A GPU Implementation of a Spatial GLMM: Assessing Spatially Varying - PowerPoint PPT Presentation

A GPU Implementation of a Spatial GLMM: Assessing Spatially Varying Coefficients of Multiple Sclerosis Lesions Timothy D. Johnson Department of Biostatistics University of Michigan Johnson (University of Michigan) MS-GPU Jan 6, 2014 1 / 18

Outline Disease Background 1 The Model 2 Intro to GPUs 3 Results 4 Acknowledgements 5 Johnson (University of Michigan) MS-GPU Jan 6, 2014 2 / 18

Disease Background Multiple Sclerosis Autoimmune disease affecting the central nervous system Johnson (University of Michigan) MS-GPU Jan 6, 2014 3 / 18

Disease Background Multiple Sclerosis Autoimmune disease affecting the central nervous system Affects women more than men Johnson (University of Michigan) MS-GPU Jan 6, 2014 3 / 18

Disease Background Multiple Sclerosis Autoimmune disease affecting the central nervous system Affects women more than men Commonly diagnosed between 20 and 40 years of age. Johnson (University of Michigan) MS-GPU Jan 6, 2014 3 / 18

Disease Background Multiple Sclerosis Autoimmune disease affecting the central nervous system Affects women more than men Commonly diagnosed between 20 and 40 years of age. Immune system attacks the myelin sheath surrounding axons Slows nerve impulse Johnson (University of Michigan) MS-GPU Jan 6, 2014 3 / 18

Disease Background Multiple Sclerosis Autoimmune disease affecting the central nervous system Affects women more than men Commonly diagnosed between 20 and 40 years of age. Immune system attacks the myelin sheath surrounding axons Slows nerve impulse Immune system attacks the myelin Johnson (University of Michigan) MS-GPU Jan 6, 2014 3 / 18

Disease Background Multiple Sclerosis Autoimmune disease affecting the central nervous system Affects women more than men Commonly diagnosed between 20 and 40 years of age. Immune system attacks the myelin sheath surrounding axons Slows nerve impulse Immune system attacks the myelin Causes inflammation visible on MRI Johnson (University of Michigan) MS-GPU Jan 6, 2014 3 / 18

Disease Background Multiple Sclerosis Autoimmune disease affecting the central nervous system Affects women more than men Commonly diagnosed between 20 and 40 years of age. Immune system attacks the myelin sheath surrounding axons Slows nerve impulse Immune system attacks the myelin Causes inflammation visible on MRI Cause of autoimmune disease is unknown, theories include Viral infection Genetics Environmental factors Johnson (University of Michigan) MS-GPU Jan 6, 2014 3 / 18

Disease Background Multiple Sclerosis Autoimmune disease affecting the central nervous system Affects women more than men Commonly diagnosed between 20 and 40 years of age. Immune system attacks the myelin sheath surrounding axons Slows nerve impulse Immune system attacks the myelin Causes inflammation visible on MRI Cause of autoimmune disease is unknown, theories include Viral infection Genetics Environmental factors No known cure Johnson (University of Michigan) MS-GPU Jan 6, 2014 3 / 18

Disease Background Multiple Sclerosis Functional Systems Scores FSS Johnson (University of Michigan) MS-GPU Jan 6, 2014 4 / 18

Disease Background Multiple Sclerosis Functional Systems Scores FSS Visual function — blind spots, decrease in visual acuity Johnson (University of Michigan) MS-GPU Jan 6, 2014 4 / 18

Disease Background Multiple Sclerosis Functional Systems Scores FSS Visual function — blind spots, decrease in visual acuity Cerebellar function — coordination Johnson (University of Michigan) MS-GPU Jan 6, 2014 4 / 18

Disease Background Multiple Sclerosis Functional Systems Scores FSS Visual function — blind spots, decrease in visual acuity Cerebellar function — coordination Brainstem function — difficulty in speech, swallowing, ... Johnson (University of Michigan) MS-GPU Jan 6, 2014 4 / 18

Disease Background Multiple Sclerosis Functional Systems Scores FSS Visual function — blind spots, decrease in visual acuity Cerebellar function — coordination Brainstem function — difficulty in speech, swallowing, ... Pyramidal function — walking Johnson (University of Michigan) MS-GPU Jan 6, 2014 4 / 18

Disease Background Multiple Sclerosis Functional Systems Scores FSS Visual function — blind spots, decrease in visual acuity Cerebellar function — coordination Brainstem function — difficulty in speech, swallowing, ... Pyramidal function — walking Sensory function — touch and pain Johnson (University of Michigan) MS-GPU Jan 6, 2014 4 / 18

Disease Background Multiple Sclerosis Functional Systems Scores FSS Visual function — blind spots, decrease in visual acuity Cerebellar function — coordination Brainstem function — difficulty in speech, swallowing, ... Pyramidal function — walking Sensory function — touch and pain Bowel and Bladder function Johnson (University of Michigan) MS-GPU Jan 6, 2014 4 / 18

Disease Background Multiple Sclerosis Functional Systems Scores FSS Visual function — blind spots, decrease in visual acuity Cerebellar function — coordination Brainstem function — difficulty in speech, swallowing, ... Pyramidal function — walking Sensory function — touch and pain Bowel and Bladder function Cerebral function — memory, mood, dementia Johnson (University of Michigan) MS-GPU Jan 6, 2014 4 / 18

Disease Background Multiple Sclerosis Functional Systems Scores FSS Visual function — blind spots, decrease in visual acuity Cerebellar function — coordination Brainstem function — difficulty in speech, swallowing, ... Pyramidal function — walking Sensory function — touch and pain Bowel and Bladder function Cerebral function — memory, mood, dementia PASAT score Paced auditory serial addition test Assesses auditory speed/flexibility + calculation ability Johnson (University of Michigan) MS-GPU Jan 6, 2014 4 / 18

Disease Background MS high-resolution imaging Data are T 2 hyperintense lesions Johnson (University of Michigan) MS-GPU Jan 6, 2014 5 / 18

Disease Background MS high-resolution imaging Data are T 2 hyperintense lesions Johnson (University of Michigan) MS-GPU Jan 6, 2014 5 / 18

The Model Notation s j , j = 1 , . . . , M will denote the j th voxel at location ( x , y , z ) (lexicographical ordering) Johnson (University of Michigan) MS-GPU Jan 6, 2014 6 / 18

The Model Notation s j , j = 1 , . . . , M will denote the j th voxel at location ( x , y , z ) (lexicographical ordering) Y i ( s j ) ∈ { 0 , 1 } : outcome for subject i = 1 , . . . , N at voxel, or site, s j Johnson (University of Michigan) MS-GPU Jan 6, 2014 6 / 18

The Model Notation s j , j = 1 , . . . , M will denote the j th voxel at location ( x , y , z ) (lexicographical ordering) Y i ( s j ) ∈ { 0 , 1 } : outcome for subject i = 1 , . . . , N at voxel, or site, s j X i : subject specific covariate vector. Johnson (University of Michigan) MS-GPU Jan 6, 2014 6 / 18

The Model Notation s j , j = 1 , . . . , M will denote the j th voxel at location ( x , y , z ) (lexicographical ordering) Y i ( s j ) ∈ { 0 , 1 } : outcome for subject i = 1 , . . . , N at voxel, or site, s j X i : subject specific covariate vector. β ( s j ) : parameter vector at voxel s j . Johnson (University of Michigan) MS-GPU Jan 6, 2014 6 / 18

The Model Notation s j , j = 1 , . . . , M will denote the j th voxel at location ( x , y , z ) (lexicographical ordering) Y i ( s j ) ∈ { 0 , 1 } : outcome for subject i = 1 , . . . , N at voxel, or site, s j X i : subject specific covariate vector. β ( s j ) : parameter vector at voxel s j . MRF (Markov Random Field) model Johnson (University of Michigan) MS-GPU Jan 6, 2014 6 / 18

The Model Notation s j , j = 1 , . . . , M will denote the j th voxel at location ( x , y , z ) (lexicographical ordering) Y i ( s j ) ∈ { 0 , 1 } : outcome for subject i = 1 , . . . , N at voxel, or site, s j X i : subject specific covariate vector. β ( s j ) : parameter vector at voxel s j . MRF (Markov Random Field) model Voxels are rectangular prisms (commonly cubes) Johnson (University of Michigan) MS-GPU Jan 6, 2014 6 / 18

The Model Notation s j , j = 1 , . . . , M will denote the j th voxel at location ( x , y , z ) (lexicographical ordering) Y i ( s j ) ∈ { 0 , 1 } : outcome for subject i = 1 , . . . , N at voxel, or site, s j X i : subject specific covariate vector. β ( s j ) : parameter vector at voxel s j . MRF (Markov Random Field) model Voxels are rectangular prisms (commonly cubes) If s j and s k are neighboring sites, we denote this by s j ∼ s k Johnson (University of Michigan) MS-GPU Jan 6, 2014 6 / 18

The Model Notation s j , j = 1 , . . . , M will denote the j th voxel at location ( x , y , z ) (lexicographical ordering) Y i ( s j ) ∈ { 0 , 1 } : outcome for subject i = 1 , . . . , N at voxel, or site, s j X i : subject specific covariate vector. β ( s j ) : parameter vector at voxel s j . MRF (Markov Random Field) model Voxels are rectangular prisms (commonly cubes) If s j and s k are neighboring sites, we denote this by s j ∼ s k The set of neighbors of s j is denoted by ∂ s j Johnson (University of Michigan) MS-GPU Jan 6, 2014 6 / 18