3fde059568f2ab13330be685106440de appsci_a2021v11n18p8568.pdf d56a621ab9785f0894c65143f990482ac39b9d85 appsci_a2021v11n18p8568.pdf bc5ac9a6e0febfac6c8af1f071dde226cce4f737e9fd8daef60e5e638fceacc8 appsci_a2021v11n18p8568.pdf Title: Physically Consistent Scar Tissue Dynamics from Scattered Set of Data: A Novel Computational Approach to Avoid the Onset of the Runge Phenomenon Subject: The foreign body reaction is a complex biological process leading to the insulation of implanted artificial materials through a capsule of scar tissue. In particular, in chronic implantations of neural electrodes, the prediction of the scar tissue evolution is crucial to assess the implant reliability over time. Indeed, the capsule behaves like an increasing insulating barrier between electrodes and nerve fibers. However, no explicit and physically based rules are available to computationally reproduce the capsule evolution. In addition, standard approaches to this problem (i.e., Vandermonde-based and Lagrange interpolation) fail for the onset of the Runge phenomenon. More specifically, numerical oscillations arise, thus standard procedures are only able to reproduce experimental detections while they result in non physical values for inter-interval times (i.e., times before and after experimental detections). As a consequence, in this work, a novel framework is described to model the evolution of the scar tissue thickness, avoiding the onset of the Runge phenomenon. This approach is able to provide novel approximating functions correctly reproducing experimental data (R20.92) and effectively predicting inter-interval detections. In this way, the overall performances of previous approaches, based on phenomenological fitting polynomials of low degree, are improved. Keywords: neural implants; foreign body reaction; scar tissue; Vandermonde matrix; Lagrange polynomials; Runge phenomenon Author: Pier Nicola Sergi, Natalia De la Oliva, Jaume del Valle, Xavier Navarro and Silvestro Micera Creator: LaTeX with hyperref Producer: pdfTeX-1.40.21 CreationDate: Wed Sep 15 12:39:19 2021 CEST ModDate: Wed Sep 15 12:41:26 2021 CEST Tagged: no UserProperties: no Suspects: no Form: none JavaScript: no Pages: 14 Encrypted: no Page size: 595.276 x 841.89 pts (A4) Page rot: 0 File size: 856821 bytes Optimized: no PDF version: 1.7 name type encoding emb sub uni object ID ------------------------------------ ----------------- ---------------- --- --- --- --------- KPUWTT+URWPalladioL-Ital Type 1 Custom yes yes no 10 0 FLCHLC+URWPalladioL-Bold Type 1 Custom yes yes no 15 0 KQOIFU+URWPalladioL-Roma Type 1 Custom yes yes no 19 0 DUJZYM+CMSY10 Type 1 Builtin yes yes no 23 0 CRVMKC+TimesNewRomanPS-BoldItalicMT Type 1C WinAnsi yes yes no 31 0 MCBCCI+SourceSansRoman-Regular Type 1C Custom yes yes no 53 0 MCBCCM+SourceSansRoman.613wght Type 1C Custom yes yes no 57 0 MCBCCO+SourceSansRoman-Bold Type 1C Custom yes yes no 61 0 GKYCJO+CMEX10 Type 1 Builtin yes yes no 76 0 SOSTRQ+CMR10 Type 1 Builtin yes yes no 80 0 XTTGGP+PazoMath-Italic Type 1 Builtin yes yes no 84 0 QXRYTF+PazoMath Type 1 Builtin yes yes no 88 0 OVNEXW+EURM10 Type 1 Builtin yes yes no 92 0 RLYTRW+CMMI10 Type 1 Builtin yes yes no 99 0 GNHOUD+MSBM10 Type 1 Builtin yes yes no 103 0 TCXUGD+ArialMT TrueType WinAnsi yes yes yes 113 0 BBCWFW+URWPalladioL-BoldItal Type 1 Custom yes yes no 157 0 FKZRZM+ArialMT TrueType WinAnsi yes yes yes 167 0 JFRJWO+ArialMT TrueType WinAnsi yes yes yes 185 0 IUEHQB+ArialMT TrueType WinAnsi yes yes yes 445 0 Jhove (Rel. 1.22.1, 2019-04-17) Date: 2023-05-27 03:28:57 CEST RepresentationInformation: appsci_a2021v11n18p8568.pdf ReportingModule: PDF-hul, Rel. 1.12.1 (2019-04-17) LastModified: 2023-03-31 11:58:15 CEST Size: 856821 Format: PDF Version: 1.7 Status: Well-Formed and valid SignatureMatches: PDF-hul MIMEtype: application/pdf PDFMetadata: Objects: 708 FreeObjects: 123 IncrementalUpdates: 0 DocumentCatalog: PageLayout: SinglePage PageMode: UseNone Outlines: Item: Title: Introduction Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@44c8afef Item: Title: Methods Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@7b69c6ba Item: Title: Results Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@46daef40 Item: Title: Discussion Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@12f41634 Item: Title: Conclusions Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@13c27452 Item: Title: Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@262b2c86 Item: Title: References Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@371a67ec Info: Title: Physically Consistent Scar Tissue Dynamics from Scattered Set of Data: A Novel Computational Approach to Avoid the Onset of the Runge Phenomenon Author: Pier Nicola Sergi, Natalia De la Oliva, Jaume del Valle, Xavier Navarro and Silvestro Micera Subject: The foreign body reaction is a complex biological process leading to the insulation of implanted artificial materials through a capsule of scar tissue. In particular, in chronic implantations of neural electrodes, the prediction of the scar tissue evolution is crucial to assess the implant reliability over time. Indeed, the capsule behaves like an increasing insulating barrier between electrodes and nerve fibers. However, no explicit and physically based rules are available to computationally reproduce the capsule evolution. In addition, standard approaches to this problem (i.e., Vandermonde-based and Lagrange interpolation) fail for the onset of the Runge phenomenon. More specifically, numerical oscillations arise, thus standard procedures are only able to reproduce experimental detections while they result in non physical values for inter-interval times (i.e., times before and after experimental detections). As a consequence, in this work, a novel framework is described to model the evolution of the scar tissue thickness, avoiding the onset of the Runge phenomenon. This approach is able to provide novel approximating functions correctly reproducing experimental data (R20.92) and effectively predicting inter-interval detections. In this way, the overall performances of previous approaches, based on phenomenological fitting polynomials of low degree, are improved. 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