final press 8ecm

kalman/graphics/figure3.py

@@ -146,27 +146,12 @@ def plot_parameters(dat, input_file, deparameterize=False, ref=None):
 
 
     for i in range(len(ids)):
-        cur_key = ids[i]
-
-        true_level =  np.log(true_values[ids[i]]/current_val[i])/np.log(2)
-        rec_value = np.round(2**theta[-1, idx]*current_val[i],2)
-
-        
-        #curve = theta[:,idx] + line_split*idx - true_level
-        #dash_curve = line_split*idx + t*0
-
-        curve = 2**theta[:, idx]*current_val[i]
-        std_down =  2**(-np.sqrt(P[:, idx, idx]))*curve
-        std_up =  2**np.sqrt(P[:, idx, idx])*curve
-        dash_curve = true_values[ids[i]]  + t*0
-        
-
         if ids_type[i] == 'dirichlet':
             fig3, axes3 = plt.subplots(1,1,figsize=(12,5))
             axes3.plot(t, curve , '-', color=col_,label= legends_ + '= ' + str(rec_value) + '/' + str(true_values[cur_key])  + '$', linewidth = 4)
             axes3.fill_between(t, std_down, std_up, alpha=0.3, color=col_)
             legends_=next(legends)
-            axes3.plot(t, dash_curve , color=col_,ls='--')
+            axes3.plot(t, dash_curve , color=col_,ls='--' , linewidth = 3)
             axes3.set_ylabel(r'$U$',fontsize=36)
             axes3.legend(fontsize=36,loc='upper right')
             axes3.set_xlim([-0.01,0.81])
@@ -177,28 +162,34 @@ def plot_parameters(dat, input_file, deparameterize=False, ref=None):
             plt.savefig('U.png')
             plt.close(fig3)
         else:
+
+            cur_key = ids[i]
+            rec_value = np.round(2**theta[-1, idx]*current_val[i],2)
+            curve = 2**theta[:, idx]*current_val[i]
+            std_down =  2**(-np.sqrt(P[:, idx, idx]))*curve
+            std_up =  2**np.sqrt(P[:, idx, idx])*curve
+            dash_curve = true_values[ids[i]]  + t*0
+
             axes1.plot(t, curve , '-', color=col_,label= legends_ + '= ' + str(rec_value) + '/' + str(true_values[cur_key])  + '$', linewidth = 3)
             axes1.fill_between(t, std_down, std_up, alpha=0.3, color=col_)
-            axes1.plot(t, dash_curve , color=col_,ls='--')
+            axes1.plot(t, dash_curve , color=col_,ls='--',linewidth = 3)
             legends_=next(legends)
 
+            if RC_flag:
+                if i<len(current_val_C):
+                    rec_value_C = np.round(2**theta[-1, idx+1]*current_val_C[idc],6)
 
-        if RC_flag:
-            if i<len(current_val_C):
-                true_level_C = np.log(true_values_C[ids[i]]/current_val_C[i])/np.log(2)
-                rec_value_C = np.round(2**theta[-1, idc]*current_val_C[idc],6)
-
-                curve_C = 2**theta[:, idx+1]*current_val_C[idc]
-                dash_curve_C = true_values_C[ids[i]] + t*0
-                std_C_down =  2**(-np.sqrt(P[:, idx+1, idx+1]))*curve_C
-                std_C_up =  2**np.sqrt(P[:, idx+1, idx+1])*curve_C
-                
-                axes2.plot(t, curve_C , '-', color=col_,label= legends_ + '= ' + str(rec_value_C) + '/' + str(true_values_C[cur_key])  + '$', linewidth = 2)
-                axes2.fill_between(t, std_C_down, std_C_up, alpha=0.3, color=col_)
-                axes2.plot(t, dash_curve_C , color=col_,ls='--')
-                legends_=next(legends)
-                idx +=1
-                idc +=1
+                    curve_C = 2**theta[:, idx+1]*current_val_C[idc]
+                    dash_curve_C = true_values_C[ids[i]] + t*0
+                    std_C_down =  2**(-np.sqrt(P[:, idx+1, idx+1]))*curve_C
+                    std_C_up =  2**np.sqrt(P[:, idx+1, idx+1])*curve_C
+                    
+                    axes2.plot(t, curve_C , '-', color=col_,label= legends_ + '= ' + str(rec_value_C) + '/' + str(true_values_C[cur_key])  + '$', linewidth = 3)
+                    axes2.fill_between(t, std_C_down, std_C_up, alpha=0.3, color=col_)
+                    axes2.plot(t, dash_curve_C , color=col_,ls='--',linewidth = 3)
+                    legends_=next(legends)
+                    idx +=1
+                    idc +=1
 
 
         if meas_flag:
@@ -221,10 +212,12 @@ def plot_parameters(dat, input_file, deparameterize=False, ref=None):
 
     if RC_flag:
 
-        axes2.set_ylabel(r'$C$',fontsize=24)
-        axes2.legend(fontsize=18,loc='upper right')
+        axes2.set_ylabel(r'$C$',fontsize=36)
+        axes2.legend(fontsize=36,loc='upper right')
         axes2.set_xlim([-0.01,0.81])
-        axes2.set_xlabel(r'$t  (s)$',fontsize=24)
+        plt.xticks(fontsize=28)
+        plt.yticks(fontsize=28)
+        axes2.set_xlabel(r'$t  (s)$',fontsize=36)
         fig2.savefig('C.png')
 
     fig1.savefig('Rd.png')

kalman/input_files/aorta.yaml

@@ -8,7 +8,7 @@ fluid:
     implicit_windkessel: True
 
 io:
-    write_path: 'results/HRz_Pb_V70'
+    write_path: 'results/impl_1ms'
     restart:
         path: ''  # './projects/nse_coa3d/results/test_restart2/' 
         time: 0
@@ -27,7 +27,8 @@ boundary_conditions:
         value: ['0','0','-U*sin(DOLFIN_PI*t/Th)*(t<=Th) + (Th<t)*(U*DOLFIN_PI/Th*(t-Th)*exp(-(t-Th)*beta))']
         parameters:
             #U: 75  #REFERENCE
-            U: 150 #Pa Pb
+            U: 80  
+            #U: 150 #Pa/Pb
             #U: 40 #Pc
             Th: 0.36
             beta: 70
@@ -55,9 +56,9 @@ boundary_conditions:
             #C: 0.0010   # Pb
             #C: 0.0001   # Pc
             #C: 0.0008   # Pg
-            #R_d: 7200  # REFERENCE
+            R_d: 7200  # REFERENCE
             #R_d:  8760  #Pa
-            R_d: 17520 #Pb x2
+            #R_d: 17520 #Pb x2
             #R_d: 4000  #Pc
             p0: 85
             conv: 1333.223874   
@@ -71,9 +72,9 @@ boundary_conditions:
             #C: 0.0010 # Pb
             #C: 0.0001 # Pc
             #C: 0.0008 # Pg
-            #R_d: 11520 # REFERENCE
+            R_d: 11520 # REFERENCE
             #R_d:  8760  #Pa
-            R_d: 17520 #Pb x2
+            #R_d: 17520 #Pb x2
             #R_d: 4000 #Pc
             p0: 85
             conv: 1333.223874   
@@ -86,9 +87,9 @@ boundary_conditions:
             #C: 0.0005 #Pa
             #C: 0.0010 #Pb
             #C: 0.0001 #Pc
-            #R_d: 11520 # REFERENCE
+            R_d: 11520 # REFERENCE
             #R_d:  8760 #Pa
-            R_d: 17520 #Pb x2
+            #R_d: 17520 #Pb x2
             #R_d: 4000 #Pc
             p0: 85
             conv: 1333.223874   
@@ -131,7 +132,7 @@ fem:
     convection_skew_symmetric: True    # aka Temam term
     stabilization:
         forced_normal:
-            enabled: True
+            enabled: False
             boundaries: [3,4,5,6]
             gamma: 20
         backflow_boundaries: [3,4,5,6]
@@ -162,17 +163,17 @@ estimation:
         - 
             id: 4
             type: 'windkessel'
-            mode: 'Rd'
+            mode: 'RdC'
             initial_stddev: 1
         - 
             id: 5
             type: 'windkessel'
-            mode: 'Rd'
+            mode: 'RdC'
             initial_stddev: 1
         - 
             id: 6
             type: 'windkessel'
-            mode: 'Rd'
+            mode: 'RdC'
             initial_stddev: 1
         - 
             id: 2
@@ -186,12 +187,12 @@ estimation:
             mesh: '/home/yeye/NuMRI/kalman/meshes/coaortaH3_leo2.0.h5'
             #mesh: './meshes/coaortaH1.h5'
             fe_degree: 1
-            xdmf_file: 'measurements/aorta_zdir/Perturbation/Mg15V70/u_all.xdmf'
-            file_root: 'measurements/aorta_zdir/Perturbation/Mg15V70/u{i}.h5'
-            #xdmf_file: 'measurements/aorta/u_all.xdmf'
-            #file_root: 'measurements/aorta/u{i}.h5'
+            #xdmf_file: 'measurements/aorta_dt1ms/Perturbation/Mg15V70/u_all.xdmf'
+            #file_root: 'measurements/aorta_dt1ms/Perturbation/Mg15V70/u{i}.h5'
+            xdmf_file: 'measurements/aorta_exp_dt1ms/u_all.xdmf'
+            file_root: 'measurements/aorta_exp_dt1ms/u{i}.h5'
             indices: 0 # indices of checkpoints to be processed. 0 == all
-            velocity_direction: ~
+            velocity_direction: [0,0,1]
             noise_stddev: 45     # standard deviation of Gaussian noise
     
     roukf:
@@ -199,5 +200,5 @@ estimation:
         observation_operator: 'postprocessing'         #state or postprocessing
         reparameterize: True
         ODV_functional:
-            enable: True
-            VENC: 142
+            enable: False
+            VENC: 138

presentations/press_8ecm/press.aux

@@ -0,0 +1,162 @@
+\relax 
+\providecommand\hyper@newdestlabel[2]{}
+\providecommand\HyperFirstAtBeginDocument{\AtBeginDocument}
+\HyperFirstAtBeginDocument{\ifx\hyper@anchor\@undefined
+\global\let\oldcontentsline\contentsline
+\gdef\contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}}
+\global\let\oldnewlabel\newlabel
+\gdef\newlabel#1#2{\newlabelxx{#1}#2}
+\gdef\newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}}
+\AtEndDocument{\ifx\hyper@anchor\@undefined
+\let\contentsline\oldcontentsline
+\let\newlabel\oldnewlabel
+\fi}
+\fi}
+\global\let\hyper@last\relax 
+\gdef\HyperFirstAtBeginDocument#1{#1}
+\providecommand\HyField@AuxAddToFields[1]{}
+\providecommand\HyField@AuxAddToCoFields[2]{}
+\providecommand\pbs@newkey[2]{}
+\providecommand\pbs@seq@push@cx[2]{}
+\providecommand\pbs@at@end@dvi@check{}
+\pbs@at@end@dvi@check
+\providecommand\mix@newkey[2]{}
+\pbs@newkey{pbs@last@page}{1}
+\babel@aux{english}{}
+\@writefile{nav}{\headcommand {\slideentry {0}{0}{1}{1/1}{}{0}}}
+\@writefile{nav}{\headcommand {\beamer@framepages {1}{1}}}
+\pbs@newkey{pbs@last@page}{2}
+\@writefile{nav}{\headcommand {\slideentry {0}{0}{2}{2/2}{}{0}}}
+\@writefile{nav}{\headcommand {\beamer@framepages {2}{2}}}
+\pbs@newkey{pbs@last@page}{3}
+\@writefile{toc}{\beamer@sectionintoc {1}{4D flow MRI}{3}{0}{1}}
+\@writefile{nav}{\headcommand {\beamer@sectionpages {1}{2}}}
+\@writefile{nav}{\headcommand {\beamer@subsectionpages {1}{2}}}
+\@writefile{nav}{\headcommand {\sectionentry {1}{4D flow MRI}{3}{4D flow MRI}{0}}}
+\pbs@newkey{pbs@last@page}{4}
+\pbs@newkey{pbs@last@page}{5}
+\@writefile{nav}{\headcommand {\slideentry {1}{0}{1}{3/5}{}{0}}}
+\@writefile{nav}{\headcommand {\beamer@framepages {3}{5}}}
+\pbs@newkey{pbs@last@page}{6}
+\@writefile{toc}{\beamer@sectionintoc {2}{The mathematical model}{6}{0}{2}}
+\@writefile{nav}{\headcommand {\beamer@sectionpages {3}{5}}}
+\@writefile{nav}{\headcommand {\beamer@subsectionpages {3}{5}}}
+\@writefile{nav}{\headcommand {\sectionentry {2}{The mathematical model}{6}{The mathematical model}{0}}}
+\@writefile{nav}{\headcommand {\slideentry {2}{0}{1}{6/6}{}{0}}}
+\@writefile{nav}{\headcommand {\beamer@framepages {6}{6}}}
+\pbs@newkey{pbs@last@page}{7}
+\@writefile{nav}{\headcommand {\slideentry {2}{0}{2}{7/7}{}{0}}}
+\@writefile{nav}{\headcommand {\beamer@framepages {7}{7}}}
+\pbs@newkey{pbs@last@page}{8}
+\pbs@newkey{pbs@last@page}{9}
+\pbs@newkey{pbs@last@page}{10}
+\@writefile{nav}{\headcommand {\slideentry {2}{0}{3}{8/10}{}{0}}}
+\@writefile{nav}{\headcommand {\beamer@framepages {8}{10}}}
+\pbs@newkey{pbs@last@page}{11}
+\@writefile{nav}{\headcommand {\slideentry {2}{0}{4}{11/11}{}{0}}}
+\@writefile{nav}{\headcommand {\beamer@framepages {11}{11}}}
+\pbs@newkey{pbs@last@page}{12}
+\pbs@newkey{pbs@last@page}{13}
+\pbs@newkey{pbs@last@page}{14}
+\pbs@newkey{pbs@last@page}{15}
+\pbs@newkey{pbs@last@page}{16}
+\pbs@newkey{pbs@last@page}{17}
+\pbs@newkey{pbs@last@page}{18}
+\pbs@newkey{pbs@last@page}{19}
+\pbs@newkey{pbs@last@page}{20}
+\@writefile{nav}{\headcommand {\slideentry {2}{0}{5}{12/20}{}{0}}}
+\@writefile{nav}{\headcommand {\beamer@framepages {12}{20}}}
+\pbs@newkey{pbs@last@page}{21}
+\@writefile{nav}{\headcommand {\slideentry {2}{0}{6}{21/21}{}{0}}}
+\@writefile{nav}{\headcommand {\beamer@framepages {21}{21}}}
+\pbs@newkey{pbs@last@page}{22}
+\@writefile{nav}{\headcommand {\slideentry {2}{0}{7}{22/22}{}{0}}}
+\@writefile{nav}{\headcommand {\beamer@framepages {22}{22}}}
+\pbs@newkey{pbs@last@page}{23}
+\@writefile{toc}{\beamer@sectionintoc {3}{The inverse problem}{23}{0}{3}}
+\@writefile{nav}{\headcommand {\beamer@sectionpages {6}{22}}}
+\@writefile{nav}{\headcommand {\beamer@subsectionpages {6}{22}}}
+\@writefile{nav}{\headcommand {\sectionentry {3}{The inverse problem}{23}{The inverse problem}{0}}}
+\@writefile{nav}{\headcommand {\slideentry {3}{0}{1}{23/23}{}{0}}}
+\@writefile{nav}{\headcommand {\beamer@framepages {23}{23}}}
+\pbs@newkey{pbs@last@page}{24}
+\pbs@newkey{pbs@last@page}{25}
+\pbs@newkey{pbs@last@page}{26}
+\pbs@newkey{pbs@last@page}{27}
+\pbs@newkey{pbs@last@page}{28}
+\pbs@newkey{pbs@last@page}{29}
+\pbs@newkey{pbs@last@page}{30}
+\pbs@newkey{pbs@last@page}{31}
+\@writefile{nav}{\headcommand {\slideentry {3}{0}{2}{24/31}{}{0}}}
+\@writefile{nav}{\headcommand {\beamer@framepages {24}{31}}}
+\pbs@newkey{pbs@last@page}{32}
+\pbs@newkey{pbs@last@page}{33}
+\pbs@newkey{pbs@last@page}{34}
+\pbs@newkey{pbs@last@page}{35}
+\pbs@newkey{pbs@last@page}{36}
+\@writefile{nav}{\headcommand {\slideentry {3}{0}{3}{32/36}{}{0}}}
+\@writefile{nav}{\headcommand {\beamer@framepages {32}{36}}}
+\pbs@newkey{pbs@last@page}{37}
+\@writefile{toc}{\beamer@sectionintoc {4}{Numerical Experiments}{37}{0}{4}}
+\@writefile{nav}{\headcommand {\beamer@sectionpages {23}{36}}}
+\@writefile{nav}{\headcommand {\beamer@subsectionpages {23}{36}}}
+\@writefile{nav}{\headcommand {\sectionentry {4}{Numerical Experiments}{37}{Numerical Experiments}{0}}}
+\@writefile{nav}{\headcommand {\slideentry {4}{0}{1}{37/37}{}{0}}}
+\@writefile{nav}{\headcommand {\beamer@framepages {37}{37}}}
+\pbs@newkey{pbs@last@page}{38}
+\pbs@newkey{pbs@last@page}{39}
+\pbs@newkey{pbs@last@page}{40}
+\pbs@newkey{pbs@last@page}{41}
+\@writefile{nav}{\headcommand {\slideentry {4}{0}{2}{38/41}{}{0}}}
+\@writefile{nav}{\headcommand {\beamer@framepages {38}{41}}}
+\pbs@newkey{pbs@last@page}{42}
+\pbs@newkey{pbs@last@page}{43}
+\@writefile{nav}{\headcommand {\slideentry {4}{0}{3}{42/43}{}{0}}}
+\@writefile{nav}{\headcommand {\beamer@framepages {42}{43}}}
+\pbs@newkey{pbs@last@page}{44}
+\@writefile{nav}{\headcommand {\slideentry {4}{0}{4}{44/44}{}{0}}}
+\@writefile{nav}{\headcommand {\beamer@framepages {44}{44}}}
+\pbs@newkey{pbs@last@page}{45}
+\pbs@newkey{pbs@last@page}{46}
+\@writefile{nav}{\headcommand {\slideentry {4}{0}{5}{45/46}{}{0}}}
+\@writefile{nav}{\headcommand {\beamer@framepages {45}{46}}}
+\pbs@newkey{pbs@last@page}{47}
+\pbs@newkey{pbs@last@page}{48}
+\@writefile{nav}{\headcommand {\slideentry {4}{0}{6}{47/48}{}{0}}}
+\@writefile{nav}{\headcommand {\beamer@framepages {47}{48}}}
+\pbs@newkey{pbs@last@page}{49}
+\pbs@newkey{pbs@last@page}{50}
+\pbs@newkey{pbs@last@page}{51}
+\@writefile{nav}{\headcommand {\slideentry {4}{0}{7}{49/51}{}{0}}}
+\@writefile{nav}{\headcommand {\beamer@framepages {49}{51}}}
+\pbs@newkey{pbs@last@page}{52}
+\@writefile{nav}{\headcommand {\slideentry {4}{0}{8}{52/52}{}{0}}}
+\@writefile{nav}{\headcommand {\beamer@framepages {52}{52}}}
+\pbs@newkey{pbs@last@page}{53}
+\pbs@newkey{pbs@last@page}{54}
+\pbs@newkey{pbs@last@page}{55}
+\@writefile{nav}{\headcommand {\slideentry {4}{0}{9}{53/55}{}{0}}}
+\@writefile{nav}{\headcommand {\beamer@framepages {53}{55}}}
+\pbs@newkey{pbs@last@page}{56}
+\@writefile{toc}{\beamer@sectionintoc {5}{Conclusions}{56}{0}{5}}
+\@writefile{nav}{\headcommand {\beamer@sectionpages {37}{55}}}
+\@writefile{nav}{\headcommand {\beamer@subsectionpages {37}{55}}}
+\@writefile{nav}{\headcommand {\sectionentry {5}{Conclusions}{56}{Conclusions}{0}}}
+\@writefile{nav}{\headcommand {\slideentry {5}{0}{1}{56/56}{}{0}}}
+\@writefile{nav}{\headcommand {\beamer@framepages {56}{56}}}
+\pbs@newkey{pbs@last@page}{57}
+\pbs@newkey{pbs@last@page}{58}
+\pbs@newkey{pbs@last@page}{59}
+\pbs@newkey{pbs@last@page}{60}
+\pbs@newkey{pbs@last@page}{61}
+\pbs@newkey{pbs@last@page}{62}
+\@writefile{nav}{\headcommand {\slideentry {5}{0}{2}{57/62}{}{0}}}
+\@writefile{nav}{\headcommand {\beamer@framepages {57}{62}}}
+\pbs@newkey{pbs@last@page}{63}
+\@writefile{nav}{\headcommand {\slideentry {5}{0}{3}{63/63}{}{0}}}
+\@writefile{nav}{\headcommand {\beamer@framepages {63}{63}}}
+\@writefile{nav}{\headcommand {\beamer@partpages {1}{63}}}
+\@writefile{nav}{\headcommand {\beamer@subsectionpages {56}{63}}}
+\@writefile{nav}{\headcommand {\beamer@sectionpages {56}{63}}}
+\@writefile{nav}{\headcommand {\beamer@documentpages {63}}}
+\@writefile{nav}{\headcommand {\gdef \inserttotalframenumber {25}}}

presentations/press_8ecm/press.blg

@@ -0,0 +1,48 @@
+This is BibTeX, Version 0.99d (TeX Live 2017/Debian)
+Capacity: max_strings=100000, hash_size=100000, hash_prime=85009
+The top-level auxiliary file: press.aux
+I found no \citation commands---while reading file press.aux
+I found no \bibdata command---while reading file press.aux
+I found no \bibstyle command---while reading file press.aux
+You've used 0 entries,
+            0 wiz_defined-function locations,
+            83 strings with 484 characters,
+and the built_in function-call counts, 0 in all, are:
+= -- 0
+> -- 0
+< -- 0
++ -- 0
+- -- 0
+* -- 0
+:= -- 0
+add.period$ -- 0
+call.type$ -- 0
+change.case$ -- 0
+chr.to.int$ -- 0
+cite$ -- 0
+duplicate$ -- 0
+empty$ -- 0
+format.name$ -- 0
+if$ -- 0
+int.to.chr$ -- 0
+int.to.str$ -- 0
+missing$ -- 0
+newline$ -- 0
+num.names$ -- 0
+pop$ -- 0
+preamble$ -- 0
+purify$ -- 0
+quote$ -- 0
+skip$ -- 0
+stack$ -- 0
+substring$ -- 0
+swap$ -- 0
+text.length$ -- 0
+text.prefix$ -- 0
+top$ -- 0
+type$ -- 0
+warning$ -- 0
+while$ -- 0
+width$ -- 0
+write$ -- 0
+(There were 3 error messages)

presentations/press_8ecm/press.nav

@@ -0,0 +1,70 @@
+\headcommand {\slideentry {0}{0}{1}{1/1}{}{0}}
+\headcommand {\beamer@framepages {1}{1}}
+\headcommand {\slideentry {0}{0}{2}{2/2}{}{0}}
+\headcommand {\beamer@framepages {2}{2}}
+\headcommand {\beamer@sectionpages {1}{2}}
+\headcommand {\beamer@subsectionpages {1}{2}}
+\headcommand {\sectionentry {1}{4D flow MRI}{3}{4D flow MRI}{0}}
+\headcommand {\slideentry {1}{0}{1}{3/5}{}{0}}
+\headcommand {\beamer@framepages {3}{5}}
+\headcommand {\beamer@sectionpages {3}{5}}
+\headcommand {\beamer@subsectionpages {3}{5}}
+\headcommand {\sectionentry {2}{The mathematical model}{6}{The mathematical model}{0}}
+\headcommand {\slideentry {2}{0}{1}{6/6}{}{0}}
+\headcommand {\beamer@framepages {6}{6}}
+\headcommand {\slideentry {2}{0}{2}{7/7}{}{0}}
+\headcommand {\beamer@framepages {7}{7}}
+\headcommand {\slideentry {2}{0}{3}{8/10}{}{0}}
+\headcommand {\beamer@framepages {8}{10}}
+\headcommand {\slideentry {2}{0}{4}{11/11}{}{0}}
+\headcommand {\beamer@framepages {11}{11}}
+\headcommand {\slideentry {2}{0}{5}{12/20}{}{0}}
+\headcommand {\beamer@framepages {12}{20}}
+\headcommand {\slideentry {2}{0}{6}{21/21}{}{0}}
+\headcommand {\beamer@framepages {21}{21}}
+\headcommand {\slideentry {2}{0}{7}{22/22}{}{0}}
+\headcommand {\beamer@framepages {22}{22}}
+\headcommand {\beamer@sectionpages {6}{22}}
+\headcommand {\beamer@subsectionpages {6}{22}}
+\headcommand {\sectionentry {3}{The inverse problem}{23}{The inverse problem}{0}}
+\headcommand {\slideentry {3}{0}{1}{23/23}{}{0}}
+\headcommand {\beamer@framepages {23}{23}}
+\headcommand {\slideentry {3}{0}{2}{24/31}{}{0}}
+\headcommand {\beamer@framepages {24}{31}}
+\headcommand {\slideentry {3}{0}{3}{32/36}{}{0}}
+\headcommand {\beamer@framepages {32}{36}}
+\headcommand {\beamer@sectionpages {23}{36}}
+\headcommand {\beamer@subsectionpages {23}{36}}
+\headcommand {\sectionentry {4}{Numerical Experiments}{37}{Numerical Experiments}{0}}
+\headcommand {\slideentry {4}{0}{1}{37/37}{}{0}}
+\headcommand {\beamer@framepages {37}{37}}
+\headcommand {\slideentry {4}{0}{2}{38/41}{}{0}}
+\headcommand {\beamer@framepages {38}{41}}
+\headcommand {\slideentry {4}{0}{3}{42/43}{}{0}}
+\headcommand {\beamer@framepages {42}{43}}
+\headcommand {\slideentry {4}{0}{4}{44/44}{}{0}}
+\headcommand {\beamer@framepages {44}{44}}
+\headcommand {\slideentry {4}{0}{5}{45/46}{}{0}}
+\headcommand {\beamer@framepages {45}{46}}
+\headcommand {\slideentry {4}{0}{6}{47/48}{}{0}}
+\headcommand {\beamer@framepages {47}{48}}
+\headcommand {\slideentry {4}{0}{7}{49/51}{}{0}}
+\headcommand {\beamer@framepages {49}{51}}
+\headcommand {\slideentry {4}{0}{8}{52/52}{}{0}}
+\headcommand {\beamer@framepages {52}{52}}
+\headcommand {\slideentry {4}{0}{9}{53/55}{}{0}}
+\headcommand {\beamer@framepages {53}{55}}
+\headcommand {\beamer@sectionpages {37}{55}}
+\headcommand {\beamer@subsectionpages {37}{55}}
+\headcommand {\sectionentry {5}{Conclusions}{56}{Conclusions}{0}}
+\headcommand {\slideentry {5}{0}{1}{56/56}{}{0}}
+\headcommand {\beamer@framepages {56}{56}}
+\headcommand {\slideentry {5}{0}{2}{57/62}{}{0}}
+\headcommand {\beamer@framepages {57}{62}}
+\headcommand {\slideentry {5}{0}{3}{63/63}{}{0}}
+\headcommand {\beamer@framepages {63}{63}}
+\headcommand {\beamer@partpages {1}{63}}
+\headcommand {\beamer@subsectionpages {56}{63}}
+\headcommand {\beamer@sectionpages {56}{63}}
+\headcommand {\beamer@documentpages {63}}
+\headcommand {\gdef \inserttotalframenumber {25}}

presentations/press_8ecm/press.out

@@ -0,0 +1,5 @@
+\BOOKMARK [2][]{Outline0.1}{4D flow MRI}{}% 1
+\BOOKMARK [2][]{Outline0.2}{The mathematical model}{}% 2
+\BOOKMARK [2][]{Outline0.3}{The inverse problem}{}% 3
+\BOOKMARK [2][]{Outline0.4}{Numerical Experiments}{}% 4
+\BOOKMARK [2][]{Outline0.5}{Conclusions}{}% 5

presentations/press_8ecm/press.tex

@@ -135,14 +135,11 @@ University of Groningen\\[0.5cm]
 \footnotesize
 
 \begin{itemize}
-\item<2-> Full 3D coverage of the region of interest
+\item<2-> Velocities encoded into the magnetization phase
 \item<3-> Rich post-proccesing: derived parameters 
 \end{itemize}
 
-\onslide<4-> Disadvantages:
-\begin{itemize}
-\item<5-> Long scan time
-\end{itemize}
+
 
 
 \column{.54\textwidth} % Right column and width
@@ -232,16 +229,26 @@ P_l = R_{p,l} \ Q_l + \pi_l
 
 \begin{frame}
  \frametitle{The mathematical model}
- 
  \begin{columns}[c] 
 \column{.5\textwidth} % Left column and width
 \footnotesize
 \begin{itemize}
-\item<1-> $u_{inlet} = -U f(t) \hat{n}$, with $f(t)$ the weaveform.
-\item<2-> Fractional step scheme.
-\item<3-> Semi-implicit Windkessel model.
-\item<4-> Stabilized $\mathbb{P}1/\mathbb{P}1$ finite elements.
-\item<4-> Implemented in FEniCS.
+\item Incompressible Navier-Stokes equations:
+\begin{equation}
+\begin{cases}
+\displaystyle \rho \frac{\partial \vec{u}}{\partial t} + \rho \big ( \vec{u}  \cdot \nabla \big) \vec{u} - \mu \Delta \vec{u} + \nabla p  =  0  \\[0.2cm]
+\nabla \cdot \vec{u}  =  0 \quad \text{in} \quad \Omega \\[0.2cm]
+\vec{u}  =  \vec{u}_{inlet}  \quad \text{on} \quad \Gamma_{in} \\[0.2cm]
+\vec{u} = 0 \quad \text{on} \quad \Gamma_{walls}
+\end{cases}
+\end{equation}
+ \emph{Three-element} Windkessel coupling at every outlet:
+\begin{equation}
+\begin{cases}
+\displaystyle C_{d,l} \frac{d \pi_l}{dt} + \frac{\pi_l}{R_{d,l}} = Q_l \\[0.2cm]
+P_l = R_{p,l} \ Q_l + \pi_l
+\end{cases}
+\end{equation}
 \end{itemize}
 
 
@@ -258,57 +265,68 @@ P_l = R_{p,l} \ Q_l + \pi_l
 
 
 
+%\begin{frame}
+% \frametitle{The mathematical model}
+% 
+% \begin{columns}[c] 
+%\column{.5\textwidth} % Left column and width
+%\footnotesize
+%\begin{itemize}
+%\item<1-> $u_{inlet} = -U f(t) \hat{n}$, with $f(t)$ the weaveform.
+%\item<2-> Fractional step scheme.
+%\item<3-> Semi-implicit Windkessel model.
+%\item<4-> Stabilized $\mathbb{P}1/\mathbb{P}1$ finite elements.
+%\item<4-> Implemented in FEniCS.
+%\end{itemize}
+%
+%
+%\column{.54\textwidth} % Right column and width
+%\begin{figure}[!hbtp]
+% \begin{center}
+%  \includegraphics[height=0.9\textwidth]{images/ref.png}
+%  \caption{\footnotesize Reference solution at peak systole}
+% \end{center}
+% \end{figure}
+%\end{columns} 
+% 
+%\end{frame}
+
+
+
 \begin{frame}
  \frametitle{The inverse problem}
 \begin{itemize}
 \item<1-> Upon this solution $\Longrightarrow$ build a set of measurements
-\item<2-> Induce typical arifacts via a Magnetization vector: $M(\vec{x},t)= M_0(\vec{x}) exp(i\phi_0 + i \frac{\pi}{venc} u(\vec{x},t))$
+\item<2->  $M(\vec{x},t)= M_0(\vec{x}) exp(i\phi_0 + i \frac{\pi}{venc} u(\vec{x},t))$
+\item<3-> reconstructed velocity: $u \in \big ( -venc, + venc  \big )$
+\item<4-> $VNR \sim 1/venc$
 \end{itemize}
-\onslide<3-> 
- \begin{columns}
- \column{.3\textwidth}
- \flushleft
- \begin{figure}
-        \includegraphics[width=1.1\textwidth]{images/ref_int.png}
-  \caption*{(a) Interpolated reference solution}
-\end{figure}
-\column{.67\textwidth}
 \centering
-\onslide<4-> \textbf{The measurements:}
+\onslide<5-> \textbf{The measurements:}
 \begin{itemize}
-\item<5-> Gaussian noise into the magnetization
-\item<6-> Different levels of aliasing varying the $venc$ parameter
-\item<7-> Only using the dominant component of the velocity: $u_z$
-\item<8-> Time interpolation $dt = 1 \ ms  \Longrightarrow dt = 30 \ ms$ 
+\item<6-> Gaussian noise into the magnetization
+\item<7-> Spatial and temporal interpolation
+\item<8-> Only using the dominant component of the velocity: $u_z$
+\item<9-> Different levels of aliasing varying the $venc$ parameter
 \end{itemize}
-\end{columns} 
 \end{frame}
 
 
 
-\section{The inverse problem}
 
 \begin{frame}
  \frametitle{The inverse problem}
 \begin{itemize}
 \item Upon this solution $\Longrightarrow$ build a set of measurements
-\item Induce typical arifacts via a Magnetization vector: $M(\vec{x},t)= M_0(\vec{x}) exp(i\phi_0 + i \frac{\pi}{venc} u(\vec{x},t))$
+\item $M(\vec{x},t)= M_0(\vec{x}) exp(i\phi_0 + i \frac{\pi}{venc} u(\vec{x},t))$
+\item reconstructed velocity: $u \in \big ( -venc, + venc  \big )$
+\item $VNR \sim 1/venc$
 \end{itemize}
- \begin{columns}
- \column{.3\textwidth}
- \flushleft
  \begin{figure}
-        \includegraphics[width=1.1\textwidth]{images/ref_int.png}
-  \caption*{(a) Interpolated reference solution}
-\end{figure}
-\column{.67\textwidth}
-\flushleft
- \begin{figure}
-        \includegraphics[width=1.1\textwidth]{images/supra_venc.png}
-  \caption*{(b) Aliased measurements with different $vencs = 120,70,30 \%$ of $u_{max}$}
+        \includegraphics[width=0.7\textwidth]{images/supra_venc.png}
+  \caption*{Aliased measurements with different $vencs = 120,70,30 \%$ of $u_{max}$}
   \hfill
 \end{figure}
-\end{columns} 
 \end{frame}
 
 
@@ -317,31 +335,35 @@ P_l = R_{p,l} \ Q_l + \pi_l
  \frametitle{The inverse problem}
 \begin{itemize}
 \item Upon this solution $\Longrightarrow$ build a set of measurements
-\item Induce typical arifacts via a Magnetization vector: $M(\vec{x},t)= M_0(\vec{x}) exp(i\phi_0 + i \frac{\pi}{venc} u(\vec{x},t))$
+\item $M(\vec{x},t)= M_0(\vec{x}) exp(i\phi_0 + i \frac{\pi}{venc} u(\vec{x},t))$
+\item reconstructed velocity: $u \in \big ( -venc, + venc  \big )$
+\item $VNR \sim 1/venc$
 \end{itemize}
- \begin{columns}
- \column{.3\textwidth}
- \flushleft
  \begin{figure}
-        \includegraphics[width=1.1\textwidth]{images/ref_int.png}
-  \caption*{(a) Interpolated reference solution}
-\end{figure}
-\column{.67\textwidth}
-\flushleft
- \begin{figure}
-        \includegraphics[width=1.1\textwidth]{images/coartation.png}
-  \caption*{(b) Aliased measurements with different $vencs = 120,70,30 \%$ of $u_{max}$}
+        \includegraphics[width=0.7\textwidth]{images/coartation.png}
+  \caption*{ Aliased measurements with different $vencs = 120,70,30 \%$ of $u_{max}$}
   \hfill
 \end{figure}
-\end{columns} 
 \end{frame}
 
 
+\section{The inverse problem}
+
+
+\begin{frame}
+ \frametitle{The inverse problem}
+\begin{center}
+Parameter optimization
+\end{center}
+\end{frame}
+
+
+
 
 \begin{frame}
  \frametitle{The Kalman Filter}
 \begin{itemize}
-\item<1-> We use a Reduced Order Unscendent Kalman Filter (ROUKF) to reconstruct the parameter vector $\theta$ solving the next optimization problem:
+\item<1-> We use a Reduced Order Unscendent Kalman Filter (ROUKF) to reconstruct the parameter vector $\theta$:
 
 \onslide<2->
 \begin{equation*}
@@ -350,7 +372,7 @@ P_l = R_{p,l} \ Q_l + \pi_l
 \begin{equation}
 J(\theta) = \displaystyle \frac{1}{2} || \theta - \theta_0  ||^2_{P_0^{-1}}  + \sum_{k=1}^N \frac{1}{2}  || Z_k - \mathbb{H} X_k(\theta)   ||^2_{W^{-1}}
 \end{equation}
-\onslide<3-> Where:
+\onslide<4-> Where:
 \begin{itemize}
 \item<4-> $Z$ the measurements and $X = (\vec{u} , \pi)$ the state variable
 \item<5-> $\mathbb{H}$ observation operator 
@@ -372,32 +394,41 @@ The parameter vector:
  
 \begin{itemize}
 \item<1->  Amplitude of the inlet velocity: $U$ 
-\item<2-> Since $R_p << R_d$, we only consider an optimization dependent on $\big ( R_{d,l}, C_l \big )$ for $l=1,...,n_l$
+\item<2-> Only the higher resistence: $R_d$
 \end{itemize}
 
-\onslide<3-> $$\theta =  (U,\vec{R_d},\vec{C})$$ \\  with $\vec{R_d} = R_{d,l}$,  $\vec{C} = C_l$ for $l=1,..., \color{red} n_{l-1}$ \\[0.3cm]
-\onslide<4-> \color{red} Not all the resistences can be recovered at once $\Longrightarrow$ desc. aorta fixed.
+\onslide<4-> $$\theta =  (U,\vec{R_d})$$ \\  with $\vec{R_d} = R_{d,l}$ for $l=1,..., \color{red} n_{l-1}$ \\[0.3cm]
+\onslide<5-> \color{red} Not all the resistences can be recovered at once $\Longrightarrow$ desc. aorta fixed.
 
 \end{frame}
 
 
 
+
+\section{Numerical Experiments}
+
+
+\begin{frame}
+ \frametitle{Numerical Experiments}
+\begin{center}
+Numerical Experiments
+\end{center}
+\end{frame}
+
+
 \begin{frame}
- \frametitle{Easy example}
+ \frametitle{Numerical Experiments}
  \footnotesize
-\begin{itemize}
-\item<1-> $\theta_{ref} = (U,\vec{R_d})$ , $U=75$, $\vec{R_d} = (7200,11520,11520)$
-\end{itemize}
+\onslide<1-> $\theta_{ref} = (U,\vec{R_d})$ , $U=75$, $\vec{R_d} = (7200,11520,11520)$
  \begin{columns}
   \footnotesize
- \column{.4\textwidth}
+ \column{.45\textwidth}
  \begin{figure}
- \onslide<2-> \textbf{Test I:} $U_0 = 150$  $\vec{R_{d,0}}= (8760,8760,8760)$
-  \onslide<3->
-        \includegraphics[width=1.2\textwidth]{images/U_Pb.png}
+ \onslide<2-> \textbf{Test I:} $U_0 = 150$  $\vec{R_{d,0}}= (17520,17520,17520)$
+  \onslide<3-> \includegraphics[width=1.2\textwidth]{images/U_Pb.png}
          \includegraphics[width=1.2\textwidth]{images/Rd_Pb.png}
 \end{figure}
-\column{.4\textwidth}
+\column{.45\textwidth}
 \begin{figure}
  \onslide<2-> \textbf{Test II:} $U_0 = 40$  $\vec{R_{d,0}}= (4000,4000,4000)$
  \onslide<4->
@@ -412,35 +443,51 @@ The parameter vector:
 
 
 
+\begin{frame}
+ \frametitle{Aliased data}
+\begin{center}
+\onslide<1-> What happend when $venc < u_{max}$ ?
+\begin{figure}
+ \onslide<2-> \includegraphics[width=0.45\textwidth]{images/v120.png}
+ \caption{Measurement set with $venc = 120 \% u_{max}$}
+\end{figure}
+\end{center}
+\end{frame}
+
+
 \begin{frame}
  \frametitle{Aliased data}
 \begin{center}
 What happend when $venc < u_{max}$ ?
+\begin{figure}
+ \includegraphics[width=0.45\textwidth]{images/v70.png}
+ \caption{Measurement set with $venc = 70 \% u_{max}$}
+\end{figure}
 \end{center}
 \end{frame}
 
 
+
+
 \begin{frame}
  \frametitle{Easy example: with $venc = 70 \% u_{max}$}
  \footnotesize
-\begin{itemize}
-\item $\theta_{ref} = (U,\vec{R_d})$ , $U=75$, $\vec{R_d} = (7200,11520,11520)$
-\end{itemize}
+$\theta_{ref} = (U,\vec{R_d})$ , $U=75$, $\vec{R_d} = (7200,11520,11520)$
  \begin{columns}
   \footnotesize
- \column{.4\textwidth}
+ \column{.45\textwidth}
  \begin{figure}
-  \onslide<1-> \textbf{Test I:} $U_0 = 150$  $\vec{R_{d,0}}= (8760,8760,8760)$
+  \onslide<1-> \textbf{Test I:} $U_0 = 150$  $\vec{R_{d,0}}= (17520,17520,17520)$
   \onslide<2->
-        \includegraphics[width=1.2\textwidth]{images/U_Pb.png}
-         \includegraphics[width=1.2\textwidth]{images/Rd_Pb.png}
+        \includegraphics[width=1.2\textwidth]{images/U_Pb_V70.png}
+         \includegraphics[width=1.2\textwidth]{images/Rd_Pb_V70.png}
 \end{figure}
-\column{.4\textwidth}
+\column{.45\textwidth}
 \begin{figure}
   \onslide<1->  \textbf{Test II:} $U_0 = 40$  $\vec{R_{d,0}}= (4000,4000,4000)$
  \onslide<2->
-        \includegraphics[width=1.2\textwidth]{images/U_Pc.png}
-         \includegraphics[width=1.2\textwidth]{images/Rd_Pc.png}
+        \includegraphics[width=1.2\textwidth]{images/U_Pc_V70.png}
+         \includegraphics[width=1.2\textwidth]{images/Rd_Pc_V70.png}
 \end{figure}
 \end{columns} 
 \end{frame}
@@ -465,42 +512,106 @@ J(\theta) = \displaystyle \frac{1}{2} || \theta - \theta_0  ||^2_{P_0^{-1}}  + \
 
 
 
+\begin{frame}
+ \frametitle{Easy example: with $venc = 70 \% u_{max}$}
+ \footnotesize
+$\theta_{ref} = (U,\vec{R_d})$ , $U=75$, $\vec{R_d} = (7200,11520,11520)$
+ \begin{columns}
+  \footnotesize
+ \column{.45\textwidth}
+ \begin{figure}
+  \onslide<1-> \textbf{Test I:} $U_0 = 150$  $\vec{R_{d,0}}= (17520,17520,17520)$
+  \onslide<2->
+        \includegraphics[width=1.2\textwidth]{images/HU_Pb_V70.png}
+         \includegraphics[width=1.2\textwidth]{images/HRd_Pb_V70.png}
+\end{figure}
+\column{.45\textwidth}
+\begin{figure}
+  \onslide<1->  \textbf{Test II:} $U_0 = 40$  $\vec{R_{d,0}}= (4000,4000,4000)$
+ \onslide<3->
+        \includegraphics[width=1.2\textwidth]{images/HU_Pc_V70.png}
+         \includegraphics[width=1.2\textwidth]{images/HRd_Pc_V70.png}
+\end{figure}
+\end{columns} 
+\end{frame}
 
 
+\begin{frame}
+ \frametitle{Aliased data}
+\begin{center}
+Or even higher aliasing...
+\begin{figure}
+ \includegraphics[width=0.45\textwidth]{images/v30.png}
+ \caption{Measurement set with $venc = 30 \% u_{max}$}
+\end{figure}
+\end{center}
+\end{frame}
 
 
 
 
+\begin{frame}
+ \frametitle{Easy example: with $venc = 30 \% u_{max}$}
+ \footnotesize
+$\theta_{ref} = (U,\vec{R_d})$ , $U=75$, $\vec{R_d} = (7200,11520,11520)$
+ \begin{columns}
+  \footnotesize
+ \column{.45\textwidth}
+ \begin{figure}
+  \onslide<1-> \textbf{Test I:} $U_0 = 150$  $\vec{R_{d,0}}= (17520,17520,17520)$
+  \onslide<2->
+        \includegraphics[width=1.2\textwidth]{images/HU_Pb_V30.png}
+         \includegraphics[width=1.2\textwidth]{images/HRd_Pb_V30.png}
+\end{figure}
+\column{.45\textwidth}
+\begin{figure}
+  \onslide<1->  \textbf{Test II:} $U_0 = 40$  $\vec{R_{d,0}}= (4000,4000,4000)$
+ \onslide<3->
+        \includegraphics[width=1.2\textwidth]{images/HU_Pc_V30.png}
+         \includegraphics[width=1.2\textwidth]{images/HRd_Pc_V30.png}
+\end{figure}
+\end{columns} 
+\end{frame}
+
+
 
-\section{Numerical Experiments}
 
+\section{Conclusions}
 
 \begin{frame}
- \frametitle{Numerical Experiments}
 \begin{center}
-Numerical Experiments
+Conclusions
 \end{center}
 \end{frame}
 
+
+
 \begin{frame}
- \frametitle{Numerical Experiments}
+\frametitle{Conclusions}
+ \footnotesize
+\begin{itemize}
+\item<1-> 4D Flow measurements are promising for extracting data via inverse problems
+\item<2-> Noise and aliasing are the typical artifacts involved.
+\item<3-> Using a suitable Kalman filter, have shown to bypass aliasing defining the funcional in terms of the frequencies.
+\end{itemize}
 
-\end{frame}
+\onslide<4-> Future Work
 
+\begin{itemize}
+\item<5-> To include the capacitancies in the inverse problem (adding some pressure meas.)
+\item<6-> Real data!
+\end{itemize}
 
+\end{frame}
 
-\section{Conclusions}
 
 \begin{frame}
 \begin{center}
-Conclusions
+Thank you for your time!
 \end{center}
-\end{frame}
-
-
-
 
 
+\end{frame}
 
 
 

presentations/press_8ecm/press.toc

@@ -0,0 +1,6 @@
+\babel@toc {english}{}
+\beamer@sectionintoc {1}{4D flow MRI}{3}{0}{1}
+\beamer@sectionintoc {2}{The mathematical model}{6}{0}{2}
+\beamer@sectionintoc {3}{The inverse problem}{23}{0}{3}
+\beamer@sectionintoc {4}{Numerical Experiments}{37}{0}{4}
+\beamer@sectionintoc {5}{Conclusions}{56}{0}{5}