{"doi":"10.1016/j.cma.2023.116450","title":"Discontinuous Galerkin methods for Fisher–Kolmogorov equation with application to <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" altimg=\"si556.svg\" display=\"inline\" id=\"d1e2166\"><mml:mi>α</mml:mi></mml:math>-synuclein spreading in Parkinson’s disease","abstract":"This spreading of prion proteins is at the basis of brain neurodegeneration. This paper deals with the numerical modelling of the misfolding process of α-synuclein in Parkinson’s disease. We introduce and analyse a discontinuous Galerkin method for the semi-discrete approximation of the Fisher–Kolmogorov (FK) equation that can be employed to model the process. We employ a discontinuous Galerkin method on polygonal and polyhedral grids (PolyDG) for space discretization, to accurately simulate the wavefronts typically observed in the prionic spreading and we prove stability and a priori error estimates. Next, we use a Crank–Nicolson scheme to advance in time. For the numerical verification of our numerical model, we first consider a manufactured solution, and then we consider a case with wavefront propagation in two-dimensional polygonal grids. Next, we carry out a simulation of α-synuclein spreading in a two-dimensional brain slice in the sagittal plane with a polygonal agglomerated grid that takes full advantage of the flexibility of PolyDG approximation. Finally, we present a simulation in a three-dimensional geometry reconstructed from magnetic resonance images of a patient’s brain.","journal":"Computer Methods in Applied Mechanics and Engineering","year":2023,"id":332465,"datarank":0.0,"base_score":0.0,"endowment":0.0,"self_citation_contribution":0.0,"citation_network_contribution":0.0,"self_endowment_contribution":0.0,"citer_contribution":0.0,"corpus_percentile":null,"corpus_rank":null,"citation_count":25,"citer_count":0,"citers_with_citation_signal":0,"citers_with_endowment":0,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":0.9475,"is_data_producer":false,"deposit_databanks":null,"is_oa":true,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":"2023-01-01","fair_score":null,"fair_percentile":null,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":1058633,"name":"Francesca Bonizzoni","orcid":"0000-0002-6222-3352","position":1,"is_corresponding":false},{"id":1047340,"name":"Luca Dede’","orcid":"0000-0002-6558-8277","position":2,"is_corresponding":false},{"id":1047341,"name":"Alfio Quarteroni","orcid":"0000-0002-5947-6885","position":3,"is_corresponding":false},{"id":1047339,"name":"Paola F. Antonietti","orcid":"0000-0002-2138-3878","position":4,"is_corresponding":false},{"id":1047338,"name":"Mattia Corti","orcid":"0000-0002-7014-972X","position":0,"is_corresponding":true}],"reference_count":42,"raw_metadata":null,"created_at":"2026-07-19T01:09:30.139849Z","pmid":null,"pmcid":null,"fwci":null,"citation_percentile":null,"influential_citations":0,"oa_status":null,"license":null,"views":0,"total_file_size_bytes":0,"version_count":0,"fair_f":null,"fair_a":null,"fair_i":null,"fair_r":null,"fair_zscore":null,"fair_rationale":null,"fair_model":null,"fair_agent_version":null,"fair_fulltext_source":null,"fair_has_llm":null,"fair_computed_at":null,"clinical_trials":[],"software_tools":[],"db_accessions":[],"linked_datasets":[],"topics":[]}