Elif Hindié
email: elif.hindie@chu-bordeaux.fr

Kenneth B Ain
email: kenneth.ain@uky.edu

Slimane Zerdoud
email: zerdoud.slimane@iuct-oncopole.fr

Anca M Avram
email: ancaa@umich.edu

Discussion on Radioactive Iodine Treatment of Hyperthyroidism and The Risk of Induced cancer Traitement par iode-131 des hyperthyroïdies et risque de cancer : mythe ou réalité

Iodine-131 ( 131 I, radioiodine) has been used for over eight decades for the treatment of Graves' disease, either as initial therapy or following failure of thionamides, as well as for the treatment of autonomous thyroid nodules. 131 I treatment is simple to administer, effective, and relatively inexpensive. Recently, there has been some turmoil after a study published in JAMA Internal Medicine reported an increased risk of cancer from 131 I treatment. The impact was of short duration however, as the paper received severe criticisms from many nuclear medicine physicians as well as from endocrinologists. Here we explain why that paper's conclusions are doubtful. We also review the major data on the topic of 131 I therapy of hyperthyroidism and the risk of cancer.

Hyperthyroidism, 131 I, radioactive iodine, cancer, secondary cancer, radioiodine therapy

Résumé

L'iode-131 est utilisé depuis presque huit décennies dans le traitement de l'hyperthyroïdie liée à une maladie Basedow ou à une pathologie nodulaire toxique. Le traitement par 131 I est simple à administrer, efficace, et relativement peu onéreux par rapport aux autres alternatives thérapeutiques. Récemment, il y a eu une certaine turbulence suite à une publication dans « JAMA Internal Medicine » signalant un excès de cancer lié au traitement par 131 I. L'impact a toutefois été de courte durée, cette étude ayant essuyé un grand nombre de critiques méthodologiques de médecins nucléaires à travers le monde mais aussi d'endocrinologues.

Dans ce papier nous expliquons les faiblesses de cette étude et résumons les données de diverses autres études sur le sujet.

Hyperthyroïdie, 131 I, « irathérapie », cancer, cancer radio-induit

Concerns on whether iodine-131 ( 131 I, radioactive iodine, RAI) treatment for hyperthyroidism confers an increased risk of cancer have always been a subject of high interest. Recently there has been a transient decline in the number of patients referred for 131 I after a paper published in a major journal "JAMA Internal Medicine" reported an increased risk of cancer [START_REF] Kitahara | Association of Radioactive Iodine Treatment With Cancer Mortality in Patients With Hyperthyroidism[END_REF]. This trend was of short duration, however; here we explain why that paper's conclusions are doubtful.

The study by Kitahara et al. was a new analysis of the Cooperative Thyrotoxicosis Therapy

Follow-up Study (CTTFS) which was last updated in 1998 [START_REF] Doody | Cancer mortality following treatment for adult hyperthyroidism. Cooperative Thyrotoxicosis Therapy Follow-up Study Group[END_REF]. In this new analysis, Kitahara et al introduced a biokinetic model of multi-organ dosimetry to retrospectively estimate patient-specific radiation doses at organ level and projected that 131 I therapy was responsible for 14% of the breast cancer deaths and 7% of deaths from other solid cancers [START_REF] Kitahara | Association of Radioactive Iodine Treatment With Cancer Mortality in Patients With Hyperthyroidism[END_REF]. Their analysis included 18805 patients (mean study entry age 49 years; 78% women; 93.7% had Graves' disease; 34.1% had multiple 131 I treatments). The mean total administered 131 I activity was 391 MBq (~10.6 mCi) (tertiles: 160, 289, and 724 MBq). In a projection of their findings, considering patients receiving 370-555 MBq 131 I for Graves' disease, the authors concluded that for every 1000 patients treated with 131 I at the age of 50, an estimated lifetime excess of 18 to 31 solid cancer deaths would occur (including 4 to 6 breast cancers) and that the majority of them (~80%) would occur more than 20 years after treatment [START_REF] Kitahara | Association of Radioactive Iodine Treatment With Cancer Mortality in Patients With Hyperthyroidism[END_REF].

Although the publication received extreme attention from the media, with an Altmetric score exceeding 300, many nuclear physicians around the world, having scrutinized the data, raised skepticism as to the method and conclusions, with many letters and editorials rapidly appearing in the main nuclear medicine journals [START_REF] Zhang | Regarding the manuscript entitled "Association of Radioactive Iodine Treatment With Cancer Mortality in Patients With Hyperthyroidism[END_REF][START_REF] Giovanella | Use of anti-thyroid drugs in patients with hyperthyroidism: a case for shared decision-making[END_REF][START_REF] Greenspan | There Is No Association of Radioactive Iodine Treatment with Cancer Mortality in Patients with Hyperthyroidism[END_REF][START_REF] Chen | Radioactive Iodine Treatment and Cancer Mortality in Hyperthyroid Patients: Questioning Standard Clinical Practice Requires Indisputable Scientific Data[END_REF].

In an Invited Commentary published in the Journal of Endocrinology and Metabolism we called attention to significant design flaws in the Kitahara et al. study highlighting the following points [START_REF] Hindié | Association of Radioactive Iodine Treatment of Hyperthyroidism With Cancer Mortality: An Unjustified Warning?[END_REF].

The analysis assessed whether greater absorbed radiation doses to specific organs were associated with increased mortality risk from specific cancers; however, because this analysis was negative for haematological cancers and for the 16 analyzed solid cancers (except borderline significance for breast cancer), the authors decided to sum-up all solid cancers, while arbitrarily using the dose to stomach as the reference [START_REF] Kitahara | Association of Radioactive Iodine Treatment With Cancer Mortality in Patients With Hyperthyroidism[END_REF]. The rationale for this additional analysis, which is not based on the initially planned analysis of absorbed organ dose, is unclear and unjustified [START_REF] Hindié | Association of Radioactive Iodine Treatment of Hyperthyroidism With Cancer Mortality: An Unjustified Warning?[END_REF].

CTTFS included patients treated between 1946 and 1964 with clinical follow-up to 1968, and many patients were lost to follow-up, with no information available for a large percentage of patients in this last analysis [START_REF] Kitahara | Association of Radioactive Iodine Treatment With Cancer Mortality in Patients With Hyperthyroidism[END_REF][START_REF] Hindié | Association of Radioactive Iodine Treatment of Hyperthyroidism With Cancer Mortality: An Unjustified Warning?[END_REF].

The CTTFS study was initially designed to compare cancer risk between RAI-treated patients and those treated differently. The last report of the CTTFS data by Ron et al. [START_REF] Doody | Cancer mortality following treatment for adult hyperthyroidism. Cooperative Thyrotoxicosis Therapy Follow-up Study Group[END_REF], with 21 years mean follow-up, concluded that RAI was not linked to cancer deaths (except thyroid cancer, with the underlying thyroid disease appearing to play a role).

In 1998 Ron et al. found increased risk of breast and lung cancer in patients treated with surgery (most of them had also received thionamides), but not in those treated with RAI [START_REF] Doody | Cancer mortality following treatment for adult hyperthyroidism. Cooperative Thyrotoxicosis Therapy Follow-up Study Group[END_REF]. Surprisingly, Kitahara et al. decided not to report data on patients who were not treated with 131 I, which constituted the control groups of the CTTFS study [START_REF] Kitahara | Association of Radioactive Iodine Treatment With Cancer Mortality in Patients With Hyperthyroidism[END_REF][START_REF] Hindié | Association of Radioactive Iodine Treatment of Hyperthyroidism With Cancer Mortality: An Unjustified Warning?[END_REF].

The CTTFS study used data collected in the 1960s, when even smoking was not a known confounder of cancer risk and severity of Graves' disease. When studying cancer incidence, the risk of confounding factors in Graves' disease and hyperthyroidism in general is now well recognized [START_REF] Ryödi | Cancer Incidence and Mortality in Patients Treated Either With RAI or Thyroidectomy for Hyperthyroidism[END_REF]. Establishing dose-response relationships does not fully protect against this risk. Confounding factors can be associated with the severity of hyperthyroidism and also with the total administered 131 I activity [START_REF] Hindié | Association of Radioactive Iodine Treatment of Hyperthyroidism With Cancer Mortality: An Unjustified Warning?[END_REF].

In addition to CTTFS, there are other major studies that also concluded that RAI does not contribute to increased cancer risk [START_REF] Ryödi | Cancer Incidence and Mortality in Patients Treated Either With RAI or Thyroidectomy for Hyperthyroidism[END_REF][START_REF] Franklyn | Cancer incidence and mortality after radioiodine treatment for hyperthyroidism: a population-based cohort study[END_REF]. We also raise concern on the absence of analysis or discussion of the increased morbidity that would be caused by alternative therapies for hyperthyroidism [START_REF] Hindié | Association of Radioactive Iodine Treatment of Hyperthyroidism With Cancer Mortality: An Unjustified Warning?[END_REF].

Interestingly, two of the co-authors of the study by Kitahara et al., later published data showing that the increase in standardized mortality ratio (SMR) for breast cancer was higher for patients treated only with anti-thyroid drugs (SMR 1.86; CI 1.29-2.58) than in patients treated with 131 I (SMR 1.11; CI 0.94-1.3) [START_REF] Tulchinsky | Spotlight on the Association of Radioactive Iodine Treatment With Cancer Mortality in Patients With Hyperthyroidism is Keeping the Highest Risk From Antithyroid Drugs in the Blind Spot[END_REF]. This finding of higher mortality with the use of thionamides was also reported in the previous report by Ron et al. [START_REF] Doody | Cancer mortality following treatment for adult hyperthyroidism. Cooperative Thyrotoxicosis Therapy Follow-up Study Group[END_REF].

Concomitant with our Commentary in JCEM, the British Thyroid Association and the Society for Endocrinology published a joint statement in the journal "Clinical Endocrinology", where they expressed concerns that the article by Kitahara et al may lead patients to reject the use of RAI therapy to manage hyperthyroidism [START_REF] Taylor | Executive Committees of the Society for Endocrinology and the British Thyroid Association. Joint statement from the Society for Endocrinology and the British Thyroid Association regarding 'Association of Radioactive Iodine Treatment with cancer mortality in patients with hyperthyroidism[END_REF]. They stated: "Recent observations have shown the importance of achieving good control of hyperthyroidism in a timely fashion to improve long-term cardiovascular and mortality outcomes. In this context, it would be unfortunate if patients were deprived of the option of rapid, effective control of their hyperthyroidism with radioiodine, due to concerns of cancer risk" [START_REF] Taylor | Executive Committees of the Society for Endocrinology and the British Thyroid Association. Joint statement from the Society for Endocrinology and the British Thyroid Association regarding 'Association of Radioactive Iodine Treatment with cancer mortality in patients with hyperthyroidism[END_REF].

When considering diverse confounding factors, it is important to recognize that hyperthyroidism itself increases the risk of several solid malignancies, including breast cancer [START_REF] Søgaard | Hypothyroidism and hyperthyroidism and breast cancer risk: a nationwide cohort study[END_REF][START_REF] Davis | How thyroid hormone works depends upon cell type, receptor type, and hormone analogue: implications in cancer growth[END_REF][START_REF] Krashin | Thyroid Hormones and Cancer: A Comprehensive Review of Preclinical and Clinical Studies[END_REF][START_REF] Verburg | Errare humanum est, sed in errare perseverare diabolicum: methodological errors in the assessment of the relationship between I-131 therapy and possible increases in the incidence of malignancies[END_REF]. Because thyroid cancer patients receive higher radioiodine activities as adjuvant therapy than those used for the treatment of hyperthyroidism, it would be helpful to also point out that results of a recent systematic review were also reassuring concerning risks of second cancers after radioiodine therapy [START_REF] Yu | A Systematic Review and Meta-Analysis of Subsequent Malignant Neoplasm Risk After Radioactive Iodine Treatment of Thyroid Cancer[END_REF]. We need to be careful, however, because the comparison between hyperthyroidism and thyroid cancer is not straightforward, requiring consideration of, not only the administered activities, but also the effective half-life of 131 I, the area under the activity curve in the whole body and specific organs, and additional other parameters. Furthermore, thyroid cancer patients can have increased underlying genetic risk for developing other cancers. The timely publication of the systematic review by Yu et al.

dispelled the conclusions of two papers from one team that tried to cast doubt on the riskbenefit from adjuvant 131 I therapy in low and intermediate-risk thyroid cancer [START_REF] Molenaar | Risk of Hematologic Malignancies After Radioiodine Treatment of Well-Differentiated Thyroid Cancer[END_REF][START_REF] Molenaar | Risk of developing chronic myeloid neoplasms in well-differentiated thyroid cancer patients treated with radioactive iodine[END_REF]; again based on biased data and incomplete analysis [START_REF] Verburg | Errare humanum est, sed in errare perseverare diabolicum: methodological errors in the assessment of the relationship between I-131 therapy and possible increases in the incidence of malignancies[END_REF][START_REF] Hindié | Risk of Hematologic Malignancies After Radioactive Iodine Treatment of Thyroid Cancer: An Unjustified Warning[END_REF].

Attesting to the safety and effectiveness of RAI treatment in patients with hyperthyroidism, the UK National Institute for Health and Care Excellence (NICE) published new guidelines recommending 131 I for first line therapy "Radioactive iodine is recommended as first line treatment for thyrotoxicosis with hyperthyroidism unless antithyroid drugs are likely to achieve remission or it is unsuitable" [START_REF] Vasileiou | Thyroid disease assessment and management: summary of NICE guidance[END_REF]. At present, the use of RAI for a first episode of hyperthyroidism varies widely from one country to another; being somewhat higher in the United States than in many European countries and rather low in Asian countries, as summarized in one recent report [START_REF] Sriphrapradang | Diagnosis and Management of Graves' Disease in Thailand: A Survey of Current Practice[END_REF].

Importantly, a novel study by Gronich et al., reported on 16,637 patients treated for hyperthyroidism with 131 I or thionamides (propylthiouracil, thiamazole), with 123,166 personyears of follow-up [START_REF] Gronich | Cancer Risk After Radioactive Iodine Treatment for Hyperthyroidism: A Cohort Study[END_REF]. While the Kitahara et al. findings were based on a hypothetical model and derived cancer mortality, Gronich reported on actual observed cancer rates. With longterm follow-up, there was no association between radioiodine treatment and increased risk of overall cancer in univariate analysis (HR = 0.99, p = 0.91) or in multivariate analysis (HR = 1.01, p = 0.95) [START_REF] Gronich | Cancer Risk After Radioactive Iodine Treatment for Hyperthyroidism: A Cohort Study[END_REF]. In an analysis of specific cancer types, an association with non-Hodgkin lymphoma was noted on univariate analysis, but not in multivariate analysis. The univariate analysis finding was not significant as a statistical (Bonferroni) correction was not performed for analysis of 20 cancer types (requiring a P value of < 0.0025 to gain statistical significance).

In summary, 131 I has been used for over eight decades for the treatment of Graves' disease, either as initial therapy or following failure of thionamides, as well as for the treatment of autonomous thyroid nodules. 131 I treatment is simple to administer, effective, and relatively inexpensive [START_REF] Vasileiou | Thyroid disease assessment and management: summary of NICE guidance[END_REF][START_REF] Ross | American Thyroid Association Guidelines for Diagnosis and Management of Hyperthyroidism and Other Causes of Thyrotoxicosis[END_REF]. Besides classical contraindications (i.e., pregnancy, breastfeeding), it is important to identify patients at risk for exacerbating Graves' orbitopathy and to use appropriate preventive measures [START_REF] Ross | American Thyroid Association Guidelines for Diagnosis and Management of Hyperthyroidism and Other Causes of Thyrotoxicosis[END_REF][START_REF] Kahaly | European Thyroid Association Guideline for the Management of Graves' Hyperthyroidism[END_REF]. Major studies have concluded that 131 I therapy does not contribute to increased cancer risk [START_REF] Doody | Cancer mortality following treatment for adult hyperthyroidism. Cooperative Thyrotoxicosis Therapy Follow-up Study Group[END_REF][START_REF] Ryödi | Cancer Incidence and Mortality in Patients Treated Either With RAI or Thyroidectomy for Hyperthyroidism[END_REF][START_REF] Franklyn | Cancer incidence and mortality after radioiodine treatment for hyperthyroidism: a population-based cohort study[END_REF][START_REF] Gronich | Cancer Risk After Radioactive Iodine Treatment for Hyperthyroidism: A Cohort Study[END_REF]. Also, when discussing potential risks from 131 I therapy, it is important to take into account risks from alternative treatments, including: cardiac and neurological consequences from uncontrolled thyrotoxicosis [START_REF] Boelaert | Comparison of mortality in hyperthyroidism during periods of treatment with thionamides and after radioiodine[END_REF][START_REF] Lillevang-Johansen | Excess Mortality in Treated and Untreated Hyperthyroidism Is Related to Cumulative Periods of Low Serum TSH[END_REF][START_REF] Okosieme | Primary therapy of Graves' disease and cardiovascular morbidity and mortality: a linked-record cohort study[END_REF][START_REF] Folkestad | Graves' Disease and Toxic Nodular Goiter, Aggravated by Duration of Hyperthyroidism, Are Associated with Alzheimer's and Vascular Dementia: A Registry-Based Long-Term Follow-Up of Two Large Cohorts[END_REF], surgical complications from increased use of thyroidectomies, marrow suppression (agranulocytosis) or hepatotoxicity from increased use of thionamides as well as small risks of thionamideassociated vasculitis and pancreatitis [START_REF] Brix | Methimazole and risk of acute pancreatitis[END_REF]. A study by Boelaert et al. on hyperthyroid patients aged ≥ 40 yrs showed that mortality was increased during periods of thionamide treatment and after radioiodine not resulting in hypothyroidism, but not during follow-up after radioiodine-induced hypothyroidism [START_REF] Boelaert | Comparison of mortality in hyperthyroidism during periods of treatment with thionamides and after radioiodine[END_REF]. It is only in understanding specific and related risks that clinicians can formulate the best therapeutic choices [START_REF] Hindié | Association of Radioactive Iodine Treatment of Hyperthyroidism With Cancer Mortality: An Unjustified Warning?[END_REF][START_REF] Giovanella | Quid autem vides festucam in oculo fratris tui et trabem in oculo tuo non vide" on the hyperthyroidism-induced mortality and antithyroid drug-induced side effects in the era of radioiodine fake news[END_REF][START_REF] Francis | Current controversies in the management of Graves' hyperthyroidism[END_REF]. It is also important that we deliver valid information, for the patient to have a fully informed role in the choice of therapy [START_REF] Hindié | Association of Radioactive Iodine Treatment of Hyperthyroidism With Cancer Mortality: An Unjustified Warning?[END_REF]. This can be organized at an international level through a multidisciplinary work involving representatives of various medical specialties and patients' associations.


Aurélie Moreau
email: aurelie.moreau@lyon.unicancer.fr

Edouard Marie
email: edouard.marie@lyon.unicancer.fr

Alice Bonneville-Levard
email: bonneville-levard@lyon.unicancer.fr

Alexandre Basle
email: alexandre.basle@lyon.unicancer.fr

David Kryza
email: david.kryza@univ-lyon1.fr

Skull vault hemangioma mimicking neoplastic lesion on [ 68 Ga]Ga-PSMA-11 PET/CT in a patient with glioblastoma: A case report

Keywords: 68Ga]Ga-PSMA-11 PET/CT, [ 18 F]-F-DOPA PET/CT, calvarial hemangioma, glioblastoma

We present the case of a 47 years old woman treated by radiochimotherapy for a glioblastoma which underwent a [68Ga]Ga-PSMA-11-PET/CT to distinguish post-radiation changes from an evolutionary process. This demonstrated a weak homogeneous uptake surrounding the lesion. There was a focal and moderate uptake of a pseudo lytic skull diploe lesion near to the glioblastoma, finally attributed to a calvaria hemangioma. Calvaria hemangiomas are less frequent than vertebral hemangiomas and may demonstrate a modest psma uptake that one should keep in mind so as not to misinterpret the examination in patients followed for glioblastomas.

Introduction

The [68Ga]Ga-PSMA-11 PET/CT holds an important and growing place in the management of patients followed for prostate cancers. This examination tends to replace [ 18 F]-Fluorocholine PET/CT thanks to a better performance, particularly in the exploration of biological recurrences with low PSA levels [START_REF] Afshar-Oromieh | The diagnostic value of PET/CT imaging with the 68Ga-labelled PSMA ligand HBED-CC in the diagnosis of recurrent prostate cancer[END_REF][START_REF] Afshar-Oromieh | Diagnostic performance of 68Ga-PSMA-11 (HBED-CC) PET/CT in patients with recurrent prostate cancer: evaluation in 1007 patients[END_REF][START_REF] Afshar-Oromieh | Comparison of PET imaging with a 68Ga-labelled PSMA ligand and 18F-choline-based PET/CT for the diagnosis of recurrent prostate cancer[END_REF][START_REF] Fendler | 68Ga-PSMA PET/CT: Joint EANM and SNMMI procedure guideline for prostate cancer imaging: version 1.0[END_REF]. PSMA is a transmembrane glycoprotein which is over-expressed in prostate adenocarcinomas.

It is also overexpressed by the endothelium of tumour-associated neovasculature such as glioblastomas multiform, but neither in malignant tumours cells themselves nor in normal vessels. A few articles have highlighted the possible role of [68Ga]Ga-PSMA-11 in glioma imaging [START_REF] Sasikumar | Diagnostic Value of 68Ga PSMA-11 PET/CT Imaging of Brain Tumors-Preliminary Analysis[END_REF][START_REF] Sasikumar | Utility of 68Ga-PSMA-11 PET/CT in Imaging of Glioma-A Pilot Study[END_REF]. We present here the case of an incidental discovery of a Skull Vault Hemangioma (SVH) in a patient explored with [68Ga]Ga-PSMA-11 PET/CT for an irradiated glioblastoma.

Case report

A 47 years-old woman was followed up for a non-operated left fronto parietal glioblastoma treated by radiochemotherapy. The MRI performed one month after the end of chemotherapy concluded in morphological stability with a perilesional oedema enlargement. Clinically, there was a difficulty in achieving cortisone withdrawal which was associated with a symptoms recrudescence (paresthesias, dysesthesias and right hemicorps clonies). [68Ga]Ga-PSMA-11 PET/CT was performed to assess the therapeutic response after radiochemotherapy to confirm inflammatory changes and to rule out an evolutionary process. [68Ga]Ga-PSMA-11 PET/CT was conducted to assess these lesions, one hour after the intra-venous injection of 98MBq of [68Ga]Ga-PSMA-11. The examination displayed a low and homogeneous uptake surrounding the lesion (Fig. 1 and Fig. 2) concording with post radiation changes. There was also a focal mild uptake of what seemed like a parietal lytic skull diploe lesion (Fig. 3A) near to the glioblastoma (Fig. 1 and Fig. 2). This image was seen a posteriori on the MRI follow-up, stable appearing in continuity with skull vessels, demonstrating an hyperT2-FLAIR and homogenous enhancement (Fig. 3B and Fig. 3C). This was attributed to a skull vault hemangioma (SVH). The patient underwent Avastin® (bevacizumab) as a test treatment for inflammatory changes, which was well tolerated, resulting in a partial clinical and imaging improvement at 3 months.

Written informed consent was obtained from the patient.

Discussion

This image was attributed to a skull vault hemangioma (SVH) and not to a rare adjacent calvarial destruction [START_REF] Gheyi | Glioblastoma Multiforme Causing Calvarial Destruction: An Unusual Manifestation Revisited[END_REF]. Several benign lesion PSMA positives have been reported, such as splenic and vertebral hemangiomas [START_REF] Artigas | Vertebral Hemangioma Mimicking Bone Metastasis in 68Ga-PSMA Ligand PET/CT[END_REF], which are well described. SVH are lesions more rarely observed. SVH accounts for about 0.2% of all bone tumours and 10% of benign skull tumours. SVH consists of dilated blood vessels separated by fibrous tissue. The pathogenesis is not clearly elucidated [START_REF] Yang | Primary Intraosseous Cavernous Hemangioma in the Skull[END_REF].

Patients are rarely symptomatic (pain, mass effect) [START_REF] Pons Escoda | Imaging of skull vault tumors in adults[END_REF]. On the CT SVH usually presents a well delineated and limited intradiploid osteolytic lesion with sharp edges with a "honeycomb" appearance. It can sometimes demonstrate an erosion of the tables. On the MRI SVH presents an hypersignal T2/FLAIR, a variable signal T1, and an enhancement after gadolinium injection. To our knowledge, this is the first PSMA-fixing SVH described. This case report is interesting for two reasons.

First of all it reminds us that any bone lesion close to glioblastoma is not necessarily related to a contiguous bone lesion but may be related to a benign lesion such as a SVH. Moreover this benign hemangiomatous uptake could serve as a reference, to help defining the intensities of benign uptake due to inflammatory remodeling from pathological fixations related do recurrence. In our case, glioblastoma (white arrow) was the site of a modest homogeneous uptake (SUVmax 3.2), about the same intensity as the cranial vault hemangioma (SUVmax 3.3). Therefore we considered the glioblastoma uptake as related to post radiation changes. Many articles have stressed the potential role of 18F-or 68Ga-radiolabelled PSMA in the evaluation of glioblastomas, especially in discriminating recurrences from post radiations changes [START_REF] Sasikumar | Utility of 68Ga-PSMA-11 PET/CT in Imaging of Glioma-A Pilot Study[END_REF]. But there is currently no threshold or validated interpretation criterion to define relapse from post radiation changes. Some authors have highlighted the over expression of PSMA by endothelial cells of reparative neovasculature and the moderate uptake of radionecrosis lesions [START_REF] Gordon | Prostate-specific membrane antigen expression in regeneration and repair[END_REF][START_REF] Salas Fragomeni | Uptake of Prostate-Specific Membrane Antigen-Targeted 18F-DCFPyL in Cerebral Radionecrosis: Implications for Diagnostic Imaging of High-Grade Gliomas[END_REF]. Conversely, some authors have reported intense uptake of venous variants [START_REF] Sgard | Pulmonary Vein Varix Mimicking Prostate Cancer Metastasis on 68Ga-Prostate Specific Membrane Antigen-11 PET/CT[END_REF]. Thus, the uptake of inflammatory remodeling and benign vascular variants therefore appears to be variable. The use of an uptake threshold based on vascular uptake to interpret the examination (post radiation changes vs. relapse) seems contentious at this time.

Other authors have used the Tumor-to-Background Ratio (TBR) in addition to visual analysis to diagnose recurrences [START_REF] Kunikowska | 68Ga-Prostate-Specific Membrane Antigen-11 PET/CT: A New Imaging Option for Recurrent Glioblastoma Multiforme?[END_REF]. The interest of this ratio in exploring recurrence versus post radiation changes has not been investigated. Larger prospective studies have to be conducted in order to clarify the place of [68Ga]Ga-PSMA PET/CT in the distinction between evolutivity versus inflammatory changes and to better define the interpretation criteria. The therapeutic role should also be evaluated [START_REF] Kunikowska | Tumor uptake in glioblastoma multiforme after IV injection of [177Lu]Lu-PSMA-617[END_REF].

In conclusion, this clinical case highlights the possibility of false positives that can be encountered with [68Ga]Ga-PSMA-11 PET/CT as well as with 18F-FDG. This fact must be taken into consideration so as not to ignore possible rare and benign lesions such as SVH and not to confuse them with bone destruction due to contiguous glioblastoma, or with prostate cancer bone metastases. More generally, when interpreting a [68Ga]Ga-PSMA-11 PET/CT, one should keep in mind that every malignant, and less frequently benign, vascularized lesions may fix the tracer. This point may hinder the distinction between inflammatory post radiation changes and recurrences in patients treated with radiotherapy for glioblastoma.

Figures

Figure 1 .

 1 Figure 1. Maximum Intensity Projection images with [ 68 Ga]Ga-PSMA-11 PET revealed a low and homogeneous uptake surrounding the lesion, and a focal mild uptake near to the glioblastoma.

Figure 2 .

 2 Figure 2. The axial [ 68 Ga]Ga-PSMA-11PET/CT fusion images showed a focal mild uptake near to the glioblastoma (A. bone scanner) and a low and homogeneous uptake surrounding the lesion (B. tissular scanner).

Figure 3 .

 3 Figure 3. The axial morphological examinations displayed a parietal lytic skull diploe lesion on bone scanner (part A: CT) and homogenous enhancement on the MRI (part B: MRI axial T1 postgadolinium; Part C: MRI T2 Flair).

Figure 1 .

 1 Figure 1.

Figure 2

 2 Figure 2.

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

Declaration of competing interest

The authors declare that they have no conflict of interest.


S Bancora
email: simone.bancora@ec-nantes.fr

C Binetruy

S Advani

S Comas-Cardona

Inverse methodology as applied to reconstruct local textile features from measured pressure field

Keywords: Textiles, Pressure sensors, Inverse method, Digital twin, Geometry reconstruction, Hyperelasticity

One can compute the final deformation of a known geometry under specific boundary conditions using the constitutive laws of mechanics that describe their stress strain behavior.

In such cases the initial geometry is known, and all operators mapping the deformation are defined on the reference domain. However, there are situations in which the final configuration of a deformation might be known but not the initial. The inverse formulation allows one to determine the initial geometry of a domain, given its final deformation state, the material behavior law and a set of boundary conditions. In the present work we propose a method to reconstruct the mesoscale geometry of a textile based on its mechanical response during compaction. To do so, stress boundary conditions are acquired by means of a pressuresensitive film. By adopting an appropriate material law, the thickness and width information of the yarns are deduced from the pressure field experienced by the compacted textile. Unlike 3D scanning techniques such as -CT, the proposed method can be applied on any domain size, allowing long-range variability to be captured. To the best of the authors' knowledge, there are no previous works that use a pressure-sensitive film on a large domain to capture the

Introduction

Inverse formulations in mechanics allow to compute unknown properties of the study domain starting from available response or external boundary conditions. Many kinds of such methods exist: perhaps the most common example in mechanics is the identification of material parameters [1,2] or boundary conditions [START_REF] Dennis | Inverse Problems in Engineering Mechanics[END_REF].

One possible application of inverse formulation is the detection of the unknown initial shape of a domain, when some information is available such as its deformed configuration or the boundary conditions applied. An extensive work on such application was presented in [START_REF] Yamada | Computational Mechanics' 95[END_REF],

where a full inverse finite element method was deployed to determine the initial shape of a rubber domain given some final conditions. Another example [START_REF] Lu | [END_REF] is the reconstruction of the initial shape of an aortic aneurysm from the final configuration and the pressure experienced by the tissue. One big challenge in inverse methods is that they often rely on knowing some field variables of the final configuration: for example, in a mechanical deformation problem one might need to know the Cauchy stress experienced by the deformed domain, or the displacement field on some boundaries. An extensive theoretical treatment of the inverse application of boundary values can be found in [6]. The actual values however are not always easy to obtain due to physical shortcomings such as difficult sensors placement or limited measurable domain.

In this work we propose an inverse methodology for initial shape identification of a deformed domain from the knowledge of the final geometry and boundary pressure. The method is applied to the reconstruction of a glass-fiber textile composed of many yarns, which is subject to a planar compaction state between two parallel rigid plates. The final thickness of the domain is known, while the initial geometry (thickness, width and path) of each yarn are unknown and subject to individual variability from one yarn to another. This material was chosen for several reasons. First, textiles are engineering materials widely used in composites manufacturing with applications in biomedical, automotive and aerospace. Second, textiles are a fitting example of materials which are compressed in a mould where the final thickness is known but the initial one is not, nor is the real pressure field experienced by the material. Furthermore, textiles present a periodic architecture which is subject to intrinsic local variability at the scale of the single yarns [7,[START_REF] Potter | International Conference on Composite Materials (ICCM)-17[END_REF]. Being able to identify these variations in geometry can be of great benefit to process control and digital characterization of properties such as hydraulic permeability [START_REF] Bahrami | [END_REF]. Lastly, yarn deformation obeys the general framework of compressible hyperelasticity [10,11], therefore such behaviour could be adopted for many other classes of materials.

The measurement of the boundary pressure is achieved using a flexible pressure sensor.

Technical developments of recent years spawned many examples of similar sensors based on current-resistive cells [12]. These sensors are typically very limited in both size and resolution due to added manufacturing costs and applications range from biological measurements [13,14] to process monitoring [15]. In this work the purely mechanical Prescale® sensor by Fujifilm is used. This is a pressure-sensitive film capable of registering a distributed pressure applied normally on its surface, yielding a quantification of the field in the form of a color intensity map. Since the measurement is carried out by the rupture of color-releasing microcapsules, this system is cheaper than the aforementioned electrical sensors. The Prescale® sensor has been extensively used in biomechanics to study contact surfaces, in articular joints [16,[START_REF] Liggins | Optical Measurement Methods in Biomechanics[END_REF] or other mechanical applications [START_REF] Aritomi | [END_REF]19]. Other fields of application include studies on wheel/road [START_REF] Backx | Tyre/road Contact Measurement Using Pressure Sensitive Films[END_REF] or wheel/rail [START_REF] Dörner | [END_REF] contact. This particular sensor works well with the chosen material, as it can be laid under the textile when a mould is closed during the compaction stage.

In addition to the mentioned cost effectiveness, another interesting advantage of this film is that the measurement has no limitations in size, unlike electrical sensors or direct geometry measurement techniques such as -CT which yield extremely accurate results but limited to a small material sample [22].

To the best of the authors' knowledge this is the first time a pressure-sensitive film is used as an input in an inverse identification method. The boundary pressure information and the final imposed thickness are used to compute the initial dimensions (thickness, width) of each individual yarn in the textile. As these dimensions are in the order of millimiters, an additional interest of this study is to assess if the measurement resolution of the Prescale® pressure film is still reliable at this scale.

Ultimately this work aims at providing a detailed methodology of inverse geometry reconstruction based on real pressure measurement, which could be extended to any other class of materials subject to a similar compression deformation.

Materials

The example textile we selected to be reconstructed is the UDT400 glass fabric ( = 423g/m 2 ) from Chomarat. This unbalanced quasi-unidirectional woven fabric was chosen because the complexity of the structure is reduced due to the absence of noticeable yarn waviness, so that bending effects can be neglected. The fabric material is shown in Fig. 1.

Methodology

To reconstruct the initial geometry of the textile, an inverse formulation methodology of reconstruction is applied to every yarn. The method will be illustrated for one generic yarn, and later will be extended to the entire textile. The following assumptions are made:

-the length of the yarn is assumed to be much larger than the cross-sectional dimensions, therefore a 2D plane strain formulation can be justified. The yarn is oriented with its major axis (width) and minor axis (thickness) as illustrated in Fig. 2.

-the yarn cross section geometry of a yarn is described as a power ellipse as detailed in [START_REF] Sherburn | Geometric and Mechanical Modelling of Textiles[END_REF], with a measured shape parameter = 0.3. Therefore identifying the crosssection geometry reduces to finding the value of thickness ( ℎ ) and width ( ) dimensions.

-The geometry is symmetric with respect to planes passing through the center with normals and .

-The yarn is modeled as a continuum.

Based on this premise, the stress state on the domain is only known at the boundaries, where the magnitude of the normal distributed traction vector Γ can be measured (on the deformed domain) by the pressure sensor. By Cauchy's theorem the admissible stress state will imply:

= Γ meas ∀ ∈ ∂Ω film 1
where is the position vector of a point in the deformed configuration, Γ meas is the boundary pressure measured by the sensor and ∂Ω mould is the boundary subregion in contact with the mould. By describing the deformation behavior by an appropriate constitutive law the stress state can be related to the deformation state. The inverse formulation then reduces to finding the deformation gradient that satisfies Eq. ( 1) for the known final configuration.

The methodology will be detailed in several steps.

-A suitable constitutive law will be chosen to relate the deformation of the yarn to the stress state (section 3.1)

-The identification of the material parameter of the constitutive law will be undertaken

(section 3.2)
-The inverse problem will be formulated and validated on the reconstruction of a single yarn cross-sectional geometry (sections 3.3, 3.4)

-An example of large scale reconstruction will be given, by applying the method on a full textile (section 4)

Yarn constitutive law

Previous efforts have described the mechanical behavior of yarns under compaction. The reported modeling approaches can be broadly classified into micro-mechanical or continuum descriptions of the yarn. In our study, continuum approach to describe the yarn mechanical behavior is adopted.

This choice is justified by the fact that, although composed of many filaments or fibers, a yarn often behaves as a continuum body due to the closely packed small diameter filaments that form the yarn bundle and the presence of sizing which maintains its cohesion. However, it will be highly non-linear mechanical behavior, since a yarn deformation under a load is a motion of the fibers within. Dixit [START_REF] Dixit | [END_REF] modeled the yarn as an elastic material, transversely isotropic in directions normal to the yarn orientation and described the evolution of the elastic modulus as a function of fiber volume fraction. Recently Dharmalingam [10], Lectez [11] and Hemmer [25] studied the evolution of yarn cross sections under compaction and described the material behavior with a compressible hyperelastic constitutive law. They used a variation on the Ogden [START_REF] Ogden | Non-linear Elastic Deformations[END_REF] strain energy density function known as hyperfoam material, that was proposed in 2000 by Jemiolo and Turtletaub [START_REF] Jemiolo | [END_REF]. This model is adopted in the present work.

The strain energy density function of the hyperfoam material is defined in terms of principal stretches λ as:

λ , λ , λ " = 2μ α %λ & + λ & + λ " & -3 + 1 β *+ ,&--1./ 2
where the principal stretches λ = |d |/|d3| are the eigenvalues of , 3 is the position vector of a point in the initial configuration, + is the determinant of the deformation gradient and α, β, μ are parameters that need to be identified. The orthonormal basis is placed so that " is aligned along the direction of the fibers and is oriented in the thickness direction out of plane. Furthermore, inextensibility of the material in the fibers direction is assumed by setting λ " = 1 . According to classical hyperelastic material theory, the eigenvalues of the Cauchy stress tensor are derived from Eq.( 2) as:

σ = λ + ∂ ∂λ 3
where Voigt notation was adopted for the stresses:

= 5σ , σ , σ "" , σ " , σ " , σ 6 4

As stated in the assumptions, we simplify the problem according to plane strain theory. The principal Cauchy stresses in the cross-sectional plane are:

σ = 2μ αλ 7λ &, -λ ,&- λ ,&-, 8 5 σ = 2μ αλ 7λ &, -λ ,&- λ ,&-, 8 6
The yarn is free to laterally expand under compression in the , direction so we adopt the assumption that σ = 0 at all locations of the domain. This yields from Eq. ( 5) a relation between principal stretches:

λ = λ , - ;-
and Eq.( 6) can be simplified to:

σ = 2μ α %λ &;&-; ;- -λ ,&-, ;- / 8
The coefficients α, β, μ need to be characterized for this specific material in order to exercise the model.

Material parameters identification

A set of compression tests were performed in order to identify the parameters of the model.

The experimental apparatus used is shown in Fig. 3. It consists of an Instron 5584 machine, on which a ball joint was mounted to ensure parallelism between the top and bottom plates. A small punch-die compression assembly was used to better control the placement of the yarn.

For each test, a single yarn of 5 cm of length was placed between the plates of the device and compacted at very low deformation velocity of 0.5mm/min. Values of force, displacement and time were recorded from the machine. The cross-section transformation during the compaction was recorded by a camera placed in front of the apparatus as shown in Fig. 4.

Measurements were taken from 8 compression repetitions. The evolution of width and thickness ℎ was extracted by image analysis from the bounding box of the cross sections, using the software ImageJ [28]. Consequently, the values of stretch in the principal directions are obtained as λ = ℎ/ℎ > , λ = / > where ℎ > and > are respectively the thickness and width of the initial configuration (stress free). The β parameter is calculated first by fitting Eq. ( 7) to the recorded experimental measurements of λ , λ and used to determine the yarn width according to the vertical compression λ to obtain a Cauchy stress curve from the measured force. An assumption of homogeneous stress state is made. It is reasonable as the geometry of the yarn is almost rectangular. Although this simplification could lead to some inaccuracy in the material characterization, relaxing this assumption would require knowing the complete strain field in the cross section, which is not practical to achieve. The raw data collected is processed and the machine compliance is eliminated to yield a stress-deformation curve for 8 yarns tested. Measurements between all samples followed a coherent trend, with some differences due to the intrinsic variability that characterizes fiber yarns [22]. From this experimental data the material parameters α, μ are calibrated by mean square error minimization. Experimental and fitted curves are plotted in Fig. 5. The values found for the model coefficients are: α = 44.8178, β = 0.1857, μ = 0.8341 MPa.

Inverse formulation

The objective of the problem is to determine the initial yarn cross section geometry in terms of width ( > ) and thickness (ℎ > ) of a yarn under compression, given a final thickness ℎ and a measured boundary pressure Γ meas . The final thickness ℎ is an arbitrary imposed value (ℎ < ℎ > ) and corresponds to the final gap between the compression plates. In the case of composite materials, it is a design parameter determined to obtain the desired fiber volume fraction [START_REF] Advani | Process Modeling in Composites Manufacturing[END_REF].

Adopting the hyperfoam material law allows one to use Eq. ( 1) to formulate the problem stated below in Eq. ( 9):

λ = arg min F G | , λ H -Γ meas | ∀ ∈ ∂Ω mould 9
One simple formulation would be to use Eq. ( 9) to determine λ for a given boundary pressure Γ meas that could be measured by the mentioned pressure sensitive film whose color density evolves with pressure. Being λ the eigenvalues of the deformation gradient λ , the reference configuration could be determined with the pull-back operation:

3 = , 10
which in the chosen basis and for our simple transformation yields:

ℎ > = λ , ℎ 11 > = λ , = λ J ;J 12
This approach however would only work if the stress state was perfectly homogeneous and for a simple rectangular geometry. When a yarn is compressed instead the measured stress Γ meas exhibits a gradient of intensity, with a maximum value on the centerline, as shown in Fig. (10c).

Furthermore, since the final width is unknown, Eq. ( 12) is not applicable right away. For this reason we look for some further condition to link > to known quantities. The cross section geometries of a population of 8 yarns in the initial state were measured using a confocal scanner (profilometer). As already stated in the assumptions, these cross sections fit into power ellipses [START_REF] Sherburn | Geometric and Mechanical Modelling of Textiles[END_REF]. Width ( > ) and thickness ℎ > ) for each sample were extracted as the bounding box dimensions, and the area > of each cross section is computed numerically from the profile, as listed in Table (1). From this sample space the average area ̅ = 1.08mm and the standard deviation L = 0.049mm ≈ 5% are calculated. The very low deviation allows us to assume that for this particular material the initial cross section area remains constant in the reference state even though the yarn initial dimensions are affected by variability. Adopting this assumption the width > of a yarn in the reference state can be directly expressed as a function of a given thickness ℎ > :

> ℎ > = arg min O *P ℎ > , > -P. 13
Using this assumption of constant initial cross section area, a finite element solution of the stress field is adopted to extract the inhomogeneous left-hand side term of Eq. ( 9).

To obtain such a solution, the compaction of the yarn is simulated iteratively in ABAQUS using an explicit method. An initial yarn cross section geometry is generated numerically, with an initial guess for thickness ℎ > * and width > * that satisfies Eq. ( 13) for a fixed value of . The yarn is assigned the hyperfoam material law with the identified parameters α, β, μ in the plane strain framework. A rigid 1D element which represents the mould is used to impose the final thickness ℎ on the domain. From the finite element solution, the σ Cauchy stress is computed, which as expected is quite homogeneous along the H direction and inhomogeneous in the H direction, as shown in Fig. (7). From the computed stress field, the normal pressure Γ num ℎ > * at the rigid element boundary ∂Ω mould is extracted.

Finally, using the stress value Γ meas acquired from the Prescale® pressure-sensitive film, the error is calculated as:

ξ = |Γ num ℎ > * -Γ meas | 14
Details on pressure acquisition and calibration of the film are provided in the Appendix A.

The initial thickness ℎ > of the yarn is found as:

ℎ > = arg min S O * T ℎ > * 15
and initial width > is determined using Eq. ( 13) under the assumption of constant initial cross-section area .

This optimization is performed iteratively by assigning an arbitrary initial value ℎ > * , performing the analysis and saving the resulting Γ num ℎ > * to a file before starting over with a new value of ℎ > * . The steps of this numerical optimization are summarized in Fig. 6.

The interest of saving all values of Γ num ℎ > * for all possible values of ℎ > * is to create a database that can be readily used to quickly evaluate Eq. ( 14) for a given ℎ when multiple yarns are being reconstructed, each with their local value of Γ meas . An example of Γ num ℎ > * database for different yarn reference dimensions and a given final ℎ is shown in Fig. 8.

Cross-section validation

The validation of the initial geometry reconstruction is performed by comparison with experimental measurements. A set of yarns were compressed up to an imposed thickness ℎ and the whole transformation was recorded from a camera placed in front of the cross section as in Fig. 9(left). A Prescale® film was also placed under the yarn, and the pressure profile Fig. 9 (right) was used to identify the yarn geometry following the procedure just described.

The geometry calculated from the pressure information was compared with the real yarn geometry measured from the video information for error quantification.

The results and a quantification of error are reported in Table 2, where > and ℎ > are the reference dimensions. The superscripts "meas" and "calc" indicate the measured and calculated values respectively. The imposed final thickness is ℎ = 0.25mm. The percentage relative errors in the calculated quantities with respect to the measured ones are reported in parentheses.

The results of this section show that:

-it is possible to reconstruct with accuracy a yarn geometry in its initial configuration from a compressive test and a pressure field sensor.

-the resolution of the Prescale® pressure sensitive film is high enough to work well even on the relatively small yarn dimensions.

Full textile reconstruction

The interest of this work is to detail and showcase how stress boundary conditions can be applied for inverse method reconstruction of more complex domains and geometries. To

showcase the potential of the technique presented in Section 3 for a single yarn, the reconstruction will be extended to a full textile which contains several yarns.

Cross sections

To address this scenario, the method is simply repeated for each yarn, since by laying the entire textile sample over a layer of Prescale® film and compressing it is possible to know the pressure field Γ meas experienced by every U th yarn individually. A UDT400 textile was placed on the pressure film and compressed up to an imposed final thickness ℎ. From the resulting pressure print an area of 98 mm × 98 mm, corresponding to a collection of 33 weft yarns and 27 warp yarns, was extracted to be analyzed. This frame can be seen in Fig. 11(b).

For each individual yarn, multiple intensity measures are sampled from the pressure print along its length and in between crossover points, as shown in Fig. 10(b). The measures are averaged length-wise to compute the curve of pressure Γ meas relative to the U-th yarn as shown in Fig. 10(c). Assigning a length-averaged pressure profile and therefore a constant crosssection identification to each yarn simplifies the geometry identification process. Each pressure curve is used in Eq. ( 15) to find the corresponding yarn reference dimensions (ℎ > , > ) under the assumption of known initial cross-section area = 1.08 mm . It should be noted that this method can allow for the cross-section to vary along the yarn length by simply repeating the identification at every sampling instead of length-averaging the pressure print. However this was not taken into account as it would be material specific and the number of identifications to carry out increases especially on a large domain.

Yarn paths

When a full textile is being reconstructed it is not sufficient to determine the yarn cross section geometries, but yarn paths are needed as well as this is important for investigating dual scale flow when these textiles are impregnated with resin [START_REF] Slade | [END_REF]. These could easily be measured by imaging techniques, taking a picture of the textile to have realistic yarn paths as was done by Gommer et al. [7]. However since the pressure field measured by the Prescale® film contains spatial information as well, the yarn paths can be directly extracted from that measurement. The complexity of this step depends on the complexity of the textile architecture. In this study, since the textile is woven material, the regions where the weft and warp yarns cross over are clearly visible as spikes in pressure since the thickness is locally higher. The yarn paths are easily measured by interpolating a spline through these regions. At the current level of implementation, the yarn paths definition is performed manually by using the ImageJ software to select and output the nodal positions W X, Y of crossover regions on the domain as shown in Fig. 10(a). To these in-plane coordinates the Z information is added by shifting the nodes out of plane following the weaving pattern to account for the thickness of the warp yarn, which was assumed to be non-deformable. These nodes W X, Y, Z are used for the definition of each yarn path when the textile geometry is generated.

Geometry generation

Following the method proposed, the information of initial cross section and yarn path for each individual yarn has been obtained. In order to generate the 3D geometry, the textile geometry generator TexGen [31] is used through scripting.

The original textile, compaction pressure map and reconstructed geometry can be seen in Fig. 11. It is clearly visible that the yarn paths and geometries are not idealized, but exhibit instead the variability in cross-section and path that was captured from the pressure print.

Summary and conclusions

Through a specific application, an inverse methodology was detailed to identify the dimensional parameters of a domain and reconstruct its initial geometry. The procedure has been showcased on the reconstruction of a textile under compression, but the principle could be applied to other contexts. The method is based on the acquisition of boundary values of pressure experienced by the material in the process, which was achieved using a pressure sensitive film. The hyperfoam material model was used to relate the pressure to the deformation of the yarns, and therefore to the reference geometry.

A final example of reconstruction of an extended textile was provided, by using the pressure film to extract the yarn paths as well as the cross sectional geometries of each yarn. This large scale reconstruction showcases the potential of using Prescale® film, as there are no limitations in domain size with this sensor and methodology (unlike for example μ-CT or image processing). Answering one stated objective, validation carried out yarn-wise showed a good match between the reconstructed and measured geometry, proving that the sensitivity of the film is satisfactory even on very small scales.

Being able to reconstruct the detailed textile geometry opens up the possibility of performing further analysis on the domain, such as computing the expected hydraulic permeability or assessing quality control over variability. However it is important to state that the reconstruction of a single layer of textile has very little direct application, and the material was chosen for this study as representative for the motivations listed in the introduction. This approach could be extended to curved surfaces due to textile deformation [32,33] or any other class of materials which exhibit similarities in mechanical behaviour and deformation mode.

Figure list:Fig. 1 .

 1 Figure list:

Fig. 2 .Fig. 3 .

 23 Fig. 2. Schematic of Yarn cross section where is the width and ℎ is the thickness subjected to normal distributed traction vector, Γ

Fig. 4 .

 4 Fig. 4. Camera recorded yarn compression.

Fig. 5 .

 5 Fig. 5. Stress/stretch best curve fitting provided the model coefficients: α = 44.8178, β = 0.1857, μ = 0.8341 MPa in Eq. (2).

Fig. 6 .

 6 Fig. 6. Flowchart to create the stress/initial geometry database.

Fig. 7 .

 7 Fig. 7. Finite element yarn compression, σ stress field on a quarter of yarn.

Fig. 8 .

 8 Fig. 8. Γ num database for imposed final ℎ = 0.25mm, half yarn normalized width (vertical symmetry). Units in legend are [mm].

Fig. 9 .

 9 Fig. 9. Visual validation of yarn geometry reconstruction (left) and pressure print of one yarn (right).

Fig. 10 .

 10 Fig. 10. Pressure field analysis for the textile reconstruction.

Fig. 11 .

 11 Fig. 11. Synoptic comparison of real and reconstructed geometry of a 98 × 98mm UDT400 textile.

Table list :

 list Table 1 Measured reference cross-section area > from an 8 samples population.

	Yarn sample > 5mm 6	1 1.10	2 1.11	3 1.11	4 1.09	5 1.12	6 1.08	7 1.04	8 1.12

Table 2

 2 Comparison of reconstructed vs measured yarn geometries [mm].

	Specimen 1	> meas 2.94	ℎ > meas 0.35	> calc (err) 3.192(8.5%)	calc (err) ℎ > 0.34(2.8%)
	2	3.39	0.33	3.392(0.05%)	0.32(3%)
	3	2.7	0.41	2.65(1.8%)	0.405(1.2%)
	4	2.7	0.41	2.77(2.6%)	0.4(4.8%)
	5	3.42	0.34	3.39(1%)	0.32(5.8%)
	6	2.75	0.39	2.855(3.8%)	0.38(2.6%)

Acknowledgements

This research was partially funded by Conseil Regional Pays de la Loire (grant number TEU29). The authors wish to thank A. Hautefeuille and the team at ECN GeM laboratory for the help with the experimental setup.