Adán Israel Rodríguez-Hernández

Eva Salinas

Deli Nazmín

Tirado González

Carlos Velasco Benitez

Mariela Jiménez

Laura E Córdova-Dávalos

Daniel Cervantes-García

Victor Federico

Rodríguez Nava
email: israel.rodriguez@edu.uaa.mx

Luis G Bermúdez-Humarán

A I ; Salinas

E ; Tirado González

D N ; Velasco Benitez

C ; Jiménez

M ; Córdova-Dávalos

Adán Israel Rodrígu-Hernández

Tirado Gonzál

Laura E Córdo-Dávalos

Effects of a Modern Kefir on Conditions Associated with Moderate Severe Spastic Quadriparesis Cerebral Palsy

Keywords: probiotics, cerebral palsy, digestive disorders, constipation, dyspepsia, common cold, malnutrition

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

Introduction

Cerebral palsy (CP) is a posture and movement disorder that results from damage to the immature brain or abnormal brain development. According to a recent report from the Center for Disease Control and Prevention (CDC) [1], it is estimated that the worldwide prevalence of CP ranges from 1 to almost 4 per 1000 newborns. In Mexico, there are around 500,000 people with CP and around 12,000 new cases are reported each year [2]. In the Rehabilitation Center Telethon (CRIT) in Aguascalientes, the registered population oscillates above 2000 patients in recent years, of which 110 have the problem of hypertonia or severe spasticity [3].

of 18

The CP is associated with various conditions such as malnutrition [4,[START_REF] De Zabarte Fernández | Nutritional status of a population with moderate-severe cerebral palsy: Beyond the weight[END_REF], alterations in swallowing mechanics [START_REF] Caramico Favero | Food intake, nutritional status and gastrointestinal symptoms in children with cerebral palsy[END_REF], respiratory diseases [START_REF] Boel | Respiratory morbidity in children with cerebral palsy: An overview[END_REF], as well as inflammatory bowel diseases (IBD) [START_REF] Jiménez | Patología gastrointestinal en niños con parálisis cerebral infantil y otras discapacidades neurológicas[END_REF][START_REF] Colson | Inflammatory Bowel Disease in Pediatric Patients with Cerebral Palsy[END_REF] and constipation [START_REF] Colson | Inflammatory Bowel Disease in Pediatric Patients with Cerebral Palsy[END_REF][START_REF] Faleiros-Castro | Paralisia cerebral tetraplégica e constipação intestinal: Avaliação da reeducação intestinal com uso de massagens e dieta laxante[END_REF]. These conditions, in turn, determine a loss or little gain in body weight and a limited muscle mass gain, represented as poor growth and muscle atrophy [START_REF] Day | Growth patterns in a population of children and adolescents with cerebral palsy[END_REF]. Additionally, children with CP present neuromotor and gastrointestinal limitations that influence improper diet, such as poor mouth opening, respiratory secretions, poor chewing, etc. [START_REF] García Zapata | La alimentación del niño con parálisis cerebral un reto para el nutricionista dietista: Perspectivas desde una revisión[END_REF].

Different symptomatic manifestations of gastrointestinal disorders are present in children with CP. Besides, laboratory studies have confirmed that those children show different grades of inflammation, characterized by leukocytosis (an excess of leukocytes in the blood), elevated erythrocyte sedimentation rate, high blood levels of C-reactive protein (CRP) (a marker of an acute phase of inflammation), hypoalbuminemia, and anemia (which could be normocytic due to chronic disease, microcytic due to iron deficiency, or more frequently combined) [START_REF] Chermesh | El papel de la microbiota en la enfermedad inflamatoria intestinal[END_REF]14].

In a study by Colson et al. [START_REF] Colson | Inflammatory Bowel Disease in Pediatric Patients with Cerebral Palsy[END_REF] an incidence of 198 IBD cases per 100,000 children with CP was observed, with ulcerative colitis, Crohn's disease, and indeterminate colitis the most frequently encountered types of IBD. Some of the symptoms were bloody stools and poor body weight gain. Recently, Roma Foundation published, through collaborators in Latin America, an update of the Rome IV Criteria for Functional Digestive Disorders (FDD) questionnaire in its Spanish version of three different pediatric age groups [START_REF] Velasco-Benítez | Utilidad de los cuestionarios de Roma IV en español para identificar desórdenes gastrointestinales funcionales en pediatría. Grupo de trabajo de la Sociedad Latinoamericana de Gastroenterología, Hepatología[END_REF]. Through this tool, it was detected the presence of functional dyspepsia, epigastric pain syndrome, irritable bowel syndrome (IBS), functional abdominal pain, functional abdominal migraine, functional constipation, fecal incontinence, adolescent rumination syndrome, and aerophagia. It may be present one or several FDDs.

Malnutrition is common in CP and its prevalence is more common in spastic CP [4]. This condition is strongly related to a deficient response of the immune system [START_REF] Sullivan | Nutrition and growth in children with cerebral palsy: Setting the scene[END_REF], as an insufficient and poor-quality food intake translates into a deficit of nutrients for the synthesis of molecules or cells of the immune system. In addition, a correlation between a poor immune response, dysbiosis, and chronicity of respiratory infections has also been established [START_REF] Marimón | The Lung Microbiome in Health and Respiratory Diseases[END_REF].

Probiotics are "live microorganisms that, when administered in adequate amounts, confer health benefits to the host" [START_REF] Sanders | Probiotics: Definition, sources, selection, and uses[END_REF]. Probiotic-based treatments to improve human health are associated with the "brain-gut-immune axis", as an adequate microbiota benefits these three main systems [START_REF] Lombardi | Nutritional modulation of the intestinal microbiota; future opportunities for the prevention and treatment of neuroimmune and neuroinflammatory disease[END_REF]. Clinical trials have proven that the intake of probiotics reduces inflammation of the intestinal and respiratory mucosa, in addition to inducing other immunomodulatory properties [START_REF] Gómez Eguílaz | El eje microbiota-intestino-cerebro y sus grandes proyecciones[END_REF][START_REF] Oelschlaeger | Mechanisms of probiotic actions-A review[END_REF][START_REF] Zolnikova | Application of probiotics for acute respiratory tract infections[END_REF]. To date, there have been few clinical trials that show an increase or improvement in weight or body mass index in children with CP that have been treated with probiotics, particularly children with a history of prematurity and poor neurological development [START_REF] Upadhyay | Effect of prebiotic and probiotic supplementation on neurodevelopment in preterm very low birth weight infants: Findings from a meta-analysis[END_REF][START_REF] Upadhyay | Cerebral palsy: Aetiology, pathophysiology and therapeutic interventions[END_REF][START_REF] Jacobs | prematurity and neurodevelopment: Follow-up of a randomised trial[END_REF].

Traditional kefir, also called milk kefir, is based on the fermentation of milk by kefir grains and includes several microorganisms. It is basically composed of a large variety of probiotic microorganisms, mainly bacteria from genera Bifidobacterium, Lactococcus, Leuconostoc, and Lactobacillus, as well as yeasts from Saccharomyces, containing an average range of up to 50 probiotic species [START_REF] Altay | A review on traditional Turkish fermented non-alcoholic beverages: Microbiota, fermentation process and quality characteristics[END_REF][START_REF] Dertli | Microbial diversity of traditional kefir grains and their role on kefir aroma[END_REF][START_REF] Lopitz-Otsoa | A symbiotic yeasts-bacteria community with alleged healthy capabilities[END_REF]. Anti-inflammatory, immunomodulatory, antiviral, antimicrobial, and antifungal properties have been attributed to the intake of milk kefir [START_REF] Mishra | Probiotics as Potential Antioxidants: A Systematic Review[END_REF][START_REF] Van Wyk | Kefir: The Champagne of Fermented Beverages[END_REF][START_REF] Kesenkaş | Fermented Foods in Health and Disease Prevention[END_REF]. A version of lyophilized or powdered kefir probiotic species can be added to conventional milk for the corresponding fermentation process, which is known as modern kefir. It contains an average of 10 to 14 probiotic species, mainly species of Bifidobacterium, Lactobacillus, and Streptococcus, but without yeasts [START_REF] Hansen | eXact ® KEFIR 12[END_REF][START_REF] Bozova | Effects of Kefir Powder Fortification on Yogurt Qual[END_REF][START_REF] Song | Reconstituted yogurt from yogurt cultured milk powder mix has better overall characteristics than reconstituted yogurt from commercial yogurt powder[END_REF]. In this sense, modern kefir is a modified version that has been designed to improve the organoleptic characteristics of traditional kefir while preserving most of the beneficial properties for host health [START_REF] Bozova | Effects of Kefir Powder Fortification on Yogurt Qual[END_REF][START_REF] Hansen | FD-DVS eXact®KEFIR 1[END_REF]. Both traditional and modern kefir are similar in aspect to yogurt, but with better sensorial properties; nevertheless, only modern kefir guarantees the presence of 1 × 10 8 colony-forming unit (CFU) of each probiotic species during the fermentation process [START_REF] Bozova | Effects of Kefir Powder Fortification on Yogurt Qual[END_REF].

The modern kefir of the Sello Rojo brand (Mexico), is a fermented dairy drink from the inoculation of 14 probiotic species isolated from traditional kefir [START_REF] Hansen | [END_REF]. Based on this argument, the objective of this study was to evaluate the effects of this modern beverage on the main pathological conditions associated with CP.

Materials and Methods

Subjects and Type of Study

A double-blind randomized clinical trial was conducted on 24 children between 4 and 8 years of age with moderate severe spastic CP from the Rehabilitation Center Telethon (CRIT) in Aguascalientes, Mexico, who attended in the 2020-2021 period (Figure A1). Children included presented CP originated due to postnatal causes. Besides, they were diagnosed with III and IV Asworth spastic level, and IV Gross Motor Function Classification System (GMFCS). Those children who had basic pharmacological treatment and did not have a special diet (ad libitum) due to some comorbidities were included; however, those whose parents did not agree to participate or were on an antibiotic treatment were eliminated. Those subjects whose parents decided to withdraw from the study or did not meet the scheduled evaluation dates were eliminated. The sample size was calculated using the Lachenbruch formula for the calculation of the sample of "Difference of two proportions" with a confidence level of 90% and a power of 80%, with a 30% adjustment for losses using the free Win Epi calculator. A simple random probabilistic sampling (randomized) was applied, using the STATS 2.0 software. The "Random Number Generator" subprogram was used to automatically generate patient numbers. Participants were randomly assigned to control (n = 12) or model kefir (n = 12) groups.

Treatment Composition and Clinical Trial Design

Commercial yogurt (kindly donated by Láctica Creativa, Mexico) was administered to the control group (yogurt group) and modern kefir (kindly gifted by Alimentos Sello Rojo S.A. of C.V, Mexico) to the experimental group (kefir group) for 49 days (7 weeks). The different evaluations were carried out at time zero and at week (W) number 7 of the treatment. Nutritional composition of the commercial yogurt was: 5.9 g of protein, 0.8 g of fat, 210 mg of calcium, 10.8 g of carbohydrates and 89 mg of sodium per 240 mL (100 calories). It also contained two probiotic species: Streptococcus thermophilus, and Lactobacillus bulgaricus. In addition, acesulfame-K (5 mg/100 mL) was included as sweetener. Nutritional composition of modern kefir was: 5.9 g of protein, 0.9 g of fat, 220 mg of calcium, 10.8 g of carbohydrates, 104 mg of sodium and 0.6 g of lactase per 240 mL (108.3 calories). The 12 probiotic species contained in modern kefirwere: (1) Bifidobacterium infantis, (2) Bifidobacterium lactis, (3) Lactobacillus acidophilus, (4) Lactobacillus delbrueckii spp. lactis, (5) Lactobacillus fermentum, (6) Lactobacillus paracasei, (7) Lactobacillus rhamnosus, (8) Lactococcus lactis spp. cremoris, (9) Lactococcus lactis spp. lactis, (10) Lactococcus lactis spp. lactis biovar. diacetylactis, (11) Leuconostoc mesenteroides, (12) Leuconostoc pseudomesenteroides. Sucralose (7.2 mg/100 g) was included as a sweetener. Participant of both groups were administered orally 250 mL of the corresponding beverage per day.

At the end of the study, a survey on the perception of effects and satisfaction of the product was applied to parents or guardians of children and was validated through a concordance test (test retest). A Likert scale survey was used to obtain responses such as: 1, particularly good; 2, good; 3, regular; 4, bad; 5, particularly bad.

Anthropometric Measurements

Height was obtained under the Stevenson et al. [START_REF] Stevenson | Use of Segmental Measures to Estimate Stature in Children with Cerebral Palsy[END_REF] segmental measurement criteria through the upper arm length equation while weight by using a wheelchair weighing scale (PWC-620 model, Tanita, Tokyo, Japan). In addition, body mass index (BMI) was calculated.

Evaluation of Resting Energy Expenditure

Resting energy expenditure (REE) was measured through the indirect calorimetry technique with a CardioCoach calorimeter (KORR Medical Technology, Salt Lake City, UT, USA), using the petit mask for children. Subjects were evaluated for 15 min in a reclining chair.

Diagnosis of Intestinal Disorders and Respiratory Problems in Children

A digital survey was applied before (W0) and after (W7) treatment administration using the FDD questionnaire under the Rome IV Criteria (Figure A2) for parents or guardians of children between 4 and 10 years of age in the Latin American Spanish language and under the legal permission of the foundation. This instrument could determine the presence or absence of up to 12 disorders. Besides, this survey included an item about stool consistence and parent responses were evaluated using Bristol scale, in which feces are classified in 7 types as follows: type 1, separate hard lumps like nuts; type 2, sausage-shape but lumpy; type 3, like a sausage but with cracks on its surface; type 4, like a sausage or snake, smooth and soft; type 5, soft blobs with clear-cut edges; type 6, mushy consistency with ragged edges; type 7, liquid consistency with no solid pieces; type 8, it is always different.

Other digital survey was applied under the criteria of the program "Integrated attention to prevalent childhood diseases" to know the frequency of respiratory problems for periods ranging from weekly to monthly.

The perception of the beneficial digestive and respiratory effects after applying the treatments was evaluated through a digital survey applied to parents or guardians of children, in which a Liker scale mentioned 5 items: 1, particularly good; 2, good; 3, regular; 4, bad; 5, particularly bad.

Blood Leukocyte Count and Serum CRP Analysis

For differential (lymphocytes, monocytes, and granulocytes) count of leucocytes, five mL of blood was drawn by venipuncture and collected in tubes with EDTA (Vacutest Kima, Italy). Two hundred µL of each blood sample were evaluated in an automated hematologic analyzer Orphée Mythic 18 (Diamond Diagnostics, Holliston, MA, USA). Clinical abnormalities in white cells, such as leukocytosis, lymphocytosis, leukopenia, or lymphocytopenia, were diagnosed using the 2018 Spanish pediatric hematology guidelines [START_REF] Aragonés | Hematología práctica: Interpretación del hemograma y de las pruebas de coagulación[END_REF].

To the qualitative (negative or positive) determination of CRP, 1 mL of undiluted serum was analyzed by latex agglutination plate test (LICON, Mexico). A negative result indicates that the CRP serum level was lower than 6 mg/L (healthy condition) and a positive result that it was higher than 6 mg/L (inflammatory condition).

Statistical Analysis

Statistical analysis was performed using the SPSS software (SPSS Inc., Chicago, IL, USA). Comparisons among groups were made with the chi-square test to compare nonparametric type variables with respect to baseline and final time between independent samples, McNemar test for analyzing dichotomous variables, the Wilcoxon test for ordinal variables, and Mann Whitney U test for related samples. Meanwhile, to analyze parametric variables a Student's t-test was used for independent samples and related samples. For the correlation of the variables of presence or absence of FDD and the perception of beneficial effects of the parents after treatment, a Pearson's R was used, where R = 0.4-0.9. Differences were considered statistically significant when p < 0.05.

Results

Characteristics of the Subjects

From the 24 patients that were included in this study, just 19 completed the treatments. The average age was 6.05 years, and 36.8% were female and 63.2% male. The level of classification of gross motor function was group 4 in 100% of the population, while the distribution based on the degree of hypertonia according to the Asworth scale was: 21.1% were classified as grade 3 (moderate), 36.8% as grade 4 (severe) and 68.4% as grade 3-4 (moderate severe). No significant differences were found between the variables age, weight, height, BMI, and REE at the beginning of the study, as shown in Table 1. Regarding the anthropometric parameters and the needs of energy expenditure at rest or REE, no statistically responses were found using the Student's t-test among the independent samples of the groups "before" and "after" the study. However, when the Student's t-test from related samples (that compared data before (W0) and after (W7) the treatment) showed that not only the height of kefir group increased significantly (p = 0.003) but also the weight (p = 0.027) as is shown in Table 2. In addition, we found a significantly positive correlation between Weight W0 and W7 with REE W0 and W7 (r = 789, p = 0.003, Spearman r). Regarding the results for the weight, we also found a significant negative correlation among the diagnostic Asworth hypertonic grade and the weight and BMI, which means that the higher the hypertonia is related to a lower body weight (r = 0.6) or BMI (r = 0.8) (p < 0.01, Pearson r).

Effects of Kefir Administration on Functional Digestive Disorders

Figure 1 shows the prevalence of different FDDs in the kefir group before and after the intervention. The most recurrent FDD detected at W0 was the functional constipation with a prevalence of 90.9% (n = 10) from those 45.45% presented as a unique disorder (not accompanied by another FDD), followed by functional dyspepsia (27.3%; n = 3), which in most cases was accompanied by other FDDs, such as aerophagia (9.1%, n = 1), and pain syndrome in epigastrium (9.1%, n = 1) combined with functional constipation. One of the children presented functional abdominal migraine and other IBS, accompanied by constipation. Finally, functional abdominal pain was diagnosed in other participant as a sole disorder. Interestingly, there was a decrease in the presence of FDDs detected after the intervention with modern kefir. In addition, it was observed a notable reduction in constipation, going from 90.9% to just 9.1%, and those children that had some other FDD, no longer was present after 7 weeks of kefir intake.

children presented functional abdominal migraine and other IBS, accompanied by constipation. Finally, functional abdominal pain was diagnosed in other participant as a sole disorder. Interestingly, there was a decrease in the presence of FDDs detected after the intervention with modern kefir. In addition, it was observed a notable reduction in constipation, going from 90.9% to just 9.1%, and those children that had some other FDD, no longer was present after 7 weeks of kefir intake. On the other hand, 75% of the control group (n = 6) presented constipation at the beginning of the study but the proportion was reduced to 12.5% (n = 1) after the treatment with kefir (Figure 2). However, from the 37.5% of the cases that presented functional dyspepsia, 12.5% who presented functional nausea at the beginning of the study did not improve after the kefir intake. In addition, an unexpected finding was the appearance of a case of dyspepsia and cyclic vomiting syndrome in one of the patients. Table 3 shows that the most reported cases of FDD in kefir group at week 0 or basal time were not present at the end of the study in 100% of subjects, with the exception of functional constipation that shows the 88.8% of the recovery. Only in the case of functional constipation, the decreasing of the cases mediated by kefir intake was statistically significant due to the high number of cases present at baseline time. On the other hand, 75% of the control group (n = 6) presented constipation at the beginning of the study but the proportion was reduced to 12.5% (n = 1) after the treatment with kefir (Figure 2). However, from the 37.5% of the cases that presented functional dyspepsia, 12.5% who presented functional nausea at the beginning of the study did not improve after the kefir intake. In addition, an unexpected finding was the appearance of a case of dyspepsia and cyclic vomiting syndrome in one of the patients.

W I T H O U T F D D F D / F C N F D / F N / … F D / C Y V O M F D F C N NUMBER OF PATIENTS WO n =8 W7 n = 8
Microorganisms 2022, 10, x FOR PEER REVIEW 6 of 18 children presented functional abdominal migraine and other IBS, accompanied by constipation. Finally, functional abdominal pain was diagnosed in other participant as a sole disorder. Interestingly, there was a decrease in the presence of FDDs detected after the intervention with modern kefir. In addition, it was observed a notable reduction in constipation, going from 90.9% to just 9.1%, and those children that had some other FDD, no longer was present after 7 weeks of kefir intake. On the other hand, 75% of the control group (n = 6) presented constipation at the beginning of the study but the proportion was reduced to 12.5% (n = 1) after the treatment with kefir (Figure 2). However, from the 37.5% of the cases that presented functional dyspepsia, 12.5% who presented functional nausea at the beginning of the study did not improve after the kefir intake. In addition, an unexpected finding was the appearance of a case of dyspepsia and cyclic vomiting syndrome in one of the patients. Table 3 shows that the most reported cases of FDD in kefir group at week 0 or basal time were not present at the end of the study in 100% of subjects, with the exception of functional constipation that shows the 88.8% of the recovery. Only in the case of functional constipation, the decreasing of the cases mediated by kefir intake was statistically significant due to the high number of cases present at baseline time. Table 3 shows that the most reported cases of FDD in kefir group at week 0 or basal time were not present at the end of the study in 100% of subjects, with the exception of functional constipation that shows the 88.8% of the recovery. Only in the case of functional constipation, the decreasing of the cases mediated by kefir intake was statistically significant due to the high number of cases present at baseline time. Regarding the evaluation of stool consistency using Bristol scale, a statistically significant improvement was found in kefir group using the Wilcoxon test for ordinal variables (p = 0.007). Specifically, there was a reduction in severity of the hardness of the stool (Figure 3), as the majority of the population (72.7%) had stools type 2, sausage-shape but lumpy (almost the worst level of hardness) before the intake of kefir, but at the end of the treatment the majority of children presented smooth and soft elongated stools (54.5%) or other lower levels of stool hardness. Only in one subject there was no improvement (9.1%). On the contrary, in the yogurt group (Figure 4) there were not significant improvement in stool consistency. Regarding the evaluation of stool consistency using Bristol scale, a statistically significant improvement was found in kefir group using the Wilcoxon test for ordinal variables (p = 0.007). Specifically, there was a reduction in severity of the hardness of the stool (Figure 3), as the majority of the population (72.7%) had stools type 2, sausage-shape but lumpy (almost the worst level of hardness) before the intake of kefir, but at the end of the treatment the majority of children presented smooth and soft elongated stools (54.5%) or other lower levels of stool hardness. Only in one subject there was no improvement (9.1%). On the contrary, in the yogurt group (Figure 4) there were not significant improvement in stool consistency. On the other hand, when it was compared the perception of the included children's parents at the end of the study, regarding the gastrointestinal benefits of the kefir addition in diets, 63.6% of them perceived the kefir treatment as particularly good but no one of the in the yogurt group perceived the treatment as particularly good, the 25% of kefir group qualified it as good and 37.5% as regular. However, the difference between groups using the Mann Whitney U test at the end of the study was not significant (p = 0.103). On the other hand, when it was compared the perception of the included children's parents at the end of the study, regarding the gastrointestinal benefits of the kefir addition in diets, 63.6% of them perceived the kefir treatment as particularly good but no one of the in the yogurt group perceived the treatment as particularly good, the 25% of kefir group qualified it as good and 37.5% as regular. However, the difference between groups using the Mann Whitney U test at the end of the study was not significant (p = 0.103).

0 - - 1 0 100 - Abdominal functional migraine 0 0 - - 1 0 100 - Functional abdominal pain 0 0 - - 1 0 100 - Irritable bowel syndrome 0 0 - - 1 0 100 - Functional nausea 1 1 0 0 0 - - Cyclic vomiting syndrome 0 1 1CI - 0 0 - - Aerophagia 0 0 - - 1

Effects of Kefir Administration on Respiratory Problems

Table 4 shows that there were significant differences by chi 2 test between W0 and W7 in relation to the presence of the frequency of respiratory problems that ranged from higher to lower frequency on an ordinal scale per week, per month, at two or 3 months, twice a year and never. However, these results were not significant by Wilcoxon test. Figure 5 shows that in the kefir group, the small population that got sick every week or every 2 months before treatment (W0), reduced the presence of colds in 100% of the cases compared to the end of the kefir treatment (W7). There was no change in cold frequency in the control group.

Effects of Kefir Administration on Respiratory Problems

Table 4 shows that there were significant differences by chi 2 test between W0 and W7 in relation to the presence of the frequency of respiratory problems that ranged from higher to lower frequency on an ordinal scale per week, per month, at two or 3 months, twice a year and never. However, these results were not significant by Wilcoxon test. Figure 5 shows that in the kefir group, the small population that got sick every week or every 2 months before treatment (W0), reduced the presence of colds in 100% of the cases compared to the end of the kefir treatment (W7). There was no change in cold frequency in the control group.

On the other hand, when comparing the effect that the treatment had according to the perception of improvement in the presence of respiratory problems between the two treated groups, the difference was not significant (p = 0.06). However, 45.5% of the parents of the patients treated in the kefir group referred to the product as particularly good vs. 12.5% of the control group. On the other hand, when comparing the effect that the treatment had according to the perception of improvement in the presence of respiratory problems between the two treated groups, the difference was not significant (p = 0.06). However, 45.5% of the parents of the patients treated in the kefir group referred to the product as particularly good vs.12.5% of the control group.

Effect of kefir Administration on the Differential Count of Leukocytes and Serum CRP Level

The percentage of lymphocytes, monocytes, and granulocytes of the patients in each group before and after treatment with yogurt or kefir remained unchanged (Figure 6). Likewise, there was no change in the percentage of each leucocyte at weeks 0 and 7 when comparing between groups. On the other hand, there were no significant differences in the absolute values of monocytes, granulocytes, and lymphocytes of the patients in each group before and after treatment with yogurt or kefir (Figure 7). Interestingly, the absolute value of lymphocytes in children that received treatment with kefir for 7 weeks (W7) was 40.82% higher than in those treated with yogurt for the same time (4.66 ± 0.43 vs. 3.31 ± 0.38 × 10 3 lymphocytes/μL of blood, p < 0.05), with no differences between the absolute values of these cells in the patients of both groups before starting treatment (W0; 4.07 ± 0.44 vs. 3.58 ± 0.45 × 10 3 lymphocytes/μL of blood, respectively). The absolute number of monocytes and granulocytes

Effect of kefir Administration on the Differential Count of Leukocytes and Serum CRP Level

The percentage of lymphocytes, monocytes, and granulocytes of the patients in each group before and after treatment with yogurt or kefir remained unchanged (Figure 6). Likewise, there was no change in the percentage of each leucocyte at weeks 0 and 7 when comparing between groups. On the other hand, when comparing the effect that the treatment had according to the perception of improvement in the presence of respiratory problems between the two treated groups, the difference was not significant (p = 0.06). However, 45.5% of the parents of the patients treated in the kefir group referred to the product as particularly good vs.12.5% of the control group.

Effect of kefir Administration on the Differential Count of Leukocytes and Serum CRP Level

The percentage of lymphocytes, monocytes, and granulocytes of the patients in each group before and after treatment with yogurt or kefir remained unchanged (Figure 6). Likewise, there was no change in the percentage of each leucocyte at weeks 0 and 7 when comparing between groups. On the other hand, there were no significant differences in the absolute values of monocytes, granulocytes, and lymphocytes of the patients in each group before and after treatment with yogurt or kefir (Figure 7). Interestingly, the absolute value of lymphocytes in children that received treatment with kefir for 7 weeks (W7) was 40.82% higher than in those treated with yogurt for the same time (4.66 ± 0.43 vs. 3.31 ± 0.38 × 10 3 lymphocytes/μL of blood, p < 0.05), with no differences between the absolute values of these cells in the patients of both groups before starting treatment (W0; 4.07 ± 0.44 vs. 3.58 ± 0.45 × 10 3 lymphocytes/μL of blood, respectively). The absolute number of monocytes and granulocytes On the other hand, there were no significant differences in the absolute values of monocytes, granulocytes, and lymphocytes of the patients in each group before and after treatment with yogurt or kefir (Figure 7). Interestingly, the absolute value of lymphocytes in children that received treatment with kefir for 7 weeks (W7) was 40.82% higher than in those treated with yogurt for the same time (4.66 ± 0.43 vs. 3.31 ± 0.38 × 10 3 lymphocytes/µL of blood, p < 0.05), with no differences between the absolute values of these cells in the patients of both groups before starting treatment (W0; 4.07 ± 0.44 vs. 3.58 ± 0.45 × 10 3 lymphocytes/µL of blood, respectively). The absolute number of monocytes and granulocytes was similar when comparing the values obtained before (W0) and after (W7) the treatments between the groups.

was similar when comparing the values obtained before (W0) and after (W7) the treatments between the groups. Regarding the total count of lymphocytes in kefir group, although there was not significant change between W0 and W7, it is worthy to mention the case of a child that presented less than 2000 lymphocytes/μL (which indicates the risk of immunodepleting or mild protein malnutrition [START_REF] Kumarasamy | Total lymphocyte count (TLC) is a useful tool for the timing of opportunistic infection prophylaxis in India and other resource-constrained countries[END_REF]) at W0, but increased considerably at W7.

In relation to serum CPR analysis, it was found a positive result (CRP > 0.06 mg/dL according to the LICON qualitative Test) in one child of the kefir population at W1 and W7, while all children in the yogurt group were negative. It has been reported CRP values above 17.1 mg/dL are associated with IBD [START_REF] Manzano | Markers for bacterial infection in children with fever without source[END_REF]. However, as the test we used is a qualitative type, we cannot confirm the association among these two criteria. In this regard, we found significant correlation between the presence of IBS and CRP in W0 (r = 1, p < 0.005; Spearman r)

Unexpected Findings and Secondary Effects

Unexpected side effects were found in the commercial yogurt group, an exacerbation of gastroesophageal reflux was observed in a controlled patient who presented cyclic vomiting syndrome at the end of the study, as well as the appearance of two cases of dyspepsia. In the kefir group, one case of exacerbation of constipation was reported at the end of the study. No subjects excluded due to severity or respiratory complications were reported during the study.

Regarding the hematological markers not included in present study, after the blood analysis it was found the presence of hypochromic anemia before and after treatments in both kefir (54.7%) and yogurt (87.5%) groups, as well as granulocytopenia at 36% in kefir and 25% in yogurt group. Regarding the total count of lymphocytes in kefir group, although there was not significant change between W0 and W7, it is worthy to mention the case of a child that presented less than 2000 lymphocytes/µL (which indicates the risk of immunodepleting or mild protein malnutrition [START_REF] Kumarasamy | Total lymphocyte count (TLC) is a useful tool for the timing of opportunistic infection prophylaxis in India and other resource-constrained countries[END_REF]) at W0, but increased considerably at W7.

In relation to serum CPR analysis, it was found a positive result (CRP > 0.06 mg/dL according to the LICON qualitative Test) in one child of the kefir population at W1 and W7, while all children in the yogurt group were negative. It has been reported CRP values above 17.1 mg/dL are associated with IBD [START_REF] Manzano | Markers for bacterial infection in children with fever without source[END_REF]. However, as the test we used is a qualitative type, we cannot confirm the association among these two criteria. In this regard, we found significant correlation between the presence of IBS and CRP in W0 (r = 1, p < 0.005; Spearman r)

Unexpected Findings and Secondary Effects

Unexpected side effects were found in the commercial yogurt group, an exacerbation of gastroesophageal reflux was observed in a controlled patient who presented cyclic vomiting syndrome at the end of the study, as well as the appearance of two cases of dyspepsia. In the kefir group, one case of exacerbation of constipation was reported at the end of the study. No subjects excluded due to severity or respiratory complications were reported during the study.

Regarding the hematological markers not included in present study, after the blood analysis it was found the presence of hypochromic anemia before and after treatments in both kefir (54.7%) and yogurt (87.5%) groups, as well as granulocytopenia at 36% in kefir and 25% in yogurt group.

Discussion

Our results are similar to those reported in previous studies that have described poor weight gain and growth in children with CP [START_REF] Day | Growth patterns in a population of children and adolescents with cerebral palsy[END_REF][START_REF] Sullivan | Nutrition and growth in children with cerebral palsy: Setting the scene[END_REF][START_REF] Krick | Pattern of growth in children with cerebral palsy[END_REF][START_REF] Karim | Nutritional Status of Children with Cerebral Palsy-Findings from Prospective Hospital-Based Surveillance in Vietnam Indicate a Need for Action[END_REF][START_REF] Bandini | Body composition and energy expenditure in adolescents with cerebral palsy or myelodysplasia[END_REF]. Therefore, the weight gain obtained in the kefir group represents an important strategy to contribute to nutritional status in this population of children. According to Krick et al. [START_REF] Krick | Pattern of growth in children with cerebral palsy[END_REF], the weight-for-age curves in children with spastic quadriparesis show an annual weight gain trend of 1 kg per year (approximately) between 4 and 10 years of age. This means that the average gain of 375 g in the kefir group during the 7 weeks of exposure to treatment represents a considerable benefit. It has also been reported an increase in the weight of infants diagnosed with the highest risk of neurological damage and treated with various probiotic species such as Bifidobacterium infantis, Streptococcus thermophilus, and Bifidobacterium lactis [START_REF] Upadhyay | Cerebral palsy: Aetiology, pathophysiology and therapeutic interventions[END_REF][START_REF] Jacobs | prematurity and neurodevelopment: Follow-up of a randomised trial[END_REF]. Garcia et al. [START_REF] García Contreras | Lactobacillus reuteri DSM 17938 and Agave Inulin in Children with Cerebral Palsy and Chronic Constipation: A Double-Blind Randomized Placebo Controlled Clinical Trial[END_REF] found no significant differences in the weight of children with CP treated with pre-, pro-and synbiotics (Lactobacillus reuteri DSM 17938, and Agave inulin as a prebiotic). Moreover, it has been described that weight is lower in ambulatory children with a higher degree of athetosis, which is caused to energy expenditure due to this alteration in muscle tone [START_REF] Marchand | Nutrition Support for Neurologically Impaired Children[END_REF]. However, this study also revealed a significant correlation between having a higher degree of hypertonia or spasticity and having a lower weight or body mass index. Results on the weight status of children with CP are sometimes controversial, while Perenc et al. [4] reported an association between greater motor disability and low weight and nutritional risk Martínez de Zabarte et al. [START_REF] De Zabarte Fernández | Nutritional status of a population with moderate-severe cerebral palsy: Beyond the weight[END_REF] showed that the weight of children with CP tends to be in excess, although no significant differences were reported between overweight and GMFCS grade IV.

Regarding the REE, a relationship between the weight gain and the increase in REE has been reported in children with spastic quadriparesis CP in a malnutrition state who underwent in-hospital nutritional treatment [START_REF] Contreras | Gasto energético en niños con parálisis cerebral infantil y desnutrición moderada y grave durante la recuperación nutricia[END_REF], while a decrease in hypertonia but not a reduction in REE was shown in patients underwent physical and robotic therapy treatment [START_REF] El-Shamy | WalkAide Efficacy on Gait and Energy Expenditure in Children with Hemiplegic Cerebral Palsy[END_REF]. Our results agree with those reported by García et al. [START_REF] Contreras | Gasto energético en niños con parálisis cerebral infantil y desnutrición moderada y grave durante la recuperación nutricia[END_REF], since in the present study an association was found between weight gain and height, and with the increase in REE, when the children were treated with kefir. An inverse correlation was also found between the hypertonic degree and BMI, so that the greater the hypertonia the lower the BMI.

About the effect of kefir on FDDs, there is no similar type of study in children with disabilities, due to the fact that the diagnostic criteria and the version of the measurement instrument in Latin American Spanish of the Roma Foundation have been recently updated. However, different studies have suggested or reported the efficacy of the use of probiotics in the treatment of FDD in children, such is the case of IBS, functional dyspepsia, abdominal pain and migraine, mostly in controlled clinical trials using a single strain or combination with prebiotics [START_REF] Alberto | Trastornos Digestivos Funcionales, una Visión Latino-Iberoamericana[END_REF][START_REF] Rahmani | Evaluating the effects of probiotics in pediatrics with recurrent abdominal pain[END_REF][START_REF] Capozza | Probiotics and Functional Gastrointestinal Disorders in Pediatric Age: A Narrative Review[END_REF][START_REF] Ding | Probiotics for paediatric functional abdominal pain disorders: A rapid review[END_REF]. Although studies with multi-probiotic species intervention in children are limited, Guandalini et al. [START_REF] Capozza | Probiotics and Functional Gastrointestinal Disorders in Pediatric Age: A Narrative Review[END_REF] reported the benefits of various combinations of probiotic bacteria, including Bifidobacterium breve, Bifidobacterium longum, Bifidobacterium infantis, Lactobacillus acidophilus, Lactobacillus plantarum, Lactobacillus casei, Lactobacillus bulgaris, and Streptococcus thermophilus (a formulation currently available as Vivomixx in Europe and Visbiome in the US and very similar to the modern kefir formulation), on dyspepsia, IBS, functional abdominal pain, flatulence, bloating, among others. Interestingly, our results show that the few cases of dyspepsia, aerophagia, irritable bowel, functional abdominal pain and migraine, as well as several of these FDDs grouped into functional constipation that were diagnosed in children with CP at the beginning of the study, did not appear at the end of the modern kefir treatment, which corroborates that the supplementation with various combinations of probiotic bacteria contributes to the reduction in symptoms of various FDDs. In this same sense, it has also been described that traditional kefir helps to eradicate conditions such as dyspepsia and irritable bowel [START_REF] Bekar | Kefir Improves the Efficacy and Tolerability of Triple Therapy in Eradicating Helicobacter pylori[END_REF]. On the other hand, in a study carried out by Colson et al. [START_REF] Colson | Inflammatory Bowel Disease in Pediatric Patients with Cerebral Palsy[END_REF], it was reported an incidence of 198 cases of IBD per 100,000 children with CP, that is to say a higher prevalence than in the generall population. The unique case of IBD diagnosed in one child with CP in our study, showed them getting significantly better after modern kefir treatment. Strikingly, it was the only children with a positive CRP test, corroborating the association between IBD and CRP previously described [START_REF] Manzano | Markers for bacterial infection in children with fever without source[END_REF]. Although IBD was not present after modern kefir treatment, CRP test was still positive. However, it is important to consider that we used a qualitative test, so we can not exclude that modern kefir treatment decreased CRP levels, as it has been described to traditional kefir [START_REF] O'brien | The effects of postexercise consumption of a kefir beverage on performance and recovery during intensive endurance training[END_REF].

Particularly, in children with CP and chronic constipation, it has been reported that different probiotics contribute significantly to the reduction in this FDD, mainly with the strain L. reuteri DSM 17938 (1 × 10 8 UFC) combined with inulin as a prebiotic [START_REF] García Contreras | Lactobacillus reuteri DSM 17938 and Agave Inulin in Children with Cerebral Palsy and Chronic Constipation: A Double-Blind Randomized Placebo Controlled Clinical Trial[END_REF]. However, multi probiotic species combinations studies are limited. Our results show that constipation and stool consistency were significantly improved in children with CP treated with modern kefir. In adults, there is also evidence of the efficacy of multi-probiotics species treatment and a prebiotic (fructooligosaccharide) against constipation [START_REF] Jayasimhan | Efficacy of microbial cell preparation in improving chronic constipation: A randomized, double-blind, placebo-controlled trial[END_REF], using a granulated multi-probiotic species preparation (Hexbio) containing Lactobacillus acidophilus, Lactobacillus casei, Lactobacillus lactis, Bifidobacterium bifidum, Bifidobacterium longum, and Bifidobacterium infantis, (with 3 × 10 10 cfu per envelope) [START_REF] Jayasimhan | Efficacy of microbial cell preparation in improving chronic constipation: A randomized, double-blind, placebo-controlled trial[END_REF], or through the formulation of the strains L. paracasei Lpc-37, B. lactis Bl-04, L. acidophilus La-14, and L. plantarum Lp-115 [START_REF] Latvala | ACO Health Benefits of a Combination Probiotics; FlorMidabil TM[END_REF]. On the other hand, reflux (that under the Rome IV criteria is called functional vomiting syndrome) usually occurs in children with CP [START_REF] Jiménez | Patología gastrointestinal en niños con parálisis cerebral infantil y otras discapacidades neurológicas[END_REF][START_REF] Faleiros-Castro | Paralisia cerebral tetraplégica e constipação intestinal: Avaliação da reeducação intestinal com uso de massagens e dieta laxante[END_REF][START_REF] Maisawa | Characteristics of inflammatory bowel disease with an onset before eight years of age: A multicenter epidemiological survey in Japan[END_REF]. However, in the present study, it occurred in a reduced number of participants and in two cases of the control group that consumed conventional yogurt for 7 weeks, an unexpected finding that was considered as a negative effect of commercial yogurt in this population.

Regarding respiratory infections, the use of traditional kefir has shown significant effects in reducing the frequency of respiratory problems and complications, even against SARS-CoV2 [START_REF] Hamida | A protective dietary supplementation against viral infection[END_REF]. In our study, treatment exposure and the size of the sample were not enough to show an association between modern kefir intake and the reduction in respiratory infections. Moreover, it is known that the diversity of species contained in traditional kefir can reach more than 50 probiotics species [START_REF] Hamida | A protective dietary supplementation against viral infection[END_REF]. Particularly, the reduction in the frequency of viral respiratory infections and of the duration of related symptoms, including the common cold, has been associated with treatments composed of species of the lactobacillus genus: L. acidophilus, L. rhamnosus, L. fermentum, L. plantarum, Lactobacillus delbrueckii spp. Lactis, as well as bifidobacteria, Lactococcus lactis spp. cremoris, and Streptococcus thermophilus [START_REF] Lehtoranta | Probiotics in respiratory virus infections[END_REF]. Thus, the cases that showed reduction in common cold in the kefir group of the present study could be associated with the presence of similar probiotic species in the modern kefir, and although the results were not significant, 100% of the cases in which the common cold occurred frequently from one week to two months reduced this respiratory problem.

Different works have reported an association between kefir intake and lymphocyte number. Himada et al. [START_REF] Hamida | A protective dietary supplementation against viral infection[END_REF] showed an increase and improvement in the production of lymphocytes after the consumption of traditional kefir, and Kranewitter et al. [START_REF] Kranewitter | Beneficios de incorporar un simbiótico a la dieta de adultos mayores con infecciones recurrentes[END_REF] reported a growth and increase in the number of lymphocytes, especially CD4 and CD8 lymphocytes. Besides, the treatment with a kefir designed from lyophilizates of traditional kefir bacteria showed an increase in the number of lymphocytes at the level of intestinal villi [START_REF] Hsu | Supplementation Modifies Gut Microbiota Composition, Reduces Physical Fatigue, and Improves Exercise Performance in Mice[END_REF]. Our results are in accordance with the mentioned works, since it was possible to demonstrate an increase in the absolute number of lymphocytes in the kefir group. This effect of modern kefir might be mediating the decrease in the frequency of respiratory problems observed in children with CP, as it has been reported that a reduction in lymphocytes is associated with greater severity and poor prognosis of respiratory infections [START_REF] Illg | Analysis of absolute lymphocyte count in patients with COVID-19[END_REF], even now used for prognosis of complications from COVID-19. It is know that intestinal microbiota can exert an important immunoregulatory activity on airway immune response through intestinal dendritic cell activation that can be translocated to lungs and induce the differentiation of regulatory T cells, and by producing short-chain fatty acids (SCFAs) that influence the epithelial and immune cells for a better adaptive immune response [START_REF] Zolnikova | Application of probiotics for acute respiratory tract infections[END_REF]. In this sense, traditional kefir intake by adult individuals has been associated with an increase in the levels of SCFAs in plasma and intestinal lumen, especially butyrate, and to a reduced amount of circulating lipopolysaccharide [START_REF] St-Onge | Kefir consumption does not alter plasma lipid levels or cholesterol fractional synthesis rates relative to milk in hyperlipidemic men: A randomized controlled trial [ISRCTN10820810[END_REF][START_REF] Smoak | Kefir Is a Viable Exercise Recovery Beverage for Cancer Survivors Enrolled in a Structured Exercise Program[END_REF]. Probiotics have the ability to positively modulate the composition of the intestinal microbiota and hence reduce intestinal permeability, oxidative stress and inflammation [START_REF] Hiippala | The Potential of Gut Commensals in Reinforcing Intestinal Barrier Function and Alleviating Inflammation[END_REF][START_REF] Peluzio | Kefir and Intestinal Microbiota Modulation: Implications in Human Health[END_REF][START_REF] Gomes | Gut microbiota, probiotics and diabetes[END_REF][START_REF] Bell | Fermented Foods, and Gut Microbiota[END_REF]. Particularly, individual kefir probiotic species, such as Bifidobacteria, improving gut barrier function, and attenuate bacterial/endotoxin translocation [START_REF] Wang | The Role of Bifidobacteria in Gut Barrier Function After Thermal Injury in Rats[END_REF]. Whether modern kefir induces a change on gut microbiome of children with CP needs to be investigated. Thus, the aim of our current research is to evaluate microbiome and quantify SCFAs from children fecal samples included in this study.

Finally, we found clinical evidence of hypochromic anemia and granulocytopenia in a high percentage of the participating children with CP. Iron deficiencies and anemia have been reported in children with CP [4,[START_REF] Roy | Deficiencia de vitamina D y de hierro en niños y adolescentes con parálisis cerebral[END_REF][START_REF] El Shemy | Impact of Iron Deficiency Anemia on Functional Abilities and Muscle Strength in Children with Spastic Cerebral Palsy[END_REF], specifically relating this deficit to a greater degree of disability. The other unexpected finding was granulocytopenia, a condition not yet described for the population with CP. Although more research is needed, it could be associated with the intake of multiple drugs by children, as it usually occurs in this population due to various associated pathological conditions, including epilepsy [START_REF] Ibáñez | Population-based drug-induced agranulocytosis[END_REF].

Conclusions

In children with infantile CP, the addition in diets of a dairy-fermented drink called modern kefir, which contains 12 probiotics species might be a strategy not only for gaining body weight but also for reducing some digestive disorders, particularly the functional constipation, as well as inducing a positive regulation of the immune status that includes an increase in the total number of lymphocytes. These positive effects might contribute in the short or medium term to a better quality of life of children with CP. The administration of modern kefir might also be considered as a potential treatment in other conditions with immune or intestinal dysfunction.

Figure 1 .

 1 Figure 1.Presence of functional digestive disorders before and after treatment with modern kefir. FDD, functional digestive disorders; FCN, functional constipation; FD, functional dyspepsia, FN functional nausea FN; FAM, functional abdominal migraine; FAP, functional abdominal pain; IBS, irritable bowel syndrome; SEP, syndrome epigastrium pain.

Figure 2 .

 2 Figure 2. Presence of functional digestive disorders before and after treatment with conventional yogurt. FDD, functional digestive disorders; FCN, functional constipation; FD, functional dyspepsia; FN, functional nausea; CYVON, cyclic vomiting.

Figure 2 .

 2 Figure 2. Presence of functional digestive disorders before and after treatment with conventional yogurt. FDD, functional digestive disorders; FCN, functional constipation; FD, functional dyspepsia; FN, functional nausea; CYVON, cyclic vomiting.

8 Figure 2 .

 82 Figure 2. Presence of functional digestive disorders before and after treatment with conventional yogurt. FDD, functional digestive disorders; FCN, functional constipation; FD, functional dyspepsia; FN, functional nausea; CYVON, cyclic vomiting.

*

  McNemar test; ** FDD improvement percentage (W0 versus W7); 1CI, one case increment.

Figure 3 .

 3 Figure 3. Differences in stool consistency according to the Bristol scale before and after consumption of modern kefir. Wilcoxon test p = 0.007.

Figure 3 .

 3 Figure 3. Differences in stool consistency according to the Bristol scale before and after consumption of modern kefir. Wilcoxon test p = 0.007.

Figure 4 .

 4 Figure 4. Differences in stool consistency according to the Bristol scale before and after consumption of commercial yogurt. Wilcoxon Test p = 0.167.

Figure 4 .

 4 Figure 4. Differences in stool consistency according to the Bristol scale before and after consumption of commercial yogurt. Wilcoxon Test p = 0.167.

Figure 5 .

 5 Figure 5. Frequency of the common cold at week 0 and week 7 of the intervention. A, weekly; B, monthly; C, every 2 months; D, 2 times per year; E, never.

Figure 6 .

 6 Figure 6. Effect of Kefir on relative differential values of leukocytes in peripheral blood. The percentages of lymphocytes, monocytes and granulocytes were analyzed. Data are expressed as mean ± standard error of mean; n = 7 yogurt group and n = 9 kefir group.

Figure 5 .

 5 Figure 5. Frequency of the common cold at week 0 and week 7 of the intervention. A, weekly; B, monthly; C, every 2 months; D, 2 times per year; E, never.

Figure 5 .

 5 Figure 5. Frequency of the common cold at week 0 and week 7 of the intervention. A, weekly; B, monthly; C, every 2 months; D, 2 times per year; E, never.

Figure 6 .

 6 Figure 6. Effect of Kefir on relative differential values of leukocytes in peripheral blood. The percentages of lymphocytes, monocytes and granulocytes were analyzed. Data are expressed as mean ± standard error of mean; n = 7 yogurt group and n = 9 kefir group.

Figure 6 .

 6 Figure 6. Effect of Kefir on relative differential values of leukocytes in peripheral blood. The percentages of lymphocytes, monocytes and granulocytes were analyzed. Data are expressed as mean ± standard error of mean; n = 7 yogurt group and n = 9 kefir group.

Figure 7 .

 7 Figure 7. Effect of Kefir on absolute differential values of leukocytes in peripheral blood. The absolute number of lymphocytes, monocytes and granulocytes were analyzed. Data are expressed as mean ± standard error of mean; n = 7 yogurt group and n = 9 kefir group, * p < 0.05.

Figure 7 .

 7 Figure 7. Effect of Kefir on absolute differential values of leukocytes in peripheral blood. The absolute number of lymphocytes, monocytes and granulocytes were analyzed. Data are expressed as mean ± standard error of mean; n = 7 yogurt group and n = 9 kefir group, * p < 0.05.

Table 1 .

 1 Baseline characteristics of the study population.

		Yogurt Group n = 8	Kefir Group n = 11	p *
	Age	5.88 (4-9)	6.18 (4-8)	0.907
	Weight	14.21 (11.30-23.3)	14.41 (9.1-18.7)	0.590
	Height	1.00 (0.90-0.122)	1.03 (0.91-1.22)	0.399
	BMI	13.89 (11.74-15.65)	13.30 (11.15-15.32)	0.488
	REE	882 (677-1093)	992.72 (732-1252)	0.176

* Student's t-test. Data are expressed as mean and minimum and maximum value.

Table 2 .

 2 Anthropometric parameters and rest energy expenditure (REE) of the study population at initial (W0) and final 7 (W7) time.

			Weight (g)			Height (cm)			BMI (kg/m 2 )			REE (Kcal)
		W0	W7	p *	p **	W0	W7	p *	p **	W0	W7	p *	p **	W0	W7	p *	p **
	Yogurt (n = 8)	14.21 ±1.45	14.40 ±1.57		0.19	1.00 0.11 ±	1.01 0.04 ±		0.06	13.89 0.46 ±	13.80 0.47 ±		0.47	882.02 52.08 ±	835.25 71.42 ±		0.26
		14.41	14.77			1.03	1.045			13.35	13.36			992.72	1001.54
	Kefir (n = 11)	±	±		0.02	±	±		0.003	±	±		0.34	±	±		0.84
		0.91	1.00			0.02	0.02			0.40	0.40			58.72	74.61
				0.84				0.51				0.48				0.12

W, week; Data are expressed as mean ± SEM. * Student's t-test for independent samples ** Student's t-test for related samples.

Table 3 .

 3 Comparison of functional digestive disorders present at week 0 and week 7 of treatment.

	Functional Digestive Disorders under Rome IV Criteria
			YOGURT				KEFIR
		Cases W0	Cases W7	% **	p *	Cases W0	Cases W7	% **	p *
	Functional constipation	6	1	83.3	0.5	9	1	88.8	0.016
	Functional dyspepsia/postprandial distress syndrome	3	4	1CI	1.00	3	0	100	1.00
	Epigastric pain syndrome	0

Table 3 .

 3 Comparison of functional digestive disorders present at week 0 and week 7 of treatment.

	Functional Digestive Disorders under Rome IV Criteria
			YOGURT				KEFIR
		Cases W0	Cases W7 % **	p *	Cases W0	Cases W7	% **	p *
	Functional constipation	6	1	83.3	0.5	9	1	88.8	0.016
	Functional dyspepsia/postprandial dis-tress syndrome	3	4	1CI	1.00	3	0	100	1.00
	Epigastric pain syndrome	0	0	-	-	1	0	100	-
	Abdominal functional migraine	0	0	-	-	1	0	100	-
	Functional abdominal pain	0	0	-	-	1	0	100	-
	Irritable bowel syndrome	0	0	-	-	1	0	100	-
	Functional nausea	1	1	0		0	0	-	-
	Cyclic vomiting syndrome	0	1	1CI	-	0	0	-	-
	Aerophagia	0	0	-	-	1	0	100	-
	* McNemar test; ** FDD improvement percentage (W0 versus W7); 1CI, one case increment.

Table 4 .

 4 Comparison of significant differences for the presence of respiratory problems according to the IMCI criteria.

	Frequency

of Throat Infections W0 vs. W7 Frequency of Ear Infections W0 vs. W7 Frequency of the Common Cold W0 vs. W7 Frequency of Cough or Shortness of Breath W0 vs. W7 Frequency of the Pres- ence of Respiratory Se- cretions W0 vs. W7

	KEFIR	p * p **	0.081 0.157	0.003 0.317	0.012 0.257	0.39 0.157	0.285 1.000
	YOGURT	p * p **	0.480 0.157	0.064 0.317	0.101 0.564	1.000 0.157	0.490 0.083

p * Chi 2 test for differences between independent groups, p ** Wilcoxon signed rank test, asymptotic significance bilateral.

Table 4 .

 4 Comparison of significant differences for the presence of respiratory problems according to the IMCI criteria.

			Frequency of Throat Infections W0 vs. W7	Frequency of Ear Infections W0 vs. W7	Frequency of the Common Cold W0 vs. W7	Frequency of Cough or Shortness of Breath W0 vs. W7	Frequency of the Presence of Respiratory Secretions W0 vs. W7
	KEFIR	p * p **	0.081 0.157	0.003 0.317	0.012 0.257	0.39 0.157	0.285 1.000
	YOGURT	p * p **	0.480 0.157	0.064 0.317	0.101 0.564	1.000 0.157	0.490 0.083

p * Chi 2 test for differences between independent groups, p ** Wilcoxon signed rank test, asymptotic significance bilateral.

Microorganisms 2022, 10, x FOR PEER REVIEW

Acknowledgments:

We particularly thank the medical area and nursing staff of the CRIT Aguascalientes (Esther Hernández, Antonio Ponce) and cerebral palsy clinic coordinator, Alejandro Mendoza S. We appreciate the donation of kefir modern made by the company Alimentos Sello Rojo S.A. of C.V. (México) and of yogurt designed by Ing. David Velasco from Láctica Creativa (México). We also thank the families that participated in the study for their commitment, UAA students of the Biotechnology or Pharmaco-biology Chemist degrees for their technical assistance, Martin Rodriguez, Dra. Argentina Magallanes, Dra Mariana Sabas, for his advice in the conceptualization of this study.

Funding: This research was financed by Universidad Autónoma De Aguascalientes, (grant PIBB20-12C and MP-20-056).

Institutional Review Board Statement:

The investigation was adjusted to the provisions of the Universal Declaration of Human Rights of 1948 and the ethical standards of the Nuremberg Code in 1947. Similarly, compliance with current standards and laws was also monitored. Regarding the protection of personal data for minors in the possession of individuals, Law DOF O5-07-2010 and the General Law on the rights of children and adolescents, Law DOF 06-20-2018, México. The protocol did not put any participant at risk and was strictly adhered to the Declaration of Helsinki according to its last correction made during the 64th Annual Assembly organized by The World Medical Association (2013). The study was approved by the bioethics committees of the CRIT (Agreement: Externo 2020:001), as well as the committee of the Universidad Internacional Iberoamericana (UNINI) (Agreement number CR-054).

Informed Consent Statement:

According to laws in Mexico to allow and regulate scientific research that involve humans (Norma Oficial Mexicana NOM-012-SSA3-2012), informed consents were elaborated and signed from all parent's subjects involved in the study.

Conflicts of Interest:

The authors declare that they have no conflict of interest.


Rima Daoudi
email: rima.daoudi@ibisc.univ-evry.fr

Khalifa Djemal
email: khalifa.djemal@ibisc.univ-evry.fr

Abdelkader Benyettou
email: aek.benyettou@univ-usto.dz

Using Artificial Immune Algorithm for Fast Convergence of Multi Layer Perceptron in Breast Cancer Diagnosis Application

Keywords: Multi Layer Perceptron, Artificial Immune System, Classification, Breast Cancer, Mean Squared Error, Speed Convergence

In this paper, a Multi Layer Perceptron (MLP) based Artificial Immune System (AIS) is presented for breast cancer classification. The proposed algorithm integrates clonal selection principle of AIS in MLP learning to reduce its computational costs and accelerate its convergence to a Mean Squared Error Threshold (MSE th ) set by the user. Applied on the Wisconsin Diagnosis Breast Cancer database (WDBC), the results show that combining Artificial Immune Systems and Neural Networks is effective. Indeed, a significant reduction of computation time has been obtained with a slight improvement of classification accuracy.

97.2%, respectively. Classification accuracy obtained by the application of a feature extraction algorithm using a hybrid of K-Means and Support Vector Machine algorithms in [START_REF] Zheng | Breast cancer diagnosis based on feature extraction using a hybrid of k-means and support vector machine algorithms[END_REF] is 97.38%. Work in paper [START_REF] Marcano-Cedeño | Wbcd breast cancer database classification applying artificial metaplasticity neural network[END_REF] presented an Artificial Metaplasticity Neural Network reaching a classification accuracy of 99.26%. Authors in [START_REF] Katsis | Using artificial immune recognition systems in order to detect early breast cancer[END_REF] presented a decision support system for early breast cancer detection; the proposed method employs a Correlation Feature Selection procedure and AIRS algorithm for classification, the classification accuracy obtained is 83.33%. Work in [START_REF] Sharma | Clonal selection algorithm for classification[END_REF] proposed a new artificial immune algorithm which uses the clonal selection principle obtaining a classification accuracy of 93.4%. Several Improvements on the artificial immune algorithm CLONALG were applied in [START_REF] Daoudi | An immune-inspired approach for breast cancer classification[END_REF] and [START_REF]Cells clonal selection for breast cancer classification[END_REF], classification accuracies were 94.40% and 98.58% respectively. This work aims to use the advantages of Artificial Immune Systems (AIS), to enhance the learning of Multi Layer Perceptron neural network in order to perform a quick and efficient diagnosis of breast cancer.

A. Multi Layer Perceptron Neural Network (MLP)

Artificial Neural Networks (ANNs) are computational models that simulate the functions of recognition of human forms. They are powerful parallel models that provide excellent resolution of problems in many areas. Neurons are interconnected with connection links which have weights that are multiplied by the signal transmitted in the network [START_REF] Kandel | Principles of neural science[END_REF]. The output of each network is determined by use of an activating function as the Sigmoid or Gaussian [START_REF] Andina | Error weighting in artificial neural networks learning interpreted as a metaplasticity model[END_REF].

Among all the various types of ANN architectures, Multi Layer Perceptron is the well known and the most frequently used [START_REF] Hamid | Accelerating learning performance of back propagation algorithm by using adaptive gain together with adaptive momentum and adaptive learning rate on classification problems[END_REF]. Basically MLP network is composed of an input layer, one or more hidden layers and one output layer. It is a supervised learning model which uses the Back Propagation (BP) algorithm to improve its efficiency. That consists of adjusting the network weights in order to reduce the Mean Squared Error (MSE) obtained by:

𝑀𝑆𝐸 = ∑ 𝑁 𝑘=1 (𝐷 𝑘 -𝑌 𝑘 ) 2 𝑁 ( 1
)
Where 𝑁 is the total number of data, 𝐷 𝑘 is the desired output of the 𝑘 𝑡ℎ data, and 𝑌 𝑘 is the actual output of the 𝑘 𝑡ℎ

I. INTRODUCTION

The correct diagnosis of breast cancer has become a major problem in the medical field since this type of cancer is ranked among the leading causes of death among the ladies. Although some risk reduction can be achieved through prevention, strategies in this sense are not able to eliminate the majority of breast cancers that occur in low-and middle-income countries. Early detection remains the main way to fight against this disease; it improves the chances of survival as well as breast cancer outcome. Indeed, if the cancerous cells are detected before spreading to other organs, the survival rate for patients is more than 97% [1]. For an ultimate diagnosis, the patient undergoes several tests which go from the mammography until the biopsy in certain difficult cases. In order to help experts to reduce the number of errors they can do and minimize the number of unnecessary biopsies, Computer-Aided Diagnosis systems (CAD) are increasingly used to directly reach the final diagnosis.

Several articles have been published presenting new CAD systems, authors in [START_REF] Karabatak | An expert system for detection of breast cancer based on association rules and neural network[END_REF] proposed an automatic diagnosis system for detecting breast cancer based on Association Rules (AR) and Neural Network, they used AR for reducing the dimension of breast cancer database and the MLP neural network as classifier, the classification accuracies were 95.6% for four inputs and 97.4% for eight inputs. In [START_REF] Goodman | Artificial immune system classification of multiple-class problems[END_REF] three different methods, Optimized Learning Vvector quantization (LVQ), big LVQ, and Artificial Immune Recognition System (AIRS), were applied and the obtained accuracies are 96.7%, 96.8%, and data obtained by:

𝑌 𝑘 = 𝑓 ( ∑ 𝑖 𝑊 𝑖 .𝑋 𝑖 ) (2)
Where 𝑋 𝑖 corresponds to the input vector, and 𝑊 𝑖 is the weight vector and 𝑓 the activation function.

Despite its great success, MLPs showed some limitations and problems during training. A serious drawback of MLPs is the slow rate of convergence [START_REF] Rumelhart | Learning internal representations by error propagation[END_REF]. Several modifications have been proposed to enhance this algorithm, but no one is able of producing satisfactory results with fast convergence, thus the search for an approach to speed-up its convergence and improve its performance still remains important.

B. Artificial Immune System (AIS)

As ANNs, models of Artificial Immune Systems have been mainly developed for analyzing the behavior of the Natural Immune System (NIS) in the field of medicine, but later its properties as pattern recognition, robustness; its hybrid structures, distributed processing and self-organization took the attention of some researchers. AIS is a distributed system that can perform classification tasks, recognition and learning using the extraction process, communication and memorization.

The major part of AIS work to date has been the development of three algorithms derived from more simplified models; negative selection [START_REF] Dasgupta | Anomaly detection in multidimensional data using negative selection algorithm[END_REF], clonal selection [START_REF] De Castro | The clonal selection algorithm with engineering applications[END_REF] and immune networks [START_REF] De Castro | ainet: an artificial immune network for data analysis[END_REF]. The immune principles used in the most AIS algorithms are: evaluation of affinity, selection, cloning and mutation. The goal is to build a consistent set of memory cells that will be used in classification step for the recognition of unknown examples by the system.

Because the human immune system operates as a cognitive mechanism that recognizes patterns that may not be recognized by the nervous system, the AIS can be used as a complement to the neural network architectures. As well, new structures based on immunology can be proposed as an alternative to ANNs, or structures of hybrid networks composed of both systems .

In this study, a Multi Layer Perceptron based Artificial Immune System is presented for classifying breast lesions in Benign / Malignant. This method consists of using the clonal selection principle in MLP learning to accelerate its convergence for a specified error without decreasing its accuracy.

The rest of the paper is organized as follows: in the next section, we present the Wisconsin Diagnosis Breast Cancer database used in evaluation. The description of the proposed algorithm is given in section3. Section 4 provides a discussion of the obtained results and we conclude our work in section 5.

II. WISCONSIN DIAGNOSIS BREAST CANCER DATABASE (WDBC)

In this study, the Wisconsin Diagnosis Breast Cancer Database is used [START_REF] Repository | Breast cancer wisconsin (diagnostic) data set[END_REF]. WDBC consists of data from 569 breast fine needle aspirate (FNA) cases containing 32 descriptive features where the two first features correspond to a unique identification number and the diagnosis status (benign or malignant). The rest 30 features are computed from a digitized image of a FNA of a breast mass. They describe characteristics of the cell nuclei present in the image. Samples of FNA images are shown in figure 1. The case distribution includes 357 cases of benign breast changes and 212 cases of malignant breast cancer. The descriptive features are recorded with four significant digits and include:

III. PROPOSED MLP-AIS ALGORITHM

In this section, the MLP based AIS approach. In order to increase convergence speed and reduce computational costs without affecting accuracy, this study uses a Clonal Selection Artificial Immune System to assist the MLP to converge more quickly towards a Mean Squared Error Threshold (𝑀𝑆𝐸 𝑡ℎ ) set by the user. The proposed AIS-MLP algorithm adds the principles of cloning and mutation to the training algorithm of MLP to help in search for optimal weights that minimize the mean squared error. The main purpose of an immune system is to recognize foreign cells that attack the body, if the difference between the antibody and the foreign cell (antigen) is little, affinity between this antigen and the antibody is great which mean that recognition is more likely. For a neural network the objective is to update the connection weights in order to minimize the distance between the obtained output and the desired output. This distance is represented by Mean Squared Error (MSE) between the two outputs, in our algorithm the affinity itself the MSE (1). We present in next subsections a description of each step of the proposed algorithm.

A. Normalization

Before starting the algorithm, the database is normalized in [0, 1], according to the following equation:

𝑅 = 𝑋 𝑖 -𝑋 𝑚𝑖𝑛 𝑋 𝑚𝑎𝑥 -𝑋 𝑚𝑖𝑛 (3)
Where 𝑋 𝑚𝑖𝑛 is the minimum of the data 𝑋 𝑖 for all 𝑖, 𝑋 𝑚𝑎𝑥 is the maximum of the data 𝑋 𝑖 for all 𝑖, and 𝑋 𝑖 is the 𝑖 𝑡ℎ data of data 𝑋.

B. MLP Weights Initialization

Randomly generate the initial weights of the neural network. The goal of this work is to update these weights in every iteration of the algorithm to find the optimal weights that minimize the mean squared error in minimal time. The choice of these initial weights directly affects the results of the algorithm. Calculate the MSE using these initial weights.

C. Repeat until the 𝑀𝑆𝐸 <= 𝑀𝑆𝐸 𝑡ℎ set by the user 1) Backpropagation and weights update :

To correct obtained error, we must change the weight 𝑊 𝑗,𝑖 so as to minimize the error 𝐸 calculated by:

𝐸 = ∑ (𝐷 𝑗 -𝑌 𝑗 ) 2 (4)
Where 𝐷 𝑗 and 𝑌 𝑗 are respectively the desired and the actual outputs of the 𝑗 𝑡ℎ neuron.

The principle of backpropagation is used to calculate Δ𝑊 𝑗,𝑖 to update the weights of MLP according to the equation:

𝑊 𝑗,𝑖+1 = 𝑊 𝑗,𝑖 +Δ𝑊 𝑗,𝑖 (5)
Where:

• The index 𝑗 represents the neuron for which the weight is to adapt.

• The index 𝑖 represents a neuron of the previous layer relative to neuron 𝑗.

The variation of Δ𝑊 𝑗,𝑖 will depend on the gradient of this error, according to the gradient descent algorithm. This can be expressed by the following equation:

Δ𝑊 𝑗,𝑖 = -𝜇. ∂𝐸 ∂𝑊 𝑗,𝑖 (6)
With 0 ≤ 𝜇 ≤ 1 representing the Learning Step-Size. A detailed description of PB algorithm can be found in [START_REF] Abid | Accelerating the multilayer perceptron learning with the davidon fletcher powell algorithm[END_REF] 2) Evaluation: This step consists in computing the mean squared error using the new updated weights (𝑀𝑆𝐸 𝐵𝑃 ).

3) Cloning: In AIS cloning consists in creating copies of selected antibodies to increase their competitiveness. At the end of this step we dispose of a number of identical copies of the updated weights matrix, these clones shall undergo to the operator of mutation in the following step.

4) Mutation:

The mutation is a random change in one or more positions of the attribute values of the clone. This process is intended to train the clones to become better or worse antibodies, less good clones are eliminated by selection, there will remain only the best. In our algorithm, the mutation consists of reviewing some clones values by a random process in order to find a better weight matrix than the original (the updated one).

5) Evaluation and selection of the best mutated clone:

In this step we compute the affinity of all the mutated clones in the previous step and we select the one who maximizes the value of affinity (minimizes MSE). A comparison between this minimal MSE and 𝑀𝑆𝐸𝐵𝑃 calculated in step C.2 is made, if the affinity of the best clone is better than that of the original one, then an update of the weights matrix is done by replacing the original matrix by the best mutated clone and the 𝑀𝑆𝐸 𝐵𝑃 by the MSE of this best clone.

At the end of the iteration, we test if it fulfils the criterion for termination (𝑀𝑆𝐸 ≤ 𝑀𝑆𝐸 𝑡ℎ ), If not, we return to step C.1 If yes, the algorithm ends. The final weights matrix represents the solution of the algorithm i.e. the optimal weights of the MLP which will be used for the classification of breast cancer. The algorithmic description of the proposed modified MLP is given by pseudo-code shown in algorithm 1.

IV. EXPERIMENTAL RESULTS

The overall results of this research are determined in this section. First we present the parameters used in evaluation, then all achieved tests are given and discussed in subsequent sections.

A. Algorithm parameters

In our analysis the MLP model is composed of 30 inputs which represent the 30 features of the WDBC, and one hidden layer. The Mean squared Error (𝑀𝑆𝐸 𝑡ℎ ) Threshold was set to 10 -4 and the activation function used is the sigmoid function defined by:

𝑓 ( )= 1 1+𝑒 -𝑥 (7)
It is necessary to control two parameters of the MLP: the Number of Neurons in the Hidden Layer, and the Learning Step-Size (𝜇). To determine the best combination of these two parameters, we selected five values for the Learning Rate (LR): 0.1, 0.2, 0. From table 1 we can see that the best classification result is obtained with a learning step-size of 0.25 and 10 neurons in the hidden layer. For the AIS algorithm, we fixed the number of clones to 5 and the affinity measure is the MSE.

B. 2) Results and Discussion

Based on tests performed above to set the parameters of the algorithm, the performance of AIS-MLP is studied on WDBC using in Matlab R ⃝ (Matlab R2013a 1.1.0.604. We shared the database into 75% for training and 25% for the test. Table 3 presents the results of five successive runs of MLP and AIS-MLP using different examples for train and test in each run. The average of this five runs is taken as final result.

From the table above it is easily noticeable that the proposed approach greatly reduces the convergence time of the MLP to the (𝑀𝑆𝐸 𝑡ℎ ) set by the user, with a slight improvement of classification accuracy. The necessary number of iterations to converge is reduced by more than 75%, and execution time is reduced by 50%. This reduction of computational costs is done thanks to the mutation operator that helps the algorithm to converge faster to the desired error by changing the values of the weight of MLP by a random process, and update the weights only if they have better affinity than their original cell. Figures 2 and3 plot respectively comparisons of convergence curves and computational costs of the two approaches on WDBC. To validate our method, Table 4 provides final evaluation based on the comparison of classification accuracies of our algorithm and previous methods from literature applied on WDBC. As can be seen from the results AIS-MLP approach obtains excellent classification accuracy.

Mean Squared Error

  Fig. 1. Images taken using the Fine Needle Aspirate test

Fig. 2 .Fig. 3 .

 23 Fig. 2. Comparison between Convergence curves of MLP and AIS-MLP on WDBC

Table 1

 1 5, 0.8 and 1 and five other values for the Number of Neurons in the Hidden Layer (NNHL) : 2, 5, 10, 15and 20 neurons. The classification accuracies of each test are listed in table 1.

	NNHL	𝜇	0.1	0.25	0.5	0.75	1
	2		98.50 98.50 98.12 97.75 96.25
	5		98.50 97.75 98.32 93.63 90.63
	10		98.50 99.06 89.51 82.39 72.28
	15		96.62 95.88 77.15 56.92 56.92
	20		95.88 93.63 53.08 43.44 44.19

. Classification accuracies of different values of training rate and hidden neurons on WDBC

Table 2

 2 summarizes the setting used in evaluation.

	Parameter	Value
	Number of inputs	30
	Number of hidden layers	1
	𝑀𝑆 𝑇ℎ𝑟𝑒𝑠ℎ𝑜𝑙𝑑	10 -4
	𝜇	0.25
	NNHL	10
	Number of clones	5
	Affinity measure	MSE

Table 2 .

 2 Optimal parameters used in evaluation

Table 3 .

 3 Average of Performances of 5 successive runs of MLP and AIS-MLP on WDBC

	Algorithm	Accuracy (%) iterations Nb	Execution Time (s)
	MLP	99.32	2705	44.01
	AIS-MLP	99.39	670	22.84

Author

Method

Classification Accuracy [START_REF] Vazirani | Diagnosis of breast cancer by modular neural network[END_REF] MNN 98.22% RBFNN 97.25% [START_REF] Guo | Breast cancer diagnosis using genetic programming generated feature[END_REF] SVM 96.32% This study MLP 99.32% AIS-MLP 99.39% In this paper, we presented an improved MLP neural network algorithm. The approach uses the Artificial Immune Systems to find the optimal weights of the neural nnetwork which minimize the MSE in a minimum of time. Based on the principles of Back Propagation of MLP and the mutation of the AISs, the proposed hybrid algorithm shows a great performance obtaining a total classification accuracy of 99.39% while significantly reducing the calculation costs comparing to the classical MLP neural network. Moreover, the results show that the combination of the AIS and the MLP can enhance the performance of the neural networks. Based on this work, we can say that the proposed approach can be used as a diagnostic tool in conjunction with other medical tests for early detection of breast cancer.


Sylvain Magne
email: sylvain.magne@cea.fr

Nicolas Legrand

Stéphane Ertz

Gwenael Jouvin

Julien Lebecq

Guillaume Laffont

Pierre Ferdinand

Vivien André

Pascale Pommier

Laurent Boissonnet

Pour Le Controle En

Ligne De

L A Planeite

MINCES PRODUITES PAR LAMINAGE A FROID D E Toles

Hamid Zahrouni

Stressomètre haute performance à réseaux de Bragg pour le contrôle en ligne de la planéité de toles minces produites par laminage à froid

Keywords: laminage, bande, planéité, rouleau, fibre optique, réseaux de Bragg

teaching and research institutions in France or abroad, or from public or private research centers.

INTRODUCTION

Les marchés de l'emballage et de l'automobile poursuivent un objectif de réduction des épaisseurs des produits laminés. Dans l'emballage, cette tendance conduit à une réduction de matière et des déchets à recycler. Pour l'automobile, elle est essentiellement motivée par des réductions de coût, de poids et indirectement de consommation et de pollution des véhicules.

Les problèmes de planéité constituent un souci majeur pour les industriels du laminage car leurs produits sont toujours plus larges, plus minces et plus durs. Les problèmes de flambage des tôles minces (quelques dixièmes de mm) obtenues par laminage à froid deviennent alors critiques. Les fortes réductions d'épaisseurs peuvent créer des contraintes résiduelles importantes (surtractions) en bords de rives avec un risque de rupture du produit et des défauts de type « frisettes » (sous-traction) peuvent également apparaitre. Les défauts de planéité qui en résultent (inhomogénéité de pression dans l'emprise) conduisent à une différence de traction dans la largeur.

Un dispositif de contrôle en ligne de la planéité agit en boucle fermée. Le signal utile pour l'exploitant (donnée d'entrée des actionneurs en cage de laminoir) est le vecteur de planéité, indicateur de la planéité latente, vecteur différentiel de pression obtenu par soustraction du relevé linéaire avec la pression moyenne induite par la traction de bande. Celui-ci est injecté dans la boucle de contre-réaction du système d'asservissement des actionneurs pour agir sur la distribution de pression de laminage dans l'emprise et ainsi corriger les défauts de planéité.

Le contrôle des faibles épaisseurs constitue également un défi technologique en termes de cadence d'acquisition, de résolution spatiale et en effort. La planéité latente est essentiellement évaluée à l'aide de rouleaux de planéité ou stressomètres (stressometer, shapemeter) insérés dans le circuit de défilement de bande dans le but de mesurer le profil de pression appliqué par la bande le long de sa génératrice (i.e. parallèlement à son axe) [START_REF] Legrand | Review of shapemeter rolls technologies to measure strip share in hot and cold rolling conditions[END_REF][START_REF] Molleda | On-line flatness measurement in the steelmaking industry[END_REF]. La bande est alors délibérément mise en flexion afin de générer un effort moyen proportionnel à la traction de bande et à l'angle d'embarrage (compris entre 5° et 180°). Les rouleaux commerciaux (ABB, BFI, …) sont constitués d'un cylindre plein comportant une ou plusieurs génératrices (typ. 1,5 m de longueur, 4 mesures par tour) incorporant des capteurs de différentes technologies (piezorésistif, inductif, etc.), de conception ancienne et d'encombrement important. De plus, la résolution spatiale des stressomètres actuels (~ 25 à 50 mm) est insuffisante à proximité des rives des produits laminés où des variations brusques de contraintes (prédites par simulation) sont indétectables. Le développement d'un stressomètre de haute résolution spatiale (millimétrique) et de grande sensibilité de mesure (pouvoir distinguer un défaut de 5 UI, soit 50 µm/m) est donc nécessaire pour mesurer la planéité sous traction dans ces conditions. De plus, pour éviter de marquer les pièces laminées, les rouleaux sont souvent chemisés par une frette continue de faible épaisseur (~ 2 mm) transmettant les efforts aux capteurs logés dessous, mais qui a néanmoins l'inconvénient de dégrader la résolution spatiale (couplage axial des efforts). Une résolution en pression de l'ordre du kPa est recherchée pour une gamme de plus de 3 ordres de grandeur ([kPa-MPa]) (e.g. la pression de contact exercée par une bande de 0,2 mm d'épaisseur est d'environ 50 kPa pour un angle d'embarrage   20° et une traction de 10 MPa). Enfin, la vitesse de défilement de bande peut atteindre 1 000 m/min en production, imposant une cadence d'acquisition minimale de l'ordre du kHz.

La métrologie par réseaux de Bragg, également mise en oeuvre pour des rouleaux destinés à l'industrie papetière [START_REF] Ecke | Continuous pressure and temperature monitoring in fast rotating machine rolls using optical FBG sensor technology[END_REF], est proposée par le CEA LIST et Arcelor-Mittal (AM R&D) dans le contexte d'un projet ANR (PLATFORM) afin d'aboutir à une preuve de concept d'un stressomètre innovant à fibres optiques.

PRINCIPE DE FONCTIONNEMENT DU STRESSOMETRE A FIBRES OPTIQUES

Le stressomètre prototype mis au point par le CEA LIST et AM R&D se présente sous la forme d'un cylindre de 30 cm de diamètre et de 30 cm de longueur (Fig. 1 -gauche).

Un logement de section en forme d'écusson a été usiné sous la surface, formant une frette de 1 mm d'épaisseur et un second logement d'équilibrage (Ø = 54,5 mm) a été aménagé à 180°. La frette ainsi formée a été découpée en lamelles afin de réduire le couplage axial des efforts. Une série de 25 réseaux a été photo-inscrite sur la même fibre, déployée à l'intérieur du logement en écusson. Chaque réseau de Bragg est ainsi collé de façon orthoradiale et subit une déformation proportionnelle à la pression exercée sur la lamelle dont le dimensionnement a été mené par AM R&D à l'aide d'un logiciel de simulation par éléments-finis (Abaqus, Dassault Systèmes).

Un premier étalonnage en effort est réalisé à l'aide d'une presse et d'un capteur d'effort (sensibilité ~ 50 à 60 pm/N). Un second étalonnage statique en pression est réalisé sur pilote de défilement de bande (Fig. 1 -droite). Les sensibilités obtenues sont de l'ordre de 6 à 13 µm/m.kPa. La performance de détection est évaluée par un critère de « capabilité » C = 0,25. m / c où  m et  c sont respectivement l'incertitude recherchée sur la mesure de planéité (5 UI) et l'incertitude sur la mesure différentielle (~ 4 µm/m). Pour une bande d'acier de 0,1 mm, ce critère est de l'ordre de 3, proche de ceux des meilleurs dispositifs commerciaux. En rotation, le signal optique est extrait à l'aide d'un joint tournant optique monomode (Princetel MJXA-155) connecté sur l'un des paliers. La pression dans le contact est déduite par soustraction d'un premier signal obtenu lorsque la bande est en contact avec un second signal de référence acquis lorsque la bande est hors contact. La compensation en température est ainsi obtenue naturellement lors de la rotation du rouleau.

ESSAIS SUR CIRCUITS DE DEFILEMENT DE BANDES ACIER (AM) ET ALUMINIUM (C-TEC)

La figure 2

CONCLUSION

Un stressomètre prototype à fibres optiques a été mis au point par AM R&D et le CEA LIST, de « capabilité » équivalente aux meilleurs dispositifs commerciaux. L'emploi de réseaux de Bragg comme jauges extensométriques permet d'améliorer la résolution spatiale (5 mm) tout en simplifiant la connectique et en assurant une mesure synchrone sur une génératrice grâce au multiplexage spectral, rendant la mesure de planéité moins sensible aux perturbations de production. La répartition de la pression sur une génératrice est ainsi mesurée à haute cadence (kHz) et présente une dynamique de plus de 3 ordres de grandeur ([kPa-MPa]) et une résolution de l'ordre du kPa. Une preuve de concept a été apportée sur lignes pilotes (AM) acier et aluminium (C-TEC).

Fig. 1 :

 1 Fig. 1 : Vue du stressomètre à fibres optiques mis au point par le CEA LIST et ARCELOR-MITTAL (gauche) et insertion dans un circuit de défilement de bande (AM R&D, droite).

  illustre le schéma expérimental mettant en oeuvre l'unité de mesure BraggLight (CEA LIST) pour les démonstrations. Cette unité incorpore une source optique (fibre dopée erbium émettant en régime d'émission spontanée amplifiée) générant un spectre continu dans la bande C+L ([1510 nm-1580 nm]) et un spectromètre intégré (IMON-512, Ibsen) équipé d'une barrette CMOS de 512 photodétecteurs InGaAs (G11620, Hamamatsu). Les longueurs d'onde de Bragg sont déterminées par un algorithme d'ajustement gaussien et stockées en mémoire à la cadence de 1 kHz.

Fig. 2 :

 2 Fig. 2 : Schéma optique de montage du stressomètre prototype sur circuits de défilement de bande

Fig. 3 :

 3 Fig.3: Signal de déformation obtenu sur un réseau de Bragg équipant le stressomètre prototype durant un test de défilement de bande acier (   X % de 300 kg).