Longitudinal modeling of appearance and shape and its potential for clinical use

Subphenotypes of platelet count trajectories in sepsis from multi-center ICU data

Although thrombocytopenia on admission to the ICU is associated with increased in-hospital mortality in septic patients, the role of longitudinally measured platelet counts, which are dynamically changing, is unclear. We aimed to identify patterns of dynamic platelet count trajectories and evaluate their association with outcomes and thrombocytopenia in septic patients. We tested the longitudinal platelet trajectory patterns of sepsis patients within the first four days of ICU admission in the MIMIC-IV database and their association with 28-day mortality, and independently validated our findings in the eICU-CRD database. Statistical methods used included multivariate regression, propensity score analysis, doubly robust estimation, gradient boosting model, and inverse probability weighting to ensure the robustness of our findings. A total of 22,866 septic patients were included in our study. The trajectory analysis categorizes patients into ascending (AS), stable (ST), or descending (DS) patterns. The risk of 28-day mortality was increased in the DS patients (OR = 2.464, 95%CI 1.895-3.203, p < 0.001) and ST patients (OR = 1.302, 95%CI 1.067-1.589, p = 0.009) compared to AS patients. The AS patients had lower ICU length of stay (2.36 vs. 4.32, p < 0.001) and 28-day maximum SOFA scores (5.00 vs. 6.00, p < 0.001) than the DS patients, but had more ventilator-free days within 28 days than the DS group (26.00 vs. 24.00, p < 0.001). The mediating effect of thrombocytopenia was significant (p < 0.001 for the average causal mediation effect (ACME)). Longitudinal platelet trajectory was associated with risk-adjusted 28-day mortality among patients with sepsis and was proportionally mediated through thrombocytopenia.

Association of inflammatory trajectory with subarachnoid hemorrhage mortality

OBJECTIVE

White blood cells (WBC) play an important role in the inflammatory response of the body. Elevated WBC counts on admission in patients with subarachnoid hemorrhage (SAH) correlate with a poor prognosis. However, the role of longitudinal WBC trajectories based on repeated WBC measurements during hospitalization remains unclear. We explored the association between different WBC trajectory patterns and in-hospital mortality.

METHODS

We analyzed a cohort of consecutive patients with SAH between 2012 and 2020. Group-based trajectory modeling (GBTM) was used to group the patients according to their white blood cell patterns over the first 4 days. Stabilized inverse probability treatment weighting (sIPTW) was used to balance baseline demographic and clinical characteristics. We analyzed the association between the WBC trajectory groups and in-hospital mortality using a Cox proportional hazards model.

RESULTS

In total, 506 patients with SAH were included in this retrospective cohort. The final model identified two distinct longitudinal WBC trajectories. After adjusting for confounding factors, multivariate regression analysis suggested that an elevated longitudinal WBC trajectory increased the risk of in-hospital mortality (hazard ratio [HR], 2.476; 95% confidence interval [CI] 1.081-5.227; P = 0.024) before sIPTW, and (HR, 2.472; 95%CI 1.489-4.977; P = 0.018) after sIPTW.

CONCLUSION

In patients with SAH, different clinically relevant groups could be identified using WBC trajectory analysis. The WBC count trajectory-initially elevated and then decreased- may lead to an increased risk of in-hospital mortality following SAH.

Spatiotemporal Cardiac Statistical Shape Modeling: A Data-Driven Approach

Clinical investigations of anatomy's structural changes over time could greatly benefit from population-level quantification of shape, or spatiotemporal statistic shape modeling (SSM). Such a tool enables characterizing patient organ cycles or disease progression in relation to a cohort of interest. Constructing shape models requires establishing a quantitative shape representation (e.g., corresponding landmarks). Particle-based shape modeling (PSM) is a data-driven SSM approach that captures population-level shape variations by optimizing landmark placement. However, it assumes cross-sectional study designs and hence has limited statistical power in representing shape changes over time. Existing methods for modeling spatiotemporal or longitudinal shape changes require predefined shape atlases and pre-built shape models that are typically constructed cross-sectionally. This paper proposes a data-driven approach inspired by the PSM method to learn population-level spatiotemporal shape changes directly from shape data. We introduce a novel SSM optimization scheme that produces landmarks that are in correspondence both across the population (inter-subject) and across time-series (intra-subject). We apply the proposed method to 4D cardiac data from atrial-fibrillation patients and demonstrate its efficacy in representing the dynamic change of the left atrium. Furthermore, we show that our method outperforms an image-based approach for spatiotemporal SSM with respect to a generative time-series model, the Linear Dynamical System (LDS). LDS fit using a spatiotemporal shape model optimized via our approach provides better generalization and specificity, indicating it accurately captures the underlying time-dependency.

Association of longitudinal platelet count trajectory with ICU mortality: A multi-cohort study

Objective

Platelet (PLT) engages in immune and inflammatory responses, all of which are related to the prognosis of critically ill patients. Although thrombocytopenia at ICU admission contributes to in-hospital mortality, PLT is repeatedly measured during ICU hospitalization and the role of longitudinal PLT trajectory remains unclear. We aimed to identify dynamic PLT trajectory patterns and evaluate their relationships with mortality risk and thrombocytopenia.

Methods

We adopted a three-phase, multi-cohort study strategy. Firstly, longitudinal PLT trajectory patterns within the first four ICU days and their associations with 28-day survival were tested in the eICU Collaborative Research Database (eICU-CRD) and independently validated in the Medical Information Mart for Intensive Care IV (MIMIC-IV) database. Secondly, the relationships among PLT trajectory patterns, thrombocytopenia, and 28-day mortality were explored and validated. Finally, a Mortality GRade system for ICU dynamically monitoring patients (Mortality-GRID) was developed to quantify the mortality risk based on longitudinal PLT, which was further validated in the Molecular Epidemiology of Acute Respiratory Distress Syndrome (MEARDS) cohort.

Results

A total of 35,332 ICU patients were included from three cohorts. Trajectory analysis clustered patients into ascending (AS), stable (ST), or descending (DS) PLT patterns. DS patients with high baseline PLT decline quickly, resulting in poor prognosis. AS patients have low baseline PLT but recover quickly, favoring a better prognosis. ST patients maintain low PLT, having a moderate prognosis in between (HRSTvsAS = 1.26, 95% CI: 1.14–1.38, P = 6.15 × 10−6; HRDSvsAS = 1.58, 95% CI: 1.40–1.79, P = 1.41 × 10−13). The associations remained significant in patients without thrombocytopenia during the entire ICU hospitalization and were robust in sensitivity analyses and stratification analyses. Further, the trajectory pattern was a warning sign of thrombocytopenia, which mediated 27.2% of the effects of the PLT trajectory on 28-day mortality (HRindirect = 1.11, 95% CI: 1.06–1.17, P = 9.80 × 10−6). Mortality-GRID well predicts mortality risk, which is in high consistency with that directly estimated in MEARDS (r = 0.98, P = 1.30 × 10−23).

Conclusion

Longitudinal PLT trajectory is a complementary predictor to baseline PLT for patient survival, even in patients without risk of thrombocytopenia. Mortality-GRID could identify patients at high mortality risk.

A predictive paradigm for COVID-19 prognosis based on the longitudinal measure of biomarkers

Novel coronavirus disease 2019 (COVID-19) is an emerging, rapidly evolving crisis, and the ability to predict prognosis for individual COVID-19 patient is important for guiding treatment. Laboratory examinations were repeatedly measured during hospitalization for COVID-19 patients, which provide the possibility for the individualized early prediction of prognosis. However, previous studies mainly focused on risk prediction based on laboratory measurements at one time point, ignoring disease progression and changes of biomarkers over time. By using historical regression trees (HTREEs), a novel machine learning method, and joint modeling technique, we modeled the longitudinal trajectories of laboratory biomarkers and made dynamically predictions on individual prognosis for 1997 COVID-19 patients. In the discovery phase, based on 358 COVID-19 patients admitted between 10 January and 18 February 2020 from Tongji Hospital, HTREE model identified a set of important variables including 14 prognostic biomarkers. With the trajectories of those biomarkers through 5-day, 10-day and 15-day, the joint model had a good performance in discriminating the survived and deceased COVID-19 patients (mean AUCs of 88.81, 84.81 and 85.62% for the discovery set). The predictive model was successfully validated in two independent datasets (mean AUCs of 87.61, 87.55 and 87.03% for validation the first dataset including 112 patients, 94.97, 95.78 and 94.63% for the second validation dataset including 1527 patients, respectively). In conclusion, our study identified important biomarkers associated with the prognosis of COVID-19 patients, characterized the time-to-event process and obtained dynamic predictions at the individual level.

Hierarchical geodesic modeling on the diffusion orientation distribution function for longitudinal DW-MRI analysis

The analysis of anatomy that undergoes rapid changes, such as neuroimaging of the early developing brain, greatly benefits from spatio-temporal statistical analysis methods to represent population variations but also subject-wise characteristics over time. Methods for spatio-temporal modeling and for analysis of longitudinal shape and image data have been presented before, but, to our knowledge, not for diffusion weighted MR images (DW-MRI) fitted with higher-order diffusion models. To bridge the gap between rapidly evolving DW-MRI methods in longitudinal studies and the existing frameworks, which are often limited to the analysis of derived measures like fractional anisotropy (FA), we propose a new framework to estimate a population trajectory of longitudinal diffusion orientation distribution functions (dODFs) along with subject-specific changes by using hierarchical geodesic modeling. The dODF is an angular profile of the diffusion probability density function derived from high angular resolution diffusion imaging (HARDI) and we consider the dODF with the square-root representation to lie on the unit sphere in a Hilbert space, which is a well-known Riemannian manifold, to respect the nonlinear characteristics of dODFs. The proposed method is validated on synthetic longitudinal dODF data and tested on a longitudinal set of 60 HARDI images from 25 healthy infants to characterize dODF changes associated with early brain development.

Hierarchical Multi-Geodesic Model for Longitudinal Analysis of Temporal Trajectories of Anatomical Shape and Covariates

Longitudinal regression analysis for clinical imaging studies is essential to investigate unknown relationships between subject-wise changes over time and subject-specific characteristics, represented by covariates such as disease severity or a level of genetic risk. Image-derived data in medical image analysis, e.g. diffusion tensors or geometric shapes, are often represented on nonlinear Riemannian manifolds. Hierarchical geodesic models were suggested to characterize subject-specific changes of nonlinear data on Riemannian manifolds as extensions of a linear mixed effects model. We propose a new hierarchical multi-geodesic model to enable analysis of the relationship between subject-wise anatomical shape changes on a Riemannian manifold and multiple subject-specific characteristics. Each individual subject-wise shape change is represented by a univariate geodesic model. The effects of subject-specific covariates on the estimated subject-wise trajectories are then modeled by multivariate intercept and slope models which together form a multi-geodesic model. Validation was performed with a synthetic example on a S ² manifold. The proposed method was applied to a longitudinal set of 72 corpus callosum shapes from 24 autism spectrum disorder subjects to study the relationship between anatomical shape changes and the autism severity score, resulting in statistics for the population but also for each subject. To our knowledge, this is the first longitudinal framework to model anatomical developments over time as functions of both continuous and categorical covariates on a nonlinear shape space.

Statistical Shape Models: Understanding and Mastering Variation in Anatomy

In our chapter we are describing how to reconstruct three-dimensional anatomy from medical image data and how to build Statistical 3D Shape Models out of many such reconstructions yielding a new kind of anatomy that not only allows quantitative analysis of anatomical variation but also a visual exploration and educational visualization. Future digital anatomy atlases will not only show a static (average) anatomy but also its normal or pathological variation in three or even four dimensions, hence, illustrating growth and/or disease progression.Statistical Shape Models (SSMs) are geometric models that describe a collection of semantically similar objects in a very compact way. SSMs represent an average shape of many three-dimensional objects as well as their variation in shape. The creation of SSMs requires a correspondence mapping, which can be achieved e.g. by parameterization with a respective sampling. If a corresponding parameterization over all shapes can be established, variation between individual shape characteristics can be mathematically investigated.We will explain what Statistical Shape Models are and how they are constructed. Extensions of Statistical Shape Models will be motivated for articulated coupled structures. In addition to shape also the appearance of objects will be integrated into the concept. Appearance is a visual feature independent of shape that depends on observers or imaging techniques. Typical appearances are for instance the color and intensity of a visual surface of an object under particular lighting conditions, or measurements of material properties with computed tomography (CT) or magnetic resonance imaging (MRI). A combination of (articulated) Statistical Shape Models with statistical models of appearance lead to articulated Statistical Shape and Appearance Models (a-SSAMs).After giving various examples of SSMs for human organs, skeletal structures, faces, and bodies, we will shortly describe clinical applications where such models have been successfully employed. Statistical Shape Models are the foundation for the analysis of anatomical cohort data, where characteristic shapes are correlated to demographic or epidemiologic data. SSMs consisting of several thousands of objects offer, in combination with statistical methods or machine learning techniques, the possibility to identify characteristic clusters, thus being the foundation for advanced diagnostic disease scoring.

Nonparametric Aggregation of Geodesic Trends for Longitudinal Data Analysis

We propose a technique for analyzing longitudinal imaging data that models individual changes with diffeomorphic geodesic regression and aggregates these geodesics into a nonparametric group average trend. Our model is specifically tailored to the unbalanced and sparse characteristics of longitudinal imaging studies. That is, each individual has few data points measured over a short period of time, while the study population as a whole spans a wide age range. We use geodesic regression to estimate individual trends, which is an appropriate model for capturing shape changes over a short time window, as is typically found within an individual. Geodesics are also adept at handling the low sample sizes found within individuals, and can model the change between as few as two timepoints. However, geodesics are limited for modeling longer-term trends, where constant velocity may not be appropriate. Therefore, we develop a novel nonparametric regression to aggregate individual trends into an average group trend. We demonstrate the power of our method to capture non-geodesic group trends on hippocampal volume (real-valued data) and diffeomorphic registration of full 3D MRI from the longitudinal OASIS data.

4D CONTINUOUS MEDIAL REPRESENTATION BY GEODESIC SHAPE REGRESSION

Longitudinal shape analysis has shown great potential to model anatomical processes from baseline to follow-up observations. Shape regression estimates a continuous trajectory of time-discrete anatomical shapes to quantify temporal changes. The need for shape alignment and point-to-point correspondences represent limitations of current shape analysis methodologies, and present significant challenges in shape evaluation. We propose a method that estimates a continuous trajectory of continuous medial representations (CM-Rep) from a set of time-discrete observed shapes. To avoid the traditional step of aligning individual objects, shape changes are modeled via diffeomorphic ambient space deformations. Using a medial shape representation, we separately capture object pose changes and intrinsic geometry changes. Tests and validation with synthetic and real anatomical shapes demonstrate that the new method captures extrinsic shape changes as well as intrinsic shape changes encoded with CM-Reps, a highly relevant property for studying growth and disease processes.

3D Registration of mpMRI for Assessment of Prostate Cancer Focal Therapy

RATIONALE AND OBJECTIVES

This study aimed to assess a novel method of three-dimensional (3D) co-registration of prostate magnetic resonance imaging (MRI) examinations performed before and after prostate cancer focal therapy.

MATERIALS AND METHODS

We developed a software platform for automatic 3D deformable co-registration of prostate MRI at different time points and applied this method to 10 patients who underwent focal ablative therapy. MRI examinations were performed preoperatively, as well as 1 week and 6 months post treatment. Rigid registration served as reference for assessing co-registration accuracy and precision.

RESULTS

Segmentation of preoperative and postoperative prostate revealed a significant postoperative volume decrease of the gland that averaged 6.49 cc (P = .017). Applying deformable transformation based on mutual information from 120 pairs of MRI slices, we refined by 2.9 mm (max. 6.25 mm) the alignment of the ablation zone, segmented from contrast-enhanced images on the 1-week postoperative examination, to the 6-month postoperative T2-weighted images. This represented a 500% improvement over the rigid approach (P = .001), corrected by volume. The dissimilarity by Dice index of the mapped ablation zone using deformable transformation vs rigid control was significantly (P = .04) higher at the ablation site than in the whole gland.

CONCLUSIONS

Our findings illustrate our method's ability to correct for deformation at the ablation site. The preliminary analysis suggests that deformable transformation computed from mutual information of preoperative and follow-up MRI is accurate in co-registration of MRI examinations performed before and after focal therapy. The ability to localize the previously ablated tissue in 3D space may improve targeting for image-guided follow-up biopsy within focal therapy protocols.

Joint prediction of longitudinal development of cortical surfaces and white matter fibers from neonatal MRI

The human brain can be modeled as multiple interrelated shapes (or a multishape), each for characterizing one aspect of the brain, such as the cortex and white matter pathways. Predicting the developing multishape is a very challenging task due to the contrasting nature of the developmental trajectories of the constituent shapes: smooth for the cortical surface and non-smooth for white matter tracts due to changes such as bifurcation. We recently addressed this problem and proposed an approach for predicting the multishape developmental spatiotemporal trajectories of infant brains based only on neonatal MRI data using a set of geometric, dynamic, and fiber-to-surface connectivity features. In this paper, we propose two key innovations to further improve the prediction of multishape evolution. First, for a more accurate cortical surface prediction, instead of simply relying on one neonatal atlas to guide the prediction of the multishape, we propose to use multiple neonatal atlases to build a spatially heterogeneous atlas using the multidirectional varifold representation. This individualizes the atlas by locally maximizing its similarity to the testing baseline cortical shape for each cortical region, thereby better representing the baseline testing cortical surface, which founds the multishape prediction process. Second, for temporally consistent fiber prediction, we propose to reliably estimate spatiotemporal connectivity features using low-rank tensor completion, thereby capturing the variability and richness of the temporal development of fibers. Experimental results confirm that the proposed variants significantly improve the prediction performance of our original multishape prediction framework for both cortical surfaces and fiber tracts shape at 3, 6, and 9 months of age. Our pioneering model will pave the way for learning how to predict the evolution of anatomical shapes with abnormal changes. Ultimately, devising accurate shape evolution prediction models that can help quantify and predict the severity of a brain disorder as it progresses will be of great aid in individualized treatment planning.

Subject-Specific Longitudinal Shape Analysis by Coupling Spatiotemporal Shape Modeling with Medial Analysis

Modeling subject-specific shape change is one of the most important challenges in longitudinal shape analysis of disease progression. Whereas anatomical change over time can be a function of normal aging; anatomy can also be impacted by disease related degeneration. Shape changes to anatomy may also be affected by external structural changes from neighboring structures, which may cause non-linear pose variations. In this paper, we propose a framework to analyze disease related shape changes by coupling extrinsic modeling of the ambient anatomical space via spatiotemporal deformations with intrinsic shape properties from medial surface analysis. We compare intrinsic shape properties of a subject-specific shape trajectory to a normative 4D shape atlas representing normal aging to separately quantify shape changes related to disease. The spatiotemporal shape modeling establishes inter/intra subject anatomical correspondence, which in turn enables comparisons between subjects and the 4D shape atlas, and also quantitative analysis of disease related shape change. The medial surface analysis captures intrinsic shape properties related to local patterns of deformation. The proposed framework simultaneously models extrinsic longitudinal shape changes in the ambient anatomical space, as well as intrinsic shape properties to give localized measurements of degeneration. Six high risk subjects and six controls are randomly sampled from a Huntington's disease image database for quantitative and qualitative comparison.