The first international workshop on the role and impact of mathematics in medicine: a collective account

The First International Workshop on The Role and Impact of Mathematics in Medicine (RIMM) convened in Paris in June 2010. A broad range of researchers discussed the difficulties, challenges and opportunities faced by those wishing to see mathematical methods contribute to improved medical outcomes. Finding mechanisms for inter- disciplinary meetings, developing a common language, staying focused on the medical problem at hand, deriving realistic mathematical solutions, obtainin

Arterial pressure: agreement between a brachial cuff-based device and radial tonometry

Objectives: Aortic (central) blood pressure (BP) differs from brachial BP and may be a superior predictor of cardiovascular events. However, its measurement is currently restricted to research settings, owing to a moderate level of operator dependency. We tested a new noninvasive device in a large UK cohort. The device estimates central BP using measurements obtained with an upper arm cuff inflated to suprasystolic pressure. We compared these estimates with those obtained using radial tonometry as well as with invasively acquired measurements of aortic BP in a limited number of individuals. Methods: Consecutive cuff-based and tonometry-based estimates of the pressure waveform and the central BP were obtained from 1107 individuals (70 ± 6 years). Short-term and long-term reproducibility studies were performed on 28 individuals. Simultaneous cuff-based and invasively measured pressure traces were acquired and compared in an additional six individuals (65 ± 20 years). Results: Central systolic BP, as estimated by the cuff-based device, was found to be highly reproducible (coefficient of variation 4 and 8% for short and long-term reproducibility, respectively) and was comparable to that estimated by tonometry (average difference 3 ± 6 mmHg, intraclass correlation coefficient = 0.91). The cuff-based pressure waveforms were similar to those acquired invasively (cross-correlation coefficient 0.93), and the difference in the estimated central systolic BP was −5 ± 8 mmHg (P = 0.2). Conclusion: Cuff-based devices show promise to simplify the measurement of central BP, whilst maintaining a similar fidelity to tonometry. This could lead to improved adoption of estimates of central BP in clinical practice

The Maestro (Mro) Gene Is Dispensable for Normal Sexual Development and Fertility in Mice

The mammalian gonad arises as a bipotential primordium from which a testis or ovary develops depending on the chromosomal sex of the individual. We have previously used DNA microarrays to screen for novel genes controlling the developmental fate of the indifferent embryonic mouse gonad. Maestro (Mro), which encodes a HEAT-repeat protein, was originally identified as a gene exhibiting sexually dimorphic expression during mouse gonad development. Wholemount in situ hybridisation analysis revealed Mro to be expressed in the embryonic male gonad from approximately 11.5 days post coitum, prior to overt sexual differentiation. No significant expression was detected in female gonads at the same developmental stage. In order to address its physiological function, we have generated mice lacking Maestro using gene targeting. Male and female mice homozygous for a Mro null allele are viable and fertile. We examined gonad development in homozygous male embryos in detail and observed no differences when compared to wild-type controls. Immunohistochemical analysis of homozygous mutant testes of adult mice revealed no overt abnormalities. Expression profiling using DNA microarrays also indicated no significant differences between homozygote embryonic male gonads and controls. We conclude that Maestro is dispensable for normal male sexual development and fertility in laboratory mice; however, the Mro locus itself does have utility as a site for insertion of transgenes for future studies in the fields of sexual development and Sertoli cell function

Minor Abnormalities of Testis Development in Mice Lacking the Gene Encoding the MAPK Signalling Component, MAP3K1

In mammals, the Y chromosome is a dominant male determinant, causing the bipotential gonad to develop as a testis. Recently, cases of familial and spontaneous 46,XY disorders of sex development (DSD) have been attributed to mutations in the human gene encoding mitogen-activated protein kinase kinase kinase 1, MAP3K1, a component of the mitogen-activated protein kinase (MAPK) signal transduction pathway. In individuals harbouring heterozygous mutations in MAP3K1, dysregulation of MAPK signalling was observed in lymphoblastoid cell lines, suggesting a causal role for these mutations in disrupting XY sexual development. Mice lacking the cognate gene, Map3k1, are viable and exhibit the eyes open at birth (EOB) phenotype on a mixed genetic background, but on the C57BL/6J genetic background most mice die at around 14.5 dpc due to a failure of erythropoiesis in the fetal liver. However, no systematic examination of sexual development in Map3k1-deficient mice has been described, an omission that is especially relevant in the case of C57BL/6J, a genetic background that is sensitized to disruptions to testis determination. Here, we report that on a mixed genetic background mice lacking Map3k1 are fertile and exhibit no overt abnormalities of testis development. On C57BL/6J, significant non-viability is observed with very few animals surviving to adulthood. However, an examination of development in Map3k1-deficient XY embryos on this genetic background revealed no significant defects in testis determination, although minor abnormalities were observed, including an increase in gonadal length. Based on these observations, we conclude that MAP3K1 is not required for mouse testis determination. We discuss the significance of these data for the functional interpretation of sex-reversing MAP3K1 mutations in humans

A quantitative systems pharmacology approach, incorporating a novel liver model, for predicting pharmacokinetic drug-drug interactions

All pharmaceutical companies are required to assess pharmacokinetic drug-drug interactions (DDIs) of new chemical entities (NCEs) and mathematical prediction helps to select the best NCE candidate with regard to adverse effects resulting from a DDI before any costly clinical studies. Most current models assume that the liver is a homogeneous organ where the majority of the metabolism occurs. However, the circulatory system of the liver has a complex hierarchical geometry which distributes xenobiotics throughout the organ. Nevertheless, the lobule (liver unit), located at the end of each branch, is composed of many sinusoids where the blood flow can vary and therefore creates heterogeneity (e.g. drug concentration, enzyme level). A liver model was constructed by describing the geometry of a lobule, where the blood velocity increases toward the central vein, and by modeling the exchange mechanisms between the blood and hepatocytes. Moreover, the three major DDI mechanisms of metabolic enzymes; competitive inhibition, mechanism based inhibition and induction, were accounted for with an undefined number of drugs and/or enzymes. The liver model was incorporated into a physiological-based pharmacokinetic (PBPK) model and simulations produced, that in turn were compared to ten clinical results. The liver model generated a hierarchy of 5 sinusoidal levels and estimated a blood volume of 283 mL and a cell density of 193 × 106 cells/g in the liver. The overall PBPK model predicted the pharmacokinetics of midazolam and the magnitude of the clinical DDI with perpetrator drug(s) including spatial and temporal enzyme levels changes. The model presented herein may reduce costs and the use of laboratory animals and give the opportunity to explore different clinical scenarios, which reduce the risk of adverse events, prior to costly human clinical studies

A Novel Mouse Fgfr2 Mutant, Hobbyhorse (hob), Exhibits Complete XY Gonadal Sex Reversal

The secreted molecule fibroblast growth factor 9 (FGF9) plays a critical role in testis determination in the mouse. In embryonic gonadal somatic cells it is required for maintenance of SOX9 expression, a key determinant of Sertoli cell fate. Conditional gene targeting studies have identified FGFR2 as the main gonadal receptor for FGF9 during sex determination. However, such studies can be complicated by inefficient and variable deletion of floxed alleles, depending on the choice of Cre deleter strain. Here, we report a novel, constitutive allele of Fgfr2, hobbyhorse (hob), which was identified in an ENU-based forward genetic screen for novel testis-determining loci. Fgr2hob is caused by a C to T mutation in the invariant exon 7, resulting in a polypeptide with a mis-sense mutation at position 263 (Pro263Ser) in the third extracellular immunoglobulin-like domain of FGFR2. Mutant homozygous embryos show severe limb and lung defects and, when on the sensitised C57BL/6J (B6) genetic background, undergo complete XY gonadal sex reversal associated with failure to maintain expression of Sox9. Genetic crosses employing a null mutant of Fgfr2 suggest that Fgr2hob is a hypomorphic allele, affecting both the FGFR2b and FGFR2c splice isoforms of the receptor. We exploited the consistent phenotype of this constitutive mutant by analysing MAPK signalling at the sex-determining stage of gonad development, but no significant abnormalities in mutant embryos were detected