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Add derived harmonized volumes to dataset for availability in age trends
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@melhemr
melhemr committed Feb 24, 2022
1 parent dfb5556 commit dc57ff8
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Showing 5 changed files with 313 additions and 7 deletions.
15 changes: 14 additions & 1 deletion NiBAx/core/model/datamodel.py
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Original file line number Diff line number Diff line change
Expand Up @@ -36,10 +36,15 @@ def __init__(self):
self.ADModel = None


def SetMUSEDictionaries(self, MUSEDictNAMEtoID, MUSEDictIDtoNAME):
def SetMUSEDictionaries(self, MUSEDictNAMEtoID, MUSEDictIDtoNAME,MUSEDictDataFrame):
"""Setter for MUSE dictionary"""
self.MUSEDictNAMEtoID = MUSEDictNAMEtoID
self.MUSEDictIDtoNAME = MUSEDictIDtoNAME
self.MUSEDictDataFrame = MUSEDictDataFrame

def SetDerivedMUSEDictionary(self,DerivedMUSEDict):
"""Setter for Derived MUSE dictionary"""
self.DerivedMUSEDict = DerivedMUSEDict


def SetDataFilePath(self,p):
Expand All @@ -65,6 +70,14 @@ def GetHarmonizationModelFilePath(self):
def GetMUSEDictionaries(self):
"""Get the MUSE dictionaries to map from ID to name and vice-versa"""
return self.MUSEDictNAMEtoID, self.MUSEDictIDtoNAME

def GetDerivedMUSEDictionary(self):
"""Get the derived MUSE dictionary to map from SINGLE to DERIVED ROIs"""
return self.DerivedMUSEDict

def GetMUSEDictDataFrame(self):
"""Get the MUSE dictionaries to map from ID to name and vice-versa"""
return self.MUSEDictDataFrame


def SetData(self,d):
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259 changes: 259 additions & 0 deletions NiBAx/plugins/data/MUSE_DerivedROIs_Mappings.csv
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Original file line number Diff line number Diff line change
@@ -0,0 +1,259 @@
702,ICV
701,TOTALBRAIN,4,11,23,30,31,32,35,36,37,38,39,40,41,47,48,49,50,51,52,55,56,57,58,59,60,61,62,71,72,73,75,76,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,100,101,102,103,104,105,106,107,108,109,112,113,114,115,116,117,118,119,120,121,122,123,124,125,128,129,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207
601,GM,23,30,31,32,36,37,38,39,47,48,55,56,57,58,59,60,71,72,73,75,76,100,101,102,103,104,105,106,107,108,109,112,113,114,115,116,117,118,119,120,121,122,123,124,125,128,129,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207
604,WM,40,41,61,62,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95
606,GM_L,30,32,37,39,48,56,58,60,75,101,103,105,107,109,113,115,117,119,121,123,125,129,133,135,137,139,141,143,145,147,149,151,153,155,157,161,163,165,167,169,171,173,175,177,179,181,183,185,187,191,193,195,197,199,201,203,205,207
607,WM_L,41,62,82,84,86,88,90,92,94
613,GM_R,23,31,36,38,47,55,57,59,76,100,102,104,106,108,112,114,116,118,120,122,124,128,132,134,136,138,140,142,144,146,148,150,152,154,156,160,162,164,166,168,170,172,174,176,178,180,182,184,186,190,192,194,196,198,200,202,204,206
614,WM_R,40,61,81,83,85,87,89,91,93
501,CORPUS_CALLOSUM,95
502,CEREBELLUM,38,39,40,41,71,72,73
503,DEEP_WM_GM,23,30,31,32,36,37,47,48,55,56,57,58,59,60,75,76,89,90,91,92,93,94
504,FRONTAL,81,82,102,103,104,105,112,113,118,119,120,121,124,125,136,137,140,141,142,143,146,147,150,151,152,153,162,163,164,165,172,173,174,175,178,179,182,183,186,187,190,191,192,193,204,205
505,LIMBIC,100,101,116,117,138,139,166,167,170,171
506,OCCIPITAL,83,84,108,109,114,115,128,129,134,135,144,145,156,157,160,161,196,197
507,PARIETAL,85,86,106,107,148,149,168,169,176,177,194,195,198,199
508,TEMPORAL,87,88,122,123,132,133,154,155,180,181,184,185,200,201,202,203,206,207
509,VENTRICLE,4,11,49,50,51,52
510,CEREBELLUM_L,39,41
511,DEEP_WM_GM_L,30,32,37,48,56,58,60,75,90,92,94
512,FRONTAL_L,82,103,105,113,119,121,125,137,141,143,147,151,153,163,165,173,175,179,183,187,191,193,205
513,LIMBIC_L,101,117,139,167,171
514,OCCIPITAL_L,84,109,115,129,135,145,157,161,197
515,PARIETAL_L,86,107,149,169,177,195,199
516,TEMPORAL_L,88,123,133,155,181,185,201,203,207
517,VENTRICLE_L,50,52
518,CEREBELLUM_R,38,40
519,DEEP_WM_GM_R,23,31,36,47,55,57,59,76,89,91,93
520,FRONTAL_R,81,102,104,112,118,120,124,136,140,142,146,150,152,162,164,172,174,178,182,186,190,192,204
521,LIMBIC_R,100,116,138,166,170
522,OCCIPITAL_R,83,108,114,128,134,144,156,160,196
523,PARIETAL_R,85,106,148,168,176,194,198
524,TEMPORAL_R,87,122,132,154,180,184,200,202,206
525,VENTRICLE_R,49,51
401,BASAL_GANGLIA,23,30,36,37,55,56,57,58
402,DEEP_GM,59,60
403,DEEP_WM,89,90,91,92,93,94
404,FRONTAL_GM,102,103,104,105,112,113,118,119,120,121,124,125,136,137,140,141,142,143,146,147,150,151,152,153,162,163,164,165,172,173,174,175,178,179,182,183,186,187,190,191,192,193,204,205
405,FRONTAL_WM,81,82
406,LIMBIC_GM,100,101,116,117,138,139,166,167,170,171
407,OCCIPITAL_GM,108,109,114,115,128,129,134,135,144,145,156,157,160,161,196,197
408,OCCIPITAL_WM,83,84
409,PARIETAL_GM,106,107,148,149,168,169,176,177,194,195,198,199
410,PARIETAL_WM,85,86
411,TEMPORAL_GM,122,123,132,133,154,155,180,181,184,185,200,201,202,203,206,207
412,TEMPORAL_WM,87,88
413,BASAL_GANGLIA_L,30,37,56,58
414,DEEP_GM_L,60
415,DEEP_WM_L,90,92,94
416,FRONTAL_GM_L,103,105,113,119,121,125,137,141,143,147,151,153,163,165,173,175,179,183,187,191,193,205
417,FRONTAL_WM_L,82
418,LIMBIC_GM_L,101,117,139,167,171
419,OCCIPITAL_GM_L,109,115,129,135,145,157,161,197
420,OCCIPITAL_WM_L,84
421,PARIETAL_GM_L,107,149,169,177,195,199
422,PARIETAL_WM_L,86
423,TEMPORAL_GM_L,123,133,155,181,185,201,203,207
424,TEMPORAL_WM_L,88
425,BASAL_GANGLIA_R,23,36,55,57
426,DEEP_GM_R,59
427,DEEP_WM_R,89,91,93
428,FRONTAL_GM_R,102,104,112,118,120,124,136,140,142,146,150,152,162,164,172,174,178,182,186,190,192,204
429,FRONTAL_WM_R,81
430,LIMBIC_GM_R,100,116,138,166,170
431,OCCIPITAL_GM_R,108,114,128,134,144,156,160,196
432,OCCIPITAL_WM_R,83
433,PARIETAL_GM_R,106,148,168,176,194,198
434,PARIETAL_WM_R,85
435,TEMPORAL_GM_R,122,132,154,180,184,200,202,206
436,TEMPORAL_WM_R,87
301,FRONTAL_INFERIOR_GM,104,105,136,137,146,147,178,179
302,FRONTAL_INSULAR_GM,102,103,172,173
303,FRONTAL_LATERAL_GM,120,121,142,143,162,163,164,165,182,183,190,191,204,205
304,FRONTAL_MEDIAL_GM,124,125,140,141,150,151,152,153,186,187,192,193
305,FRONTAL_OPERCULAR_GM,112,113,118,119,174,175
306,LIMBIC_CINGULATE_GM,100,101,138,139,166,167
307,LIMBIC_MEDIALTEMPORAL_GM,116,117,170,171
308,OCCIPITAL_INFERIOR_GM,160,161
309,OCCIPITAL_LATERAL_GM,128,129,144,145,156,157,196,197
310,OCCIPITAL_MEDIAL_GM,108,109,114,115,134,135
311,PARIETAL_LATERAL_GM,106,107,176,177,194,195,198,199
312,PARIETAL_MEDIAL_GM,148,149,168,169
313,TEMPORAL_INFERIOR_GM,122,123
314,TEMPORAL_LATERAL_GM,132,133,154,155,200,201,202,203
315,TEMPORAL_SUPRATEMPORAL_GM,180,181,184,185,206,207
316,FRONTAL_INFERIOR_GM_L,105,137,147,179
317,FRONTAL_INSULAR_GM_L,103,173
318,FRONTAL_LATERAL_GM_L,121,143,163,165,183,191,205
319,FRONTAL_MEDIAL_GM_L,125,141,151,153,187,193
320,FRONTAL_OPERCULAR_GM_L,113,119,175
321,LIMBIC_CINGULATE_GM_L,101,139,167
322,LIMBIC_MEDIALTEMPORAL_GM_L,117,171
323,OCCIPITAL_INFERIOR_GM_L,161
324,OCCIPITAL_LATERAL_GM_L,129,145,157,197
325,OCCIPITAL_MEDIAL_GM_L,109,115,135
326,PARIETAL_LATERAL_GM_L,107,177,195,199
327,PARIETAL_MEDIAL_GM_L,149,169
328,TEMPORAL_INFERIOR_GM_L,123
329,TEMPORAL_LATERAL_GM_L,133,155,201,203
330,TEMPORAL_SUPRATEMPORAL_GM_L,181,185,207
331,FRONTAL_INFERIOR_GM_R,104,136,146,178
332,FRONTAL_INSULAR_GM_R,102,172
333,FRONTAL_LATERAL_GM_R,120,142,162,164,182,190,204
334,FRONTAL_MEDIAL_GM_R,124,140,150,152,186,192
335,FRONTAL_OPERCULAR_GM_R,112,118,174
336,LIMBIC_CINGULATE_GM_R,100,138,166
337,LIMBIC_MEDIALTEMPORAL_GM_R,116,170
338,OCCIPITAL_INFERIOR_GM_R,160
339,OCCIPITAL_LATERAL_GM_R,128,144,156,196
340,OCCIPITAL_MEDIAL_GM_R,108,114,134
341,PARIETAL_LATERAL_GM_R,106,176,194,198
342,PARIETAL_MEDIAL_GM_R,148,168
343,TEMPORAL_INFERIOR_GM_R,122
344,TEMPORAL_LATERAL_GM_R,132,154,200,202
345,TEMPORAL_SUPRATEMPORAL_GM_R,180,184,206
4,3rd Ventricle,4
11,4th Ventricle,11
23,Right Accumbens Area,23
30,Left Accumbens Area,30
31,Right Amygdala,31
32,Left Amygdala,32
35,Brain Stem,35
36,Right Caudate,36
37,Left Caudate,37
38,Right Cerebellum Exterior,38
39,Left Cerebellum Exterior,39
40,Right Cerebellum White Matter,40
41,Left Cerebellum White Matter,41
47,Right Hippocampus,47
48,Left Hippocampus,48
49,Right Inf Lat Vent,49
50,Left Inf Lat Vent,50
51,Right Lateral Ventricle,51
52,Left Lateral Ventricle,52
55,Right Pallidum,55
56,Left Pallidum,56
57,Right Putamen,57
58,Left Putamen,58
59,Right Thalamus Proper,59
60,Left Thalamus Proper,60
61,Right Ventral DC,61
62,Left Ventral DC,62
71,Cerebellar Vermal Lobules I-V,71
72,Cerebellar Vermal Lobules VI-VII,72
73,Cerebellar Vermal Lobules VIII-X,73
75,Left Basal Forebrain,75
76,Right Basal Forebrain,76
81,frontal lobe WM right,81
82,frontal lobe WM left,82
83,occipital lobe WM right,83
84,occipital lobe WM left,84
85,parietal lobe WM right,85
86,parietal lobe WM left,86
87,temporal lobe WM right,87
88,temporal lobe WM left,88
89,fornix right,89
90,fornix left,90
91,anterior limb of internal capsule right,91
92,anterior limb of internal capsule left,92
93,posterior limb of internal capsule inc. cerebral peduncle right,93
94,posterior limb of internal capsule inc. cerebral peduncle left,94
95,corpus callosum,95
100,Right ACgG anterior cingulate gyrus,100
101,Left ACgG anterior cingulate gyrus,101
102,Right AIns anterior insula,102
103,Left AIns anterior insula,103
104,Right AOrG anterior orbital gyrus,104
105,Left AOrG anterior orbital gyrus,105
106,Right AnG angular gyrus,106
107,Left AnG angular gyrus,107
108,Right Calc calcarine cortex,108
109,Left Calc calcarine cortex,109
112,Right CO central operculum,112
113,Left CO central operculum,113
114,Right Cun cuneus,114
115,Left Cun cuneus,115
116,Right Ent entorhinal area,116
117,Left Ent entorhinal area,117
118,Right FO frontal operculum,118
119,Left FO frontal operculum,119
120,Right FRP frontal pole,120
121,Left FRP frontal pole,121
122,Right FuG fusiform gyrus,122
123,Left FuG fusiform gyrus,123
124,Right GRe gyrus rectus,124
125,Left GRe gyrus rectus,125
128,Right IOG inferior occipital gyrus,128
129,Left IOG inferior occipital gyrus,129
132,Right ITG inferior temporal gyrus,132
133,Left ITG inferior temporal gyrus,133
134,Right LiG lingual gyrus,134
135,Left LiG lingual gyrus,135
136,Right LOrG lateral orbital gyrus,136
137,Left LOrG lateral orbital gyrus,137
138,Right MCgG middle cingulate gyrus,138
139,Left MCgG middle cingulate gyrus,139
140,Right MFC medial frontal cortex,140
141,Left MFC medial frontal cortex,141
142,Right MFG middle frontal gyrus,142
143,Left MFG middle frontal gyrus,143
144,Right MOG middle occipital gyrus,144
145,Left MOG middle occipital gyrus,145
146,Right MOrG medial orbital gyrus,146
147,Left MOrG medial orbital gyrus,147
148,Right MPoG postcentral gyrus medial segment,148
149,Left MPoG postcentral gyrus medial segment,149
150,Right MPrG precentral gyrus medial segment,150
151,Left MPrG precentral gyrus medial segment,151
152,Right MSFG superior frontal gyrus medial segment,152
153,Left MSFG superior frontal gyrus medial segment,153
154,Right MTG middle temporal gyrus,154
155,Left MTG middle temporal gyrus,155
156,Right OCP occipital pole,156
157,Left OCP occipital pole,157
160,Right OFuG occipital fusiform gyrus,160
161,Left OFuG occipital fusiform gyrus,161
162,Right OpIFG opercular part of the inferior frontal gyrus,162
163,Left OpIFG opercular part of the inferior frontal gyrus,163
164,Right OrIFG orbital part of the inferior frontal gyrus,164
165,Left OrIFG orbital part of the inferior frontal gyrus,165
166,Right PCgG posterior cingulate gyrus,166
167,Left PCgG posterior cingulate gyrus,167
168,Right PCu precuneus,168
169,Left PCu precuneus,169
170,Right PHG parahippocampal gyrus,170
171,Left PHG parahippocampal gyrus,171
172,Right PIns posterior insula,172
173,Left PIns posterior insula,173
174,Right PO parietal operculum,174
175,Left PO parietal operculum,175
176,Right PoG postcentral gyrus,176
177,Left PoG postcentral gyrus,177
178,Right POrG posterior orbital gyrus,178
179,Left POrG posterior orbital gyrus,179
180,Right PP planum polare,180
181,Left PP planum polare,181
182,Right PrG precentral gyrus,182
183,Left PrG precentral gyrus,183
184,Right PT planum temporale,184
185,Left PT planum temporale,185
186,Right SCA subcallosal area,186
187,Left SCA subcallosal area,187
190,Right SFG superior frontal gyrus,190
191,Left SFG superior frontal gyrus,191
192,Right SMC supplementary motor cortex,192
193,Left SMC supplementary motor cortex,193
194,Right SMG supramarginal gyrus,194
195,Left SMG supramarginal gyrus,195
196,Right SOG superior occipital gyrus,196
197,Left SOG superior occipital gyrus,197
198,Right SPL superior parietal lobule,198
199,Left SPL superior parietal lobule,199
200,Right STG superior temporal gyrus,200
201,Left STG superior temporal gyrus,201
202,Right TMP temporal pole,202
203,Left TMP temporal pole,203
204,Right TrIFG triangular part of the inferior frontal gyrus,204
205,Left TrIFG triangular part of the inferior frontal gyrus,205
206,Right TTG transverse temporal gyrus,206
207,Left TTG transverse temporal gyrus,207
8 changes: 6 additions & 2 deletions NiBAx/plugins/data/data.py
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Original file line number Diff line number Diff line change
Expand Up @@ -107,8 +107,12 @@ def ReadData(self,filename):
logger.info('New data read from file: %s', filename)

#also read MUSE dictionary
MUSEDictNAMEtoID, MUSEDictIDtoNAME = dio.ReadMUSEDictionary()
self.datamodel.SetMUSEDictionaries(MUSEDictNAMEtoID, MUSEDictIDtoNAME)
MUSEDictNAMEtoID, MUSEDictIDtoNAME, MUSEDictDataFrame = dio.ReadMUSEDictionary()
self.datamodel.SetMUSEDictionaries(MUSEDictNAMEtoID, MUSEDictIDtoNAME,MUSEDictDataFrame)

#also read Derived MUSE dictionary
DerivedMUSEDict = dio.ReadDerivedMUSEDictionary()
self.datamodel.SetDerivedMUSEDictionary(DerivedMUSEDict)

#set data in model
self.datamodel.SetDataFilePath(filename)
Expand Down
14 changes: 13 additions & 1 deletion NiBAx/plugins/data/dataio.py
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Original file line number Diff line number Diff line change
Expand Up @@ -36,9 +36,21 @@ def ReadMUSEDictionary(self):
# e.g. ID to name; MUSE_Volume_48 -> Hippocampus right
MUSEDictIDtoNAME = dict(zip(MUSEDict['ROI_COL'], MUSEDict['ROI_NAME']))

MUSEDictDataFrame = MUSEDict

logger.info('MUSE dictionary read from file: %s', MUSEDictfile)

return MUSEDictNAMEtoID, MUSEDictIDtoNAME
return MUSEDictNAMEtoID, MUSEDictIDtoNAME, MUSEDictDataFrame

def ReadDerivedMUSEDictionary(self):
# Load MUSE dictionary file
DerivedDictfile = os.path.join(os.path.dirname(__file__), 'MUSE_DerivedROIs_Mappings.csv')
DerivedMUSEDict = pd.read_csv(DerivedDictfile,
header=None, engine='python').reset_index().rename(columns={'level_0':'ROI_INDEX','level_1':'ROI_NAME'}).set_index('ROI_INDEX').drop(columns=['ROI_NAME'])

logger.info('Derived MUSE dictionary read from file: %s', DerivedDictfile)

return DerivedMUSEDict


def ReadSPAREModel(self, filename):
Expand Down
24 changes: 21 additions & 3 deletions NiBAx/plugins/harmonization/harmonization.py
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Original file line number Diff line number Diff line change
Expand Up @@ -292,7 +292,14 @@ def plotMUSE(self,plotOptions):

def OnAddToDataFrame(self):
print('Saving modified data to pickle file...')
H_ROIs = ['H_'+x for x in self.datamodel.harmonization_model['ROIs']]
MUSEDictDataFrame= self.datamodel.GetMUSEDictDataFrame()
Derived_numbers = list(MUSEDictDataFrame[MUSEDictDataFrame['ROI_LEVEL']=='DERIVED']['ROI_INDEX'])
Derived_MUSE_Volumes = list('MUSE_Volume_' + str(x) for x in Derived_numbers)
ROI_list = list(self.datamodel.harmonization_model['ROIs']) + Derived_MUSE_Volumes
ROI_list.remove('MUSE_Volume_702')
print(ROI_list)
H_ROIs = list('H_' + str(x) for x in ROI_list)
print(H_ROIs)
ROIs_ICV_Sex_Residuals = ['RES_ICV_Sex_' + x for x in self.datamodel.harmonization_model['ROIs']]
ROIs_Residuals = ['RES_' + x for x in self.datamodel.harmonization_model['ROIs']]
RAW_Residuals = ['RAW_RES_' + x for x in self.datamodel.harmonization_model['ROIs']]
Expand Down Expand Up @@ -354,9 +361,9 @@ def DoHarmonization(self):
continue

print('Harmonizing '+ site)
gamma_hat_site = np.mean(((Raw_ROIs_Residuals[new_site_is_train,:])/np.dot(np.sqrt(var_pooled),np.ones((1,Raw_ROIs_Residuals[new_site_is_train,:].shape[0]))).T),0)
gamma_hat_site = np.nanmean(((Raw_ROIs_Residuals[new_site_is_train,:])/np.dot(np.sqrt(var_pooled),np.ones((1,Raw_ROIs_Residuals[new_site_is_train,:].shape[0]))).T),0)
gamma_hat_site = gamma_hat_site[:,np.newaxis]
delta_hat_site = pow(np.std(((Raw_ROIs_Residuals[new_site_is_train,:])/np.dot(np.sqrt(var_pooled),np.ones((1,Raw_ROIs_Residuals[new_site_is_train,:].shape[0]))).T),0),2)
delta_hat_site = pow(np.nanstd(((Raw_ROIs_Residuals[new_site_is_train,:])/np.dot(np.sqrt(var_pooled),np.ones((1,Raw_ROIs_Residuals[new_site_is_train,:].shape[0]))).T),0),2)
delta_hat_site = delta_hat_site[:,np.newaxis]

site_gamma = pd.DataFrame(gamma_hat_site.T,columns=gamma_ROIs,index=[site])
Expand All @@ -378,8 +385,19 @@ def DoHarmonization(self):

if 'isTrainMUSEHarmonization' in self.datamodel.data.columns:
muse = pd.concat([self.datamodel.data['isTrainMUSEHarmonization'].copy(), covars, pd.DataFrame(bayes_data, columns=['H_' + s for s in self.datamodel.harmonization_model['ROIs']])],axis=1)
if 'UseForComBatGAMHarmonization' in self.datamodel.data.columns:
muse = pd.concat([self.datamodel.data['UseForComBatGAMHarmonization'].copy(), covars, pd.DataFrame(bayes_data, columns=['H_' + s for s in self.datamodel.harmonization_model['ROIs']])],axis=1)
else:
muse = pd.concat([covars,pd.DataFrame(bayes_data, columns=['H_' + s for s in self.datamodel.harmonization_model['ROIs']])],axis=1)

# harmonize derived volumes
MUSEDictDataFrame= self.datamodel.GetMUSEDictDataFrame()
muse_mappings = self.datamodel.GetDerivedMUSEDictionary()
for ROI in MUSEDictDataFrame[MUSEDictDataFrame['ROI_LEVEL']=='DERIVED']['ROI_INDEX']:
single_ROIs = muse_mappings.loc[ROI].replace('NaN',np.nan).dropna().astype(np.float)
single_ROIs = ['H_MUSE_Volume_%0d' % x for x in single_ROIs]
muse['H_MUSE_Volume_%d' % ROI] = muse[single_ROIs].sum(axis=1)
muse.drop(columns=['H_MUSE_Volume_702'], inplace=True)

start_index = len(self.datamodel.harmonization_model['SITE_labels'])
sex_icv_effect = np.dot(muse[['Sex','DLICV_baseline']].copy(), self.datamodel.harmonization_model['B_hat'][start_index:(start_index+2),:])
Expand Down

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