility of integrating a hyper-elastic law will be analyzed as in previous work of our team Danan et al. (2017). In futur works, the right ventricle will be included in order to improve simulations of strain morphologies. Some limitations are also related to the manual adjustment of model parameters. In future developments, identification algorithms will be implemented to reduce the error between simulated and experimental strains, as done in our previous works Le [START_REF] Le Rolle | Model-based analysis of myocardial strain data acquired by tissue Doppler imaging[END_REF][START_REF] Le Rolle | A tissue-level electromechanical model of the left ventricle: application to the analysis of intraventricular pressure[END_REF]. Finally, this study is based on a small population of IHD patients leading to moderately significant results and, thus, conclusions should be extracted by means of a larger clinical series.

Conclusion

The objective of this study was to propose a model-based interpretation of the different patterns of LV contraction observed in the case of preserved contractility and myocardial scarring. A mathematical model of the left ventricle, including the coupling between the 3D description of electro-mechanical activity and the influence of circulation, was proposed and analyzed. One contribution of this work is the description of the coupling algorithm between the FEM and lumped-parameter models. The integration algorithm is essential to describe both cardiac electrical, mechanical, and hemodynamic influence on LV contraction patterns. The integrated model reproduced the reduction of minimum strains observed in myocardial ischemia. The ischemic segments presented reduced contractility, as expressed by the smaller active parameters. The results are promising for the analysis of cardiac strains in the context of IHD and provide novel insights into the complex deformations of the left ventricle.

CRediT authorship contribution statement

Figure 1 :

 1 Figure 1: Left panel: Strain-derived curves obtained from each patient were compared to the outputs of the model and used to adjust the model's parameters. Right panel: Coupling between the lumped-parameter model of the circulation and the 3D model of the LV, which was divided in 16 segment according to the standardized segmentation of the AHA.

Figure 2 :

 2 Figure 2: Pressure-generating algorithm used to obtain hemodynamic coupling

Figure 3 :

 3 Figure 3: Aortic/endocardial pressure and endocardial volume through a cardiac cycle

Figure 4 :

 4 Figure 4: Comparison between simulated and experimental strain signals for 2 healthy cases (Upper panel). Minimum simulated and experimental strains in % (Bottom panel)

Figure 5 :

 5 Figure 5: Comparison between simulated and experimental strain signals for inferior and anterior IHD patients (Upper panel). Minimum simulated and experimental strains in % (Bottom panel)

Figure 6 :

 6 Figure 6: Bull-eye of maximum stress values in kPa (A)

O

  . Duport: Formal analysis, Data curation, Methodology, Software, Writing -review & editing. V. Le Rolle: Conceptualization, Funding acquisition, Data curation, formal analysis, Methodology, Software, Supervision, Writing -Original draft, Writing -review & editing. E. Galli: Data curation, Supervision, Writing -review & editing. D. Danan: formal analysis, Methodology, Software, Writing -review & editing. E. Darrigrand: Formal analysis, Methodology, Writing -review & editing. E. Donal: Data curation, Writing -Original draft preparation, Supervision, Writingreview & editing. A.I. Hernández: Conceptualization, Data curation, formal analysis, Methodology, Software, Writing -original draft, Supervision, Writing -review & editing.

⋆ This document is the results of the research project funded by the French National Research Agency (ANR) (ANR-16-CE19-0008-01) (project MAESTRo).

Funding

This work did not receive any grant from funding agencies in the public, commercial, or not-for-profit sectors.

This work has been supported by:

V5.0 -27/08/19 -For use with journals published by Elsevier Masson SAS, France

Model-based analysis of myocardial contraction patterns in ischemic heart disease

CONCLUSION:

A close match is observed between minimum strains obtain from simulation and clinical data.

Duport et al., 2021

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Integrated model of the left ventricle for the analysis of regional di l t i i th t t f i h i h t di