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<h3>Simulation Guide</h3>
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<div class="manFlowSolver"> <section id="intro" class="group"><h2>Introduction</h2>
<p><strong>SV Simulation</strong> tool can solve the three-dimensional incompressible Navier-Stokes equations in an arbitrary domain, generally a vascular model reconstructed from image data. This is a complex subject with extensive underlying theory, and therefore this document will focus mainly on the practical aspects of simulation and analysis. </p>
<p><strong>Notice</strong>: To get full functions from the Simulation tool, it uses three solvers: <strong>Presolver (svPre), Flowsolver (svSolver), Postsolver (svPost)</strong>. Normally, SimVascular already includes the solvers and can find them automatically. Users don’t need to set up the solvers. However, in case SimVascular can’t find them while users are using the Simulation tool, refer to <a href="#solverconfiguration">Solver Configuration</a>.</p>
<p>The <strong>svSolver</strong> evolved from the academic finite element code PHASTA (Parallel, Hierarchical, Adaptive, Stabilized, Transient Analysis), developed mainly at RPI (Rensselaer Polytechnic Institute, Troy, NY) by Professor Kenneth Jansen. This code was in turned inspired by the Stabilized Finite Element theory developed by Professor Thomas J.R. Hughes during his Stanford years.</p>
<p>Building on the original PHASTA code, there have been a number of important additions and modifications. Professor Charles Taylor’s group at Stanford University developed key additions in the areas of Boundary Conditions and Fluid-Solid Interaction (FSI) coupling. These additions are crucial to represent with a high level of realism the way blood flows in arteries, since this flow is highly dependent on the characteristics of the vascular trees that are downstream of our three-dimensional model, and the compliance of the three-dimensional vascular tree.</p>
<h3>What’s New?</h3>
<p>Building on the above features, the Marsden lab at Stanford has added additional key functionality enabling efficient and stable solutions with models of the circulatory physiology:</p>
<ul>
<li><p><a href="/docsRefs.html#refSec2"><strong>Backflow stabilization.</strong></a> This problem usually arises in large vessels that are exposed to backflow in 3D and 2D flow simulations. This phenomenon may be a cause of divergence of the numerical scheme due to bulk reversal of the flow through an outlet, localized areas of flow reversal or use of a boundary 0D circulation model. </p></li>
<li><p>Custom and efficient <a href="/docsRefs.html#refSec3"><strong>linear solver.</strong></a> Accurate simulation of blood flow in vessels require the repeated solution of linear systems of equations with millions of unknowns. Moreover, use of closed-loop boundary models significantly increases the degree of coupling between boundary degrees of freedoms. The <strong>svLS</strong> linear solver is designed to efficiently handle large cardiovascular simulations with arbitrary boundary conditions and reduce solution times. </p></li>
<li><p>Multiscale Coupling for <a href="/docsRefs.html#refSec2"><strong>closed loop boundary conditions.</strong></a> Coupling a three-dimensional finite element solver with a 0D lumped circulation model drastically improves the possibility of realistically simulate patient-specific hemodynamics and phisiology.</p></li>
</ul>
<h3>About this guide</h3>
<p>This document will teach you:</p>
<ol>
<li>setting initial conditions and boundary conditions</li>
<li>setting mechanical properties for vessel walls (if deformable)</li>
<li>setting parameters for flowsolver</li>
<li>running the flow solver</li>
<li>converting and analyzing the simualtion results </li>
</ol>
<p>In addition, this tutorial will show you a number of good practices that are important to observe during the simulation process. We will do this considering very simple geometry (a straight cylinder) to illustrate different points in a simple way.</p>
<h3>Theory and Implementation</h3>
<p>The theory and implementation details are not covered in this document. For more information about those details, please refer to our <a href="/docsRefs.html">publications page</a>.</p>
</section>
<section id="overview" class="group"><h2>Overview</h2>
<h3>Process Flow of SimVascular Simulation</h3>
<p>The following figure contains a schematic representation of the processes involved in running a simulation using SimVascular.</p>
<figure>
<img class="svImg svImgLg" src="documentation/flowsolver/imgs/simulation_flowchart.png">
<figcaption class="svCaption" >Workflow for generating hemodynamic results of a cylindrical model starting from a stereolithography of its exterior surface</figcaption>
</figure>
<p>We start off with the files coming from the <a href="/docsMeshing.html">meshing</a> of the analysis: these files contain nodal and connectivity information for the finite element mesh, located in the the folder <em>mesh-complete/mesh-surfaces/</em>.</p>
<p><strong>svPre</strong> is the preprocessor for <strong>svSolver</strong>. The input data files to svPre contain a complete description of the discrete model: nodal coordinates, element connectivity, element adjacency information and connectivity of boundary nodes and elements. The <strong>svPre</strong> program can be called either from the command line (in terminal) or the Simulation tool (in GUI). The input data files for <strong>svPresolver</strong> are created from the mesh. They are organized as shown in the example below.</p>
<figure>
<img class="svImg svImgMd" src="documentation/flowsolver/imgs/meshfiles.png">
<figcaption class="svCaption" >Folder structure and file created after clicking on <b>Write Files</b></figcaption>
</figure>
<p>These files are:</p>
<p>in the <strong>mesh-complete/</strong> folder: </p>
<ul>
<li><strong>mesh-complete.mesh.vtu</strong>, vtu file containing the solid mesh generated with TetGen.</li>
<li><strong>mesh-complete.exterior.vtp</strong>, vtp file containig all the exterior elements of the mesh generated with TetGen.</li>
<li><strong>walls_combined.vtp</strong>, vtp file containing all surface elements assigned to the wall, possibily combined from various surfaces. </li>
</ul>
<p>in the <strong>mesh-complete/mesh-surfaces/</strong> folder:</p>
<ul>
<li><strong>inflow.vtp</strong>, vtp file containing the meshed inlet surface.</li>
<li><strong>outlet.vtp</strong>, vtp file containing the meshed outlet surface.</li>
<li><strong>wall.vtp</strong>, vtp file containing the meshed wall surface.</li>
</ul>
<p>SimVascular runs <strong>Presolver(svPre)</strong> using the *.svpre_ file. The *.svpre file contains the set of instructions that define the boundary conditions, initial conditions, and geometrical configuration of our problem. The output of <strong>svPre</strong> is a set of files (<strong>bct.dat, geombc.dat.1, restart.0.1, numstart.dat</strong>) that are ready to be processed by <strong>svSolver</strong> to run a blood flow analysis. Running svSolver also need <strong>solver.inp</strong>, which provide further info for flowsolver.</p>
<p>Once the analysis is finished, the solver outputs files that characterize the finite element solution over a defined time period, typically several cardiac cycles. These files are taken by <strong>svPost</strong> to generate visualization files (typically *.vtu and *.vtp files) that are used to post-process and analyze the desired hemodynamic results. </p>
<h3>Units in Simulation</h3>
<p><strong>svSolver</strong>, just like many other Finite Element Programs, does not enforce a consistent set of physical units in the analysis, but it is up to the analyst to make sure that input data are dimensionally consistent.</p>
<p>To have a consistent set of units, users are advised to either work in CGS, MGS, or SI units; see the following table. </p>
<table class="table table-bordered">
<thead>
<tr>
<th>Quantity</th>
<th>CGS Unit</th>
<th>MGS Unit</th>
<th>SI Unit</th>
</tr>
</thead>
<tr>
<td>Length</td>
<td>cm</td>
<td>mm</td>
<td>m</td>
</tr>
<tr>
<td>Mass</td>
<td>gr</td>
<td>gr</td>
<td>Kg</td>
</tr>
<tr>
<td>Time</td>
<td>s</td>
<td>s</td>
<td>s</td>
</tr>
</table>
<h3>Useful constants in Simulation</h3>
<p>The following table gathers several important physical constants of blood given in different unit
systems.</p>
<table class="table table-bordered">
<thead>
<tr>
<th>Property</th>
<th>CGS Unit</th>
<th>MGS Unit</th>
<th>SI Unit</th>
</tr>
</thead>
<tr>
<td>Dynamic viscosity $\mu$ [M · L<sup>-1</sup> · T<sup>-1</sup>]</td>
<td>0.04 poise [gr · cm<sup>-1</sup> · s<sup>-1</sup>]</td>
<td>0.004 [gr · mm<sup>-1</sup> · s<sup>-1</sup>]</td>
<td>0.004 [Kg · m<sup>-1</sup>· s<sup>-1</sup>]</td>
</tr>
<tr>
<td>Blood density $\rho$ [M · L<sup>-3</sup>]</td>
<td>1.06 [gr · cm<sup>-3</sup>]</td>
<td>0.00106 [gr · mm<sup>-3</sup>] </td>
<td>1060 [Kg · m<sup>-3</sup>]</td>
</tr>
</table>
</section>
<section id="bcphysics" class="group"><h2>Boundary Condition Specification: the Physical Side of the Problem</h2>
<p>Boundary conditions are crucial to obtaining high quality cardiovascular simulation results. It is essential that boundary conditions accurately capture the physiology of vascular networks outside of the 3D domain of the model. <strong>SimVascular</strong> provides several different options for boundary condition assignment at inlets and outlets that are described in this section. Typically, we begin with some physiologic information about our problem, for instance:</p>
<ul>
<li>Flow rate info coming from <strong>MRI</strong> or <strong>ultrasound</strong> measurements.</li>
<li>Pressure values in the model obtained with a <strong>catheter</strong> transducer or a pressure cuff.</li>
<li>Vessel wall elastic properties (if we are modeling the vessel walls as deformable).</li>
</ul>
<figure>
<img class="svImg svImgMd" src="documentation/flowsolver/imgs/Fig_15.png">
<figcaption class="svCaption" >Inflow, outflow and wall characterization in a simple cylindrical vessel</figcaption>
</figure>
<p>From a conceptual standpoint, no matter how geometrically complex a vascular model is (we’ll refer to this as $\Omega$), its boundaries can be classified into three groups (see figure above):</p>
<ul>
<li>An <strong>inflow</strong> boundary $\Gamma_g$. This is the set of face(s) of the model where we will prescribe a flow wave as obtained from a clinical measurement.</li>
<li>A vessel <strong>wall</strong> boundary $\Gamma_s$. This boundary represents the interface between the fluid domain and the vessel wall. In the physical world, this boundary is lined by a layer of endothelial cells, the treatment of which can be complex. Many blood flow simulations have traditionally used a <strong>rigid wall assumption</strong>. Under these circumstances, a zero velocity condition is applied on these surfaces. <strong>SimVascular</strong> also offers options for fluid structure interaction as discussed below.</li>
<li>An <strong>outflow</strong> boundary $\Gamma_h$. On this boundary, we will typically prescribe a pressure value that is uniform over the face (i.e. spatially not temporally constant) in a <strong>weak manner</strong>. A <strong>weakly applied</strong> pressure means that we are not prescribing nodal values of pressure at the nodes of the outlet face as Dirichlet boundary conditions. Instead, we apply this pressure by enforcing that the integral of the pressure field on that face must be a certain value.</li>
</ul>
<p>These boundaries have an absolutely critical impact on the numerical simulation results. The SimVascular package contains several options for boundary condition assignment. All of these use a weakly prescribed pressure formulation, with the purpose of accounting for effects of the downstream vasculature on the vascular model (see figure below). These boundary conditions include:</p>
<ul>
<li><p><strong>Resistance Boundary condition</strong>. Here, the condition prescribed on the face is a relationship between flow and pressure of the form
$p = p_0 + R\,Q$, where $R$ is the resistance parameter that characterizes the downstream vasculature, $p$ is the weakly prescribed pressure, $Q$ is the flow rate passing through the face and $p_0$ is a “flag” that sets the boundary as a “weakly-prescribed pressure boundary”. This flag has a “zero” numerical value, so the total value of the pressure on that face is simply given by $R\,Q$.</p></li>
<li><p><strong>Impedance Boundary condition</strong>. Here, the condition prescribed on the face is a relationship of the form:</p></li>
</ul>
<p>$$
p(t)=p_0 + \frac{1}{T}\,\int_{t-T}^{t} Z(t−\tau) \, Q(\tau) \, d\tau
$$</p>
<p>where $Z$ is the Inverse Fourier Transform of an impedance function that characterizes the downstream vasculature, $p$ is the weakly prescribed pressure, $Q$ is the flow rate passing through the face, and $T$ is the cardiac cycle.</p>
<figure>
<img class="svImg svImgLg" src="documentation/flowsolver/imgs/Fig_16.png">
<figcaption class="svCaption" >Cardiovascular model with various boundary conditions</figcaption>
</figure>
<figure>
<img class="svImg svImgLg" src="documentation/flowsolver/imgs/Fig_17.png">
<figcaption class="svCaption" >Frequency content of impedance from the literature for the left external iliac and a canine femoral artery</figcaption>
</figure>
<p>The mathematical definition of an impedance function is:</p>
<p>$$
Z(\omega)=P(\omega)\,Q(\omega),\,\omega=0,1,2,\dots
$$</p>
<p>That is, a relationship between pressure and flow modes for different frequencies. The figure above shows the typical shape of these impedances as a function of the frequency in the human iliac artery under rest and exercise conditions. Getting a good characterization of these impedance functions is once again critical to accurately represent the way blood flows in our computational domain.</p>
<ul>
<li><strong>RCR lumped parameters condition</strong>. In this boundary condition type, we use a <em>reduced-order</em> model of the downstream vasculature, considering an electric circuit analog. In this theory, the behavior of the vasculature is represented by three parameters: a proximal resistance $R_p$, a capacitance $C$, and a distal resistance $R_d$.</li>
</ul>
<figure>
<img class="svImg svImgMd" src="documentation/flowsolver/imgs/Fig_18.png">
<figcaption class="svCaption" >Circuit representation of RCR block</figcaption>
</figure>
<ul>
<li><p><strong>Coronary boundary conditions</strong>. These conditions simulate what happens at the coronary outlets. The implementation in the <strong>svSolver</strong> follows the derivations in <a href="/docsRefs.html#refSec2">this paper</a>.</p></li>
<li><p><strong>Closed-loop boundary circulation model</strong>. The capability of coupling a 3D finite element model with a lumped parameter model is built into the <strong>svSolver</strong>. Documentation on this feature will be available with later releases of the code. </p></li>
</ul>
<h3>Boundary conditions considered in Example 1</h3>
<p>Before we move on, let us recap the type of <em>physical problem</em> (<strong>Example 1</strong>) we are solving: the geometry used in this problem consists of an idealized blood vessel, represented by a cylindrical segment with a radius $r=2$ cm and length $L=30$ cm. We prescribe an idealized constant inlet volumetric flow rate $Q$ of $100$ cc/sec to a parabolic profile at the inlet face of the model ($\Gamma_g$). The dynamic viscosity $\mu$ and density $\rho$ of the blood are 0.04 poise and 1.06 gr/cm$^3$, respectively. The lateral surface of the vessel ($\Gamma_{s}$) is considered to be rigid (therefore, we will apply a zero-velocity condition there). For the outlet boundary ($\Gamma_h$), a spatially-constant pressure boundary condition is weakly enforced via a resistance $R$.
In this problem, we will consider a resistance of $R = 1333.0$ dynes·s/cm$^5$. </p>
<p>This resistance will give a (weakly-applied) pressure at the outlet face of</p>
<p>$$
p=p_0 + R\,Q = 0.0 + 1333.0 \cdot 100.0=133300.00 \approx 100\,\text{mmHg}
$$</p>
<p>(recall that $1.0$ mmHg = $1333.2$ dyn/cm$^2$). For steady flow in a long tube with a circular cross section, the flow will develop a flow profile known as the <em>Poiseuille</em> flow profile assuming the flow remains laminar. The flow will remain laminar in a circular tube assuming that the non-dimensional parameter given by the <em>Reynolds</em> number $Re$ is $Re < 2100$.</p>
<p>The definition of the Reynolds number is given by:</p>
<p>$$
Re = \frac{\rho\,D\,V}{\mu}
$$</p>
<p>where $V$ is a representative velocity of the flow, $D$ is a characteristic dimension of the vessel where the flow is happening (in this case, the diameter), and $\mu$ and $\rho$ are the dynamic viscosity and density, respectively.</p>
<p>For this problem, the Reynolds number is about $884$, so it is well within the laminar flow regime. For a fully developed flow, the axisymmetric profile is parabolic and is given by: </p>
<p>$$
v_z(a) = v_z^{max}\left[1-\left(\frac{a}{r}\right)^2\right]
$$</p>
<p>where $v_z^{max}$ is the maximum velocity at the center of the vessel, a is the radial coordinate from center of the vessel $0\le a \le r$ . The expression for maximum velocity is given by:</p>
<p>$$
v_z^{max} = 2\frac{Q}{\pi\,r^2}
$$</p>
<p>where $Q$ is the volumetric flow rate. The wall shear stress $\tau$, is given by</p>
<p>$$
\tau = \frac{2\,\mu\,v_z^{max}}{r}
$$</p>
<p>For this example, the maximum velocity is $v_z^{max} = 15.92$ cm/s and the wall shear stress is $\tau$ = $0.64$ dynes/cm$^2$.</p>
</section>
<section id="creatingjob" class="group"><h2>Creating a Job for Simulation</h2>
<p>Let’s try Example 1. The files for Example 1 can be found from the link on the left “Cylinder Example”. Download and open the project. Now we assume you alread have the model and mesh for it.</p>
<p><strong>To create a simulation job (empty):</strong></p>
<pre class="highlight plaintext"><code>Right click the data node "Simulations" in the SV project in Data Manager
Click "Create Simulation Job" in the popup menu
Select Model: cylinder
Job Name: steady
Click "OK"
</code></pre>
<figure>
<img class="svImg svImgSm" src="documentation/flowsolver/imgs/createemptyjob.png">
<figcaption class="svCaption" ></figcaption>
</figure>
<figure>
<img class="svImg svImgSm" src="documentation/flowsolver/imgs/createjobdialog.png">
<figcaption class="svCaption" ></figcaption>
</figure>
<p>Now a new data node “steady” for the job is created under the data node “Simulations” in Data Manager. Double click the data node “steady" and the tool “SV Simulation” automatically shows up. The new job is empty and has not created input and data files yet. </p>
</section>
<section id="basic" class="group"><h2>Basic Parameters</h2>
<p>Basic parameters include fluid material properties, and initial conditions, which are some basic infor to be used for Presolver and Flowsolver. Here we use the defult values (in CSG units). Initial pressure is “0”. Initial velocities (vx, vy, vz) is “0 0 0”.</p>
<figure>
<img class="svImg svImgXl" src="documentation/flowsolver/imgs/basic.png">
<figcaption class="svCaption" ></figcaption>
</figure>
</section>
<section id="inflowbc" class="subgroup"><h2>Inlet Boundary Condition Specification</h2>
<p>Let’s first create a simple file to provide inlet flow rates before seting inlet boundary condition. Your problem may have more that one inflow wave form file. In this case, we only have a single flow file (called steady.flow). We put the file in a subfolder “flow-files” under the project folder in the disk.</p>
<p>The format of the <strong>steady.flow</strong> file is as follows:</p>
<pre class="highlight plaintext"><code># Time (sec) Flow (cc/sec)
0 -100.0
1 -100.0
</code></pre>
<p>The first line is a comment line that you don’t need to include, but it helps to remember what units you used in the analysis. Then, two columns of numbers follow. The first column contains time values, and the second column flow values.</p>
<p><strong>WARNING</strong>: please note that flow coming <strong>into</strong> the model (forward flow) will have a negative sign, (like in the example considered here), whereas flow coming <strong>out of</strong> the model (backflow) will be positive. A good way to remember that is that in the case of forward flow, the vector that gives you the direction of the flow and the normal to the face of the model point in opposite directions, and therefore their dot product will be negative.</p>
<figure>
<img class="svImg svImgMd" src="documentation/flowsolver/imgs/negativeflow.png">
<figcaption class="svCaption" >Cylinder with negative inflow</figcaption>
</figure>
<p>On the other hand, in a situation of back flow, the numerical value in the *.flow file with be positive. </p>
<figure>
<img class="svImg svImgMd" src="documentation/flowsolver/imgs/positiveflow.png">
<figcaption class="svCaption" >Cylinder with positive inflow</figcaption>
</figure>
<p>In this problem, since we are running a steady case, our physical time goes from 0.0 to 1.0 seconds, and the flow is constant with a value of 100.0 cc/sec.</p>
<p><strong>HINT</strong>: it is very important that you are absolutely sure about the physical dimensions of your model: every unit (length, time, flow, density, etc.) in your analysis must be dimensionally consistent. You can easily check the size of your model in <a href="http://www.paraview.org/">Paraview</a> before importing it into <strong>SimVascular</strong>.</p>
<p>In this case, our cylinder has a radius $r=2.0$ cm and length $L=30$ cm.</p>
<p>Let’s start setting inlet boundary condition.</p>
<pre class="highlight plaintext"><code>Go to "Inlet and Outlet BCs"
All the faces of type "cap" are already listed in the table
Double click the row for the face "inflow"
A dialog pops up and also the face is highlighted in the 3D-view window.
In the dialog:
BC Type: Prescribed Velocities
Analytic Shape: parabolic
Point Number: 2
Fourier Modes: 1
Click the tool button "..." to select the file "steady.flow" we just created as above
Period: (filled automatically based on the data from the file)
Click "OK"
</code></pre>
<figure>
<img class="svImg svImgSm" src="documentation/flowsolver/imgs/inletbcdialog.png">
<figcaption class="svCaption" ></figcaption>
</figure>
<p><font color="red"><strong>Help Hints:</strong> </font> Please make use you specify face types when you create the corresponding model;otherwise, the cap faces won’t appear.</p>
<ul>
<li><p><strong>Point Number</strong>: This is the number of <em>temporal</em> data points that you want to have in one cycle. This is not necessarily the number of time points in the *.flow file. In this case, they match (2 in both cases), but this is because this is a very simple example using steady flow and two time points is all we need to characterize a constant flow. In general, your *.flow file will have in the order of $20$ data points over the cardiac cycle (that’s about how many points you will be able to reconstruct using <strong>PC-MRI</strong>, for example), and your interpolated data from it will have on the order of $100$-$200$ points. Whatever is enough to have a smooth representation of the inflow wave mapping to velocity vectors at the inlet face.</p></li>
<li><p><strong>Fourier Modes</strong>: Fourier smoothing allows to smooth your inlet flow curve and to make sure that you have a periodic function in the specified interval. </p></li>
</ul>
<p><strong>WARNING</strong>: Be careful with this! <strong>SimVascular</strong> is doing a Fourier Series approximation of the data that you provide in the *.flow file. Since in this case, our data is constant flow, we only need one Fourier mode to capture this appropriately. For pulsatile flow problems, we will need more Fourier Modes to accurately represent the *.flow data (usually, $10$ Fourier modes is enough for a pulsatile problem).</p>
<figure>
<img class="svImg svImgLg" src="documentation/flowsolver/imgs/inflowbc.png">
<figcaption class="svCaption" > </figcaption>
</figure>
</section>
<section id="outletbc" class="subgroup"><h2>Outlet Boundary Condition Specification</h2>
<p>We are making the face <strong>outlet</strong> into a <strong>weakly-pressure</strong> face. This is mathematically expressed by the expressions we saw before:</p>
<p>$$
p = p_0 + R\,Q
$$</p>
<p>$$
p(t)=p_0 + \frac{1}{T}\,\int_{t-T}^{t} Z(t−\tau) \, Q(\tau) \, d\tau
$$</p>
<p>This expression sets $p_0 = 0$ for the face <strong>outlet</strong>. The total pressure set on that face will be the result of the flow-pressure operator considered (i.e., resistance, impedance, RCR, Coronary etc.).</p>
<p>Let’s start setting outlet boundary condition.</p>
<pre class="highlight plaintext"><code>Double click the row for the face "outlet"
A dialog pops up and also the face is highlighted in the 3D-view window.
In the dialog:
BC Type: Resistance
Resistance: 1333 (resistance value)
Distal Pressure: (0 by default)
Click "OK"
</code></pre>
<figure>
<img class="svImg svImgSm" src="documentation/flowsolver/imgs/outletbcdialog.png">
<figcaption class="svCaption" ></figcaption>
</figure>
<p><font color="red"><strong>Help Hints:</strong> </font> Please make use you specify face types when you create the corresponding model;otherwise, the cap faces won’t appear.</p>
<h3>Advanced Options for splitting BC</h3>
<p>In many clinical cases, we would like to split a total resistance or capacitance among a group of outlets, instead of explicitly assigning resistance or capacitance for each individual outlet.</p>
<p>To use this feature, first set up the group of outlets with initial zero resistance or capacitance.</p>
<p>For resistance BC:</p>
<pre class="highlight plaintext"><code>Select a group of outlets, right click
Click "Set BC"
BC Type: Resistance
Resistance: 0
Click "OK"
</code></pre>
<p>For RCR BC:</p>
<pre class="highlight plaintext"><code>Select a group of outlets, right click
Click "Set BC"
BC Type: RCR
Rp, C, Rd: 0 0 0
Click "OK"
</code></pre>
<p>For Coronary BC:</p>
<pre class="highlight plaintext"><code>Select a group of outlets, right click
Click "Set BC"
BC Type: Coronary BC
Rp, Ca, Ra-micro,Cim, RV: 0 0 0 0 0
Pim (from file): Click the button "..." to select file for Pim
Pim Period: filled automatically using the data from the file. You can change the period, SimVascular will automatically scale the time from the file
Pim Scaling: use this value to scale presure values from the file
Click "OK"
</code></pre>
<p>After you set up the group, let’s split the total resistance or capacitance.</p>
<p>To split total resistance:</p>
<pre class="highlight plaintext"><code>Select the group of outlets, right click
Click "Split Resistance"
Total Resistance: total resistance for the group of outlets
Murray's Law Coefficient: (2~3), 2 in general, 2.6 for coronary arteries, 2.3 for pulmonary arteries
Ratio of resistance for each outlet:
Rp:Rd (for RCR BC):
Ra:Ra-micro:Rv (for Coronary BC):
Click "OK"
</code></pre>
<p>To split total capacitance:</p>
<pre class="highlight plaintext"><code>Select the group of outlets, right click
Click "Split Capacitance"
Total Capacitance: total capacitance for the group of outlets
Ratio of capacitance for each outlet:
Ca:Cim (for Coronary BC):
Click "OK"
</code></pre>
</section>
<section id="wallproperties" class="subgroup"><h2>Wall Property Specification</h2>
<p>In Example 1, the wall is rigid and set no-slip boundary condition. </p>
<pre class="highlight plaintext"><code>Go to "Wall Properties"
Type: Rigid
</code></pre>
<p>SimVascular also has options like “Deformable(Constance)” and “Deformable(Variable)”. We will explain them in Examples 3 and 4.</p>
</section>
<section id="solverparameters" class="subgroup"><h2>Solver Parameters</h2>
<p>There are many parameters for flow solver, but you are only required to set explicitly a few of them. Advanced paramters are optional. To check out the meaning of all the parameters, refer to <a href="/docsFlowSolver.html#solverinp">appendix</a>.</p>
<pre class="highlight plaintext"><code>Number of Timesteps: 200
Time Step Size: 0.03
Number of Timesteps between Restarts: 10
Step Construction : 2 # standard two iterations, enough for constant problems.
</code></pre>
<figure>
<img class="svImg svImgMd" src="documentation/flowsolver/imgs/solverparameters.png">
<figcaption class="svCaption" ></figcaption>
</figure>
<h3>Time Step Parameters Block</h3>
<p><strong>Number of Timesteps: 200</strong> and <strong>Time Step Size: 0.03</strong> - These two lines control the amount of physical time that you run your problem for. In this case,</p>
<p>$$
\text{Total physical time} = \text{N. time steps} \times \text{Time Step Size} = T = N \times \Delta t = 200 \times 0.03 = 6.0\,\text{sec}
$$</p>
<p>Note that this doesn’t match the <strong>period</strong> options we specified before. In this case, like we mentioned before, it does not really make sense to talk about a <em>cardiac cycle</em> (this is a steady flow), but if we wanted to run this analysis for <em>six</em> cardiac cycles, we would have to run the problem for $6.0$ seconds of physical time. If we kept our choice of time step size the same ( $\Delta t = 0.03$ sec), we will need a total number of time steps of $N = 200$.</p>
<p><strong>WARNING</strong>: Note that this $N$ is the total number of time steps you need in your numerical simulation to model a certain physical time, given a prescribed $\Delta t$. </p>
<p><strong>WARNING</strong>: Now the question is: how do you come up with a reasonable value for $\Delta t$? There is not a straightforward answer for this. $\Delta t$ is the parameter that controls your <strong>temporal discretization</strong>, which is something that works in a similar fashion to the <strong>spatial discretization</strong> given by your mesh: the finer, the more accurate the results, but also the bigger the size of the problem and the time to solve it! We don’t want to get into a lot of theoretical details now, so we will just provide you with a reasonable <strong>recipe</strong> to evaluate this parameter. The <strong>recipe</strong> to estimate a reasonable $\Delta t$ is based on a dimensionless parameter called the <strong>CFL</strong> number. The CFL number relates the velocities happening in the fluid domain ($v$), a temporal discretization parameter ($\Delta t$), and a mesh discretization parameter (i.e. mesh size) ($h$) as follows:</p>
<p>$$
\text{CFL} = \frac{v\,\Delta t}{h}
$$</p>
<p>We want this <strong>CFL</strong> number to be around $1.0$. This will mean that, for the velocities present in our fluid domain, the temporal and spatial discretizations are <em>balanced</em>. In our problem, it can be shown that the average expected velocity is about $v = 16.7$ cm/s; the spatial discretization parameter or finite element size is $h = 0.5$. Therefore, if we shoot for a CFL number close to one, we have:</p>
<p>$$
\Delta t = \frac{h}{v} = \frac{0.5}{16.7} = 0.03
$$</p>
<p>Of course, you can imagine that in a real-world problem things are way more complicated to evaluate: it will be much harder to estimate where your model will have the largest velocities, what the mesh element size will be there, etc. The time step size $\Delta t$ is a parameter that will have a very important impact on the performance of the linear solver of equations. The smaller you make it, the <em>easier</em> you will be for the solver to find a solution, but the longer it will take you to reach a certain point in time.</p>
<p><br></p>
<h3>Output Control Block</h3>
<p><strong>Number of Timesteps between Restarts: 10</strong> - This line tells the solver how often it should save solution files. In this problem, you are really calculating $200$ solutions to the problem at $200$ different time points, but in general you do not want to save a solution file for every single time step. Keep in mind that two consecutive solutions are only $\Delta t = 0.03$ seconds apart! In this line, we are asking the solver to save one in every $10$ files. Therefore, the output files of the solver will look like this: restart.0.*, restart.10.*, restart.20.*, restart.30.*, …., restart.190.*, restart.200.*</p>
<p><br></p>
<h3>Step Construction Block</h3>
<p>This line controls the non-linear iteration loop within the time step. The syntax of the line represents a two nonlinear iteration process for each time step. Each iteration tells the solver to make a solve and an update of the solution. </p>
<p><strong>WARNING</strong>: Deciding on the adequate number of non-linear iterations for a problem is also a non-trivial problem. In principle, we need to iterate until the residual (i.e., the <em>error</em>) of our numerical solution is small enough. But doing many non-linear iterations on each time step is very costly. In general, for steady flow problems, 1 or 2 non-linear iterations are enough. For pulsatile problems, at least three non-linear iterations are needed. For deformable wall problems, 4 or more non-linear iterations are required. This parameter, together with the time step size $\Delta t$ and the quality of the spatial discretization given by the finite element mesh, will completely determine the performance of the linear solver of equations. The better chosen these parameters are, the faster and more accurately our simulation will run. We will talk more about this later.</p>
<p>The set of instructions explained here constitute a very small sample of all the possible parameters the <strong>svSolver</strong> can take. A more detailed discussion can be found in <a href="#solverinp">this section</a>.</p>
</section>
<section id="creatingdata" class="subgroup"><h2>Creating Data Files for Simulation</h2>
<p>Before running simualtion, you need to create some required data files for presolver and flowsolver.</p>
<p>For Presolver:</p>
<ul>
<li><strong>.svpre</strong>: script input file</li>
</ul>
<p>For Flowsolver:</p>
<ul>
<li><strong>geombc.dat.1</strong>: containing mesh info and boundary conditions specified in the problem, created by presolver</li>
<li><strong>restart.0.1</strong>: containing initial conditions for our problem, , created by presolver</li>
<li><strong>numstart.dat</strong>: contains a number <strong>0</strong>. This number is used by the solver to identify the restart file that should be used as initial condition.</li>
<li><strong>bct.dat</strong>: containing time-dependent velocity vectors at the inflow face of the model according to a prescribed flow wave coming from a *.flow file. See <a href="#bctfile">this section</a>.</li>
<li><strong>solver.inp</strong>: providing further info for flowsolver, specifying parameters such as time step size, number of time steps, number of nonlinear iterations, boundary condition control, etc. A detailed description is presented in <a href="#solverinp">this section</a>.</li>
</ul>
<p>These five files are the bare minimum we need to run an analysis. However, if we want to perform more complicated simulations, involving more complex boundary conditions, we will need more input files.</p>
<p><strong>Impedance Boundary Condition simulations:</strong></p>
<p>In addition to the five standard files (geombc.dat.1, restart.0.1, numstart.dat, bct.dat, solver.inp), we will need to provide impedance functions in the time domain for each impedance outlet, as well as a history of flow rates for each outlet. We will have therefore two additional ascii files: <strong>impt.dat</strong> (containing the impedance functions for each of the outlets), and <strong>Qhistor.dat</strong> (containing the flow rate history). A detailed description is <a href="#impbcfile">here</a>.</p>
<p><strong>RCR Boundary Condition simulations:</strong></p>
<p>In addition to the five standard files (geombc.dat.1, restart.0.1, numstart.dat, bct.dat, solver.inp), we will need to provide the RCR parameters in a ascii file that will set the relationship between flow and pressure on each outflow face. This is done by defining a file named <strong>rcrt.dat</strong> containing such parameters. A detailed description is <a href="#rcrtfile">here</a>.</p>
<p><strong>Coronary Boundary Condition simulations:</strong></p>
<p>In addition to the five standard files (geombc.dat.1, restart.0.1, numstart.dat, bct.dat, solver.inp), we will need to provide the coronary model parameters in a ascii file that will set the relationship between flow and pressure on each outflow face. This is done by defining a file named <strong>cort.dat</strong> containing such parameters. A detailed description is <a href="#cortfile">here</a>.</p>
<p><strong>Closed-loop boundary conditions:</strong></p>
<p>This will required an executable that implements a lumped parameter network model for the patient circulation. This will be covered in a later version of this tutorial. Stay tuned!</p>
<p><br>
<strong>HINT</strong>: In both files geombc.data.1 and restart.0.1, the number “.1” refers to the <strong>partition number</strong> of the file. Remember <strong>svSolver</strong> has the ability of running a problem <em>in parallel</em> (i.e., using multiple processors or computing cores), using MPI (message-passing interface). When we run a job using multiple processors, the first thing that happens is the “splitting” of these two files into as many processors we are going to use in our analysis, so the calculations can be performed faster. For example, if we use $4$ processors later in svSolver, these files will be split as follows:</p>
<pre class="highlight plaintext"><code>geombc.dat.1 => geombc.dat.1 , geombc.dat.2 , geombc.dat.3 , geombc.dat.4
restart.0.1 => restart.0.1 , restart.0.2 , restart.0.3 , restart.0.4
</code></pre>
<p>Roughly speaking, each of the four files is $1⁄4$ of the size of the original un-split file. For a generic time step <strong>n</strong>, the solution will be given by the following files:</p>
<pre class="highlight plaintext"><code>restart.n.1 , restart.n.2 , restart.n.3 , restart.n.4 , ...
</code></pre>
<p><br></p>
<h3>Creating Data Files</h3>
<p>This step creates files inside the job folder in the SV project</p>
<pre class="highlight plaintext"><code>Choose Mesh: cylinder
Click the button "Create Data Files for Simulation"
</code></pre>
<p>A new directory using the job name “steady” is created under the folder “Simulations” and contains the following folder/files:</p>
<pre class="highlight plaintext"><code>For presolver:
mesh-complete (folder)
inflow.flow
steady.svpre
For flowsolver
geombc.dat.1
restart.0.1
bct.dat (and bct.vtp)
solver.inp
numstart.dat
rcrt.dat (if applicable)
cort.dat (if applicable)
</code></pre>
</section>
<section id="runningjob" class="subgroup"><h2>Running Simualtion Jobs</h2>
<p>Before running simualtion, you may need to click the button “Import Extra Files into Job” to add extra file into the simualtion job. In this example, we don’t need importint extra files</p>
<p><strong>To run a simulation job:</strong></p>
<pre class="highlight plaintext"><code>Number of Processes: 8 (select the maximum number in your case)
Starting Step Number: (be default, use 0 or the last time step from previous simulation)
Click the button "Run Job"
</code></pre>
<p>This will launch a eight-processor job in your computer. Therefore, the input file are split as follows: </p>
<pre class="highlight plaintext"><code>geombc.dat.1 => geombc.dat.1, geombc.dat.2, ..., geombc.dat.8
restart.0.1 => restart.0.1, restart.0.2, ..., restart.0.8
</code></pre>
<p>During the job running, the progress of simualtion is shown at “Job Status” and the status bar at the the bottom of the main window:</p>
<figure>
<img class="svImg scImgMd" src="documentation/flowsolver/imgs/simulationstatus.png">
<figcaption class="svCaption" ></figcaption>
</figure>
<p>It shows the name of th running job, the percentage completed, and more info: [current time step] [time used(s)] [nonlinear residual] [logarithm of the redisual change] …</p>
<p>During the job running, you can terminate it before it finishes. To stop the simulation:</p>
<pre class="highlight plaintext"><code>Right click the job data node "steady" at Data Manager
Click "Stop Simulation" in the popup menu
</code></pre>
<p>After the simulation is finished. A dialog pops up to inform that the job is done. You can click the button “Show Details…” to get more info about the simulation progress. You can also check the simulation progress by open the file “histor.dat” in the folder “steady”. It contains containing details that allows to evaluate how well your numerical simulation is doing. Here’s a brief description of what each of those columns means.</p>
<table class='table borderless' id="solverTable">
<thead>
<tr>
<th>a</th>
<th>b</th>
<th>c</th>
<th>d</th>
<th>e</th>
<th>f</th>
<th>g</th>
<th>h</th>
</tr>
</thead>
<tr>
<td> 1 </td>
<td> 1.30E+001 </td>
<td> 1.16E-002 </td>
<td> (0) </td>
<td> 2.10E+002 </td>
<td> 2.62E+028 </td>
<td> < -10474 1 | 15 > </td>
<td> [199-190] </td>
</tr>
<tr>
<td> 1 </td>
<td> 2.50E+001 </td>
<td> 7.35E-003 </td>
<td> (-1) </td>
<td> 2.93E-001 </td>
<td> 5.15E+000 </td>
<td> < -3237 1 | 13> </td>
<td> [117-200] </td>
</tr>
<tr>
<td> 2 </td>
<td> 2.80E+001 </td>
<td> 5.13E-001 </td>
<td> (-16) </td>
<td> 1.75E-001 </td>
<td> 1.69E-001 </td>
<td> < -1357 1 | 5> </td>
<td> [63-1] </td>
</tr>
<tr>
<td> 2 </td>
<td> 3.00E+001 </td>
<td> 2.05E-002 </td>
<td> (-2) </td>
<td> 8.07E-002 </td>
<td> 2.67E-002 </td>
<td> < -3286 1 | 11> </td>
<td> [21-13] </td>
</tr>
<tr>
<td> 3 </td>
<td> 3.20E+001 </td>
<td> 1.20E-001 </td>
<td> (-10) </td>
<td> 8.75E-002 </td>
<td> 2.44E-002 </td>
<td> < -2342 1 | 7> </td>
<td> [36-1] </td>
</tr>
<tr>
<td> 3 </td>
<td> 3.40E+001 </td>
<td> 5.18E-003 </td>
<td> (-3) </td>
<td> 2.13E-002 </td>
<td> 3.59E-003 </td>
<td> < -3277 1 | 10> </td>
<td> [6-6] </td>
</tr>
<tr>
<td> 4 </td>
<td> 3.60E+001 </td>
<td> 2.14E-002 </td>
<td> (-2) </td>
<td> 5.57E-002 </td>
<td> 6.13E-003 </td>
<td> < -3146 1 | 9> </td>
<td> [24-2] </td>
</tr>
<tr>
<td> 4 </td>
<td> 3.80E+001 </td>
<td> 2.18E-003 </td>
<td> (-7) </td>
<td> 7.33E-003 </td>
<td> 3.15E-004 </td>
<td> < -3233 1 | 11> </td>
<td> [9-5] </td>
</tr>
<tr>
<td> 5 </td>
<td> 4.00E+001 </td>
<td> 1.52E-002 </td>
<td> (-1) </td>
<td> 4.22E-002 </td>
<td> 3.45E-004 </td>
<td> < -3141 1 | 10> </td>
<td> [27-3] </td>
</tr>
<tr>
<td> 5 </td>
<td> 4.20E+001 </td>
<td> 1.11E-003 </td>
<td> (-10) </td>
<td> 3.57E-003 </td>
<td> 1.24E-004 </td>
<td> < -3237 1 | 12> </td>
<td> [7-5] </td>
</tr>
<tr>
<td> 6 </td>
<td> 4.40E+001 </td>
<td> 1.24E-002 </td>
<td> (0) </td>
<td> 3.31E-002 </td>
<td> 3.16E-004 </td>
<td> < -3024 1 | 10> </td>
<td> [16-2] </td>
</tr>
<tr>
<td> 6 </td>
<td> 4.60E+001 </td>
<td> 1.01E-003 </td>
<td> (-10) </td>
<td> 3.98E-003 </td>
<td> 3.30E-005 </td>
<td> < -3220 1 | 11> </td>
<td> [6-5] </td>
</tr>
<tr>
<td> 7 </td>
<td> 4.80E+001 </td>
<td> 1.05E-002 </td>
<td> (0) </td>
<td> 2.70E-002 </td>
<td> 1.87E-004 </td>
<td> < -3019 1 | 10> </td>
<td> [8-2] </td>
</tr>
<tr>
<td> 7 </td>
<td> 5.00E+001 </td>
<td> 8.74E-004 </td>
<td> (-11) </td>
<td> 3.50E-003 </td>
<td> 4.35E-005 </td>
<td> < -2993 1 | 11> </td>
<td> [5-5] </td>
</tr>
<tr>
<td> 8 </td>
<td> 5.20E+001 </td>
<td> 9.09E-003 </td>
<td> (-1) </td>
<td> 2.25E-002 </td>
<td> 1.16E-004 </td>
<td> < -2993 1 | 10> </td>
<td> [8-2] </td>
</tr>
<tr>
<td> 8 </td>
<td> 5.30E+001 </td>
<td> 7.42E-004 </td>
<td> (-11) </td>
<td> 2.92E-003 </td>
<td> 5.63E-005 </td>