diff --git a/stable b/stable
index cf2dc0b..a6316f0 120000
--- a/stable
+++ b/stable
@@ -1 +1 @@
-v2.2.0
\ No newline at end of file
+v2.3.0
\ No newline at end of file
diff --git a/v2 b/v2
index cf2dc0b..a6316f0 120000
--- a/v2
+++ b/v2
@@ -1 +1 @@
-v2.2.0
\ No newline at end of file
+v2.3.0
\ No newline at end of file
diff --git a/v2.3 b/v2.3
new file mode 120000
index 0000000..a6316f0
--- /dev/null
+++ b/v2.3
@@ -0,0 +1 @@
+v2.3.0
\ No newline at end of file
diff --git a/v2.3.0/.documenter-siteinfo.json b/v2.3.0/.documenter-siteinfo.json
new file mode 100644
index 0000000..59a4dea
--- /dev/null
+++ b/v2.3.0/.documenter-siteinfo.json
@@ -0,0 +1 @@
+{"documenter":{"julia_version":"1.10.2","generation_timestamp":"2024-04-02T11:02:48","documenter_version":"1.3.0"}}
\ No newline at end of file
diff --git a/v2.3.0/assets/documenter.js b/v2.3.0/assets/documenter.js
new file mode 100644
index 0000000..c6562b5
--- /dev/null
+++ b/v2.3.0/assets/documenter.js
@@ -0,0 +1,1050 @@
+// Generated by Documenter.jl
+requirejs.config({
+ paths: {
+ 'highlight-julia': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia.min',
+ 'headroom': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/headroom.min',
+ 'jqueryui': 'https://cdnjs.cloudflare.com/ajax/libs/jqueryui/1.13.2/jquery-ui.min',
+ 'katex-auto-render': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/contrib/auto-render.min',
+ 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.7.0/jquery.min',
+ 'headroom-jquery': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/jQuery.headroom.min',
+ 'katex': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/katex.min',
+ 'highlight': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/highlight.min',
+ 'highlight-julia-repl': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia-repl.min',
+ },
+ shim: {
+ "highlight-julia": {
+ "deps": [
+ "highlight"
+ ]
+ },
+ "katex-auto-render": {
+ "deps": [
+ "katex"
+ ]
+ },
+ "headroom-jquery": {
+ "deps": [
+ "jquery",
+ "headroom"
+ ]
+ },
+ "highlight-julia-repl": {
+ "deps": [
+ "highlight"
+ ]
+ }
+}
+});
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery', 'katex', 'katex-auto-render'], function($, katex, renderMathInElement) {
+$(document).ready(function() {
+ renderMathInElement(
+ document.body,
+ {
+ "delimiters": [
+ {
+ "left": "$",
+ "right": "$",
+ "display": false
+ },
+ {
+ "left": "$$",
+ "right": "$$",
+ "display": true
+ },
+ {
+ "left": "\\[",
+ "right": "\\]",
+ "display": true
+ }
+ ]
+}
+
+ );
+})
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery', 'highlight', 'highlight-julia', 'highlight-julia-repl'], function($) {
+$(document).ready(function() {
+ hljs.highlightAll();
+})
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+let timer = 0;
+var isExpanded = true;
+
+$(document).on("click", ".docstring header", function () {
+ let articleToggleTitle = "Expand docstring";
+
+ debounce(() => {
+ if ($(this).siblings("section").is(":visible")) {
+ $(this)
+ .find(".docstring-article-toggle-button")
+ .removeClass("fa-chevron-down")
+ .addClass("fa-chevron-right");
+ } else {
+ $(this)
+ .find(".docstring-article-toggle-button")
+ .removeClass("fa-chevron-right")
+ .addClass("fa-chevron-down");
+
+ articleToggleTitle = "Collapse docstring";
+ }
+
+ $(this)
+ .find(".docstring-article-toggle-button")
+ .prop("title", articleToggleTitle);
+ $(this).siblings("section").slideToggle();
+ });
+});
+
+$(document).on("click", ".docs-article-toggle-button", function (event) {
+ let articleToggleTitle = "Expand docstring";
+ let navArticleToggleTitle = "Expand all docstrings";
+ let animationSpeed = event.noToggleAnimation ? 0 : 400;
+
+ debounce(() => {
+ if (isExpanded) {
+ $(this).removeClass("fa-chevron-up").addClass("fa-chevron-down");
+ $(".docstring-article-toggle-button")
+ .removeClass("fa-chevron-down")
+ .addClass("fa-chevron-right");
+
+ isExpanded = false;
+
+ $(".docstring section").slideUp(animationSpeed);
+ } else {
+ $(this).removeClass("fa-chevron-down").addClass("fa-chevron-up");
+ $(".docstring-article-toggle-button")
+ .removeClass("fa-chevron-right")
+ .addClass("fa-chevron-down");
+
+ isExpanded = true;
+ articleToggleTitle = "Collapse docstring";
+ navArticleToggleTitle = "Collapse all docstrings";
+
+ $(".docstring section").slideDown(animationSpeed);
+ }
+
+ $(this).prop("title", navArticleToggleTitle);
+ $(".docstring-article-toggle-button").prop("title", articleToggleTitle);
+ });
+});
+
+function debounce(callback, timeout = 300) {
+ if (Date.now() - timer > timeout) {
+ callback();
+ }
+
+ clearTimeout(timer);
+
+ timer = Date.now();
+}
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require([], function() {
+function addCopyButtonCallbacks() {
+ for (const el of document.getElementsByTagName("pre")) {
+ const button = document.createElement("button");
+ button.classList.add("copy-button", "fa-solid", "fa-copy");
+ button.setAttribute("aria-label", "Copy this code block");
+ button.setAttribute("title", "Copy");
+
+ el.appendChild(button);
+
+ const success = function () {
+ button.classList.add("success", "fa-check");
+ button.classList.remove("fa-copy");
+ };
+
+ const failure = function () {
+ button.classList.add("error", "fa-xmark");
+ button.classList.remove("fa-copy");
+ };
+
+ button.addEventListener("click", function () {
+ copyToClipboard(el.innerText).then(success, failure);
+
+ setTimeout(function () {
+ button.classList.add("fa-copy");
+ button.classList.remove("success", "fa-check", "fa-xmark");
+ }, 5000);
+ });
+ }
+}
+
+function copyToClipboard(text) {
+ // clipboard API is only available in secure contexts
+ if (window.navigator && window.navigator.clipboard) {
+ return window.navigator.clipboard.writeText(text);
+ } else {
+ return new Promise(function (resolve, reject) {
+ try {
+ const el = document.createElement("textarea");
+ el.textContent = text;
+ el.style.position = "fixed";
+ el.style.opacity = 0;
+ document.body.appendChild(el);
+ el.select();
+ document.execCommand("copy");
+
+ resolve();
+ } catch (err) {
+ reject(err);
+ } finally {
+ document.body.removeChild(el);
+ }
+ });
+ }
+}
+
+if (document.readyState === "loading") {
+ document.addEventListener("DOMContentLoaded", addCopyButtonCallbacks);
+} else {
+ addCopyButtonCallbacks();
+}
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery', 'headroom', 'headroom-jquery'], function($, Headroom) {
+
+// Manages the top navigation bar (hides it when the user starts scrolling down on the
+// mobile).
+window.Headroom = Headroom; // work around buggy module loading?
+$(document).ready(function () {
+ $("#documenter .docs-navbar").headroom({
+ tolerance: { up: 10, down: 10 },
+ });
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+$(document).ready(function () {
+ let meta = $("div[data-docstringscollapsed]").data();
+
+ if (meta?.docstringscollapsed) {
+ $("#documenter-article-toggle-button").trigger({
+ type: "click",
+ noToggleAnimation: true,
+ });
+ }
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+/*
+To get an in-depth about the thought process you can refer: https://hetarth02.hashnode.dev/series/gsoc
+
+PSEUDOCODE:
+
+Searching happens automatically as the user types or adjusts the selected filters.
+To preserve responsiveness, as much as possible of the slow parts of the search are done
+in a web worker. Searching and result generation are done in the worker, and filtering and
+DOM updates are done in the main thread. The filters are in the main thread as they should
+be very quick to apply. This lets filters be changed without re-searching with minisearch
+(which is possible even if filtering is on the worker thread) and also lets filters be
+changed _while_ the worker is searching and without message passing (neither of which are
+possible if filtering is on the worker thread)
+
+SEARCH WORKER:
+
+Import minisearch
+
+Build index
+
+On message from main thread
+ run search
+ find the first 200 unique results from each category, and compute their divs for display
+ note that this is necessary and sufficient information for the main thread to find the
+ first 200 unique results from any given filter set
+ post results to main thread
+
+MAIN:
+
+Launch worker
+
+Declare nonconstant globals (worker_is_running, last_search_text, unfiltered_results)
+
+On text update
+ if worker is not running, launch_search()
+
+launch_search
+ set worker_is_running to true, set last_search_text to the search text
+ post the search query to worker
+
+on message from worker
+ if last_search_text is not the same as the text in the search field,
+ the latest search result is not reflective of the latest search query, so update again
+ launch_search()
+ otherwise
+ set worker_is_running to false
+
+ regardless, display the new search results to the user
+ save the unfiltered_results as a global
+ update_search()
+
+on filter click
+ adjust the filter selection
+ update_search()
+
+update_search
+ apply search filters by looping through the unfiltered_results and finding the first 200
+ unique results that match the filters
+
+ Update the DOM
+*/
+
+/////// SEARCH WORKER ///////
+
+function worker_function(documenterSearchIndex, documenterBaseURL, filters) {
+ importScripts(
+ "https://cdn.jsdelivr.net/npm/minisearch@6.1.0/dist/umd/index.min.js"
+ );
+
+ let data = documenterSearchIndex.map((x, key) => {
+ x["id"] = key; // minisearch requires a unique for each object
+ return x;
+ });
+
+ // list below is the lunr 2.1.3 list minus the intersect with names(Base)
+ // (all, any, get, in, is, only, which) and (do, else, for, let, where, while, with)
+ // ideally we'd just filter the original list but it's not available as a variable
+ const stopWords = new Set([
+ "a",
+ "able",
+ "about",
+ "across",
+ "after",
+ "almost",
+ "also",
+ "am",
+ "among",
+ "an",
+ "and",
+ "are",
+ "as",
+ "at",
+ "be",
+ "because",
+ "been",
+ "but",
+ "by",
+ "can",
+ "cannot",
+ "could",
+ "dear",
+ "did",
+ "does",
+ "either",
+ "ever",
+ "every",
+ "from",
+ "got",
+ "had",
+ "has",
+ "have",
+ "he",
+ "her",
+ "hers",
+ "him",
+ "his",
+ "how",
+ "however",
+ "i",
+ "if",
+ "into",
+ "it",
+ "its",
+ "just",
+ "least",
+ "like",
+ "likely",
+ "may",
+ "me",
+ "might",
+ "most",
+ "must",
+ "my",
+ "neither",
+ "no",
+ "nor",
+ "not",
+ "of",
+ "off",
+ "often",
+ "on",
+ "or",
+ "other",
+ "our",
+ "own",
+ "rather",
+ "said",
+ "say",
+ "says",
+ "she",
+ "should",
+ "since",
+ "so",
+ "some",
+ "than",
+ "that",
+ "the",
+ "their",
+ "them",
+ "then",
+ "there",
+ "these",
+ "they",
+ "this",
+ "tis",
+ "to",
+ "too",
+ "twas",
+ "us",
+ "wants",
+ "was",
+ "we",
+ "were",
+ "what",
+ "when",
+ "who",
+ "whom",
+ "why",
+ "will",
+ "would",
+ "yet",
+ "you",
+ "your",
+ ]);
+
+ let index = new MiniSearch({
+ fields: ["title", "text"], // fields to index for full-text search
+ storeFields: ["location", "title", "text", "category", "page"], // fields to return with results
+ processTerm: (term) => {
+ let word = stopWords.has(term) ? null : term;
+ if (word) {
+ // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names
+ word = word
+ .replace(/^[^a-zA-Z0-9@!]+/, "")
+ .replace(/[^a-zA-Z0-9@!]+$/, "");
+
+ word = word.toLowerCase();
+ }
+
+ return word ?? null;
+ },
+ // add . as a separator, because otherwise "title": "Documenter.Anchors.add!", would not
+ // find anything if searching for "add!", only for the entire qualification
+ tokenize: (string) => string.split(/[\s\-\.]+/),
+ // options which will be applied during the search
+ searchOptions: {
+ prefix: true,
+ boost: { title: 100 },
+ fuzzy: 2,
+ },
+ });
+
+ index.addAll(data);
+
+ /**
+ * Used to map characters to HTML entities.
+ * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts
+ */
+ const htmlEscapes = {
+ "&": "&",
+ "<": "<",
+ ">": ">",
+ '"': """,
+ "'": "'",
+ };
+
+ /**
+ * Used to match HTML entities and HTML characters.
+ * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts
+ */
+ const reUnescapedHtml = /[&<>"']/g;
+ const reHasUnescapedHtml = RegExp(reUnescapedHtml.source);
+
+ /**
+ * Escape function from lodash
+ * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts
+ */
+ function escape(string) {
+ return string && reHasUnescapedHtml.test(string)
+ ? string.replace(reUnescapedHtml, (chr) => htmlEscapes[chr])
+ : string || "";
+ }
+
+ /**
+ * Make the result component given a minisearch result data object and the value
+ * of the search input as queryString. To view the result object structure, refer:
+ * https://lucaong.github.io/minisearch/modules/_minisearch_.html#searchresult
+ *
+ * @param {object} result
+ * @param {string} querystring
+ * @returns string
+ */
+ function make_search_result(result, querystring) {
+ let search_divider = `
`;
+ let display_link =
+ result.location.slice(Math.max(0), Math.min(50, result.location.length)) +
+ (result.location.length > 30 ? "..." : ""); // To cut-off the link because it messes with the overflow of the whole div
+
+ if (result.page !== "") {
+ display_link += ` (${result.page})`;
+ }
+
+ let textindex = new RegExp(`${querystring}`, "i").exec(result.text);
+ let text =
+ textindex !== null
+ ? result.text.slice(
+ Math.max(textindex.index - 100, 0),
+ Math.min(
+ textindex.index + querystring.length + 100,
+ result.text.length
+ )
+ )
+ : ""; // cut-off text before and after from the match
+
+ text = text.length ? escape(text) : "";
+
+ let display_result = text.length
+ ? "..." +
+ text.replace(
+ new RegExp(`${escape(querystring)}`, "i"), // For first occurrence
+ '$& '
+ ) +
+ "..."
+ : ""; // highlights the match
+
+ let in_code = false;
+ if (!["page", "section"].includes(result.category.toLowerCase())) {
+ in_code = true;
+ }
+
+ // We encode the full url to escape some special characters which can lead to broken links
+ let result_div = `
+
+
+
${escape(result.title)}
+
${result.category}
+
+
+ ${display_result}
+
+
+ ${display_link}
+
+
+ ${search_divider}
+ `;
+
+ return result_div;
+ }
+
+ self.onmessage = function (e) {
+ let query = e.data;
+ let results = index.search(query, {
+ filter: (result) => {
+ // Only return relevant results
+ return result.score >= 1;
+ },
+ });
+
+ // Pre-filter to deduplicate and limit to 200 per category to the extent
+ // possible without knowing what the filters are.
+ let filtered_results = [];
+ let counts = {};
+ for (let filter of filters) {
+ counts[filter] = 0;
+ }
+ let present = {};
+
+ for (let result of results) {
+ cat = result.category;
+ cnt = counts[cat];
+ if (cnt < 200) {
+ id = cat + "---" + result.location;
+ if (present[id]) {
+ continue;
+ }
+ present[id] = true;
+ filtered_results.push({
+ location: result.location,
+ category: cat,
+ div: make_search_result(result, query),
+ });
+ }
+ }
+
+ postMessage(filtered_results);
+ };
+}
+
+// `worker = Threads.@spawn worker_function(documenterSearchIndex)`, but in JavaScript!
+const filters = [
+ ...new Set(documenterSearchIndex["docs"].map((x) => x.category)),
+];
+const worker_str =
+ "(" +
+ worker_function.toString() +
+ ")(" +
+ JSON.stringify(documenterSearchIndex["docs"]) +
+ "," +
+ JSON.stringify(documenterBaseURL) +
+ "," +
+ JSON.stringify(filters) +
+ ")";
+const worker_blob = new Blob([worker_str], { type: "text/javascript" });
+const worker = new Worker(URL.createObjectURL(worker_blob));
+
+/////// SEARCH MAIN ///////
+
+// Whether the worker is currently handling a search. This is a boolean
+// as the worker only ever handles 1 or 0 searches at a time.
+var worker_is_running = false;
+
+// The last search text that was sent to the worker. This is used to determine
+// if the worker should be launched again when it reports back results.
+var last_search_text = "";
+
+// The results of the last search. This, in combination with the state of the filters
+// in the DOM, is used compute the results to display on calls to update_search.
+var unfiltered_results = [];
+
+// Which filter is currently selected
+var selected_filter = "";
+
+$(document).on("input", ".documenter-search-input", function (event) {
+ if (!worker_is_running) {
+ launch_search();
+ }
+});
+
+function launch_search() {
+ worker_is_running = true;
+ last_search_text = $(".documenter-search-input").val();
+ worker.postMessage(last_search_text);
+}
+
+worker.onmessage = function (e) {
+ if (last_search_text !== $(".documenter-search-input").val()) {
+ launch_search();
+ } else {
+ worker_is_running = false;
+ }
+
+ unfiltered_results = e.data;
+ update_search();
+};
+
+$(document).on("click", ".search-filter", function () {
+ if ($(this).hasClass("search-filter-selected")) {
+ selected_filter = "";
+ } else {
+ selected_filter = $(this).text().toLowerCase();
+ }
+
+ // This updates search results and toggles classes for UI:
+ update_search();
+});
+
+/**
+ * Make/Update the search component
+ */
+function update_search() {
+ let querystring = $(".documenter-search-input").val();
+
+ if (querystring.trim()) {
+ if (selected_filter == "") {
+ results = unfiltered_results;
+ } else {
+ results = unfiltered_results.filter((result) => {
+ return selected_filter == result.category.toLowerCase();
+ });
+ }
+
+ let search_result_container = ``;
+ let modal_filters = make_modal_body_filters();
+ let search_divider = `
`;
+
+ if (results.length) {
+ let links = [];
+ let count = 0;
+ let search_results = "";
+
+ for (var i = 0, n = results.length; i < n && count < 200; ++i) {
+ let result = results[i];
+ if (result.location && !links.includes(result.location)) {
+ search_results += result.div;
+ count++;
+ links.push(result.location);
+ }
+ }
+
+ if (count == 1) {
+ count_str = "1 result";
+ } else if (count == 200) {
+ count_str = "200+ results";
+ } else {
+ count_str = count + " results";
+ }
+ let result_count = `${count_str}
`;
+
+ search_result_container = `
+
+ ${modal_filters}
+ ${search_divider}
+ ${result_count}
+
+ ${search_results}
+
+
+ `;
+ } else {
+ search_result_container = `
+
+ ${modal_filters}
+ ${search_divider}
+
0 result(s)
+
+ No result found!
+ `;
+ }
+
+ if ($(".search-modal-card-body").hasClass("is-justify-content-center")) {
+ $(".search-modal-card-body").removeClass("is-justify-content-center");
+ }
+
+ $(".search-modal-card-body").html(search_result_container);
+ } else {
+ if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) {
+ $(".search-modal-card-body").addClass("is-justify-content-center");
+ }
+
+ $(".search-modal-card-body").html(`
+ Type something to get started!
+ `);
+ }
+}
+
+/**
+ * Make the modal filter html
+ *
+ * @returns string
+ */
+function make_modal_body_filters() {
+ let str = filters
+ .map((val) => {
+ if (selected_filter == val.toLowerCase()) {
+ return `${val} `;
+ } else {
+ return `${val} `;
+ }
+ })
+ .join("");
+
+ return `
+
+ Filters:
+ ${str}
+
`;
+}
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+// Modal settings dialog
+$(document).ready(function () {
+ var settings = $("#documenter-settings");
+ $("#documenter-settings-button").click(function () {
+ settings.toggleClass("is-active");
+ });
+ // Close the dialog if X is clicked
+ $("#documenter-settings button.delete").click(function () {
+ settings.removeClass("is-active");
+ });
+ // Close dialog if ESC is pressed
+ $(document).keyup(function (e) {
+ if (e.keyCode == 27) settings.removeClass("is-active");
+ });
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+$(document).ready(function () {
+ let search_modal_header = `
+
+ `;
+
+ let initial_search_body = `
+ Type something to get started!
+ `;
+
+ let search_modal_footer = `
+
+ `;
+
+ $(document.body).append(
+ `
+
+
+
+ ${search_modal_header}
+
+ ${initial_search_body}
+
+ ${search_modal_footer}
+
+
+ `
+ );
+
+ document.querySelector(".docs-search-query").addEventListener("click", () => {
+ openModal();
+ });
+
+ document
+ .querySelector(".close-search-modal")
+ .addEventListener("click", () => {
+ closeModal();
+ });
+
+ $(document).on("click", ".search-result-link", function () {
+ closeModal();
+ });
+
+ document.addEventListener("keydown", (event) => {
+ if ((event.ctrlKey || event.metaKey) && event.key === "/") {
+ openModal();
+ } else if (event.key === "Escape") {
+ closeModal();
+ }
+
+ return false;
+ });
+
+ // Functions to open and close a modal
+ function openModal() {
+ let searchModal = document.querySelector("#search-modal");
+
+ searchModal.classList.add("is-active");
+ document.querySelector(".documenter-search-input").focus();
+ }
+
+ function closeModal() {
+ let searchModal = document.querySelector("#search-modal");
+ let initial_search_body = `
+ Type something to get started!
+ `;
+
+ searchModal.classList.remove("is-active");
+ document.querySelector(".documenter-search-input").blur();
+
+ if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) {
+ $(".search-modal-card-body").addClass("is-justify-content-center");
+ }
+
+ $(".documenter-search-input").val("");
+ $(".search-modal-card-body").html(initial_search_body);
+ }
+
+ document
+ .querySelector("#search-modal .modal-background")
+ .addEventListener("click", () => {
+ closeModal();
+ });
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+// Manages the showing and hiding of the sidebar.
+$(document).ready(function () {
+ var sidebar = $("#documenter > .docs-sidebar");
+ var sidebar_button = $("#documenter-sidebar-button");
+ sidebar_button.click(function (ev) {
+ ev.preventDefault();
+ sidebar.toggleClass("visible");
+ if (sidebar.hasClass("visible")) {
+ // Makes sure that the current menu item is visible in the sidebar.
+ $("#documenter .docs-menu a.is-active").focus();
+ }
+ });
+ $("#documenter > .docs-main").bind("click", function (ev) {
+ if ($(ev.target).is(sidebar_button)) {
+ return;
+ }
+ if (sidebar.hasClass("visible")) {
+ sidebar.removeClass("visible");
+ }
+ });
+});
+
+// Resizes the package name / sitename in the sidebar if it is too wide.
+// Inspired by: https://github.com/davatron5000/FitText.js
+$(document).ready(function () {
+ e = $("#documenter .docs-autofit");
+ function resize() {
+ var L = parseInt(e.css("max-width"), 10);
+ var L0 = e.width();
+ if (L0 > L) {
+ var h0 = parseInt(e.css("font-size"), 10);
+ e.css("font-size", (L * h0) / L0);
+ // TODO: make sure it survives resizes?
+ }
+ }
+ // call once and then register events
+ resize();
+ $(window).resize(resize);
+ $(window).on("orientationchange", resize);
+});
+
+// Scroll the navigation bar to the currently selected menu item
+$(document).ready(function () {
+ var sidebar = $("#documenter .docs-menu").get(0);
+ var active = $("#documenter .docs-menu .is-active").get(0);
+ if (typeof active !== "undefined") {
+ sidebar.scrollTop = active.offsetTop - sidebar.offsetTop - 15;
+ }
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+// Theme picker setup
+$(document).ready(function () {
+ // onchange callback
+ $("#documenter-themepicker").change(function themepick_callback(ev) {
+ var themename = $("#documenter-themepicker option:selected").attr("value");
+ if (themename === "auto") {
+ // set_theme(window.matchMedia('(prefers-color-scheme: dark)').matches ? 'dark' : 'light');
+ window.localStorage.removeItem("documenter-theme");
+ } else {
+ // set_theme(themename);
+ window.localStorage.setItem("documenter-theme", themename);
+ }
+ // We re-use the global function from themeswap.js to actually do the swapping.
+ set_theme_from_local_storage();
+ });
+
+ // Make sure that the themepicker displays the correct theme when the theme is retrieved
+ // from localStorage
+ if (typeof window.localStorage !== "undefined") {
+ var theme = window.localStorage.getItem("documenter-theme");
+ if (theme !== null) {
+ $("#documenter-themepicker option").each(function (i, e) {
+ e.selected = e.value === theme;
+ });
+ }
+ }
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+// update the version selector with info from the siteinfo.js and ../versions.js files
+$(document).ready(function () {
+ // If the version selector is disabled with DOCUMENTER_VERSION_SELECTOR_DISABLED in the
+ // siteinfo.js file, we just return immediately and not display the version selector.
+ if (
+ typeof DOCUMENTER_VERSION_SELECTOR_DISABLED === "boolean" &&
+ DOCUMENTER_VERSION_SELECTOR_DISABLED
+ ) {
+ return;
+ }
+
+ var version_selector = $("#documenter .docs-version-selector");
+ var version_selector_select = $("#documenter .docs-version-selector select");
+
+ version_selector_select.change(function (x) {
+ target_href = version_selector_select
+ .children("option:selected")
+ .get(0).value;
+ window.location.href = target_href;
+ });
+
+ // add the current version to the selector based on siteinfo.js, but only if the selector is empty
+ if (
+ typeof DOCUMENTER_CURRENT_VERSION !== "undefined" &&
+ $("#version-selector > option").length == 0
+ ) {
+ var option = $(
+ "" +
+ DOCUMENTER_CURRENT_VERSION +
+ " "
+ );
+ version_selector_select.append(option);
+ }
+
+ if (typeof DOC_VERSIONS !== "undefined") {
+ var existing_versions = version_selector_select.children("option");
+ var existing_versions_texts = existing_versions.map(function (i, x) {
+ return x.text;
+ });
+ DOC_VERSIONS.forEach(function (each) {
+ var version_url = documenterBaseURL + "/../" + each + "/";
+ var existing_id = $.inArray(each, existing_versions_texts);
+ // if not already in the version selector, add it as a new option,
+ // otherwise update the old option with the URL and enable it
+ if (existing_id == -1) {
+ var option = $(
+ "" + each + " "
+ );
+ version_selector_select.append(option);
+ } else {
+ var option = existing_versions[existing_id];
+ option.value = version_url;
+ option.disabled = false;
+ }
+ });
+ }
+
+ // only show the version selector if the selector has been populated
+ if (version_selector_select.children("option").length > 0) {
+ version_selector.toggleClass("visible");
+ }
+});
+
+})
diff --git a/v2.3.0/assets/logo.png b/v2.3.0/assets/logo.png
new file mode 100644
index 0000000..2737b9d
Binary files /dev/null and b/v2.3.0/assets/logo.png differ
diff --git a/v2.3.0/assets/themes/documenter-dark.css b/v2.3.0/assets/themes/documenter-dark.css
new file mode 100644
index 0000000..53889fb
--- /dev/null
+++ b/v2.3.0/assets/themes/documenter-dark.css
@@ -0,0 +1,7 @@
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+ Theme: a11y-dark
+ Author: @ericwbailey
+ Maintainer: @ericwbailey
+
+ Based on the Tomorrow Night Eighties theme: https://github.com/isagalaev/highlight.js/blob/master/src/styles/tomorrow-night-eighties.css
+*/}html.theme--documenter-dark html{background-color:#1f2424;font-size:16px;-moz-osx-font-smoothing:grayscale;-webkit-font-smoothing:antialiased;min-width:300px;overflow-x:auto;overflow-y:scroll;text-rendering:optimizeLegibility;text-size-adjust:100%}html.theme--documenter-dark article,html.theme--documenter-dark aside,html.theme--documenter-dark figure,html.theme--documenter-dark footer,html.theme--documenter-dark header,html.theme--documenter-dark hgroup,html.theme--documenter-dark section{display:block}html.theme--documenter-dark body,html.theme--documenter-dark button,html.theme--documenter-dark input,html.theme--documenter-dark optgroup,html.theme--documenter-dark select,html.theme--documenter-dark textarea{font-family:"Lato Medium",-apple-system,BlinkMacSystemFont,"Segoe UI","Helvetica Neue","Helvetica","Arial",sans-serif}html.theme--documenter-dark code,html.theme--documenter-dark 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h1,html.theme--documenter-dark .content h2,html.theme--documenter-dark .content h3,html.theme--documenter-dark .content h4,html.theme--documenter-dark .content h5,html.theme--documenter-dark .content h6{color:#f2f2f2;font-weight:600;line-height:1.125}html.theme--documenter-dark .content h1{font-size:2em;margin-bottom:0.5em}html.theme--documenter-dark .content h1:not(:first-child){margin-top:1em}html.theme--documenter-dark .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--documenter-dark .content h2:not(:first-child){margin-top:1.1428em}html.theme--documenter-dark .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--documenter-dark .content h3:not(:first-child){margin-top:1.3333em}html.theme--documenter-dark .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--documenter-dark .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--documenter-dark .content h6{font-size:1em;margin-bottom:1em}html.theme--documenter-dark .content 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.docs-logo>img.is-5by4{padding-top:80%}html.theme--documenter-dark .image.is-4by3,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-4by3{padding-top:75%}html.theme--documenter-dark .image.is-3by2,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by2{padding-top:66.6666%}html.theme--documenter-dark .image.is-5by3,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-5by3{padding-top:60%}html.theme--documenter-dark .image.is-16by9,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-16by9{padding-top:56.25%}html.theme--documenter-dark .image.is-2by1,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-2by1{padding-top:50%}html.theme--documenter-dark .image.is-3by1,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by1{padding-top:33.3333%}html.theme--documenter-dark .image.is-4by5,html.theme--documenter-dark #documenter .docs-sidebar 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diff --git a/v2.3.0/assets/themes/documenter-light.css b/v2.3.0/assets/themes/documenter-light.css
new file mode 100644
index 0000000..2f168c7
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diff --git a/v2.3.0/assets/themeswap.js b/v2.3.0/assets/themeswap.js
new file mode 100644
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+++ b/v2.3.0/assets/themeswap.js
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+// Small function to quickly swap out themes. Gets put into the tag..
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+ // attribute not set => non-theme stylesheet => ignore
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+function maybeAddWarning() {
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+ // in siteinfo.js.
+ // If either of these are undefined something went horribly wrong, so we abort.
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diff --git a/v2.3.0/index.html b/v2.3.0/index.html
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+
+Home · openBF openBF is an open-source 1D blood flow solver based on MUSCL finite-volume numerical scheme, written in Julia and released under Apache 2.0 free software license.
openBF has been developed by Dr. A. Melis under the supervision of Dr. A. Marzo as part of the PhD project on cardiovascular modelling at INSIGNEO Institute, Department of Mechanical Engineering of The University of Sheffield. All the contributors are listed on github .
The accompaigning PhD Thesis contains the relevant theoretical background and the explanation of the numerical scheme implemented. A shorter backgound introduction is given in the Overview page.
Head over to the Quickstart section for installation and running instructions.
openBF has been used in the following works:
Ning W, Sharma K, Sourbron SP, Benemerito I, Marzo A. Distinguishing hypertensive renal injury from diabetic nephropathy using MR imaging and computational modelling of renal blood flow , VPH2022 September 2022, Porto, PO In proceedings
Benemerito I, Narata AP, Narracott A, Marzo A. Determining clinically-viable biomarkers for ischaemic stroke through a mechanistic and machine learning approach . Annals of Biomedical Engineering , 2022. DOI: 10.1007/s10439-022-02956-7
Mustafa A. An efficient computational approach to guide intervention in treatment of stroke . PhD Thesis , 2021
Benemerito I, Jordan B, Mustafa A, Marzo A. Quantification of the effects of ageing, hypertension and atherosclerosis on flow reversal during a mechanical thrombectomy procedure , BioMedEng21 September 2021, Sheffield, UK In proceedings
Benemerito I, Narata AP, Narracott A, Marzo A. Pulsatility indices can inform on distal perfusion following ischaemic stroke , CMMBE September 2021, Online event, In proceedings
Benemerito I, Narata AP, Narracott A, Marzo A. Identification of biomarkers for perfusion following an ischaemic event , CMBE September 2021, Online event, In proceedings
Melis A. Gaussian process emulators for 1D vascular models . PhD Thesis , 2017.
Melis A, Clayton RH, Marzo A. Bayesian sensitivity analysis of a 1D vascular model with Gaussian process emulators . International Journal for Numerical Methods in Biomedical Engineering , 2017. DOI: 10.1002/cnm.2882
Melis A, Clayton RH, Marzo A. A more efficient approach to perform sensitivity analyses in 0D/1D cardiovascular models , CMBE July 2015, Cachan, FR. In proceedings
Have you used openBF for your research? Let us know!
If you find openBF useful in your work, we kindly request that you cite the following figshare repository
@misc{openBF.jl-2018,
+title={openBF: Julia software for 1D blood flow modelling},
+url={https://figshare.com/articles/openBF_Julia_software_for_1D_blood_flow_modelling/7166183/1},
+DOI={10.15131/shef.data.7166183},
+abstractNote={
+openBF is an open-source 1D blood flow solver based on MUSCL finite-volume numerical scheme, written in Julia and released under Apache 2.0 free software license.
+
+See https://github.com/INSIGNEO/openBF for the git repository and https://insigneo.github.io/openBF/ for the documentation.
+},
+publisher={figshare},
+author={Melis, Alessandro},
+year={2018},
+month={Oct}}
and the accompaining PhD thesis
@phdthesis{wreo19175,
+ month = {August},
+ title = {Gaussian process emulators for 1D vascular models},
+ school = {University of Sheffield},
+ author = {Alessandro Melis},
+ publisher = {University of Sheffield},
+ year = {2017},
+ url = {https://etheses.whiterose.ac.uk/19175/},
+}
Theme
Automatic (OS) documenter-light documenter-dark
This document was generated with Documenter.jl version 1.3.0 on Tuesday 2 April 2024 . Using Julia version 1.10.2.
diff --git a/v2.3.0/man/config/index.html b/v2.3.0/man/config/index.html
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+
+Configuration · openBF Here is a description of the config file and its entries. You can also use openBF webapp to quickly fill in config files.
The first line in the configuration file contains the project_name
variable.
project_name: "my_simulation_name"
This is a string that will be used to name the results folder. At the end of the simulation, all the results files will be found in project_name_results/
directory.
inlet_file: "my_inlet.dat"
The inlet BC is given trough an ASCII file containing a list of values (pressure or volumetric flow rate) in time. For now, the inlet vessel is the one whose sn
node is 1
.
Following the write_results
list is defined.
write_results: ["P"] # ["P", "Q", "u", "A"]
Here you can specify which quantities to write in the output files (P
ressure, Q
flow, u
velocity and A
rea). These are all optional but at least one is recommended.
Then there are three main sections: solver
, blood
, and network
.
solver:
+ Ccfl: 0.9
+ cycles: 100
+ convergence_tolerance: 5.0
+ jump: 100
It contains the values for the numerical scheme parameters:
Ccfl
is the Courant's number used to compute the $\Delta t$ and it is usually taken equal to $0.9$ .
cycles
is the maximum number of cardiac cycles to be simulated. This is used to stop openBF execution in case of non-converging simulations. An openBF simulation usually takes less than 20 cardiac cycles to converge.
convergence_tolerance
is the maximum error in $mmHg$ allowed between two consecutive cardiac cycle to claim convergence.
jump
is the number of time-points to be saved in the result files.
blood:
+ rho: 1060.0
+ mu: 0.004
Blood rheological properties:
mu
dynamic viscosity in $Pa \cdot s$ ;rho
density in $kg \cdot m^{-3}$ .This contains the list of vessels in the network. Each vessel has the following mandatory properties:
label
the vessel name that will be used to name result files;sn
segment source node;tn
segment target node;L
vessel lenght in $m$ ;E
wall Young's modulus in $Pa$ ;R0
or Rp
and Rd
describe the lumen radius. If R0
is defined, the vessel is assumed to have a constant reference lumen radius; it Rp
and Rd
are specified, the vessel is set to taper linearly from the proximal lumen radius (i.e. Rp
, the lumen radius at sn
) to the distal lumen radius (i.e. Rd
, the lumen radius at tn
).Optional parameters are:
to_save
a boolean flag (default true
) to tell openBF to save results for the current vessel;
M
is the number of division along the vessels used to compute the artery $\Delta x$ . When not specified, openBF automatically meshes the arteries so that $\Delta x$ is at least $1 mm$ ;
Pext
vessel external pressure in $Pa$ , default $0.0 Pa$ ;
gamma_profile
is the radial velocity profile parameter used in the calculation of the viscous losses term, default $2$ (parabolic profile).
The system boundary conditions (BCs) are applied to inlet vessel(s) and outlet vessel(s).
In the case a vessel outlet is not connected to any other vessel, an outlet BC must be assigned by imposing a reflection coefficient Rt
or by coupling a windkessel model. In case of Rt
:
In case of two-element windkessel:
R1
peripheral resistanceCc
peripheral complianceIn case of three-element windkessel:
R1
first peripheral resistanceR2
second peripheral resistanceCc
peripheral complianceYou can also enable inlet_impedance_matching
to let openBF optimise R1
at runtime. This will match the windkessel inlet impedance and minimise artificial reflections (recommended).
The configuration file template is reported below. This contains all the mandatory and optional paramenter that can be specified in openBF. The parameter type is reported for each line after the #.
project_name: <project name> # String
+inlet_file: <inlet name>.dat
+write_results: ["P"] # ["P", "Q", "u", "A"]
+
+solver:
+ Ccfl: <Courant's number> # 0.0 < Ccfl ≤ 1.0; Float
+ cycles: <Max number of cardiac cycles> # Int
+ convergence_tolerance: <Max RMSE between two cycles> # Pressure, Float
+ jump: <Number of timepoints in result files; default 100> # Int
+
+blood:
+ mu: <dynamic viscosity> # [Pa⋅s]; Float
+ rho: <density> # [kg/m^3]; Float
+
+network:
+ - label: <vessel name> # String
+ to_save: true # Bool (default true)
+ sn: <source node> # Int
+ tn: <target node> # Int
+
+ L: <length> # [m]; Float
+ M: <number of divisions along the vessel; default so that Δx = L/M = 1.0mm; minimum M=5> # Int (optional)
+ E: <wall Young's modulus> # [Pa]; Float
+ h0: <wall thickness; default computed as h0(x) = f(R0)> # [m]; Float (optional)
+
+ R0: <constant lumen radius> # [m]; Float
+ #------ OR ------ to assign a linear tapering
+ Rp: <proximal lumen radius, i.e. lumen radius at sn>
+ Rd: <distal lumen radius, i.e. lumen radius at tn>
+
+ Pext: <external pressure; default 0.0 Pa> # [Pa]; Float (optional)
+
+ gamma_profile: <radial velocity profile parameter; default 9> # ≥ 2.0; Float
+
+ # outlet wk2
+ R1: <windkessel peripheral resistance> # [Pa⋅s⋅m^-3]; Float
+ Cc: <compliance> # [m^3⋅Pa^-1]; Float
+ #------ OR ------ outlet wk3
+ R1: <windkessel inlet impedance>
+ R2: <peripheral resistance>
+ Cc: <compliance>
+ inlet_impedance_matching: true # Bool (default false)
+ #------ OR ------ outlet reflection
+ Rt: <reflection coefficient> # 1.0 ≤ Rt ≥ -1.0; Float
Theme
Automatic (OS) documenter-light documenter-dark
This document was generated with Documenter.jl version 1.3.0 on Tuesday 2 April 2024 . Using Julia version 1.10.2.
diff --git a/v2.3.0/man/examples/index.html b/v2.3.0/man/examples/index.html
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@@ -0,0 +1,2 @@
+
+Examples · openBF The repository models folder contains configuration and inlet files for:
In-vitro model from Matthys KS, Alastruey J, Peiró J, Khir AW, Segers P, Verdonck PR, Parker KH, Sherwin SJ. Pulse wave propagation in a model human arterial network: assessment of 1-D numerical simulations against in vitro measurements . Journal of biomechanics. 2007 Dec 31;40(15):3476-86.
Circle of Willis model from Alastruey J, Parker KH, Peiró J, Byrd SM, Sherwin SJ. Modelling the circle of Willis to assess the effects of anatomical variations and occlusions on cerebral flows . Journal of biomechanics. 2007 Dec 31;40(8):1794-805
Benchmark models from Boileau E, Nithiarasu P, Blanco PJ, Müller LO, Fossan FE, Hellevik LR, Donders WP, Huberts W, Willemet M, Alastruey J. A benchmark study of numerical schemes for one‐dimensional arterial blood flow modelling . International journal for numerical methods in biomedical engineering. 2015 Oct 1;31(10).
Theme
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diff --git a/v2.3.0/man/overview/index.html b/v2.3.0/man/overview/index.html
new file mode 100644
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+
+Overview · openBF The cardiovascular system is a complex network of elastic vessels through which blood is pumped by contraction of the heart. This pulsatile regime and vessel elasticity cause pressure to propagate along the arterial circulation as waves. Mechanical discontinuities caused by bifurcation, bends or cardiovascular pathology cause pressure waves to be reflected in all directions.
Pressure waves measured at a specific location can be seen as the result of a superimposition of incident (forward) and reflected (backward) waves. The analysis of this superposition mechanism allows for the study of mechanical properties upstream and downstream of the measurement point and can be a rich source of diagnostic information about the system through which these waves propagate. However, given the vascular system complexity, it is at present difficult to ascribe a particular waveform feature to a specific trait of the arterial circulation
The understanding of the cause-effect mechanisms governing wave propagation in the cardiovascular system was used at INSIGNEO to develop a computer model that can reproduce this behaviour in a quantitative way. openBF is a Julia package for the solution of one-dimensional (1D) blood flow in networks of elastic arteries.
The 1D model is derived from the three-dimensional formulation of the viscous fluid motion equations, the Navier-Stokes equations. These are simplified by assuming the arteries to be long, narrow, and elastic tubes and the blood to be incompressible (i.e., its density is constant over time) and behaving as a Newtonian fluid (i.e., its viscosity does not depend on its velocity).
Despite all the above assumptions, the resulting partial differential equation system is complex enough to simulate the physics of pulse wave transmission and reflection. This is at the expense of results accuracy in areas where the flow structure is inherently three-dimensional, e.g., in the proximity of heart valves and bifurcations. Conversely, the computational requirements are small compared to 3D simulations, allowing the simulation of the entire cardiovascular system rather than only circumscribed parts.
The software openBF was developed at INSIGNEO Institute for in silico Medicine at The University of Sheffield (UK) as part of A. Melis’ PhD thesis under the supervision of Dr. A. Marzo . We gratefully acknowledge funding from the UK Engineering and Physical Sciences Research Council (Grant Number EP/K037145/1). openBF is based on MUSCL finite-volume numerical scheme, written in Julia, and released under Apache 2.0 free software license on GitHub.
The solver is currently used in several HPC systems within the H2020 CompBioMed Centre of Excellence in Computational Biomedicine (Grant Agreement №675451). In SURFSara ’s HPC-Cloud, it is being used for large-scale sensitivity analysis and uncertainty quantification studies, towards clinical application. The simulations reported in the thesis and in this paper where run in TUoS’s ShARC tier-3 cluster. More information can be found on the official page and in CompBioMed Software Hub .
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This document was generated with Documenter.jl version 1.3.0 on Tuesday 2 April 2024 . Using Julia version 1.10.2.
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+Quickstart · openBF The latest Julia binary can be downloaded for all platforms from the official website .
openBF can be installed via Pkg.clone
. Start julia
in a terminal session and run
using Pkg
+Pkg.clone("https://github.com/INSIGNEO/openBF.git")
openBF API consists of a single function
run_simulation(
+ yaml_config_path::String;
+ verbose::Bool = false, # show progress bars
+ out_files::Bool = false, # save .out files with the all the cycles
+ save_stats::Bool = false, # save .conv file with simulation stats
+ )
whose main argument is the name of a .yaml
file (see here for an introduction to yaml) containining the description of the vascular network, blood properties, and numerical solver parameters (see Configuration ).
Running a simulation consists in calling
using openBF
+run_simulation("input.yml", verbose=true, save_stats=true)
This will create a <project_name>_results
folder containing all the output files from the simulation.
Simulation results are saved in the <project_name>_results
directory or in the output_directory
specified. There, for each artery in your network, you'll find a file per output quantity (these are specified in the write_results
list).
By default only .last
files are saved. Thes contains only the last simulated cardiac cycle; at convergence, these are the files you want to look at.
You can also set out_files = true
when calling run_simulation
. This results in the writing of .out
files which contain the whole simulation history, i.e., all the cardiac cycles simulated.
When setting save_stats=true
, a <project_name>.conv
file is written in the results dolder. This reads
<has the simulation converged> # boolean: true or false
+<elapsed cardiac cycles> # integer
+<elapsed time> # float, seconds
+<memory allocated> # integer, bytes
+<garbace collection % time> # float, percentage
These files contain as many rows as defined in the config by the jump
parameter (default 100
), and 6 columns. The first column contains the simulation time for the current cardiac cycles; column 2-6 report waveforms at five locations along the vessel, namely inlet , 1/4th of the length, mid-point , 3/4th of the length and outlet .
Theme
Automatic (OS) documenter-light documenter-dark
This document was generated with Documenter.jl version 1.3.0 on Tuesday 2 April 2024 . Using Julia version 1.10.2.
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+[{"location":"man/overview/","page":"Overview","title":"Overview","text":"The cardiovascular system is a complex network of elastic vessels through which blood is pumped by contraction of the heart. This pulsatile regime and vessel elasticity cause pressure to propagate along the arterial circulation as waves. Mechanical discontinuities caused by bifurcation, bends or cardiovascular pathology cause pressure waves to be reflected in all directions.","category":"page"},{"location":"man/overview/","page":"Overview","title":"Overview","text":"(Image: )","category":"page"},{"location":"man/overview/","page":"Overview","title":"Overview","text":"Pressure waves measured at a specific location can be seen as the result of a superimposition of incident (forward) and reflected (backward) waves. The analysis of this superposition mechanism allows for the study of mechanical properties upstream and downstream of the measurement point and can be a rich source of diagnostic information about the system through which these waves propagate. However, given the vascular system complexity, it is at present difficult to ascribe a particular waveform feature to a specific trait of the arterial circulation","category":"page"},{"location":"man/overview/","page":"Overview","title":"Overview","text":"The understanding of the cause-effect mechanisms governing wave propagation in the cardiovascular system was used at INSIGNEO to develop a computer model that can reproduce this behaviour in a quantitative way. openBF is a Julia package for the solution of one-dimensional (1D) blood flow in networks of elastic arteries.","category":"page"},{"location":"man/overview/#Why-1D?","page":"Overview","title":"Why 1D?","text":"","category":"section"},{"location":"man/overview/","page":"Overview","title":"Overview","text":"The 1D model is derived from the three-dimensional formulation of the viscous fluid motion equations, the Navier-Stokes equations. These are simplified by assuming the arteries to be long, narrow, and elastic tubes and the blood to be incompressible (i.e., its density is constant over time) and behaving as a Newtonian fluid (i.e., its viscosity does not depend on its velocity).","category":"page"},{"location":"man/overview/","page":"Overview","title":"Overview","text":"(Image: )","category":"page"},{"location":"man/overview/#Does-it-work?","page":"Overview","title":"Does it work?","text":"","category":"section"},{"location":"man/overview/","page":"Overview","title":"Overview","text":"Despite all the above assumptions, the resulting partial differential equation system is complex enough to simulate the physics of pulse wave transmission and reflection. This is at the expense of results accuracy in areas where the flow structure is inherently three-dimensional, e.g., in the proximity of heart valves and bifurcations. Conversely, the computational requirements are small compared to 3D simulations, allowing the simulation of the entire cardiovascular system rather than only circumscribed parts.","category":"page"},{"location":"man/overview/","page":"Overview","title":"Overview","text":"(Image: )","category":"page"},{"location":"man/overview/#Acknowledgements","page":"Overview","title":"Acknowledgements","text":"","category":"section"},{"location":"man/overview/","page":"Overview","title":"Overview","text":"The software openBF was developed at INSIGNEO Institute for in silico Medicine at The University of Sheffield (UK) as part of A. Melis’ PhD thesis under the supervision of Dr. A. Marzo. We gratefully acknowledge funding from the UK Engineering and Physical Sciences Research Council (Grant Number EP/K037145/1). openBF is based on MUSCL finite-volume numerical scheme, written in Julia, and released under Apache 2.0 free software license on GitHub.","category":"page"},{"location":"man/overview/","page":"Overview","title":"Overview","text":"The solver is currently used in several HPC systems within the H2020 CompBioMed Centre of Excellence in Computational Biomedicine (Grant Agreement №675451). In SURFSara’s HPC-Cloud, it is being used for large-scale sensitivity analysis and uncertainty quantification studies, towards clinical application. The simulations reported in the thesis and in this paper where run in TUoS’s ShARC tier-3 cluster. More information can be found on the official page and in CompBioMed Software Hub.","category":"page"},{"location":"man/examples/","page":"Examples","title":"Examples","text":"The repository models folder contains configuration and inlet files for:","category":"page"},{"location":"man/examples/","page":"Examples","title":"Examples","text":"In-vitro model from Matthys KS, Alastruey J, Peiró J, Khir AW, Segers P, Verdonck PR, Parker KH, Sherwin SJ. Pulse wave propagation in a model human arterial network: assessment of 1-D numerical simulations against in vitro measurements. Journal of biomechanics. 2007 Dec 31;40(15):3476-86.\nCircle of Willis model from Alastruey J, Parker KH, Peiró J, Byrd SM, Sherwin SJ. Modelling the circle of Willis to assess the effects of anatomical variations and occlusions on cerebral flows. Journal of biomechanics. 2007 Dec 31;40(8):1794-805\nBenchmark models from Boileau E, Nithiarasu P, Blanco PJ, Müller LO, Fossan FE, Hellevik LR, Donders WP, Huberts W, Willemet M, Alastruey J. A benchmark study of numerical schemes for one‐dimensional arterial blood flow modelling. International journal for numerical methods in biomedical engineering. 2015 Oct 1;31(10).","category":"page"},{"location":"#openBF","page":"Home","title":"openBF","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"openBF is an open-source 1D blood flow solver based on MUSCL finite-volume numerical scheme, written in Julia and released under Apache 2.0 free software license.","category":"page"},{"location":"","page":"Home","title":"Home","text":"openBF has been developed by Dr. A. Melis under the supervision of Dr. A. Marzo as part of the PhD project on cardiovascular modelling at INSIGNEO Institute, Department of Mechanical Engineering of The University of Sheffield. All the contributors are listed on github.","category":"page"},{"location":"","page":"Home","title":"Home","text":"The accompaigning PhD Thesis contains the relevant theoretical background and the explanation of the numerical scheme implemented. A shorter backgound introduction is given in the Overview page.","category":"page"},{"location":"","page":"Home","title":"Home","text":"Head over to the Quickstart section for installation and running instructions.","category":"page"},{"location":"#Publications","page":"Home","title":"Publications","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"openBF has been used in the following works:","category":"page"},{"location":"","page":"Home","title":"Home","text":"Ning W, Sharma K, Sourbron SP, Benemerito I, Marzo A. Distinguishing hypertensive renal injury from diabetic nephropathy using MR imaging and computational modelling of renal blood flow, VPH2022 September 2022, Porto, PO In proceedings\nBenemerito I, Narata AP, Narracott A, Marzo A. Determining clinically-viable biomarkers for ischaemic stroke through a mechanistic and machine learning approach. Annals of Biomedical Engineering, 2022. DOI: 10.1007/s10439-022-02956-7\nMustafa A. An efficient computational approach to guide intervention in treatment of stroke. PhD Thesis, 2021\nBenemerito I, Jordan B, Mustafa A, Marzo A. Quantification of the effects of ageing, hypertension and atherosclerosis on flow reversal during a mechanical thrombectomy procedure, BioMedEng21 September 2021, Sheffield, UK In proceedings\nBenemerito I, Narata AP, Narracott A, Marzo A. Pulsatility indices can inform on distal perfusion following ischaemic stroke, CMMBE September 2021, Online event, In proceedings\nBenemerito I, Narata AP, Narracott A, Marzo A. Identification of biomarkers for perfusion following an ischaemic event, CMBE September 2021, Online event, In proceedings\nMelis A. Gaussian process emulators for 1D vascular models. PhD Thesis, 2017.\nMelis A, Clayton RH, Marzo A. Bayesian sensitivity analysis of a 1D vascular model with Gaussian process emulators. International Journal for Numerical Methods in Biomedical Engineering, 2017. DOI: 10.1002/cnm.2882\nMelis A, Clayton RH, Marzo A. A more efficient approach to perform sensitivity analyses in 0D/1D cardiovascular models, CMBE July 2015, Cachan, FR. In proceedings","category":"page"},{"location":"","page":"Home","title":"Home","text":"Have you used openBF for your research? Let us know!","category":"page"},{"location":"#Cite","page":"Home","title":"Cite","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"If you find openBF useful in your work, we kindly request that you cite the following figshare repository","category":"page"},{"location":"","page":"Home","title":"Home","text":"@misc{openBF.jl-2018,\ntitle={openBF: Julia software for 1D blood flow modelling}, \nurl={https://figshare.com/articles/openBF_Julia_software_for_1D_blood_flow_modelling/7166183/1}, \nDOI={10.15131/shef.data.7166183}, \nabstractNote={\nopenBF is an open-source 1D blood flow solver based on MUSCL finite-volume numerical scheme, written in Julia and released under Apache 2.0 free software license.\n\nSee https://github.com/INSIGNEO/openBF for the git repository and https://insigneo.github.io/openBF/ for the documentation.\n}, \npublisher={figshare}, \nauthor={Melis, Alessandro}, \nyear={2018}, \nmonth={Oct}}","category":"page"},{"location":"","page":"Home","title":"Home","text":"and the accompaining PhD thesis","category":"page"},{"location":"","page":"Home","title":"Home","text":"@phdthesis{wreo19175,\n month = {August},\n title = {Gaussian process emulators for 1D vascular models},\n school = {University of Sheffield},\n author = {Alessandro Melis},\n publisher = {University of Sheffield},\n year = {2017},\n url = {https://etheses.whiterose.ac.uk/19175/},\n}","category":"page"},{"location":"man/config/","page":"Configuration","title":"Configuration","text":"Here is a description of the config file and its entries. You can also use openBF webapp to quickly fill in config files.","category":"page"},{"location":"man/config/","page":"Configuration","title":"Configuration","text":"","category":"page"},{"location":"man/config/","page":"Configuration","title":"Configuration","text":"The first line in the configuration file contains the project_name variable. ","category":"page"},{"location":"man/config/","page":"Configuration","title":"Configuration","text":"project_name: \"my_simulation_name\"","category":"page"},{"location":"man/config/","page":"Configuration","title":"Configuration","text":"This is a string that will be used to name the results folder. At the end of the simulation, all the results files will be found in project_name_results/ directory.","category":"page"},{"location":"man/config/","page":"Configuration","title":"Configuration","text":"inlet_file: \"my_inlet.dat\"","category":"page"},{"location":"man/config/","page":"Configuration","title":"Configuration","text":"The inlet BC is given trough an ASCII file containing a list of values (pressure or volumetric flow rate) in time. For now, the inlet vessel is the one whose sn node is 1.","category":"page"},{"location":"man/config/","page":"Configuration","title":"Configuration","text":"Following the write_results list is defined.","category":"page"},{"location":"man/config/","page":"Configuration","title":"Configuration","text":"write_results: [\"P\"] # [\"P\", \"Q\", \"u\", \"A\"]","category":"page"},{"location":"man/config/","page":"Configuration","title":"Configuration","text":"Here you can specify which quantities to write in the output files (Pressure, Q flow, u velocity and Area). These are all optional but at least one is recommended.","category":"page"},{"location":"man/config/","page":"Configuration","title":"Configuration","text":"Then there are three main sections: solver, blood, and network.","category":"page"},{"location":"man/config/#solver","page":"Configuration","title":"solver","text":"","category":"section"},{"location":"man/config/","page":"Configuration","title":"Configuration","text":"solver:\n Ccfl: 0.9\n cycles: 100\n convergence_tolerance: 5.0\n jump: 100","category":"page"},{"location":"man/config/","page":"Configuration","title":"Configuration","text":"It contains the values for the numerical scheme parameters:","category":"page"},{"location":"man/config/","page":"Configuration","title":"Configuration","text":"Ccfl is the Courant's number used to compute the Delta t and it is usually taken equal to 09.\ncycles is the maximum number of cardiac cycles to be simulated. This is used to stop openBF execution in case of non-converging simulations. An openBF simulation usually takes less than 20 cardiac cycles to converge.\nconvergence_tolerance is the maximum error in mmHg allowed between two consecutive cardiac cycle to claim convergence.\njump is the number of time-points to be saved in the result files.","category":"page"},{"location":"man/config/#blood","page":"Configuration","title":"blood","text":"","category":"section"},{"location":"man/config/","page":"Configuration","title":"Configuration","text":"blood:\n rho: 1060.0\n mu: 0.004","category":"page"},{"location":"man/config/","page":"Configuration","title":"Configuration","text":"Blood rheological properties:","category":"page"},{"location":"man/config/","page":"Configuration","title":"Configuration","text":"mu dynamic viscosity in Pa cdot s;\nrho density in kg cdot m^-3.","category":"page"},{"location":"man/config/#network","page":"Configuration","title":"network","text":"","category":"section"},{"location":"man/config/","page":"Configuration","title":"Configuration","text":"This contains the list of vessels in the network. Each vessel has the following mandatory properties:","category":"page"},{"location":"man/config/","page":"Configuration","title":"Configuration","text":"label the vessel name that will be used to name result files;\nsn segment source node;\ntn segment target node;\nL vessel lenght in m;\nE wall Young's modulus in Pa;\nR0 or Rp and Rd describe the lumen radius. If R0 is defined, the vessel is assumed to have a constant reference lumen radius; it Rp and Rd are specified, the vessel is set to taper linearly from the proximal lumen radius (i.e. Rp, the lumen radius at sn) to the distal lumen radius (i.e. Rd, the lumen radius at tn).","category":"page"},{"location":"man/config/","page":"Configuration","title":"Configuration","text":"Optional parameters are:","category":"page"},{"location":"man/config/","page":"Configuration","title":"Configuration","text":"to_save a boolean flag (default true) to tell openBF to save results for the current vessel;\nM is the number of division along the vessels used to compute the artery Delta x. When not specified, openBF automatically meshes the arteries so that Delta x is at least 1 mm;\nPext vessel external pressure in Pa, default 00 Pa;\ngamma_profile is the radial velocity profile parameter used in the calculation of the viscous losses term, default 2 (parabolic profile).","category":"page"},{"location":"man/config/#Boundary-conditions","page":"Configuration","title":"Boundary conditions","text":"","category":"section"},{"location":"man/config/","page":"Configuration","title":"Configuration","text":"The system boundary conditions (BCs) are applied to inlet vessel(s) and outlet vessel(s).","category":"page"},{"location":"man/config/","page":"Configuration","title":"Configuration","text":"In the case a vessel outlet is not connected to any other vessel, an outlet BC must be assigned by imposing a reflection coefficient Rt or by coupling a windkessel model. In case of Rt:","category":"page"},{"location":"man/config/","page":"Configuration","title":"Configuration","text":"Rt 1.0 ≤ Rt ≥ -1.0","category":"page"},{"location":"man/config/","page":"Configuration","title":"Configuration","text":"In case of two-element windkessel:","category":"page"},{"location":"man/config/","page":"Configuration","title":"Configuration","text":"R1 peripheral resistance\nCc peripheral compliance","category":"page"},{"location":"man/config/","page":"Configuration","title":"Configuration","text":"In case of three-element windkessel:","category":"page"},{"location":"man/config/","page":"Configuration","title":"Configuration","text":"R1 first peripheral resistance\nR2 second peripheral resistance\nCc peripheral compliance","category":"page"},{"location":"man/config/","page":"Configuration","title":"Configuration","text":"You can also enable inlet_impedance_matching to let openBF optimise R1 at runtime. This will match the windkessel inlet impedance and minimise artificial reflections (recommended).","category":"page"},{"location":"man/config/#Template","page":"Configuration","title":"Template","text":"","category":"section"},{"location":"man/config/","page":"Configuration","title":"Configuration","text":"The configuration file template is reported below. This contains all the mandatory and optional paramenter that can be specified in openBF. The parameter type is reported for each line after the #.","category":"page"},{"location":"man/config/","page":"Configuration","title":"Configuration","text":"project_name: # String\ninlet_file: .dat\nwrite_results: [\"P\"] # [\"P\", \"Q\", \"u\", \"A\"]\n\nsolver:\n Ccfl: # 0.0 < Ccfl ≤ 1.0; Float\n cycles: # Int\n convergence_tolerance: # Pressure, Float\n jump: # Int\n\nblood:\n mu: # [Pa⋅s]; Float\n rho: # [kg/m^3]; Float\n\nnetwork:\n - label: # String\n to_save: true # Bool (default true)\n sn: # Int\n tn: # Int\n\n L: # [m]; Float\n M: # Int (optional)\n E: # [Pa]; Float\n h0: # [m]; Float (optional)\n\n R0: # [m]; Float\n #------ OR ------ to assign a linear tapering\n Rp: \n Rd: \n\n Pext: # [Pa]; Float (optional)\n\n gamma_profile: # ≥ 2.0; Float\n\n # outlet wk2\n R1: # [Pa⋅s⋅m^-3]; Float\n Cc: # [m^3⋅Pa^-1]; Float\n #------ OR ------ outlet wk3\n R1: \n R2: \n Cc: \n inlet_impedance_matching: true # Bool (default false)\n #------ OR ------ outlet reflection\n Rt: # 1.0 ≤ Rt ≥ -1.0; Float","category":"page"},{"location":"man/quickstart/#Installation","page":"Quickstart","title":"Installation","text":"","category":"section"},{"location":"man/quickstart/","page":"Quickstart","title":"Quickstart","text":"The latest Julia binary can be downloaded for all platforms from the official website.","category":"page"},{"location":"man/quickstart/","page":"Quickstart","title":"Quickstart","text":"openBF can be installed via Pkg.clone. Start julia in a terminal session and run","category":"page"},{"location":"man/quickstart/","page":"Quickstart","title":"Quickstart","text":"using Pkg\nPkg.clone(\"https://github.com/INSIGNEO/openBF.git\")","category":"page"},{"location":"man/quickstart/#Run-a-simulation","page":"Quickstart","title":"Run a simulation","text":"","category":"section"},{"location":"man/quickstart/","page":"Quickstart","title":"Quickstart","text":"openBF API consists of a single function","category":"page"},{"location":"man/quickstart/","page":"Quickstart","title":"Quickstart","text":"run_simulation(\n yaml_config_path::String;\n verbose::Bool = false, # show progress bars\n out_files::Bool = false, # save .out files with the all the cycles\n save_stats::Bool = false, # save .conv file with simulation stats\n )","category":"page"},{"location":"man/quickstart/","page":"Quickstart","title":"Quickstart","text":"whose main argument is the name of a .yaml file (see here for an introduction to yaml) containining the description of the vascular network, blood properties, and numerical solver parameters (see Configuration).","category":"page"},{"location":"man/quickstart/","page":"Quickstart","title":"Quickstart","text":"Running a simulation consists in calling","category":"page"},{"location":"man/quickstart/","page":"Quickstart","title":"Quickstart","text":"using openBF\nrun_simulation(\"input.yml\", verbose=true, save_stats=true)","category":"page"},{"location":"man/quickstart/","page":"Quickstart","title":"Quickstart","text":"This will create a _results folder containing all the output files from the simulation.","category":"page"},{"location":"man/quickstart/#Outputs","page":"Quickstart","title":"Outputs","text":"","category":"section"},{"location":"man/quickstart/","page":"Quickstart","title":"Quickstart","text":"Simulation results are saved in the _results directory or in the output_directory specified. There, for each artery in your network, you'll find a file per output quantity (these are specified in the write_results list).","category":"page"},{"location":"man/quickstart/","page":"Quickstart","title":"Quickstart","text":"By default only .last files are saved. Thes contains only the last simulated cardiac cycle; at convergence, these are the files you want to look at.","category":"page"},{"location":"man/quickstart/","page":"Quickstart","title":"Quickstart","text":"You can also set out_files = true when calling run_simulation. This results in the writing of .out files which contain the whole simulation history, i.e., all the cardiac cycles simulated.","category":"page"},{"location":"man/quickstart/","page":"Quickstart","title":"Quickstart","text":"When setting save_stats=true, a .conv file is written in the results dolder. This reads","category":"page"},{"location":"man/quickstart/","page":"Quickstart","title":"Quickstart","text":" # boolean: true or false\n # integer\n # float, seconds\n # integer, bytes\n # float, percentage","category":"page"},{"location":"man/quickstart/#.last/.out-Format","page":"Quickstart","title":".last/.out Format","text":"","category":"section"},{"location":"man/quickstart/","page":"Quickstart","title":"Quickstart","text":"These files contain as many rows as defined in the config by the jump parameter (default 100), and 6 columns. The first column contains the simulation time for the current cardiac cycles; column 2-6 report waveforms at five locations along the vessel, namely inlet, 1/4th of the length, mid-point, 3/4th of the length and outlet.","category":"page"}]
+}
diff --git a/v2.3.0/siteinfo.js b/v2.3.0/siteinfo.js
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--- /dev/null
+++ b/v2.3.0/siteinfo.js
@@ -0,0 +1 @@
+var DOCUMENTER_CURRENT_VERSION = "v2.3.0";
diff --git a/versions.js b/versions.js
index 6dbbae8..971d86a 100644
--- a/versions.js
+++ b/versions.js
@@ -1,9 +1,10 @@
var DOC_VERSIONS = [
"stable",
+ "v2.3",
"v2.2",
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"dev",
];
-var DOCUMENTER_NEWEST = "v2.2.0";
+var DOCUMENTER_NEWEST = "v2.3.0";
var DOCUMENTER_STABLE = "stable";