4D MR phase and magnitude segmentations with GPU parallel computing.

The increasing size and number of data sets of large four dimensional (three spatial, one temporal) magnetic resonance (MR) cardiac images necessitates efficient segmentation algorithms. Analysis of phase-contrast MR images yields cardiac flow information which can be manipulated to produce accurate segmentations of the aorta. Phase contrast segmentation algorithms are proposed that use simple mean-based calculations and least mean squared curve fitting techniques. The initial segmentations are generated on a multi-threaded central processing unit (CPU) in 10 seconds or less, though the computational simplicity of the algorithms results in a loss of accuracy. A more complex graphics processing unit (GPU)-based algorithm fits flow data to Gaussian waveforms, and produces an initial segmentation in 0.5 seconds. Level sets are then applied to a magnitude image, where the initial conditions are given by the previous CPU and GPU algorithms. A comparison of results shows that the GPU algorithm appears to produce the most accurate segmentation.

Effects of vaccination and population structure on influenza epidemic spread in the presence of two circulating strains.

BACKGROUND: Human influenza is characterized by seasonal epidemics, caused by rapid viral adaptation to population immunity. Vaccination against influenza must be updated annually, following surveillance of newly appearing viral strains. During an influenza season, several strains may be co-circulating, which will influence their individual evolution; furthermore, selective forces acting on the strains will be mediated by the transmission dynamics in the population. Clearly, viral evolution and public health policy are strongly interconnected. Understanding population-level dynamics of coexisting viral influenza infections, would be of great benefit in designing vaccination strategies. METHODS: We use a Markov network to extend a previous homogeneous model of two co-circulating influenza viral strains by including vaccination (either prior to or during an outbreak), age structure, and heterogeneity of the contact network. We explore the effects of changes in vaccination rate, cross-immunity, and delay in appearance of the second strain, on the size and timing of infection peaks, attack rates, and disease-induced mortality rate; and compare the outcomes of the network and corresponding homogeneous models. RESULTS: Pre-vaccination is more effective than vaccination during an outbreak, resulting in lower attack rates for the first strain but higher attack rates for the second strain, until a "threshold" vaccination level of ~30-40% is reached, after which attack rates due to both strains sharply dropped. A small increase in mortality was found for increasing pre-vaccination coverage below about 40%, due to increasing numbers of strain 2 infections. The amount of cross-immunity present determines whether a second wave of infection will occur. Some significant differences were found between the homogeneous and network models, including timing and height of peak infection(s). CONCLUSIONS: Contact and age structure significantly influence the propagation of disease in the population. The present model explores only qualitative behaviour, based on parameters derived for homogeneous influenza models, but may be used for realistic populations through statistical estimates of inter-age contact patterns. This could have significant implications for vaccination strategies in realistic models of populations in which more than one strain is circulating.

A comparative evaluation of modelling strategies for the effect of treatment and host interactions on the spread of drug resistance.

The evolutionary responses of infectious pathogens often have ruinous consequences for the control of disease spread in the population. Drug resistance is a well-documented instance that is generally driven by the selective pressure of drugs on both the replication of the pathogen within hosts and its transmission between hosts. Management of drug resistance therefore requires the development of treatment strategies that can impede the emergence and spread of resistance in the population. This study evaluates various treatment strategies for influenza infection as a case study by comparing the long-term epidemiological outcomes predicted by deterministic and stochastic versions of a homogeneously mixing (mean-field) model and those predicted by a heterogeneous model that incorporates spatial pair-wise correlation. We discuss the importance of three major parameters in our evaluation: the basic reproduction number, the population level of treatment, and the degree of clustering as a key parameter determining the structure of heterogeneous interactions. The results show that, as a common feature in all models, high treatment levels during the early stages of disease outset can result in large resistant outbreaks, with the possibility of a second wave of infection appearing in the pair-approximation model. Our simulations demonstrate that, if the basic reproduction number exceeds a threshold value, the population-wide spread of the resistant pathogen emerges more rapidly in the pair-approximation model with significantly lower treatment levels than in the homogeneous models. We tested an antiviral strategy that delays the onset of aggressive treatment for a certain amount of time after the onset of the outbreak. The findings indicate that the overall disease incidence is reduced as the degree of clustering increases, and a longer delay should be considered for implementing the large-scale treatment.

A delay differential model for pandemic influenza with antiviral treatment.

The use of antiviral drugs has been recognized as the primary public health strategy for mitigating the severity of a new influenza pandemic strain. However, the success of this strategy requires the prompt onset of therapy within 48 hours of the appearance of clinical symptoms. This requirement may be captured by a compartmental model that monitors the density of infected individuals in terms of the time elapsed since the onset of symptoms. We show that such a model can be expressed by a system of delay differential equations with both discrete and distributed delays. The model is analyzed to derive the criterion for disease control based on two critical factors: (i) the profile of treatment rate; and (ii) the level of treatment as a function of time lag in commencing therapy. Numerical results are also obtained to illustrate the feasible region of disease control. Our findings show that due to uncertainty in the attack rate of a pandemic strain, initiating therapy immediately upon diagnosis can significantly increase the likelihood of disease control and substantially reduce the required community-level of treatment. This suggests that reliable diagnostic methods for influenza cases should be rapidly implemented within an antiviral treatment strategy.

Emergence of drug resistance: implications for antiviral control of pandemic influenza.

Given the danger of an unprecedented spread of the highly pathogenic avian influenza strain H5N1 in humans, and great challenges to the development of an effective influenza vaccine, antiviral drugs will probably play a pivotal role in combating a novel pandemic strain. A critical limitation to the use of these drugs is the evolution of highly transmissible drug-resistant viral mutants. Here, we develop a mathematical model to evaluate the potential impact of an antiviral treatment strategy on the emergence of drug resistance and containment of a pandemic. The results show that elimination of the wild-type strain depends crucially on both the early onset of treatment in indexed cases and population-level treatment. Given the probable delay of 0.5-1 day in seeking healthcare and therefore initiating therapy, the findings indicate that a single strategy of antiviral treatment will be unsuccessful at controlling the spread of disease if the reproduction number of the wild-type strain (R0s) exceeds 1.4. We demonstrate the possible occurrence of a self-sustaining epidemic of resistant strain, in terms of its transmission fitness relative to the wild-type, and the reproduction number R0s. Considering reproduction numbers estimated for the past three pandemics, the findings suggest that an uncontrollable pandemic is likely to occur if resistant viruses with relative transmission fitness above 0.4 emerge. While an antiviral strategy is crucial for containing a pandemic, its effectiveness depends critically on timely and strategic use of drugs.

Bifurcations of an epidemic model with non-linear incidence and infection-dependent removal rate.

An epidemic model with a generalized non-linear incidence is extended to incorporate the effect of an infection-dependent removal strategy, which is defined as a function of the number of infected individuals. It is assumed that the removal rate decreases from a maximum capacity for removing infected individuals as their number increases. The existence and stability of the associated equilibria are analysed, and the basic reproductive number (R0) is formulated. It is shown that R0 is independent of the functional form of the incidence, but depends on the removal rate. Normal forms are derived to show the different types of bifurcation the model undergoes, including transcritical, generalized Hopf (Bautin), saddle-node and Bogdanov-Takens. A degenerate Hopf bifurcation at the Bautin point, where the first Lyapunov coefficient vanishes, is discussed. Sotomayor's theorem is applied to establish a saddle-node bifurcation at the turning point of backward bifurcation. The Bogdanov-Takens normal form is derived, from which the local bifurcation curve for a family of homoclinic orbits is formulated. Bifurcation diagrams and numerical simulations, using parameter values estimated for some infectious diseases, are also presented to provide more intuition to the theoretical findings. The results show that sufficiently increasing the removal rate can reduce R0 below a subthreshold domain, which leads to disease eradication.

Modelling strategies for controlling SARS outbreaks.

Severe acute respiratory syndrome (SARS), a new, highly contagious, viral disease, emerged in China late in 2002 and quickly spread to 32 countries and regions causing in excess of 774 deaths and 8098 infections worldwide. In the absence of a rapid diagnostic test, therapy or vaccine, isolation of individuals diagnosed with SARS and quarantine of individuals feared exposed to SARS virus were used to control the spread of infection. We examine mathematically the impact of isolation and quarantine on the control of SARS during the outbreaks in Toronto, Hong Kong, Singapore and Beijing using a deterministic model that closely mimics the data for cumulative infected cases and SARS-related deaths in the first three regions but not in Beijing until mid-April, when China started to report data more accurately. The results reveal that achieving a reduction in the contact rate between susceptible and diseased individuals by isolating the latter is a critically important strategy that can control SARS outbreaks with or without quarantine. An optimal isolation programme entails timely implementation under stringent hygienic precautions defined by a critical threshold value. Values below this threshold lead to control, but those above are associated with the incidence of new community outbreaks or nosocomial infections, a known cause for the spread of SARS in each region. Allocation of resources to implement optimal isolation is more effective than to implement sub-optimal isolation and quarantine together. A community-wide eradication of SARS is feasible if optimal isolation is combined with a highly effective screening programme at the points of entry.

Affine registration: a comparison of several programs.

Several registration programs with an affine model for the displacement field were tested on various 2D and 3D MRI of the same modality. The following programs were considered: AIR 3.0 (Woods, J. Comp. Assist. Tomogr, 22(1): 139-152, 1998), COCGV (Ostuni, JMRI, 7(2): 410-415, 1997), FLIRT (Jenkinson, Med. Image Analysis, 5(2): 143-156, 2001), Intramodal Registration (Thevenaz, IEEE Trans. Image Proc., 7(1): 27-41, 1998), SPM (Friston, Human Brain Mapping, 2: 165-189, 1995), and Patch Algorithm (Zhilkin, MRI 18(9): 1143-1150, 2000). Although some of these programs can perform multimodal registration, none was used in such a mode. This paper attempts a fair comparison of the performance of the Patch Algorithm with other programs. However, different settings of the programs' parameters may further improve the quality of the registration and/or change execution speed. The registered images, the CPU time required to perform the registration, and the error between the registered and reference images, are presented. Most of the programs give comparable accuracies of registration, but their execution times vary considerably. In general the AIR and Patch Algorithm require the least time. The Patch Algorithm can be easily parallelizable on a multi-processor computer.