Displaying all 9 publications

  1. Morton SE, Chiew YS, Pretty C, Moltchanova E, Scarrott C, Redmond D, et al.
    Math Biosci, 2017 02;284:21-31.
    PMID: 27301378 DOI: 10.1016/j.mbs.2016.06.001
    Randomised control trials have sought to seek to improve mechanical ventilation treatment. However, few trials to date have shown clinical significance. It is hypothesised that aside from effective treatment, the outcome metrics and sample sizes of the trial also affect the significance, and thus impact trial design. In this study, a Monte-Carlo simulation method was developed and used to investigate several outcome metrics of ventilation treatment, including 1) length of mechanical ventilation (LoMV); 2) Ventilator Free Days (VFD); and 3) LoMV-28, a combination of the other metrics. As these metrics have highly skewed distributions, it also investigated the impact of imposing clinically relevant exclusion criteria on study power to enable better design for significance. Data from invasively ventilated patients from a single intensive care unit were used in this analysis to demonstrate the method. Use of LoMV as an outcome metric required 160 patients/arm to reach 80% power with a clinically expected intervention difference of 25% LoMV if clinically relevant exclusion criteria were applied to the cohort, but 400 patients/arm if they were not. However, only 130 patients/arm would be required for the same statistical significance at the same intervention difference if VFD was used. A Monte-Carlo simulation approach using local cohort data combined with objective patient selection criteria can yield better design of ventilation studies to desired power and significance, with fewer patients per arm than traditional trial design methods, which in turn reduces patient risk. Outcome metrics, such as VFD, should be used when a difference in mortality is also expected between the two cohorts. Finally, the non-parametric approach taken is readily generalisable to a range of trial types where outcome data is similarly skewed.
  2. Mohamed Mokhtarudin MJ, Payne SJ
    Math Biosci, 2015 May;263:111-20.
    PMID: 25749185 DOI: 10.1016/j.mbs.2015.02.011
    Restoration of an adequate cerebral blood supply after an ischemic attack is a primary clinical goal. However, the blood-brain barrier may break down after a prolonged ischemia causing the fluid in the blood plasma to filtrate and accumulate into the cerebral tissue interstitial space. Accumulation of this filtration fluid causes the cerebral tissue to swell, a condition known as vasogenic oedema. Tissue swelling causes the cerebral microvessels to be compressed, which may further obstruct the blood flow into the tissue, thus leading to the no-reflow phenomenon or a secondary ischemic stroke. The actual mechanism of this however is still not fully understood. A new model is developed here to study the effect of reperfusion on the formation of vasogenic oedema and cerebral microvessel collapse. The formation of vasogenic oedema is modelled using the capillary filtration equation while vessel collapse is modelled using the tube law of microvessel. Tissue swelling is quantified in terms of displacement, which is modelled using poroelastic theory. The results show that there is an increase in tissue displacement and interstitial pressure after reperfusion. In addition, the results also show that vessel collapse can occur at high value of reperfusion pressure, low blood osmotic pressure, high cerebral capillary permeability and low cerebral capillary stiffness. This model provides insight on the formation of ischemia-reperfusion injury by tissue swelling and vessel collapse.
  3. Khabibor Rahman N, Bakar MZ, Hekarl Uzir M, Harun Kamaruddin A
    Math Biosci, 2009 Apr;218(2):130-7.
    PMID: 19563738 DOI: 10.1016/j.mbs.2009.01.007
    A one-dimensional biofilm model was developed based on the basic principle of conservation of mass. Three simple, generic processes were combined in the model which includes microbial growth, diffusive and convective mass transport. The final model could generate a quantitative description of the relationship between the microbial growth and the consumption of substrate (oxygen) within the fixed biofilm thickness. Mass transfer resistance contributes large influence on the substrates and microbial concentration across the biofilm thickness due to the effect of biofilm structure.
  4. Fernando WJ, Othman R
    Math Biosci, 2006 Feb;199(2):175-87.
    PMID: 16387333
    Disinfectants are generally used to inactivate microorganisms in solutions. The process of inactivation involves the disinfectant in the liquid diffusing towards the bacteria sites and thereafter reacting with bacteria at rates determined by the respective reaction rates. Such processes have demonstrated an initial lag phase followed by an active depletion phase of bacteria. This paper attempts to study the importance of the combined effects of diffusion of the disinfectant through the outer membrane of the bacteria and transport through the associated concentration boundary layers (CBLs) during the initial lag phase. Mathematical equations are developed correlating the initial concentration of the disinfectant with time required for reaching a critical concentration (C*) at the inner side of the membrane of the cell based on diffusion of disinfectant through the outer membranes of the bacteria and the formation of concentration boundary layers on both sides of the membranes. Experimental data of the lag phases of inactivation already available in the literature for inactivation of Bacillus subtilis spores with ozone and monochloramine are tested with the equations. The results seem to be in good agreement with the theoretical equations indicating the importance of diffusion process across the outer cell membranes and the resulting CBL's during the lag phase of disinfection.
  5. Smith JD
    Math Biosci, 1998 Nov;153(2):151-61.
    PMID: 9825637
    The Gibbs canonical ensemble of statistical mechanics is used to describe the probability distribution of the age classes of mothers of new-borns in an age-structured population. The Malthusian parameter emerges as a Lagrange multiplier corresponding to a generation time constraint, while a new perturbation parameter appears as the Lagrange multiplier corresponding to a maternity constraint. Classical Lotka stability reduces to the unperturbed case of the more general canonical ensemble model. The model is used in a case study of the female (peninsular) Malaysian population of 1970. The Malthusian parameter and perturbation are calculated easily by linear regression. Use of the model identifies an anomaly in the population due to the effects of World War II.
  6. Gumel AB, Kubota K, Twizell EH
    Math Biosci, 1998 Aug 15;152(1):87-103.
    PMID: 9727298
    A sequential algorithm is developed for the non-linear dual-sorption model developed by Chandrasekaran et al. [1,2] which monitors pharmacokinetic profiles in percutaneous drug absorption. In the experimental study of percutaneous absorption, it is often observed that the lag-time decreases with the increase in the donor concentration when two or more donor concentrations of the same compound are used. The dual-sorption model has sometimes been employed to explain such experimental results. In this paper, it is shown that another feature observed after vehicle removal may also characterize the dual-sorption model. Soon after vehicle removal, the plots of the drug flux versus time become straight lines on a semilogarithmic scale as in the linear model, but the half-life is prolonged thereafter when the dual-sorption model prevails. The initial half-life after vehicle removal with a low donor concentration is longer than that with a higher donor concentration. These features, if observed in experiments, may be used as evidence to confirm that the dual-sorption model gives an explanation to the non-linear kinetic behaviour of a permeant.
  7. Langdon R, Docherty PD, Chiew YS, Chase JG
    Math Biosci, 2017 02;284:32-39.
    PMID: 27513728 DOI: 10.1016/j.mbs.2016.08.001
    For patients with acute respiratory distress syndrome (ARDS), mechanical ventilation (MV) is an essential therapy in the intensive care unit (ICU). Suboptimal PEEP levels in MV can cause ventilator induced lung injury, which is associated with increased mortality, extended ICU stay, and high cost. The ability to predict the outcome of respiratory mechanics in response to changes in PEEP would thus provide a critical advantage in personalising and improving care. Testing the potentially dangerous high pressures would not be required to assess their impact. A nonlinear autoregressive (NARX) model was used to predict airway pressure in 19 data sets from 10 mechanically ventilated ARDS patients. Patient-specific NARX models were identified from pressure and flow data over one, two, three, or four adjacent PEEP levels in a recruitment manoeuvre. Extrapolation of NARX model elastance functions allowed prediction of patient responses to PEEP changes to higher or lower pressures. NARX model predictions were more successful than those using a well validated first order model (FOM). The most clinically important results were for extrapolation up one PEEP step of 2cmH2O from the highest PEEP in the training data. When the NARX model was trained on one PEEP level, the mean RMS residual for the extrapolation PEEP level was 0.52 (90% CI: 0.47-0.57) cmH2O, compared to 1.50 (90% CI: 1.38-1.62) cmH2O for the FOM. When trained on four PEEP levels, the NARX result was 0.50 (90% CI: 0.42-0.58) cmH2O, and was 1.95 (90% CI: 1.71-2.19) cmH2O for the FOM. The results suggest that a full recruitment manoeuvre may not be required for the NARX model to obtain a useful estimate of the pressure waveform at higher PEEP levels. The methodology could thus allow clinicians to make informed decisions about ventilator PEEP settings while reducing the risk associated with high PEEP, and subsequent high peak airway pressures.
  8. Ibrahim RW, Nashine HK, Kamaruddin N
    Math Biosci, 2017 10;292:10-17.
    PMID: 28728968 DOI: 10.1016/j.mbs.2017.07.007
    A biological dynamic system carries engineering properties such as control systems and signal processing (or image processing) addicted to molecular biology at the level of bio-molecular communication networks. Dynamical system features and signal reply functions of cellular signaling pathways are some of the main topics in biological dynamic systems (for example the biological segmentation). In the present paper, we introduce new generalized hybrid time-space dynamical systems of growing bacteria. We impose the approximate analytic solution for the system. The generalization adapted the concepts of the Riemann-Liouville fractional operators for time and the Srivastava-Owa fractional operators for space. Moreover, we introduce a numerical perturbation method of two operators to obtain the approximate solutions. We establish the existence and uniqueness results and impose some applications in the sequel. Moreover, we study the Ulam stability and apply these stable solutions to improve the segmentation of a class of growing bacteria.
  9. Chen C, Chong NS, Smith R
    Math Biosci, 2018 02;296:98-112.
    PMID: 29273381 DOI: 10.1016/j.mbs.2017.12.002
    Mass-media reports on an epidemic or pandemic have the potential to modify human behaviour and affect social attitudes. Here we construct a Filippov model to evaluate the effects of media coverage and quarantine on the transmission dynamics of influenza. We first choose a piecewise smooth incidence rate to represent media reports being triggered once the number of infected individuals exceeds a certain critical level [Formula: see text] . Further, if the number of infected cases increases and exceeds another larger threshold value [Formula: see text] ( [Formula: see text] ), we consider that the incidence rate tends to a saturation level due to the protection measures taken by individuals; meanwhile, we begin to quarantine susceptible individuals when the number of susceptible individuals is larger than a threshold value Sc. Then, for each susceptible threshold value Sc, the global properties of the Filippov model with regard to the existence and stability of all possible equilibria and sliding-mode dynamics are examined, as we vary the infected threshold values [Formula: see text] and [Formula: see text] . We show generically that the Filippov system stabilizes at either the endemic equilibrium of the subsystem or the pseudoequilibrium on the switching surface or the endemic equilibrium [Formula: see text] depending on the choice of the threshold values. The findings suggest that proper combinations of infected and susceptible threshold values can maintain the number of infected individuals either below a certain threshold level or at a previously given level.
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