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1. The directed landscape is a black noise

Author

Himwich, Zoe and Parekh, Shalin

Subjects
Mathematics - Probability
Abstract

We show that the directed landscape is a black noise in the sense of Tsirelson and Vershik. As a corollary, we show that for any microscopic system in which the height profile converges in law to the directed landscape, the driving noise is asymptotically independent of the height profile. This decoupling result provides one answer to the question of what happens to the driving noise in the limit under the KPZ scaling, and illustrates a type of noise sensitivity for systems in the KPZ universality class. Such decoupling and sensitivity phenomena are not present in the intermediate-disorder or weak-asymmetry regime, thus illustrating a contrast from the weak KPZ scaling regime. Along the way, we prove a strong mixing property for the directed landscape on a bounded time interval under spatial shifts, with a mixing rate $\alpha(N)\leq Ce^{-dN^3}$ for some $C,d>0$., Comment: 34 pages, 1 figure

Published
2024

2. Health-Related Quality of Life After Neonatal Treatment of Symptomatic Tetralogy of Fallot: Insights from the Congenital Cardiac Research Collaborative

Author

Nicholson, George T., Zampi, Jeffrey D., Glatz, Andrew C., Goldstein, Bryan H., Petit, Christopher J., Zhang, Yun, McCracken, Courtney E., Qureshi, Athar M., Goldberg, Caren S., Romano, Jennifer C., Law, Mark A., Meadows, Jeffery J., Shahanavaz, Shabana, Batlivala, Sarosh P., Maskatia, Shiraz A., Beshish, Asaad, O’Byrne, Michael L., Ligon, R. Allen, Stack, Kathryn O., Khan, Hala Q., Parekh, Shalin, and Ilardi, Dawn L.

Published
2024
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3. A hierarchy of KPZ equation scaling limits arising from directed random walk models in random media

Author

Parekh, Shalin

Subjects
Mathematics - Probability, Mathematical Physics
Abstract

We consider a generalized model of random walk in dynamical random environment, and we show that the multiplicative-noise stochastic heat equation (SHE) describes the fluctuations of the quenched density at a certain precise location in the tail. The distribution of transition kernels is fixed rather than changing under the diffusive rescaling of space-time, i.e., there is no critical tuning of the model parameters when scaling to the stochastic PDE limit. The proof is done by pushing the methods developed in [arxiv 2304.14279, arXiv 2311.09151] to their maximum, substantially weakening the assumptions and obtaining fairly sharp conditions under which one expects to see the SHE arise in a wide variety of random walk models in random media. In particular we are able to get rid of conditions such as nearest-neighbor interaction as well as spatial independence of quenched transition kernels. Moreover, we observe an entire hierarchy of moderate deviation exponents at which the SHE can be found, confirming a physics prediction of J. Hass., Comment: Changes in v2: changed title, added a picture of the model for clarity, fixed a crucial mistake in Section 2, found shorter arguments for some proofs, slightly weakened assumptions, fixed typos, added references (73 pages, 1 picture)

Published
2024

4. Correction: Health-Related Quality of Life After Neonatal Treatment of Symptomatic Tetralogy of Fallot: Insights from the Congenital Cardiac Research Collaborative

Author

Nicholson, George T., Zampi, Jeffrey D., Glatz, Andrew C., Goldstein, Bryan H., Petit, Christopher J., Zhang, Yun, McCracken, Courtney E., Qureshi, Athar M., Goldberg, Caren S., Romano, Jennifer C., Law, Mark A., Meadows, Jeffery J., Shahanavaz, Shabana, Batlivala, Sarosh P., Maskatia, Shiraz A., Beshish, Asaad, O’Byrne, Michael L., Ligon, R. Allen, Stack, Kathryn O., Khan, Hala Q., Parekh, Shalin, and Ilardi, Dawn L.

Published
2024
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6. KPZ equation limit of random walks in random environments

Author

Das, Sayan, Drillick, Hindy, and Parekh, Shalin

Subjects
Mathematics - Probability, Mathematical Physics
Abstract

We show that under a certain moderate deviation scaling, the multiplicative-noise stochastic heat equation (SHE) arises as the fluctuations of the quenched density of a 1D random walk whose transition probabilities are iid [0,1]-valued random variables. In contrast to the case of directed polymers in the intermediate disorder regime, the variance of our weights is fixed rather than vanishing under the diffusive rescaling of space-time. Consequently, taking a naive limit of the chaos expansion fails for this model, and a nontrivial noise coefficient is observed in the limit. Rather than using chaos techniques, our proof instead uses the fact that in this regime the quenched density solves a discrete SPDE which resembles the SHE. As a byproduct of our techniques, it is shown that independent noise is generated in the limit., Comment: 62 pages, 1 figure

Published
2023

7. A nonlinear Strassen law for singular SPDEs

Author

Parekh, Shalin

Subjects
Mathematics - Probability, Mathematics - Functional Analysis
Abstract

A result of Arcones implies that if a measure-preserving linear operator $S$ on an abstract Wiener space $(X,H,\mu)$ is strongly mixing, then the set of limit points of the random sequence $((2\log n)^{-1/2}S^n(x))_{n\in\mathbb N}$ equals the unit ball of $H$ for a.e. $x \in X$, which may be seen as a generalization of the classical Strassen's law of the iterated logarithm. We extend this result to the case of a continuous parameter $n$ and higher Gaussian chaoses, and we also prove a contraction-type principle for Strassen laws of such chaoses. We then use these extensions to recover or prove Strassen-type laws for a broad collection of processes derived from a Gaussian measure, including "nonlinear" Strassen laws for singular SPDEs such as the KPZ equation., Comment: 3rd version: fixed various small typos appearing in the published version

Published
2023
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8. KPZ equation limit of sticky Brownian motion

Author

Das, Sayan, Drillick, Hindy, and Parekh, Shalin

Subjects
Mathematics - Probability, Mathematical Physics, 60K37, 82B21, 82C22 (Primary), 60G70 (Secondary)
Abstract

We consider the motion of a particle under a continuum random environment whose distribution is given by the Howitt-Warren flow. In the moderate deviation regime, we establish that the quenched density of the motion of the particle (after appropriate centering and scaling) converges weakly to the $(1+1)$ dimensional stochastic heat equation driven by multiplicative space-time white noise. Our result confirms physics predictions and computations in [LDT17, BLD20, HCGCC23] and is the first rigorous instance of such weak convergence in the moderate deviation regime. Our proof relies on a certain Girsanov transform and works for all Howitt-Warren flows with finite and nonzero characteristic measures. Our results capture universality in the sense that the limiting distribution depends on the flow only via the total mass of the characteristic measure. As a corollary of our results, we prove that the fluctuations of the maximum of an $N$-point sticky Brownian motion are given by the KPZ equation plus an independent Gumbel on timescales of order $(\log N)^2.$, Comment: 64 pages, 2 figures. Improved introduction, added references, and corrected typos

Published
2023

9. Ergodicity results for the open KPZ equation

Author

Parekh, Shalin

Subjects
Mathematics - Probability
Abstract

We give a new proof of existence as well as two proofs of uniqueness of the invariant measure of the open-boundary KPZ equation on [0,1], for all possible choices of inhomogeneous Neumann boundary data. Both proofs yield an exponential convergence result in total variation when combined with the strong Feller property which was recently established in [Knizel-Matetski, arXiv:2211.04466]. An important ingredient in both proofs is the construction of a compact state space for the Markov operator to act on, which measurably contains all of the usual H\"older spaces modulo constants. Along the way, the strong Feller property is extended to this larger class of initial conditions. The arguments do not rely on exact descriptions of the invariant measures, and some of the results generalize to the case of a spatially colored noise and other boundary conditions., Comment: Changes in the 3rd version: added references, clarified details, corrected typos

Published
2022

10. Neurite orientation dispersion and density imaging of white matter microstructure in sensory processing dysfunction with versus without comorbid ADHD.

Author

Mark, Ian, Wren-Jarvis, Jamie, Xiao, Jaclyn, Cai, Lanya, Parekh, Shalin, Bourla, Ioanna, Lazerwitz, Maia, Rowe, Mikaela, Marco, Elysa, and Mukherjee, Pratik

Subjects
attention deficit and hyperactivity disorder, diffusion MRI, neurite orientation dispersion and density imaging, sensory processing dysfunction, white matter microstructure
Abstract

INTRODUCTION: Sensory Processing Dysfunction (SPD) is common yet understudied, affecting up to one in six children with 40% experiencing co-occurring challenges with attention. The neural architecture of SPD with Attention Deficit and Hyperactivity Disorder (ADHD) (SPD+ADHD) versus SPD without ADHD (SPD-ADHD) has yet to be explored in diffusion tensor imaging (DTI) and Neurite Orientation Dispersion and Density Imaging (NODDI) has yet to be examined. METHODS: The present study computed DTI and NODDI biophysical model parameter maps of one hundred children with SPD. Global, regional and voxel-level white matter tract measures were analyzed and compared between SPD+ADHD and SPD-ADHD groups. RESULTS: SPD+ADHD children had global WM Fractional Anisotropy (FA) and Neurite Density Index (NDI) that trended lower than SPD-ADHD children, primarily in boys only. Data-driven voxelwise and WM tract-based analysis revealed statistically significant decreases of NDI in boys with SPD+ADHD compared to those with SPD-ADHD, primarily in projection tracts of the internal capsule and commissural fibers of the splenium of the corpus callosum. CONCLUSION: We conclude that WM microstructure is more delayed/disrupted in boys with SPD+ADHD compared to SPD-ADHD, with NODDI showing a larger effect than DTI. This may represent the combined WM pathology of SPD and ADHD, or it may result from a greater degree of SPD WM pathology causing the development of ADHD.

Published
2023

11. Hemispheric lateralization of white matter microstructure in children and its potential role in sensory processing dysfunction

Author

Parekh, Shalin A, Wren-Jarvis, Jamie, Lazerwitz, Maia, Rowe, Mikaela A, Powers, Rachel, Bourla, Ioanna, Cai, Lanya T, Chu, Robyn, Trimarchi, Kaitlyn, Garcia, Rafael, Marco, Elysa J, and Mukherjee, Pratik

Subjects
Paediatrics, Biomedical and Clinical Sciences, Clinical Research, Pediatric, Bioengineering, Biomedical Imaging, Brain Disorders, Neurosciences, sensory processing disorder, lateralization, sensory over-responsivity, neurite orientation dispersion and density imaging, microstructure, Psychology, Cognitive Sciences, Biological psychology
Abstract

Diffusion tensor imaging (DTI) studies have demonstrated white matter microstructural differences between the left and right hemispheres of the brain. However, the basis of these hemispheric asymmetries is not yet understood in terms of the biophysical properties of white matter microstructure, especially in children. There are reports of altered hemispheric white matter lateralization in ASD; however, this has not been studied in other related neurodevelopmental disorders such as sensory processing disorder (SPD). Firstly, we postulate that biophysical compartment modeling of diffusion MRI (dMRI), such as Neurite Orientation Dispersion and Density Imaging (NODDI), can elucidate the hemispheric microstructural asymmetries observed from DTI in children with neurodevelopmental concerns. Secondly, we hypothesize that sensory over-responsivity (SOR), a common type of SPD, will show altered hemispheric lateralization relative to children without SOR. Eighty-seven children (29 females, 58 males), ages 8-12 years, presenting at a community-based neurodevelopmental clinic were enrolled, 48 with SOR and 39 without. Participants were evaluated using the Sensory Processing 3 Dimensions (SP3D). Whole brain 3 T multi-shell multiband dMRI (b = 0, 1,000, 2,500 s/mm2) was performed. Tract Based Spatial Statistics were used to extract DTI and NODDI metrics from 20 bilateral tracts of the Johns Hopkins University White-Matter Tractography Atlas and the lateralization Index (LI) was calculated for each left-right tract pair. With DTI metrics, 12 of 20 tracts were left lateralized for fractional anisotropy and 17/20 tracts were right lateralized for axial diffusivity. These hemispheric asymmetries could be explained by NODDI metrics, including neurite density index (18/20 tracts left lateralized), orientation dispersion index (15/20 tracts left lateralized) and free water fraction (16/20 tracts lateralized). Children with SOR served as a test case of the utility of studying LI in neurodevelopmental disorders. Our data demonstrated increased lateralization in several tracts for both DTI and NODDI metrics in children with SOR, which were distinct for males versus females, when compared to children without SOR. Biophysical properties from NODDI can explain the hemispheric lateralization of white matter microstructure in children. As a patient-specific ratio, the lateralization index can eliminate scanner-related and inter-individual sources of variability and thus potentially serve as a clinically useful imaging biomarker for neurodevelopmental disorders.

Published
2023

12. Brief Report: Characterization of Sensory Over-Responsivity in a Broad Neurodevelopmental Concern Cohort Using the Sensory Processing Three Dimensions (SP3D) Assessment

Author

Lazerwitz, Maia C, Rowe, Mikaela A, Trimarchi, Kaitlyn J, Garcia, Rafael D, Chu, Robyn, Steele, Mary C, Parekh, Shalin, Wren-Jarvis, Jamie, Bourla, Ioanna, Mark, Ian, Marco, Elysa J, and Mukherjee, Pratik

Subjects
Clinical Research, Pediatric, Autism, Mental Health, Brain Disorders, Neurosciences, Intellectual and Developmental Disabilities (IDD), 2.1 Biological and endogenous factors, Aetiology, ASD, Sensory Processing, Sensory Over-Responsivity, SP3D, Education, Psychology and Cognitive Sciences, Developmental & Child Psychology
Abstract

Sensory Over-Responsivity (SOR) is an increasingly recognized challenge among children with neurodevelopmental concerns (NDC). To investigate, we characterized the incidence of auditory and tactile over-responsivity (AOR, TOR) among 82 children with NDC. We found that 70% of caregivers reported concern for their child's sensory reactions. Direct assessment further revealed that 54% of the NDC population expressed AOR, TOR, or both - which persisted regardless of autism spectrum disorder (ASD) diagnosis. These findings support the high prevalence of SOR as well as its lack of specificity to ASD. Additionally, AOR is revealed to be over twice as prevalent as TOR. These conclusions present several avenues for further exploration, including deeper analysis of the neural mechanisms and genetic contributors to sensory processing challenges.

Published
2022

14. The Effect of Size and Asymmetry at Birth on Brain Injury and Neurodevelopmental Outcomes in Congenital Heart Disease

Author

Parekh, Shalin A, Cox, Stephany M, Barkovich, A James, Chau, Vann, Steurer, Martina A, Xu, Duan, Miller, Steven P, McQuillen, Patrick S, and Peyvandi, Shabnam

Subjects
Paediatrics, Biomedical and Clinical Sciences, Cardiovascular Medicine and Haematology, Cardiovascular, Neurosciences, Infant Mortality, Preterm, Low Birth Weight and Health of the Newborn, Pediatric, Heart Disease, Perinatal Period - Conditions Originating in Perinatal Period, Reproductive health and childbirth, Brain, Brain Injuries, Child, Female, Heart Defects, Congenital, Humans, Infant, Newborn, Magnetic Resonance Imaging, Placenta, Pregnancy, Transposition of Great Vessels, Birth asymmetry, Birth anthropometry, Brain injury, Neurodevelopment, Congenital heart disease, Cardiorespiratory Medicine and Haematology, Cardiovascular System & Hematology, Cardiovascular medicine and haematology
Abstract

Poor and asymmetric fetal growth have been associated with neonatal brain injury (BI) and worse neurodevelopmental outcomes (NDO) in the growth-restricted population due to placental insufficiency. We tested the hypothesis that postnatal markers of fetal growth (birthweight (BW), head circumference (HC), and head to body symmetry) are associated with preoperative white matter injury (WMI) and NDO in infants with single ventricle physiology (SVP) and d-transposition of great arteries (TGA). 173 term newborns (106 TGA; 67 SVP) at two sites had pre-operative brain MRI to assess for WMI and measures of microstructural brain development. NDO was assessed at 30 months with the Bayley Scale of Infant Development-II (n = 69). We tested the association between growth parameters at birth with the primary outcome of WMI on the pre-operative brain MRI. Secondary outcomes included measures of NDO. Newborns with TGA were more likely to have growth asymmetry with smaller heads relative to weight while SVP newborns were symmetrically small. There was no association between BW, HC or asymmetry and WMI on preoperative brain MRI or with measures of microstructural brain development. Similarly, growth parameters at birth were not associated with NDO at 30 months. In a multivariable model only cardiac lesion and site were associated with NDO. Unlike other high-risk infant populations, postnatal markers of fetal growth including head to body asymmetry that is common in TGA is not associated with brain injury or NDO. Lesion type appears to play a more important role in NDO in CHD.

Published
2022

15. Convergence of ASEP to KPZ with basic coupling of the dynamics

Author

Parekh, Shalin

Subjects
Mathematics - Probability
Abstract

We prove an extension of a seminal result of Bertini and Giacomin. Namely we consider weakly asymmetric exclusion processes with several distinct initial data simultaneously, then run according to the basic coupling, and we show joint convergence to the solution of the KPZ equation with the same driving noise in the limiting equation. Along the way, we analyze fine properties of nontrivially coupled solutions-in-law of KPZ-type equations., Comment: 22 pages

Published
2021

16. Limit Shape of Subpartition Maximizing Partitions

Author

Corwin, Ivan and Parekh, Shalin

Subjects
Mathematics - Probability, Mathematics - Combinatorics
Abstract

This is an expository note answering a question posed to us by Richard Stanley, in which we prove a limit shape theorem for partitions of $n$ which maximize the number of subpartitions. The limit shape and the growth rate of the number of subpartitions are explicit. The key ideas are to use large deviations estimates for random walks, together with convex analysis and the Hardy-Ramanujan asymptotics. Our limit shape coincides with Vershik's limit shape for uniform random partitions., Comment: 15 pages

Published
2019
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17. Positive random walks and an identity for half-space SPDEs

Author

Parekh, Shalin

Subjects
Mathematics - Probability
Abstract

The purpose of this article is threefold. First, we introduce a new type of boundary condition for the multiplicative-noise stochastic heat equation on the half space. This is essentially a Dirichlet boundary condition but with a nontrivial normalization near the boundary which leads to inhomogeneous transition densities (roughly, those of a Brownian \textit{meander}) within the associated chaos series. Secondly, we prove a new convergence result of the directed-polymer partition function in an octant to the multiplicative stochastic heat equation with this type of boundary condition, which in turn involves a detailed analysis of the aforementioned inhomogeneous Markov process. Thirdly, as a corollary, we prove a surprising equality-in-distribution for multiplicative-noise stochastic heat equations on the half space with \textit{different} boundary conditions. This identity may be seen as a precursor for proving Gaussian fluctuation behavior of supercritical half-space KPZ at the origin., Comment: 50 pages, 1 figure

Published
2019

19. The KPZ Limit of ASEP with Boundary

Author

Parekh, Shalin

Subjects
Mathematics - Probability, Condensed Matter - Statistical Mechanics, Mathematical Physics
Abstract

It was recently proved in [Corwin-Shen, 2016] that under weak asymmetry scaling, the height functions for open ASEP on the half-line and on a bounded interval converge to the Hopf-Cole solution of the KPZ equation with Neumann boundary conditions. In their assumptions [Corwin-Shen, 2016] chose positive values for the Neumann boundary conditions, and they assumed initial data which is close to stationarity. By developing more extensive heat-kernel estimates, we extend their results to negative values of the Neumann boundary parameters, and we also show how to generalize their results to narrow-wedge initial data (which is very far from stationarity). As a corollary via [Barraquand-Borodin-Corwin-Wheeler, 2017], we obtain the Laplace transform of the one-point distribution for half-line KPZ, and use this to prove $t^{1/3}$-scale GOE Tracy-Widom long-time fluctuations., Comment: 70 pages, 1 figure

Published
2017
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20. Abstract 13113: Health-Related Quality of Life After Neonatal Treatment of Symptomatic Tetralogy of Fallot: Insights From the Congenital Cardiac Research Collaborative

Author

Zampi, Jeffrey D, Nicholson, George T, Goldstein, Bryan H, Glatz, Andrew C, Petit, Christopher J, McCracken, Courtney E, Qureshi, Athar M, Goldberg, Caren S, Romano, Jennifer C, Law, Mark A, Meadows, Jeffery J, Shahanavaz, Shabana, Batlivala, Sarosh P, Maskatia, Shiraz A, Pettus, Joelle A, Beshish, Asaad, Stack, Kathryn O, Khan, Hala Q, Parekh, Shalin, and Ilardi, Dawn L

Published
2022
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21. Abstract 11531: Neurodevelopmental Outcomes After Neonatal Tetralogy of Fallot Repair or Palliation: Scope of The Problem and Does Treatment Strategy Matter

Author

Zampi, Jeffrey D, Ilardi, Dawn L, McCracken, Courtney E, Glatz, Andrew C, Beshish, Asaad, Goldstein, Bryan H, Petit, Christopher J, Qureshi, Athar M, Goldberg, Caren S, Law, Mark A, Meadows, Jeffery J, Shahanavaz, Shabana, Batlivala, Sarosh P, Maskatia, Shiraz A, Pettus, Joelle A, Romano, Jennifer C, Stack, Kathryn O, Khan, Hala Q, Parekh, Shalin, and Nicholson, George T

Published
2022
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25. Towards a Tropical Proof of the Gieseker-Petri Theorem

Author

Baratham, Vyassa, Jensen, David, Mata, Cristina, Nguyen, Dat, and Parekh, Shalin

Subjects
Mathematics - Algebraic Geometry, 14T05, 14H51
Abstract

We use tropical techniques to prove a case of the Gieseker-Petri Theorem. Specifically, we show that the general curve of arbitrary genus does not admit a Gieseker-Petri special pencil.

Published
2012

28. Hemispheric lateralization of white matter microstructure in children and its potential role in sensory processing dysfunction

Author

Parekh, Shalin A., primary, Wren-Jarvis, Jamie, additional, Lazerwitz, Maia, additional, Rowe, Mikaela A., additional, Powers, Rachel, additional, Bourla, Ioanna, additional, Cai, Lanya T., additional, Chu, Robyn, additional, Trimarchi, Kaitlyn, additional, Garcia, Rafael, additional, Marco, Elysa J., additional, and Mukherjee, Pratik, additional

Published
2023
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29. Brief Report: Characterization of Sensory Over-Responsivity in a Broad Neurodevelopmental Concern Cohort Using the Sensory Processing Three Dimensions (SP3D) Assessment

Author

Lazerwitz, Maia C., primary, Rowe, Mikaela A., additional, Trimarchi, Kaitlyn J., additional, Garcia, Rafael D., additional, Chu, Robyn, additional, Steele, Mary C., additional, Parekh, Shalin, additional, Wren-Jarvis, Jamie, additional, Bourla, Ioanna, additional, Mark, Ian, additional, Marco, Elysa J., additional, and Mukherjee, Pratik, additional

Published
2022
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30. Neurite orientation dispersion and density imaging of white matter microstructure in sensory processing dysfunction with versus without comorbid ADHD.

Author

Mark, Ian T., Wren-Jarvis, Jamie, Xiao, Jaclyn, Cai, Lanya T., Parekh, Shalin, Bourla, Ioanna, Lazerwitz, Maia C., Rowe, Mikaela A., Marco, Elysa J., and Mukherjee, Pratik

Subjects
WHITE matter (Nerve tissue), SENSORIMOTOR integration, ATTENTION-deficit hyperactivity disorder, DIFFUSION tensor imaging, CORPUS callosum
Abstract

Introduction: Sensory Processing Dysfunction (SPD) is common yet understudied, affecting up to one in six children with 40% experiencing co-occurring challenges with attention. The neural architecture of SPD with Attention Deficit and Hyperactivity Disorder (ADHD) (SPD+ADHD) versus SPD without ADHD (SPD-ADHD) has yet to be explored in diffusion tensor imaging (DTI) and Neurite Orientation Dispersion and Density Imaging (NODDI) has yet to be examined. Methods: The present study computed DTI and NODDI biophysical model parameter maps of one hundred children with SPD. Global, regional and voxel-level white matter tract measures were analyzed and compared between SPD+ADHD and SPD-ADHD groups. Results: SPD+ADHD children had global WM Fractional Anisotropy (FA) and Neurite Density Index (NDI) that trended lower than SPD-ADHD children, primarily in boys only. Data-driven voxelwise and WM tract-based analysis revealed statistically significant decreases of NDI in boys with SPD+ADHD compared to those with SPD-ADHD, primarily in projection tracts of the internal capsule and commissural fibers of the splenium of the corpus callosum. Conclusion: We conclude that WM microstructure is more delayed/disrupted in boys with SPD+ADHD compared to SPD-ADHD, with NODDI showing a larger effect than DTI. This may represent the combined WM pathology of SPD and ADHD, or it may result from a greater degree of SPD WM pathology causing the development of ADHD. [ABSTRACT FROM AUTHOR]

Published
2023
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31. Positive random walks and an identity for half-space SPDEs

Author

Parekh, Shalin

Subjects
Statistics and Probability, Probability (math.PR), FOS: Mathematics, Statistics, Probability and Uncertainty, Mathematics - Probability
Abstract

The purpose of this article is threefold. First, we introduce a new type of boundary condition for the multiplicative-noise stochastic heat equation on the half space. This is essentially a Dirichlet boundary condition but with a nontrivial normalization near the boundary which leads to inhomogeneous transition densities (roughly, those of a Brownian \textit{meander}) within the associated chaos series. Secondly, we prove a new convergence result of the directed-polymer partition function in an octant to the multiplicative stochastic heat equation with this type of boundary condition, which in turn involves a detailed analysis of the aforementioned inhomogeneous Markov process. Thirdly, as a corollary, we prove a surprising equality-in-distribution for multiplicative-noise stochastic heat equations on the half space with \textit{different} boundary conditions. This identity may be seen as a precursor for proving Gaussian fluctuation behavior of supercritical half-space KPZ at the origin., Comment: 50 pages, 1 figure

Published
2022

40. Abstract 15105: Comparative Analysis of Measured vs. Estimated VO2 in Sedated, Spontaneously Breathing Congenital Cardiac Catheterization Patients

Author

Juergensen, Stephan, Parekh, Shalin, Iams, Amy, and Moore, Phillip

Abstract

Background:Accurate estimation of VO2 is needed for reliable calculation of blood flow and resistance in patients with congenital heart disease. Commonly used estimates of VO2 are based on data from intubated patients (Seckeler), or normal adults (LaFarge equation) but may not be appropriate for sedated spontaneously breathing congenital cardiac patients undergoing catheterization. The aim of this study is to compare direct VO2 measurements with standard estimation of VO2 in sedated, spontaneously breathing congenital cardiac catheterization patients.Methods:Patients undergoing cardiac catheterization with moderate sedation and spontaneous breathing at UCSF from February 2016 to December 2017 with weight >12 kg had VO2 directly measured using the Ultima CPX system (MCG Diagnostics, St. Paul, MN). LaFarge, Seckeler, and primary proceduralist?s estimate were recorded prior to direct VO2 measurement. Cardiac output was measured using thermodilution on a subset of patients as clinically indicated, and VO2 measurement was derived by back calculation using Fick?s equation. More than 30% variation from directly measured VO2 was considered to be clinically significant and defined as an inaccurate VO2 estimate.Results:Analysis was performed on 140 patients (22% with single ventricle physiology), 31 had thermodilution-derived VO2 estimation. Age ranged from 2 to 75 years (median 12.5, IQR 6,20). Mean measured VO2 was 124 mL/min/m2(SD 27). Paired t-test showed significant difference between direct VO2 measurement and each of the methods of VO2 estimation; Seckeler and LaFarge overestimating measured VO2 by a mean of 15 (p<0.001) and 7.4 (p<0.001), respectively. The percentage of inaccurate VO2 results were 25%, 13%, 8% and 6% when using the Seckeler, LaFarge, interventionalist, and thermodilution, respectively (Cochran Q p<0.001 for Seckeler, LaFarge, and interventionalist estimates).Conclusion:Current methods do not accurately represent directly measured VO2, both Seckeler and LaFarge significantly overestimate VO2 in sedated spontaneously breathing patients during congenital cardiac catheterization. This may result in the overestimation of cardiac output and underestimation of resistances as calculated using Fick?s equation.

Published
2019
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41. Abstract 13228: The Effect of Gestational Age and Size at Birth on Brain Injury and Developmental Outcomes in Congenital Heart Disease

Author

Parekh, Shalin, Steurer, Martina A, Chau, Vann, Hogan, Whitnee, Xu, Duan, Miller, Steven, McQuillen, Patrick S, and Peyvandi, Shabnam

Abstract

Background:Early delivery and size at birth are known to be independent risk factors for neurodevelopmental (ND) impairments among patients with complex congenital heart disease (CHD). The aim of this study was to explore the interaction between gestational age (GA) and size at birth and their relationship with postnatal brain injury and developmental outcomes among patients with CHD.Methods:This was an analysis of a prospective study of neonates with d-transposition of the great arteries (TGA) or single ventricle physiology (SVP) that underwent pre- and post-operative brain MRIs and ND testing. The primary outcome was white matter injury (WMI) on the pre-operative MRI. Secondary outcomes included fractional anisotropy (FA) in white matter as a measure of microstructural development and psychomotor (PDI) and mental development indices (MDI) on the Bayley scale of infant development-II at 30 months. Primary predictors included z-scores for birth weight (WZ), length (LZ) and head circumference (HCZ) and GA at birth categorized as early term (37-38 weeks) or term (>39 weeks). Growth asymmetry was measured by the difference in WZ and HCZ and categorized as symmetric, asymmetric with a small head relative to body and asymmetric with a large head relative to body.Results:187 subjects (112- TGA; 75- SVP) were analyzed of which 74 were early term and 113 were term. There was no relationship between growth parameters with WMI or white matter FA on the pre-operative brain MRI. WZ, LZ and HCZ were not associated with MDI or PDI at 30 months of age in either GA category. However, there was a significant association between growth asymmetry and MDI after adjusting for hospital length of stay and GA at birth. Compared with symmetric infants, SVP infants with a small head relative to body had significantly lower MDI scores (?= -38, 95%CI: -65, -11; p= 0.01) while there was a trend in TGA infants (?= -8, 95%CI: -19, 4; p= 0.1)Conclusions:Size at birth is not associated with early measures of brain injury or development. However, asymmetric size at birth regardless of GA is associated with worse cognitive outcomes at 30 months of age, particularly for SVP patients. These findings suggest that ND impairment in CHD is multi-factorial with early origins.

Published
2019
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42. Comparing Parent Perception of Neurodevelopment after Primary versus Staged Repair of Neonatal Symptomatic Tetralogy of Fallot.

Author

Zampi JD, Ilardi DL, McCracken CE, Zhang Y, Glatz AC, Goldstein BH, Petit CJ, Qureshi AM, Goldberg CS, Law MA, Meadows JJ, Shahanavaz S, Batlivala SP, Maskatia SA, O'Byrne ML, Ligon RA, Pettus JA, Beshish A, Romano JC, Stack KO, Khan HQ, Parekh S, and Nicholson GT

Abstract

Objective: To assess the association between primary (PR) and staged repair (SR) of neonatal symptomatic tetralogy of Fallot (sTOF) and neurodevelopmental outcomes in preschool through school-age children., Study Design: Multi-center cohort (n=9 sites) study of sTOF patients who underwent neonatal intervention between 2005 and 2017. The neurodevelopmental outcomes measures included caregivers' ratings of executive function with the Behavior Rating Inventory of Executive Function (BRIEF), and psychosocial functioning with the Behavior Assessment System for Children - 3 rd Edition (BASC-3). Results were compared with normative data and by treatment strategy (PR versus SR). A parent survey assessed history of disabilities and access to services related to neurodevelopment., Results: Although the majority of patients (median age 8.3 years, interquartile range 5.7-11.2) had median BRIEF and BASC-3 scores within the normal range, a proportion had clinically elevated (abnormal) scores, especially in the school-age patient subgroup (BRIEF 24-30% and BASC 20-37%). There were no statistically significant differences based on treatment strategy for either the BRIEF or BASC-3. However, lower birth weight, genetic syndrome, and medical complexity were significantly associated with worse executive function, and lower maternal education was associated in school age children with lower executive and psychosocial functioning. Ongoing disabilities were relatively common (learning disability 35%, speech delay 33%, developmental delay 31%), although up to 50% of children were not receiving educational or developmental services., Conclusion: Elevated executive and psychosocial concerns are present in the sTOF patient population. Although initial treatment strategy appears unrelated to neurodevelopmental outcomes, lower birth weight, genetic syndrome, and medical complexity, and lower maternal education are risk factors. Early recognition of neurodevelopmental concerns can facilitate access to appropriate neuro-developmental services in this high-risk group., Competing Interests: Conflicts of Interest Dr. Jeffrey Zampi is a consultant for Medtronic, Inc and WL Gore and Associates. He also serves on the Data Safety Monitoring Board for Encore Medical. Dr. Athar Qureshi is a consultant for Medtronic, Inc, B Braun, and WL Gore and Associates. Dr. Bryan Goldstein is a consultant for Medtronic, Inc, WL Gore and Associates, PECA labs, and Mezzion Pharma, (Copyright © 2024. Published by Elsevier Inc.)

Published
2024
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