Surrogate-driven respiratory motion models relate the motion of the internal anatomy to easily acquired respiratory surrogate signals, such as the motion of the skin surface. They are usually built by first using image registration to determine the motion from a number of dynamic images, and then fitting a correspondence model relating the motion to the surrogate signals. In this paper we present a generalized framework that unifies the image registration and correspondence model fitting into a single optimization. This allows the use of 'partial' imaging data, such as individual slices, projections, or k-space data, where it would not be possible to determine the motion from an individual frame of data. Motion compensated image reconstruction can also be incorporated using an iterative approach, so that both the motion and a motion-free image can be estimated from the partial image data. The framework has been applied to real 4DCT, Cine CT, multi-slice CT, and multi-slice MR data, as well as simulated datasets from a computer phantom. This includes the use of a super-resolution reconstruction method for the multi-slice MR data. Good results were obtained for all datasets, including quantitative results for the 4DCT and phantom datasets where the ground truth motion was known or could be estimated.

Rationale: The decades-long progression of chronic obstructive pulmonary disease (COPD) renders identifying different trajectories of disease progression challenging.Objectives: To identify subtypes of patients with COPD with distinct longitudinal progression patterns using a novel machine-learning tool called "Subtype and Stage Inference" (SuStaIn) and to evaluate the utility of SuStaIn for patient stratification in COPD.Methods: We applied SuStaIn to cross-sectional computed tomography imaging markers in 3,698 Global Initiative for Chronic Obstructive Lung Disease (GOLD) 1-4 patients and 3,479 controls from the COPDGene (COPD Genetic Epidemiology) study to identify subtypes of patients with COPD. We confirmed the identified subtypes and progression patterns using ECLIPSE (Evaluation of COPD Longitudinally to Identify Predictive Surrogate Endpoints) data. We assessed the utility of SuStaIn for patient stratification by comparing SuStaIn subtypes and stages at baseline with longitudinal follow-up data.Measurements and Main Results: We identified two trajectories of disease progression in COPD: a "Tissue→Airway" subtype (n = 2,354, 70.4%), in which small airway dysfunction and emphysema precede large airway wall abnormalities, and an "Airway→Tissue" subtype (n = 988, 29.6%), in which large airway wall abnormalities precede emphysema and small airway dysfunction. Subtypes were reproducible in ECLIPSE. Baseline stage in both subtypes correlated with future FEV₁/FVC decline (r = -0.16 [P < 0.001] in the Tissue→Airway group; r = -0.14 [P = 0.011] in the Airway→Tissue group). SuStaIn placed 30% of smokers with normal lung function at elevated stages, suggesting imaging changes consistent with early COPD. Individuals with early changes were 2.5 times more likely to meet COPD diagnostic criteria at follow-up.Conclusions: We demonstrate two distinct patterns of disease progression in COPD using SuStaIn, likely representing different endotypes. One third of healthy smokers have detectable imaging changes, suggesting a new biomarker of "early COPD."