Mathematical analysis of a model for the growth of the bovine corpus luteum

The corpus luteum (CL) is an ovarian tissue that grows in the wound space created by follicular rupture. It produces the progesterone needed in the uterus to maintain pregnancy. Rapid growth of the CL and progesterone transport to the uterus require angiogenesis, the creation of new blood vessels from pre-existing ones, a process which is regulated by proteins that include fibroblast growth factor 2 (FGF2).\ud \ud In this paper we develop a system of time-dependent ordinary differential equations to model CL growth. The dependent variables represent FGF2, endothelial cells (ECs), luteal cells, and stromal cells (like pericytes), by assuming that the CL volume is a continuum of the three cell types. We assume that if the CL volume exceeds that of the ovulated follicle, then growth is inhibited. This threshold volume partitions the system dynamics into two regimes, so that the model may be classified as a Filippov (piecewise smooth) system.\ud \ud We show that normal CL growth requires an appropriate balance between the growth rates of luteal and stromal cells. We investigate how angiogenesis influences CL growth by considering how the system dynamics depend on the dimensionless EC proliferation rate, p5. We find that weak (low p5) or strong (high p5) angiogenesis leads to ‘pathological’ CL growth, since the loss of CL constituents compromises progesterone production or delivery. However, for intermediate values of p5, normal CL growth is predicted. The implications of these results for cow fertility are also discussed. For example, inadequate angiogenesis has been linked to infertility in dairy cows

Simulations and experimental demonstrations of encoding for X-ray coherent scattering

Diffraction data may be measured using approaches that lead to ambiguity in the interpretation of scattering distributions. Thus, the encoding and decoding of coherent scattering distributions have been considered with a view to enabling unequivocal data interpretation. Two encoding regimes are considered, where encoding occurs between the X-ray source and sample, and where the encoder is placed between the sample and detector. In the first case, the successful recovery of diffraction data formed from the interrogation of powder samples with annular incident beams is presented using a coded aperture approach. In the second regime, encoding of Debye cones is shown to enable recovery of the sample position relative to the detector. The errors associated with both regimes are considered and the advantages of combining the two discussed

Depth resolved snapshot energy-dispersive X-ray diffraction using a conical shell beam

We demonstrate a novel imaging architecture to collect range encoded diffraction patterns from overlapping samples in a single conical shell projection. The patterns were measured in the dark area encompassed by the beam via a centrally positioned aperture optically coupled to a pixelated energy-resolving detector. We show that a single exposure measurement of 0.3 mAs enables d-spacing values to be calculated. The axial positions of the samples were not required and the resultant measurements were robust in the presence of crystallographic textures. Our results demonstrate rapid volumetric materials characterization and the potential for a direct imaging method, which is of great relevance to applications in medicine, non-destructive testing and security screening

Mathematical analysis of a model for the growth of the bovine corpus luteum.

The corpus luteum (CL) is an ovarian tissue that grows in the wound space created by follicular rupture. It produces the progesterone needed in the uterus to maintain pregnancy. Rapid growth of the CL and progesterone transport to the uterus require angiogenesis, the creation of new blood vessels from pre-existing ones, a process which is regulated by proteins that include fibroblast growth factor 2 (FGF2). In this paper we develop a system of time-dependent ordinary differential equations to model CL growth. The dependent variables represent FGF2, endothelial cells (ECs), luteal cells, and stromal cells (like pericytes), by assuming that the CL volume is a continuum of the three cell types. We assume that if the CL volume exceeds that of the ovulated follicle, then growth is inhibited. This threshold volume partitions the system dynamics into two regimes, so that the model may be classified as a Filippov (piecewise smooth) system. We show that normal CL growth requires an appropriate balance between the growth rates of luteal and stromal cells. We investigate how angiogenesis influences CL growth by considering how the system dynamics depend on the dimensionless EC proliferation rate, ρ₅. We find that weak (low ρ₅) or strong (high ρ₅) angiogenesis leads to 'pathological' CL growth, since the loss of CL constituents compromises progesterone production or delivery. However, for intermediate values of ρ₅, normal CL growth is predicted. The implications of these results for cow fertility are also discussed. For example, inadequate angiogenesis has been linked to infertility in dairy cows

Constraining N2O emissions since 1940 using firn air isotope measurements in both hemispheres

N2O is currently the third most important anthropogenic greenhouse gas in terms of radiative forcing and its atmospheric mole fraction is rising steadily. To quantify the growth rate and its causes over the past decades, we performed a multi-site reconstruction of the atmospheric N2O mole fraction and isotopic composition using new and previously published firn air data collected from Greenland and Antarctica in combination with a firn diffusion and densification model. The multi-site reconstruction showed that while the global mean N2O mole fraction increased from (290±1)nmolmol-1 in 1940 to (322±1)nmolmol-1 in 2008, the isotopic composition of atmospheric N2O decreased by (-2.2±0.2)% for δ15Nav, (-1.0±0.3)% for δ18O, (-1.3±0.6)% for δ15Nα, and (-2.8±0.6)% for δ15Nβ over the same period. The detailed temporal evolution of the mole fraction and isotopic composition derived from the firn air model was then used in a two-box atmospheric model (comprising a stratospheric box and a tropospheric box) to infer changes in the isotopic source signature over time. The precise value of the source strength depends on the choice of the N2O lifetime, which we choose to fix at 123 years. The average isotopic composition over the investigated period is δ15Nav Combining double low line (-7.6±0.8)% (vs. air-N2), δ18O Combining double low line (32.2±0.2)% (vs. Vienna Standard Mean Ocean Water-VSMOW) for δ18O, δ15Nα Combining double low line (-3.0±1.9)% and δ15Nβ Combining double low line (-11.7±2.3)%. δ15Nav, and δ15Nβ show some temporal variability, while for the other signatures the error bars of the reconstruction are too large to retrieve reliable temporal changes. Possible processes that may explain trends in 15N are discussed. The 15N site preference (Combining double low line δ15Nα-δ15Nβ) provides evidence of a shift in emissions from denitrification to nitrification, although the uncertainty envelopes are large

X-ray absorption tomography employing a conical shell beam

We demonstrate depth-resolved absorption imaging by scanning an object through a conical shell of X-rays. We measure ring shaped projections and apply tomosynthesis to extract optical sections at different axial focal plane positions. Three-dimensional objects have been imaged to validate our theoretical treatment. The novel principle of our method is scalable with respect to both scan size and X-ray energy. A driver for this work is to complement previously reported methods concerning the measurement of diffracted X-rays for structural analysis. The prospect of employing conical shell beams to combine both absorption and diffraction modalities would provide enhanced analytical utility and has many potential applications in security screening, process control and diagnostic imaging

Combined X-ray diffraction and absorption tomography using a conical shell beam

We combine diffraction and absorption tomography by raster scanning samples through a hollow cone of pseudo monochromatic X-rays with a mean energy of 58.4 keV. A single image intensifier takes 90x90 (x,y) snapshots during the scan. We demonstrate a proof-of-principle of our technique using a heterogeneous three-dimensional (x,y,z) phantom (90x90x170 mm3) comprised of different material phases, i.e., copper and sodium chlorate. Each snapshot enables the simultaneous measurement of absorption contrast and diffracted flux. The axial resolution was ~1 mm along the (x,y) orthogonal scan directions and ~7 mm along the z-axis. The tomosynthesis of diffracted flux measurements enable the calculation of d-spacing values with ~0.1 Å full width at half maximum (FWHM) at ~2 Å. Thus the identified materials may be color-coded in the absorption optical sections. Characterization of specific material phases is of particular interest in security screening for the identification of narcotics and a wide range of homemade explosives concealed within complex "everyday objects." Other potential application areas include process control and biological imaging

JAK2 V617F hematopoietic clones are present several years prior to MPN diagnosis and follow different expansion kinetics.

TO THE EDITOR: The JAK2 V617F mutation is the most common somatic mutation in the classical myeloproliferative neoplasms (MPNs), present in >95% of cases of polycythemia vera (PV) and ∼50% of essential thrombocythemia (ET) and myelofibrosis (MF).1⇓⇓-4 It is usually the sole identifiable driver mutation in MPNs5 and was recently also identified as a driver of age-related clonal hemopoiesis in healthy individuals.6⇓⇓-9 In order to investigate the preclinical clonal evolution of MPNs, we identified 12 individuals with a JAK2 V617F mutant MPN, who 4.6 to 15.2 years previously (median 10.2 years) had also donated blood to register with the Cyprus Bone Marrow Donor Registry at the Karaiskakio FoundationThis work was supported by the Wellcome Trust Sanger Institute (WT098051). T. McKerrell is funded by a Wellcome Trust Clinician Scientist Fellowship (100678/Z/12/Z). G.S.V. is funded by a Wellcome Trust Senior Fellowship in Clinical Science (WT095663MA), and work in his laboratory is also funded by Cancer Research UK, Bloodwise, the Kay Kendall Leukaemia Fund, and Celgene. I.V. is supported by the Spanish Ministerio de Economía y Competitividad, Programa Ramón y Cajal

Mathematical models for immunology:current state of the art and future research directions

The advances in genetics and biochemistry that have taken place over the last 10 years led to significant advances in experimental and clinical immunology. In turn, this has led to the development of new mathematical models to investigate qualitatively and quantitatively various open questions in immunology. In this study we present a review of some research areas in mathematical immunology that evolved over the last 10 years. To this end, we take a step-by-step approach in discussing a range of models derived to study the dynamics of both the innate and immune responses at the molecular, cellular and tissue scales. To emphasise the use of mathematics in modelling in this area, we also review some of the mathematical tools used to investigate these models. Finally, we discuss some future trends in both experimental immunology and mathematical immunology for the upcoming years