press new

kalman/graphics/figure2.py

@@ -72,7 +72,7 @@ def plot_parameters(dat, input_file, deparameterize=False, ref=None):
                 if bnd_c['id'] == bnd_set['id']:
                     ids.append(bnd_c['id'])
                     current_val.append(bnd_set['value'][0])
-                    labels.append('R_' + str(bnd_c['id']))
+                    labels.append('$R_' + str(bnd_c['id']))
 
         elif 'dirichlet' in bnd_c['type']:
             current_val.append(inputfile['boundary_conditions'][1]['parameters']['U'])
@@ -105,13 +105,17 @@ def plot_parameters(dat, input_file, deparameterize=False, ref=None):
 
 
     for i in range(dim):
-        axes.plot(t, theta[:, i] + 1.5*i, '-', color=col_,label=legends_)
+        
+        true_level =  np.log(true_values[ids[i]]/current_val[i])/np.log(2)
+        rec_value = np.round(2**theta[-1, i]*current_val[i],1)
+        cur_key = ids[i]
+
+        axes.plot(t, theta[:, i] + 1.5*i, '-', color=col_,label=legends_ + '= ' + str(rec_value) + '/' + str(true_values[cur_key])  + '$')
         axes.fill_between(t, theta[:, i] + 1.5*i - np.sqrt(P[:, i, i]),
                         theta[:, i] + 1.5*i + np.sqrt(P[:, i, i]), alpha=0.3,
                         color=col_)
         
 
-        true_level =  np.log(true_values[ids[i]]/current_val[i])/np.log(2)
         axes.plot(t,1.5*i + t*0 + true_level , color=col_,ls='--')
         col_ = next(col)
         legends_=next(legends)

kalman/input_files/aorta.yaml

@@ -4,9 +4,10 @@ mesh: './meshes/coaortaH1.h5'
 fluid:
     density: 1.2
     dynamic_viscosity: 0.035
+    stokes: False
 
 io:
-    write_path: 'results/aorta_master'
+    write_path: 'results/aorta'
     restart:
         path: ''  # './projects/nse_coa3d/results/test_restart2/' 
         time: 0
@@ -25,38 +26,40 @@ boundary_conditions:
         type: 'dirichlet'
         value: ['0','0','-U*sin(DOLFIN_PI*t/Th)*(t<=Th) + (Th<t)*(-3.67949466208*U*sin(9*DOLFIN_PI*t/Th)*exp(-t*10))']
         parameters:
-            U: 30
+            U: 100
             Th: 0.35
             t: 0   
     - 
         id: 3
         type: 'windkessel'
-        value: [10,0,0]
-        p0: [0,1333.223874]
-        #value: [10,1000,0.01]
-        #p0: [47,1333.223874]
+        #value: [10,0,0]
+        value: [10,0.0008,2400]
+        p0: [80,1333.223874]
+        #p0: [0,1333.223874]
     - 
         id: 4
         type: 'windkessel'
-        value: [250,0,0]
-        p0: [0,1333.223874]
-        #value: [250,8000,0.0001]
-        #p0: [47,1333.223874]
-        
+        #value: [60,0,0]
+        #value: [250,0,0]
+        value: [60,0.00034,4200]
+        p0: [80,1333.223874]
+        #p0: [0,1333.223874]
     - 
         id: 5
         type: 'windkessel'
-        value: [250,0,0]
-        p0: [0,1333.223874]
-        #value: [250,8000,0.0001]
-        #p0: [47,1333.223874]
+        #value: [220,0,0]
+        #value: [250,0,0]
+        value: [220,0.00034,11000]
+        p0: [80,1333.223874]
+        #p0: [0,1333.223874]
     - 
         id: 6
         type: 'windkessel'
-        value: [250,0,0]
-        p0: [0,1333.223874]
-        #value: [250,8000,0.0001]
-        #p0: [47,1333.223874]
+        #value: [160,0,0]
+        #value: [250,0,0]
+        value: [160,0.00034,7800]
+        p0: [80,1333.223874]
+        #p0: [0,1333.223874]
 
 timemarching:
     velocity_pressure_coupling: 'fractionalstep'    # monolithic, fractionalstep
@@ -96,7 +99,7 @@ fem:
     convection_skew_symmetric: True    # aka Temam term
     stabilization:
         forced_normal:
-            enabled: True
+            enabled: False
             boundaries: [6]
             gamma: 10
         backflow_boundaries: [3,4,5,6]
@@ -120,38 +123,38 @@ linear_solver:
 
 estimation:
     boundary_conditions:
-        - 
-            id: 3
-            type: 'windkessel'
-            initial_stddev: 1
+        #- 
+        #    id: 3
+        #    type: 'windkessel'
+        #    initial_stddev: 1
         - 
             id: 4
             type: 'windkessel'
             initial_stddev: 1
-        - 
-            id: 5
-            type: 'windkessel'
-            initial_stddev: 1
-        - 
-            id: 6
-            type: 'windkessel'
-            initial_stddev: 1
-        - 
-            id: 2
-            type: 'dirichlet'
-            parameters: 'U'
-            initial_stddev: 1
+        #- 
+        #    id: 5
+        #    type: 'windkessel'
+        #    initial_stddev: 1
+        #- 
+        #    id: 6
+        #    type: 'windkessel'
+        #    initial_stddev: 1
+        #- 
+        #    id: 2
+        #    type: 'dirichlet'
+        #    parameters: 'U'
+        #    initial_stddev: 1
 
 
     measurements:
         -
             mesh: '/home/yeye/NuMRI/kalman/meshes/coaortaH3_leo2.0.h5'
             fe_degree: 1
-            xdmf_file: 'measurements/aorta_master_s100/u_all.xdmf'
-            file_root: 'measurements/aorta_master_s100/u{i}.h5'
+            xdmf_file: 'measurements/aorta/u_all.xdmf'
+            file_root: 'measurements/aorta/u{i}.h5'
             indices: 0 # indices of checkpoints to be processed. 0 == all
             velocity_direction: ~
-            noise_stddev: 5     # standard deviation of Gaussian noise
+            noise_stddev: 500     # standard deviation of Gaussian noise
     
     roukf:
         particles: 'simplex' # unique or simplex

kalman/input_files/aorta_C.yaml

@@ -1,172 +0,0 @@
-
-mesh: './meshes/coaortaH1.h5'
-# Physical parameters of the fluid
-fluid:
-    density: 1.2
-    dynamic_viscosity: 0.035
-
-io:
-    write_path: 'results/aorta'
-    restart:
-        path: ''  # './projects/nse_coa3d/results/test_restart2/' 
-        time: 0
-    write_xdmf: True
-    write_checkpoints: True
-    write_hdf5_timeseries: False
-    write_velocity: 'update'     # tentative or update
-
-boundary_conditions:
-    - 
-        id: 1
-        type: 'dirichlet'
-        value: ['0','0','0']
-    - 
-        id: 2
-        type: 'dirichlet'
-        value: ['0','0','-U*sin(DOLFIN_PI*t/Th)*(t<=Th) + (t<=Tc)*(t>Th)*(-3.67949466208*U*sin(9*DOLFIN_PI*t/Th)*exp(-t*10)) 
-                    - U*sin(DOLFIN_PI*(t-Tc)/Th)*(t>Tc)*(t<= Tc + Th) 
-                    + (t<=2*Tc)*(t>Tc+Th)*(-3.67949466208*U*sin(9*DOLFIN_PI*(t-Tc)/Th)*exp(-(t-Tc)*10)) 
-                    - U*sin(DOLFIN_PI*(t-2*Tc)/Th)*(t>2*Tc)*(t<= 2*Tc + Th) 
-                    + (t<=3*Tc)*(t>2*Tc+Th)*(-3.67949466208*U*sin(9*DOLFIN_PI*(t-2*Tc)/Th)*exp(-(t-2*Tc)*10))
-                    - U*sin(DOLFIN_PI*(t-3*Tc)/Th)*(t>3*Tc)*(t<= 3*Tc + Th) 
-                    + (t<=4*Tc)*(t>3*Tc+Th)*(-3.67949466208*U*sin(9*DOLFIN_PI*(t-3*Tc)/Th)*exp(-(t-3*Tc)*10)) 
-                    - U*sin(DOLFIN_PI*(t-4*Tc)/Th)*(t>4*Tc)*(t<= 4*Tc + Th)
-                    + (t<=5*Tc)*(t>4*Tc+Th)*(-3.67949466208*U*sin(9*DOLFIN_PI*(t-4*Tc)/Th)*exp(-(t-4*Tc)*10)) ']
-        parameters:
-            U: 100  #100
-            Th: 0.35
-            Tc: 0.8
-            t: 0   
-    - 
-        id: 3
-        type: 'windkessel'
-        value: [10,0,0]
-        #value: [10,0.0008,2400] # [R_p,C,R_d] SEPARAR 
-        #p0: [80,1333.223874]
-        p0: [0,1333.223874]
-    - 
-        id: 4
-        type: 'windkessel'
-        value: [60,0,0]
-        #value: [60,0.00034,4200]
-        #p0: [80,1333.223874]
-        p0: [0,1333.223874]
-    - 
-        id: 5
-        type: 'windkessel'
-        value: [220,0,0]
-        #value: [220,0.00034,11000]
-        #p0: [80,1333.223874]
-        p0: [0,1333.223874]
-    - 
-        id: 6
-        type: 'windkessel'
-        value: [160,0,0]
-        #value: [160,0.00034,7800]
-        #p0: [80,1333.223874]
-        p0: [0,1333.223874]
-
-timemarching:
-    velocity_pressure_coupling: 'fractionalstep'    # monolithic, fractionalstep
-
-    monolithic:
-        timescheme: 'gmp'   # generalized midpoint, steady FIXME TODO
-        theta: 1            # 1: Euler, 0.5: implicit midpoint rule (one-legged)
-        nonlinear:
-            method: 'constant_extrapolation'   # constant_extrapolation, linear_extrapolation, newton, picard, snes
-            maxit: 20
-            init_steps: 30
-            use_aitken: 1   #  0: False, 1: Picard only, 2: all
-            report: 1       # 0: None, 1: residuals, 2: residuals and energy (inflow/driving/forcing via ESSENTIAL Dbcs!)
-            atol: 1.e-6    # note: dot required!!
-            rtol: 1.e-16
-            stol: 0.0
-
-    fractionalstep:
-        scheme: 'CT'      # CT, IPCS
-        coupled_velocity: False     # False faster, True needed if robin_bc implicit
-        robin_bc_velocity_scheme: 'implicit' # explicit, semi-implicit, implicit
-        transpiration_bc_projection: 'robin'      # robin, dirichlet
-        flux_report_normalize_boundary: 1
-
-    T: 0.8      # end time
-    dt: 0.002
-    write_dt: 0.04
-    checkpoint_dt:  0.04 # <= 0: only last; else value + last
-    report: 1   # 0: print nothing, 1: print time step and writeout, 2: 1 + flux
-
-# solver setup
-fem:
-    velocity_space: p1  # p1 p1b/p1+ p2
-    pressure_space: p1  # p1 p0/dg0 dg1
-
-    strain_symmetric: False
-    convection_skew_symmetric: True    # aka Temam term
-    stabilization:
-        forced_normal:
-            enabled: False
-            boundaries: [6]
-            gamma: 10
-        backflow_boundaries: [3,4,5,6]
-        streamline_diffusion:
-            enabled: False
-            parameter: 'standard'   # standard, shakib, codina, klr
-            length_scale: 'metric' # average, max, metric
-            parameter_element_constant: True
-            Cinv: ~
-        monolithic:
-            infsup: 'pspg'    # pspg, pressure-stabilization
-            graddiv: False
-            consistent: False
-            pressure_stab_constant: 1.
-
-    fix_pressure: False
-    fix_pressure_point: [0., 0. , 0.]
-
-linear_solver:
-    method: 'lu'
-
-estimation:
-    boundary_conditions:
-        #- 
-        #    id: 3
-        #    type: 'windkessel'
-        #    initial_stddev: 1
-        - 
-            id: 4
-            type: 'windkessel'
-            initial_stddev: 1
-        #- 
-        #    id: 5
-        #    type: 'windkessel'
-        #    initial_stddev: 1
-        #- 
-        #    id: 6
-        #    type: 'windkessel'
-        #    initial_stddev: 1
-        #- 
-        #    id: 2
-        #    type: 'dirichlet'
-        #    parameters: 'U'
-        #    initial_stddev: 1
-
-    measurements:
-        -
-            mesh: './meshes/coaortaH3_leo2.0.h5'
-            #mesh: './meshes/coaortaH1.h5'
-            fe_degree: 1
-            #xdmf_file: 'measurements/aorta_C/Perturbation/Ks12V50/u_all.xdmf'
-            #file_root: 'measurements/aorta_C/Perturbation/Ks12V50/u{i}.h5'
-            xdmf_file: 'measurements/aorta_s100/u_all.xdmf'
-            file_root: 'measurements/aorta_s100/u{i}.h5'
-            indices: 0 # indices of checkpoints to be processed. 0 == all
-            velocity_direction: ~
-            noise_stddev: 15     # standard deviation of Gaussian noise
-    
-    roukf:
-        particles: 'simplex' # unique or simplex
-        observation_operator: 'postprocessing'         #state or postprocessing
-        reparameterize: True
-        ODV_functional:
-            enable: False
-            VENC: 172    #  241,172

presentations/press_course1/press.tex

@@ -25,10 +25,9 @@
 \usepackage{amssymb,graphicx,enumerate}
 \usepackage{subcaption}
 \usepackage{hyperref}
-
 \usepackage[normalem]{ulem} % for strike out command \sout
-
-
+\usepackage{tikz}
+\usetikzlibrary{arrows,shapes,positioning}
 
 
 
@@ -98,7 +97,7 @@
 
 
 
-\title[]{4D flow MRI in cardiovascular diseases}
+\title[]{4D flow MRI in the diagnosis of cardiovascular diseases}
 %\author[Jeremías Garay Labra]
 %{Jeremías Garay Labra}
 \institute[University of Groningen]
@@ -118,15 +117,42 @@ University of Groningen\\[0.5cm]
 
 % \onslide<1->
 
+\begin{frame}
+\begin{figure}[!hbtp]
+  \includegraphics[height=0.5\textwidth]{images/aorta_healthy.jpg}
+ \end{figure}
+\end{frame}
+
+
+
+\begin{frame}
+\begin{figure}[!hbtp]
+  \includegraphics[height=0.6\textwidth]{images/aortic_stenosis_1.png}
+ \end{figure}
+\end{frame}
+
+\begin{frame}
+\begin{figure}[!hbtp]
+  \includegraphics[height=0.6\textwidth]{images/aortic_stenosis_2.png}
+ \end{figure}
+\end{frame}
+
+
+\begin{frame}
+\begin{figure}[!hbtp]
+  \includegraphics[height=0.6\textwidth]{images/aortic_stenosis_3.png}
+ \end{figure}
+\end{frame}
 
 \begin{frame}
 \begin{figure}[!hbtp]
-  \includegraphics[height=0.6\textwidth]{images/aortic_stenosis.png}
+  \includegraphics[height=0.6\textwidth]{images/aortic_stenosis_4.png}
  \end{figure}
 \end{frame}
 
 
 
+
 \begin{frame}
 \begin{figure}[!hbtp]
  \begin{center}
@@ -145,10 +171,6 @@ University of Groningen\\[0.5cm]
 \end{frame}
 
 
-
-
-
-
 \begin{frame}
 \begin{figure}[!hbtp]
  \begin{center}
@@ -161,6 +183,31 @@ University of Groningen\\[0.5cm]
 
 
 
+\begin{frame}
+\begin{figure}
+\centering
+\tikzstyle{block} = [rectangle, draw, fill=blue!25,text width=15em, text centered, rounded corners, minimum height=15em, line width=1pt ]
+\tikzstyle{block2} = [rectangle, draw, fill=blue!25,text width=4em, text centered, rounded corners, minimum height=2em, line width=1pt ]
+
+\tikzstyle{line} = [draw, -latex', line width=1pt]
+\tikzstyle{alert} = [text=red, fill=red!25, draw=red]
+
+\begin{tikzpicture}[node distance = 2cm, auto]
+    % Place nodes
+    \node [block2] (mri) {velocity data \\ $\vec{u}$ };
+    \node [block, right of=mri, node distance=4.5cm] (NS) {Navier-Stokes equations \\[0.3cm] 
+    $$\rho \frac{\partial \vec{u}}{\partial t} + \rho \vec{u} \cdot \nabla \vec{u} + \mu \Delta \vec{u} + \nabla p =0 $$ $$ \nabla \cdot \vec{u} = 0$$};
+    \node [block2,alert, right of=NS, node distance=4.5cm] (press) {pressure \\ $p$ };
+    % Draw edges
+    \path [line] (mri) -> (NS);
+    \path [line] (NS) -- (press);
+\end{tikzpicture}
+\end{figure}
+\end{frame}
+
+
+
+
 
 \begin{frame}
 \begin{figure}[!hbtp]
@@ -172,11 +219,53 @@ University of Groningen\\[0.5cm]
 \end{frame}
 
 
+\begin{frame}
+\begin{figure}[!hbtp]
+ \begin{center}
+  \includegraphics[height=0.6\textwidth]{images/p2.png}
+  \caption{\footnotesize reconstructed pressure using NS equations}
+ \end{center}
+ \end{figure}
+\end{frame}
+
+
+
+
+\begin{frame}
+\begin{center}
+\huge{Conclusions}
+\end{center}
+\end{frame}
+
+
+
+
+
 
 
 
 
+\begin{frame}
+\begin{figure}[!hbtp]
+ \begin{center}
+  \includegraphics[height=0.5\textwidth]{images/catheter_curve.png}
+  \caption{\footnotesize Two different methods for pressure reconstruction (STE, PPE) against actual catheter data in two patients}
+ \end{center}
+ \end{figure}
+\end{frame}
 
+\begin{frame}
+\title{Conclusion}
+\begin{itemize}
+\item \onslide<1-> New approach for addressing cardiovascular diagnosis is presented \\[0.3cm]
+\item \onslide<2-> Consists in imagining the velocity of blood flows (4D flow)\\[0.3cm]
+\item \onslide<3-> Main limitations so far:
+\begin{itemize}
+\item \onslide<4-> Difficulties in obtaining the special type of data needed
+\item \onslide<5-> Practical resolutions are far from the desired ones
+\end{itemize}
+\end{itemize}
+\end{frame}