Mathematics and Medicine: How mathematics, modelling and simulations can lead to better diagnosis and treatments

Starting with the discovery of X-rays by Röntgen in 1895, the progress in medical imaging has been extraordinary and immensely beneficial to diagnosis and therapy. Parallel to the increase of imaging accuracy, there is the quest of moving from qualitative to quantitative analysis and patient-tailored therapy. Mathematics, modelling and simulations are increasing their importance as tools in this quest. In this paper we give an overview of relations between mathematical modelling and imaging and focus particularly on the estimation of perfusion in the brain. In the forward model, the brain is treated as a porous medium and a two compartment model (arterial/venous) is used. Motivated by the similarity with techniques in reservoir modelling, we propose an ensemble Kalman filter to perform the parameter estimation and apply the method to a simple example as an illustrative example.acceptedVersio

Oscillatory cortical forces promote three dimensional cell intercalations that shape the murine mandibular arch

Multiple vertebrate embryonic structures such as organ primordia are composed of confluent cells. Although mechanisms that shape tissue sheets are increasingly understood, those which shape a volume of cells remain obscure. Here we show that 3D mesenchymal cell intercalations are essential to shape the mandibular arch of the mouse embryo. Using a genetically encoded vinculin tension sensor that we knock-in to the mouse genome, we show that cortical force oscillations promote these intercalations. Genetic loss- and gain-of-function approaches show that Wnt5a functions as a spatial cue to coordinate cell polarity and cytoskeletal oscillation. These processes diminish tissue rigidity and help cells to overcome the energy barrier to intercalation. YAP/TAZ and PIEZO1 serve as downstream effectors of Wnt5a-mediated actomyosin polarity and cytosolic calcium transients that orient and drive mesenchymal cell intercalations. These findings advance our understanding of how developmental pathways regulate biophysical properties and forces to shape a solid organ primordium

Detection of maturity and ligament injury using magic angle directional imaging

Purpose: To investigate whether magnetic field–related anisotropies of collagen may be correlated with postmortem findings in animal models. Methods: Optimized scan planning and new MRI data‐processing methods were proposed and analyzed using Monte Carlo simulations. Six caprine and 10 canine knees were scanned at various orientations to the main magnetic field. Image intensities in segmented voxels were used to compute the orientation vectors of the collagen fibers. Vector field and tractography plots were computed. The Alignment Index was defined as a measure of orientation distribution. The knees were subsequently assessed by a specialist orthopedic veterinarian, who gave a pathological diagnosis after having dissected and photographed the joints. Results: Using 50% less scans than reported previously can lead to robust calculation of fiber orientations in the presence of noise, with much higher accuracy. The 6 caprine knees were found to range from very immature ( 3 years). Mature specimens exhibited significantly more aligned collagen fibers in their patella tendons compared with the immature ones. In 2 of the 10 canine knees scanned, partial cranial caudal ligament tears were identified from MRI and subsequently confirmed with encouragingly high consistency of tractography, Alignment Index, and dissection results. Conclusion: This method can be used to detect injury such as partial ligament tears, and to visualize maturity‐related changes in the collagen structure of tendons. It can provide the basis for new, noninvasive diagnostic tools in combination with new scanner configurations that allow less‐restricted field orientations

Three dimensional first-pass myocardial perfusion imaging at 3T: feasibility study

<p>Abstract</p> <p>Background</p> <p>In patients with ischemic heart disease, accurate assessment of the extent of myocardial perfusion deficit may be important in predicting prognosis of clinical cardiac outcomes. The aim of this study was to compare the ability of three dimensional (3D) and of two dimensional (2D) multi-slice myocardial perfusion imaging (MPI) using cardiovascular magnetic resonance (CMR) in determining the size of defects, and to demonstrate the feasibility of 3D MPI in healthy volunteers at 3 Tesla.</p> <p>Methods</p> <p>A heart phantom was used to compare the accuracy of 3D and 2D multi-slice MPI in estimating the volume fraction of seven rubber insets which simulated transmural myocardial perfusion defects. Three sets of cross-sectional planes were acquired for 2D multi-slice imaging, where each set was shifted along the partition encoding direction by ± 10 mm. 3D first-pass contrast-enhanced (0.1 mmol/kg Gd-DTPA) MPI was performed in three volunteers with sensitivity encoding for six-fold acceleration. The upslope of the myocardial time-intensity-curve and peak SNR/CNR values were calculated.</p> <p>Results</p> <p>Mean/standard deviation of errors in estimating the volume fraction across the seven defects were -0.44/1.49%, 2.23/2.97%, and 2.59/3.18% in 3D, 2D 4-slice, and 2D 3-slice imaging, respectively. 3D MPI performed in healthy volunteers produced excellent quality images with whole left ventricular (LV) coverage. Peak SNR/CNR was 57.6 ± 22.0/37.5 ± 19.7 over all segments in the first eight slices.</p> <p>Conclusion</p> <p>3D performed better than 2D multi-slice MPI in estimating the size of perfusion defects in phantoms. Highly accelerated 3D MPI at 3T was feasible in volunteers, allowing whole LV coverage with excellent image quality and high SNR/CNR.</p

Adipose segmentation in small animals at 7T: a preliminary study

<p>Abstract</p> <p>Background</p> <p>Small animal MRI at 7 Tesla (T) provides a useful tool for adiposity research. For adiposity researchers, separation of fat from surrounding tissues and its subsequent quantitative or semi- quantitative analysis is a key task. This is a relatively new field and a priori it cannot be known which specific biological questions related to fat deposition will be relevant in a specific study. Thus it is impossible to predict what accuracy and what spatial resolution will be required in all cases and even difficult what accuracy and resolution will be useful in most cases. However the pragmatic time constraints and the practical resolution ranges are known for small animal imaging at 7T. Thus we have used known practical constraints to develop a method for fat volume analysis based on an optimized image acquisition and image post processing pair.</p> <p>Methods</p> <p>We designed a fat segmentation method based on optimizing a variety of factors relevant to small animal imaging at 7T. In contrast to most previously described MRI methods based on signal intensity of T1 weighted image alone, we chose to use parametric images based on Multi-spin multi-echo (MSME) Bruker pulse sequence which has proven to be particularly robust in our laboratory over the last several years. The sequence was optimized on a T1 basis to emphasize the signal. T2 relaxation times can be calculated from the multi echo data and we have done so on a pixel by pixel basis for the initial step in the post processing methodology. The post processing consists of parallel paths. On one hand, the weighted image is precisely divided into different regions with optimized smoothing and segmentation methods; and on the other hand, a confidence image is deduced from the parametric image according to the distribution of relaxation time relationship of typical adipose. With the assistance of the confidence image, a useful software feature was implemented to which enhances the data and in the end results in a more reliable and flexible method for adipose evaluation.</p> <p>Results</p> <p>In this paper, we describe how we arrived at our recommended procedures and key aspects of the post-processing steps. The feasibility of the proposed method is tested on both simulated and real data in this preliminary research. A research tool was created to help researchers segment out fat even when the anatomical information is of low quality making it difficult to distinguish between fat and non-fat. In addition, tool is designed to allow the operator to make adjustments to many of the key steps for comparison purposes and to quantitatively assess the difference these changes make. Ultimately our flexible software lets the researcher define key aspects of the fat segmentation and quantification.</p> <p>Conclusions</p> <p>Combining the full T2 parametric information with the optimized first echo image information, the research tool enhances the reliability of the results while providing more flexible operations than previous methods. The innovation in the method is to pair an optimized and very specific image acquisition technique to a flexible but tuned image post processing method. The separation of the fat is aided by the confidence distribution of regions produced on a scale relevant to and dictated by practical aspects of MRI at 7T.</p

Data preparation protocol for low signal-to-noise ratio fluorine-19 MRI

Fluorine-19 MRI shows great promise for a wide range of applications including renal imaging, yet the typically low signal-to-noise ratios and sparse signal distribution necessitate a thorough data preparation.This chapter describes a general data preparation workflow for fluorine MRI experiments. The main processing steps are: (1) estimation of noise level, (2) correction of noise-induced bias and (3) background subtraction. The protocol is supplemented by an example script and toolbox available online.This chapter is based upon work from the COST Action PARENCHIMA, a community-driven network funded by the European Cooperation in Science and Technology (COST) program of the European Union, which aims to improve the reproducibility and standardization of renal MRI biomarkers. This analysis protocol chapter is complemented by two separate chapters describing the basic concept and experimental procedure

Oxygen-sensitive 3He-MRI in bronchiolitis obliterans after lung transplantation

Oxygen-sensitive 3He-MRI was studied for the detection of differences in intrapulmonary oxygen partial pressure (pO2) between patients with normal lung transplants and those with bronchiolitis obliterans syndrome (BOS). Using software developed in-house, oxygen-sensitive 3He-MRI datasets from patients with normal lung grafts (n = 8) and with BOS (n = 6) were evaluated quantitatively. Datasets were acqiured on a 1.5-T system using a spoiled gradient echo pulse sequence. Underlying diseases were pulmonary emphysema (n = 10 datasets) and fibrosis (n = 4). BOS status was verified by pulmonary function tests. Additionally, 3He-MRI was assessed blindedly for ventilation defects. Median intrapulmonary pO2 in patients with normal lung grafts was 146 mbar compared with 108 mbar in patients with BOS. Homogeneity of pO2 distribution was greater in normal grafts (standard deviation pO2 34 versus 43 mbar). Median oxygen decrease rate during breath hold was higher in unaffected patients (−1.75 mbar/s versus −0.38 mbar/s). Normal grafts showed fewer ventilation defects (5% versus 28%, medians). Oxygen-sensitive 3He-MRI appears capable of demonstrating differences of intrapulmonary pO2 between normal lung grafts and grafts affected by BOS. Oxygen-sensitive 3He-MRI may add helpful regional information to other diagnostic techniques for the assessment and follow-up of lung transplant recipients

Three-Dimensional Imaging of the Mouse Neurovasculature with Magnetic Resonance Microscopy

Knowledge of the three-dimensional (3D) architecture of blood vessels in the brain is crucial because the progression of various neuropathologies ranging from Alzheimer's disease to brain tumors involves anomalous blood vessels. The challenges in obtaining such data from patients, in conjunction with development of mouse models of neuropathology, have made the murine brain indispensable for investigating disease induced neurovascular changes. Here we describe a novel method for “whole brain” 3D mapping of murine neurovasculature using magnetic resonance microscopy (μMRI). This approach preserves the vascular and white matter tract architecture, and can be combined with complementary MRI contrast mechanisms such as diffusion tensor imaging (DTI) to examine the interplay between the vasculature and white matter reorganization that often characterizes neuropathologies. Following validation with micro computed tomography (μCT) and optical microscopy, we demonstrate the utility of this method by: (i) combined 3D imaging of angiogenesis and white matter reorganization in both, invasive and non-invasive brain tumor models; (ii) characterizing the morphological heterogeneity of the vascular phenotype in the murine brain; and (iii) conducting “multi-scale” imaging of brain tumor angiogenesis, wherein we directly compared in vivo MRI blood volume measurements with ex vivo vasculature data