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Body Mass Index Moderates Brain Dynamics
and Executive Function: A Structural Equation
Modeling Approach
Lauren Kupis,a Zachary T. Goodman,b Salome Kornfeld,b Celia Romero,b Bryce Dirks,b Leigha Kircher,b
Catie Chang,c,d,e Maria M. Llabre,b Jason S. Nomi,a Lucina Q. Uddina*
a Department of Psychiatry, University of California Los Angeles, Los Angeles, CA, USA
b Department of Psychology, University of Miami, Coral Gables, FL, USA
c Department of Electrical Engineering and Computer Science, Vanderbilt University, Nashville, TN, USA
d Department of Biomedical Engineering, Vanderbilt University, Nashville, TN, USA
e Vanderbilt University Institute of Imaging Science, Vanderbilt University, Nashville, TN, USA
ABSTRACT
Obesity is associated with negative physical and mental health outcomes. Being overweight/obese is also associated with execu-
tive functioning impairments and structural changes in the brain. However, the impact of body mass index (BMI) on the relationship
between brain dynamics and executive function (EF) is unknown. The goal of the study was to assess the modulatory effects of
BMI on brain dynamics and EF. A large sample of publicly available neuroimaging and neuropsychological assessment data col-
lected from 253 adults (18–45 years; mean BMI 26.95 kg/m2 ± 5.90 SD) from the Nathan Kline Institute (NKI) were included (http://
fcon_1000.projects.nitrc.org/indi/enhanced/). Participants underwent resting-state functional MRI and completed the Delis–Kaplan
Executive Function System (D-KEFS) test battery (1). Time series were extracted from 400 brain nodes and used in a co-activation
pattern (CAP) analysis. Dynamic CAP metrics including dwell time (DT), frequency of occurrence, and transitions were computed.
Multiple measurement models were compared based on model t with indicators from the D-KEFS assigned a priori (shifting,
inhibition, and uency). Multiple structural equation models were computed with interactions between BMI and the dynamic CAP
metrics predicting the three latent factors of shifting, inhibition, and uency while controlling for age, sex, and head motion. Models
were assessed for the main effects of BMI and CAP metrics predicting the latent factors. A three-factor model (shifting, inhibition,
and uency) resulted in the best model t. Signi cant interactions were present between BMI and CAP 2 (lateral frontoparietal
(L-FPN), medial frontoparietal (M-FPN), and limbic nodes) and CAP 5 (dorsal frontoparietal (D-FPN), midcingulo-insular (M-CIN),
somatosensory motor, and visual network nodes) DTs associated with shifting. A higher BMI was associated with a positive relation-
ship between CAP DTs and shifting. Conversely, in average and low BMI participants, a negative relationship was seen between
CAP DTs and shifting. Our ndings indicate that BMI moderates the relationship between brain dynamics of networks important for
cognitive control and shifting, an index of cognitive exibility. Furthermore, higher BMI is linked with altered brain dynamic patterns
associated with shifting.
Keywords: executive function, cognitive control, and decision-making, connectivity
Correspondence: Lauren Kupis, University of California Los Angeles, Los Angeles, CA 90095, Email: lkupis@g.ucla.edu
Received: January 27, 2021
Accepted: August 10, 2021
DOI: 10.52294/8944e106-c54b-40d7-a620-925f7b074f99
R E S E A R C H A R T I C L E
INTRODUCTION
Overweight and obesity are prevalent in one-third of the
global population (2) and 42.4% of adults in the United
States (3). Obesity accounts for over 2.8 million deaths
per year (4), and a body mass index (BMI) ≥30 is addi-
tionally a risk factor for greater complications as a re-
sult of the novel coronavirus (COVID-19) (5). Overweight
(BMI 25 to <30) and obesity are typically considered
physical health conditions associated with comorbid
conditions such as type II diabetes and cardiovascular
disease (6). In addition to these health concerns, obe-
sity is increasingly linked with cognitive impairments
and brain alterations (7–9). Cognitive impairments are
found to worsen with increasing BMI (10,11) throughout
the lifespan (11). Additionally, obesity during midlife is
associated with greater risks of dementia (12) and brain
atrophy in later life (13).
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Accumulating evidence supports cognitive impairment
in the form of executive function (EF) de cits in overweight/
obese individuals (14,15). EFs are higher-order cognitive
processes that enable goal-oriented behaviors (16,17) and
are important for various aspects of daily functioning in-
cluding maintaining a job (18), social functioning (19,20),
and well-being (21). EFs can be divided into distinct but
related components (22) including inhibition, cognitive
exibility, and updating (23,24). A recent meta-analysis
revealed that individuals with obesity primarily show
impairments on EF tasks that require inhibition, cognitive
exibility, working memory, decision-making, verbal uen-
cy, and planning (15). Additionally, impairments in EF and
overweight/obesity are associated with negative impacts
on mental health such as anxiety and depression (25–28).
A common neuropsychological test used to assess EF
is the Delis–Kaplan Executive Function System (D-KEFS)
(1). The D-KEFS consists of nine tests of varying EF com-
ponents; however, composite scores within the tests
have been tested as construct-speci c factors rather
than stand-alone tests (29,30). The use of latent vari-
ables as dependent variables reduces the task impurity
problem by tapping into the underlying construct rather
than relying on one impure measure of a task. The la-
tent variable is characterized by statistical extraction of
the variance shared by multiple tasks that are thought
to require thesame executive control ability, resulting in
a purer measure of the ability (31,32). The D-KEFS does
not include direct tests within the latent factor of updat-
ing (i.e., continuously monitoring working memory and
updating content), which is thought to be one of three
EF constructs in well-known latent models of executive
functioning (23). The three constructs instead include
shifting, inhibition, and uency (33). The three latent fac-
tors of D-KEFS are de ned as follows: (1) shifting or the
mental ability to switch or shift in response to changing
stimuli (an index of cognitive exibility) (34); (2) inhibition
or the ability to control one’s behavior and thoughts to
inhibit responses (16); and (3) uency, thought to under-
lie executive control and updating (35), uency in gen-
erating new designs (i.e., creativity) (36), and an index of
verbal abilities.
Recent studies examining brain functional connectivity
in overweight/obesity have identi ed alterations in brain
networks rather than speci c brain regions that may
impact EF. Studies have reported network alterations
among the midcingulo-insular/salience network (M-CIN),
medial frontoparietal/default network (M-FPN), and lat-
eral frontoparietal/central executive network (L-FPN) in
overweight/obese individuals (37–45). The M-CIN plays
a role in detecting salient information and coordinating
transitions between the L-FPN and M-FPN; the L-FPN is
involved in executive or control processes; the M-FPN
is involved in self-referential thoughts and monitoring of
the environment (46). The dynamic relationships among
these three core neurocognitive networks are additional-
ly thought to enable exible cognition (46,47), important
for EFs. Alterations among the M-CIN, L-FPN, and M-FPN
in overweight/obesity provide further support for altered
reward processing and EF, and cognitive and emotional
processing of salient food cues (48). Alterations among
these networks have also been previously associated
with various neuropsychiatric disorders (49), suggesting
these networks are important treatment targets for pop-
ulations such as obese individuals.
Evidence of brain alterations among the three large-
scale neurocognitive networks provides important in-
sights into potential neural mechanisms underlying
behavior; however, whole-brain functional connectivity
studies have revealed alterations among other regions
in overweight/obese individuals. Functional connectivity
alterations have been observed between the aforemen-
tioned three large-scale networks and visual (39,45,50),
limbic (44), sensorimotor (39,51), and dorsal frontoparietal
networks (D-FPN; dorsal attention) (39). These ndings
suggest that it is important to examine whole-brain net-
work relationships in overweight/obesity. Further, brain
regions important for monitoring external and internal
processes are altered in overweight/obesity (39–45) and
suggest that BMI may alter the way network exibility
is associated with exible behavior such that reduced
network exibility may be linked with poorer EF and
adaptive behavior.
There are very few studies to date that have examined
the relationship among EF, BMI, and the brain (52–54),
and no study to date has examined the relationship
among BMI, brain network dynamics, and EF. Brain net-
work dynamics have previously been shown to predict
EF performance irrespective of BMI (55). Recent work has
also shown that brain network dynamics of the L-FPN,
thought to underlie EFs, were correlated with BMI (56).
Additionally, increased BMI (overweight/obesity) is as-
sociated with reduced cerebral blood ow (57). Neural
activity in the brain is dependent on cerebral blood ow
(58–60), and cerebral blood ow is correlated with func-
tional connectivity strength (61). Further, brain dynamics
represent time-varying brain states (62) that may also be
modulated by cerebral blood ow (63). Combined with
the previously noted in uence of BMI on cerebral blood
ow, it is plausible to infer that the relationship between
brain dynamics and EF may be moderated by an individ-
ual’s BMI; however, this has not been previously tested.
Although there is evidence that dynamic brain function
is associated with EF performance (55,64,65), brain dy-
namic patterns are not consistently associated with each
EF (e.g., shifting but not inhibition or uency/updating)
(55,64), leading to the question of whether another vari-
able (e.g., moderator) could be accounting for the differ-
ences. Further, altered functional connectivity among re-
gions important for EF is accompanied by impaired EF in
individuals with a higher BMI, but not in individuals within
a healthy BMI (37). This suggests that the relationship be-
tween brain function and EF may vary depending on an
individual’s BMI (e.g., optimal brain function is related to
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inhibition, using structural equation modeling (SEM).
Examination of the dynamic interactions among the
M-CIN, L-FPN, and M-FPN has provided important in-
formation about the network interactions subserving
cognition; however, large-scale network interactions
with other brain regions, such as the visual network,
also lend insight into exible cognition (85). Therefore,
whole-brain network co-activations were assessed in
this study. We hypothesized that a higher BMI would be
associated with an altered relationship between brain
network dynamics among the M-CIN, M-FPN, and L-FPN
and shifting, an index of cognitive exibility (34).
METHODS
Participants
This study included a sample of 253 adults (18–45 years)
from the publicly available Nathan Kline Institute—
Rockland Sample (http://fcon_1000.projects.nitrc.org/
indi/enhanced/). Inclusionary criteria were as follows: (1)
available neuroimaging and behavioral data, (2) no cur-
rent Diagnostic and Statistical Manual of Mental Disorders
(DSM) diagnosis, and (3) mean framewise displacement
(FD) < 0.5 mm (Table 1). Institutional Review Board ap-
proval was obtained for this project, and written informed
consent was obtained for all study participants.
MEASURES
Body Mass Index
BMI was calculated from weight in kilograms divided
by height in meters squared (kg/m2) for all participants.
Weight and height were measured during the study visit
optimal EF in healthy-weight individuals, but poorer brain
function is related to poorer EF in overweight/obese indi-
viduals). Together, this implies that BMI may be tested as
a moderator of the relationship between brain dynamics
and EF as previously done in other elds (66,67) to better
understand how the relationship between two variables is
affected by varying levels of BMI (68).
In this study, BMI was tested as a moderator primar-
ily due to the following reasons: (1) previous evidence
of brain dynamics supporting EF (55,64); (2) the un-
clear directionality among BMI, EF, and brain dynamics
(69,70); (3) previous work examining brain structure and
functional connectivity rather than brain dynamics; (4) ac-
cess to cross-sectional data; (5) previous work using BMI
as a moderator; and (6) the use of a population (young
to middle-aged adults) where brain function is optimal
(71–74) and less is known in this population regarding EF
and brain function related to BMI (75,76). By adopting
a moderator framework, the relationship between brain
function and EF can be examined at different levels of
BMI. Such insight may bene t researchers and clinicians
when assessing young- to middle-aged adults at varying
BMI levels and overweight/obese adults who may be at
greater risk of altered time-varying brain function paired
with poorer cognition.
Functional connectivity and structural neuroimaging
methods have provided insight into brain organization
differences in overweight/obese individuals; however,
recent developments in neuroimaging posit dynamic
methods, such as sliding window correlations (77,78) and
co-activation patterns (CAPs) (77,79), may be applied to
capture time-varying changes in the brain architecture
(see (62)). Further, dynamic or time-varying methods may,
in some cases, better capture relationships between
brain function and cognition and behavior than static
functional connectivity methods (80,81). Dynamic meth-
ods have also been shown to reveal relationships with
BMI and behavior where static methods were unable to
(56). CAPs, in particular, identify critical co-activating pat-
terns that recur across time by averaging time points with
similar spatial distributions of brain activity at either the
whole-brain or region-of-interest level (82). Further, CAPs
require the speci cation of fewer assumptions than slid-
ing window methods as they do not rely on arbitrary de -
nitions of window size. CAPs have also been utilized to
study neuropsychiatric disorders such as autism (64,83,84)
and dynamic network changes across the lifespan (Kupis
et al. 2021). Despite the advantages to using dynamic
MRI methods over static MRI methods, no study to date
has examined dynamic brain network alterations during
rest across BMI or its association with EF. Further, explor-
ing relationships among brain networks using brain dy-
namics has shown to be bene cial for the study of EF due
to the various networks underlying EF (55).
This study aims to explore BMI as a moderator of the
relationship between whole-brain CAP dynamics and
EF, indexed by latent factors of shifting, uency, and
Table 1. Participant Demographics
N = 253
mean ± SD (minimum − maximum)
BMI (kg/m2) 26.95 ± 5.90 (16.26 − 49.96)
Age (years) 28.44 ± 7.55 (18.15 − 44.82)
Mean FD (mm) 0.23 ± 0.09 (0.08 − 0.49)
Sex 105 M/ 148 F
DF Switching 8.59 ± 2.94 (1.00 − 16.00)
TMT 9.97 ± 2.83 (1.00 − 15.00)
VF Switching 10.47 ± 3.56 (1.00 − 19.00)
CWIT Inhibition 10.26 ± 2.89 (1.00 − 16.00)
CWIT Inhibition/Switching 9.89 ± 3.04 (1.00 − 14.00)
Tower Total Achievement 9.99 ± 2.36 (2.00 − 19.00)
VF Letter Fluency 10.61 ± 3.44 (1.00 − 19.00)
VF Category Fluency 11.28 ± 3.64 (2.00 − 19.00)
DF Composite Score 10.42 ± 2.69 (4.00 − 18.00)
Note: BMI, body mass index; FD, framewise displacement; DF, Design Fluency;
TMT, Trail Making Test; VF, Verbal Fluency; CWIT, Color-Word Interference Test.
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MRI Protocol
Three-dimensional magnetization-prepared rapid gra-
dient-echo imaging (3D-MP-RAGE) structural scans
and multiband (factor of 4) EPI-sequenced resting-state
fMRI (rsfMRI) were acquired using a Siemens TrioTM 3.0
T MRI scanner. Scanning parameters were as follows:
TR = 1400 ms, 2 × 2 × 2 mm, 64 interleaved slices, TE =
30 ms, ip angle = 65 degrees, eld of view (FOV) = 224
mm, 404 volumes. Participants were instructed to keep
their eyes open and xate on a cross in the center of the
screen during the 9.4-minute rsfMRI scan. For detailed
MRI protocol information, see http://fcon_1000.projects
.nitrc.org/indi/pro/nki.html.
Preprocessing and Postprocessing
Preprocessing steps were conducted using the Data
Preprocessing Assistant for Resting-State fMRI Advanced
edition (DPARSF-A; (88)), which uses FMRIB Software
Library (FSL) and Statistical Parametric Mapping (SPM)-
12 (https://www. l.ion.ucl.ac.uk/spm/software/spm12/),
and were as follows: removal of the rst ve volumes to
allow scanner signal to reach equilibrium, despiking, re-
alignment, normalization directly to the 3 mm Montreal
Neurological Institute (MNI) template, and smoothing
(6 mm Full Width at Half Maximum (FWHM)).
Independent component analysis (ICA) was conduct-
ed using FSL’s MELODIC by means of automatic dimen-
sionality estimation. The ICA-FIX classi cation algorithm
was applied to the data (FMIRB’s ICA-FIX; (89)) using a
subset of the participants to train FIX. ICA-FIX then clas-
si ed ICA into noise and non-noise components for the
rsfMRI data for individual subjects. The fMRI data also un-
derwent nuisance covariance regression (linear detrend,
Friston 24 motion parameters, global mean signal), de-
spiking using AFNI’s 3dDespike algorithm, and bandpass
ltering (0.01–0.10 Hz). Information about the data pro-
cessed without global mean signal regression is included
in Supplementary Materials.
Parcellation
A 400 node parcellation was used containing nodes with-
in 17 networks ((90); https://github.com/ThomasYeoLab/
CBIG/tree/master/stable_projects/brain_parcellation/
Schaefer2018_LocalGlobal). The parcellation incorpo-
rates local gradient and global similarity approaches
from task-based and resting-state functional connectivity.
Co-activation Pattern Analysis
The time series were extracted from the 400 nodes for
each subject and were converted to z-statistics and con-
catenated into one (nodes × timepoints) matrix (where
the number of timepoints is 399 TR × 253 subjects).
by study staff. Participants ranged in their BMI from un-
derweight (<18.5 BMI), healthy weight (18.5 to <20 BMI),
overweight (25 to <30 BMI), and obese (30 or higher
BMI). For the purpose of this study, overweight/obesi-
ty are discussed interchangeably. See Figure S1 for a
graphical distribution of BMI in this sample.
Shifting
The D-KEFS was administered to all participants (1).
The tasks with shifting (an index of cognitive exibility)
conditions within the D-KEFS include the Trail Making
Test (TMT), the Design Fluency (DF) Test, and the Verbal
Fluency (VF) Task. The TMT consists of ve conditions,
including the Number-Letter Switching condition (86).
During the Number-Letter Switching condition, subjects
switch back and forth between connecting numbers and
letters (i.e., 1, A, 2, B, etc.) (87). The DF test consists of
three conditions including a Switching condition. In the
Switching condition, participants are asked to alternate
between connecting empty and lled dots. Lastly, the VF
test consists of three conditions, including the Category
Switching condition. During the Category Switching con-
dition, participants alternate between saying words from
two different semantic categories.
Inhibition
The D-KEFS tasks with inhibition conditions included the
Color-Word Interference Test (CWIT) and the Tower Test.
The CWIT is a modi ed Stroop task and consists of four
conditions including an inhibition and inhibition/switch-
ing condition. In the CWIT Inhibition condition, the par-
ticipant is presented with color names that are written in
incongruent ink color. The participant is required to name
the ink color and ignore the written word. Therefore, par-
ticipants have to inhibit saying the more automatic written
word response. In the Inhibition/Switching condition, par-
ticipants are presented with a page containing the words
“red,” “green,” and “blue,” written in red, green, or blue
ink. Some of the words are contained in a box, and the
subject must switch between saying the color of the ink
(word is not inside a box) or the color of the word (word in-
side a box). The Tower Test examines the participant’s abil-
ity to plan and carry out steps to attain the desired goal.
Fluency
The D-KEFS tasks with uency conditions included the
VF test and the DF test. The uency measures in the VF
test include the Letter Fluency and Category Fluency
conditions. In both conditions, participants must gen-
erate as many words as possible within 60 seconds, be-
ginning with either a speci c letter or within a speci c
category. The DF test included trials where participants
had to connect either empty or lled dots.
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Switching-total score or time to completion. The shifting
indicator in the DF Switching condition was the Switching
Total Correct score or the number of unique designs
drawn. The shifting indicator in the VF test was the total
correct number of category switches made.
The indicators for inhibition included the CWIT
Inhibition and Inhibition/Switching conditions and Tower
total achievement score. The inhibition indicator for the
CWIT Inhibition condition was the total number of cor-
rect responses. The inhibition indicator in the Tower Test
was the Total Achievement score or the sum of points
given in each trial. The CWIT shifting indicator included
the total score for the number of correct switches made.
Although the Inhibition/Switching condition could also
potentially be used as an indicator for the shifting factor,
previous work has found it to be involved in inhibition
using the SEM framework (33).
The uency indicators included the VF letter and cat-
egory uency scores, and the DF total composite score.
The uency indicators in the VF test included the Letter
Fluency Total Correct score and the Category Fluency
Total correct scores. The uency indicator from the DF
test was the total unique designs drawn across the two
DF trials.
The three-factor model including shifting, inhibition,
and uency was evaluated rst for statistical t, and one-
and two-factor models were evaluated thereafter because
of previous theoretical evidence supporting both the unity
and diversity of EFs (23). The one-factor model included
all indicators under one factor or a “common EF.” Three
two-factor models were tested with three combinations of
the latent factors (i.e., shifting with inhibition; shifting with
uency; inhibition with uency). The proposed model is
presented in Figure 1.
Structural Model
The best- tting model from the con rmatory factor
analysis was tested within the framework of SEM. The
latent variable(s) in the model were the dependent vari-
ables in the SEMs. The use of SEMs has been growing
within the eld of cognitive neuroscience (93) and brain
dynamic analyses (94). First, BMI was tested as a moder-
ator between each brain dynamic metric (DT, frequency
of occurrence, and transitions) for each of the ve CAPs
and the latent variable (shifting, inhibition, or uency)
in an exploratory analysis. A moderator is a variable
thought to affect the relationship between two other
variables (68). A moderator was tested because there
is previous evidence that brain dynamics support EF
(55,64); however, the results were not consistent across
all EFs suggesting the relationship between brain dy-
namics and EF may be dependent on a third variable
for speci c EFs. BMI was tested as the moderator due
to previous work suggesting a link between brain dy-
namics and EF, and previous evidence that functional
The matrix was then subjected to k-means clustering to
determine the optimal number of clusters. The elbow
criterion was applied to the cluster validity index (the
ratio between within-cluster to between-cluster dis-
tance) for values of k = 2–20, and an optimal value of
k = 5 was determined (Figure S2).
K-means clustering (squared Euclidean distance) was
then applied to the matrix using the optimal k = 5 to
produce ve CAPs (“brain states”). CAP metrics were cal-
culated and included: (a) dwell time (DT), calculated as
the average number of continuous TRs that a participant
stayed in a given brain state, (b) frequency of occurrence
of brain states, calculated as an overall percentage that
the brain state occurred throughout the duration of rsfM-
RI scan compared to other brain states, and (c) the num-
ber of transitions, calculated as the number of switches
between brain states.
Statistical Analysis
The normative data were age-corrected for all D-KEFS
variables. All data were screened for outliers, missingness
in data, and tests of assumptions (see Supplementary
Materials for more information about the assumptions).
Additionally, each CAP was assessed prior to statistical
modeling to determine if the brain regions co-activated
in each CAP had theoretical support behind including
the CAP in the models. Using a two-step procedure, a
measurement model was evaluated rst to ensure an
acceptable t for the data, and then a structural mod-
erated model was examined. Con rmatory factor anal-
ysis (measurement model) and SEM were conducted
in MPlus (91,92) using maximum likelihood to estimate
model parameters and full information maximum like-
lihood approach to allow data to be included regard-
less of the pattern of missingness in the data. Code for
all MPlus analyses is publicly available (https://github
.com/lkupis/NKI_BMI). Covariates included mean FD,
age, and sex. All models were assessed for the goodness
of t by examining the following: χ2, comparative t index
(CFI), standardized root-mean-square residual (SRMR),
and root-mean-square error of approximation (RMSEA).
χ2 > .05, CFI ≥ .95, SRMR values ≤ .08, and RMSEA
values ≤ .06 indicated good model t.
Con rmatory Factor Analysis
A three-factor model was tested based on prior ndings
of a three-factor model using the D-KEFS (33). The three
factors were shifting, inhibition, and uency. Additionally,
all indicators used were scaled or age-adjusted scores
(M = 10, SD = 3).
The indicators for shifting included the TMT Number-
Letter Switching condition, the DF Switching condition,
and the VF Switching condition scores. The shifting in-
dicator in the TMT condition was the Number-Letter
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connectivity may give rise to poorer EF at certain lev-
els of BMI, primarily in overweight/obese individuals
(37,95). Additionally, the use of a moderator is bene -
cial when the relationships among variables are equiv-
ocal (70), as in BMI, brain dynamics, and EF (11,37). BMI
and the brain dynamic metrics were mean centered to
reduce multicollinearity (96).
The interactions were tested separately to reduce
the effects of multicollinearity and negative impacts on
parameter estimations (97). Accordingly, each latent
factor outcome was tested while retaining all latent
factors in the model due to best model t; however,
they were predicted one at a time with the main ef-
fects and covariates as depicted in Figure 2. Variables
without a signi cant interaction were tested for main
effects using the SEM framework. Signi cant interac-
tions indicate that the effect observed between the in-
dependent variable and dependent variable is depen-
dent on a moderating variable (98,99). As in previous
work (64,100,101), only variables within nonsigni cant
Fig. 1. Con rmatory factor analysis. The proposed three-factor measurement model. VF, Verbal Fluency; TMT; Trail Making Test; DF, Design Fluency; CWIT,
Color-Word Interference Test.
Fig. 2. Structural equation model. Structural equation model linking co-activation patterns (CAPs) with executive function (shifting, inhibition, and uency) moderated
by body mass index (BMI).