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

Effects of platinum/taxane based chemotherapy on acute perfusion in human pelvic tumours measured by dynamic MRI

Dynamic contrast enhanced MRI (DCE-MRI) is being used increasingly in clinical trials to demonstrate that vascular disruptive and antiangiogenic agents target tumour microcirculation. Significant reductions in DCE-MRI kinetic parameters are seen within 4–24 and 48 h of treatment with vascular disruptive and antiangiogenic agents, respectively. It is important to know whether cytotoxic agents also cause significant acute reductions in these parameters, for reliable interpretation of results. This study investigated changes in transfer constant (Ktrans) and the initial area under the gadolinium curve (IAUGC) following the first dose of chemotherapy in patients with mostly gynaecological tumours. A reproducibility analysis on 20 patients (using two scans performed on consecutive days) was used to determine the significance of DCE-MRI parameter changes 24 h after chemotherapy in 18 patients. In 11 patients who received platinum alone or with a taxane, there were no significant changes in Ktrans or IAUGC in either group or individual patient analyses. When the remaining seven patients (treated with a variety of agents including platinum and taxanes) were included (n=18), there were also no significant changes in Ktrans. Therefore, if combination therapy does show changes in DCE-MRI parameters then the effects can be attributed to antivascular therapy rather than chemotherapy

Sensitivity of MRI Tumor Biomarkers to VEGFR Inhibitor Therapy in an Orthotopic Mouse Glioma Model

MRI biomarkers of tumor edema, vascular permeability, blood volume, and average vessel caliber are increasingly being employed to assess the efficacy of tumor therapies. However, the dependence of these biomarkers on a number of physiological factors can compromise their sensitivity and complicate the assessment of therapeutic efficacy. Here we examine the response of these MRI tumor biomarkers to cediranib, a potent vascular endothelial growth factor receptor (VEGFR) inhibitor, in an orthotopic mouse glioma model. A significant increase in the tumor volume and relative vessel caliber index (rVCI) and a slight decrease in the water apparent diffusion coefficient (ADC) were observed for both control and cediranib treated animals. This contrasts with a clinical study that observed a significant decrease in tumor rVCI, ADC and volume with cediranib therapy. While the lack of a difference between control and cediranib treated animals in these biomarker responses might suggest that cediranib has no therapeutic benefit, cediranib treated mice had a significantly increased survival. The increased survival benefit of cediranib treated animals is consistent with the significant decrease observed for cediranib treated animals in the relative cerebral blood volume (rCBV), relative microvascular blood volume (rMBV), transverse relaxation time (T2), blood vessel permeability (Ktrans), and extravascular-extracellular space (νe). The differential response of pre-clinical and clinical tumors to cediranib therapy, along with the lack of a positive response for some biomarkers, indicates the importance of evaluating the whole spectrum of different tumor biomarkers to properly assess the therapeutic response and identify and interpret the therapy-induced changes in the tumor physiology

Oral administration of the KATP channel opener diazoxide ameliorates disease progression in a murine model of multiple sclerosis

Background Multiple Sclerosis (MS) is an acquired inflammatory demyelinating disorder of the central nervous system (CNS) and is the leading cause of nontraumatic disability among young adults. Activated microglial cells are important effectors of demyelination and neurodegeneration, by secreting cytokines and others neurotoxic agents. Previous studies have demonstrated that microglia expresses ATP-sensitive potassium (KATP) channels and its pharmacological activation can provide neuroprotective and anti-inflammatory effects. In this study, we have examined the effect of oral administration of KATP channel opener diazoxide on induced experimental autoimmune encephalomyelitis (EAE), a mouse model of MS. Methods Anti-inflammatory effects of diazoxide were studied on lipopolysaccharide (LPS) and interferon gamma (IFNy)-activated microglial cells. EAE was induced in C57BL/6J mice by immunization with myelin oligodendrocyte glycoprotein peptide (MOG35-55). Mice were orally treated daily with diazoxide or vehicle for 15 days from the day of EAE symptom onset. Treatment starting at the same time as immunization was also assayed. Clinical signs of EAE were monitored and histological studies were performed to analyze tissue damage, demyelination, glial reactivity, axonal loss, neuronal preservation and lymphocyte infiltration. Results Diazoxide inhibited in vitro nitric oxide (NO), tumor necrosis factor alpha (TNF-¿) and interleukin-6 (IL-6) production and inducible nitric oxide synthase (iNOS) expression by activated microglia without affecting cyclooxygenase-2 (COX-2) expression and phagocytosis. Oral treatment of mice with diazoxide ameliorated EAE clinical signs but did not prevent disease. Histological analysis demonstrated that diazoxide elicited a significant reduction in myelin and axonal loss accompanied by a decrease in glial activation and neuronal damage. Diazoxide did not affect the number of infiltrating lymphocytes positive for CD3 and CD20 in the spinal cord. Conclusion Taken together, these results demonstrate novel actions of diazoxide as an anti-inflammatory agent, which might contribute to its beneficial effects on EAE through neuroprotection. Treatment with this widely used and well-tolerated drug may be a useful therapeutic intervention in ameliorating MS disease

A simple, reproducible method for monitoring the treatment of tumours using dynamic contrast-enhanced MR imaging

Dynamic contrast-enhanced MR imaging (DCE-MRI) may act as a biomarker for successful cancer therapy. Simple, reproducible techniques may widen this application. This paper demonstrates a single slice imaging technique. The image acquisition is performed in less than 500 ms making it relatively insensitive to respiratory motion. Data from phantom studies and a reproducibility study in solid human tumours are presented. The reproducibility study showed a coefficient of variation (CoV) of 19.1% for Ktrans and 15.8% for the initial area under the contrast enhancement curve (IAUC). This was improved to 16 and 13.9% if tumours of diameter less than 3 cm were excluded. The individual repeatability (the range within which individual measurements are expected to fall) was 30.6% for Ktrans and 26.5% for IAUC for tumours greater than 3 cm diameter. This approach to DCE–MRI image acquisition can be performed with standard clinical scanners, and data analysis is straightforward. For treatment trials with 10 patients in a cohort, the CoV implies that the method would be sensitive to a treatment effect of greater than 18%. The individual repeatability is well inside the 40% change shown to be important in clinical studies using this DCE–MRI technique

Spatiotemporal Correlations between Blood-Brain Barrier Permeability and Apparent Diffusion Coefficient in a Rat Model of Ischemic Stroke

Variations in apparent diffusion coefficient of water (ADC) and blood-brain barrier (BBB) permeability after ischemia have been suggested, though the correlation between ADC alterations and BBB opening remains to be studied. We hypothesized that there are correlations between the alteration of ADC and BBB permeability. Rats were subjected to 2 h of transient middle cerebral artery occlusion and studied at 3 and 48 h of reperfusion, which are crucial times of BBB opening. BBB permeability and ADC values were measured by dynamic contrast-enhanced MRI and diffusion-weighted imaging, respectively. Temporal and spatial analyses of the evolution of BBB permeability and ADC alteration in cortical and subcortical regions were conducted along with the correlation between ADC and BBB permeability data. We found significant increases in BBB leakage and reduction in ADC values between 3 and 48 h of reperfusion. We identified three MR tissue signature models: high Ki and low ADC, high Ki and normal ADC, and normal Ki and low ADC. Over time, areas with normal Ki and low ADC transformed into areas with high Ki. We observed a pattern of lesion evolution where the extent of initial ischemic injury reflected by ADC abnormalities determines vascular integrity. Our results suggest that regions with vasogenic edema alone are not likely to develop low ADC by 48 h and may undergo recovery

Does visual cortex lactate increase following photic stimulation in migraine without aura patients? A functional 1H-MRS study

Proton magnetic resonance spectroscopy (1H-MRS) has been used in a number of studies to assess noninvasively the temporal changes of lactate (Lac) in the activated human brain. Migraine neurobiology involves lack of cortical habituation to repetitive stimuli and a mitochondrial component has been put forward. Our group has recently demonstrated a reduction in the high-energy phosphates adenosine triphosphate (ATP) and phosphocreatine (PCr) in the occipital lobe of migraine without aura (MwoA) patients, at least in a subgroup, in a phosphorus MRS (31P-MRS) study. In previous studies, basal Lac levels or photic stimulation (PS)-induced Lac levels were found to be increased in patients with migraine with aura (MwA) and migraine patients with visual symptoms and paraesthesia, paresia and/or dysphasia, respectively. The aim of this study was to perform functional 1H-MRS at 3 T in 20 MwoA patients and 20 control subjects. Repetitive visual stimulation was applied using MR-compatible goggles with 8 Hz checkerboard stimulation during 12 min. We did not observe any significant differences in signal integrals, ratios and absolute metabolite concentrations, including Lac, between MwoA patients and controls before PS. Lac also did not increase significantly during and following PS, both for MwoA patients and controls. Subtle Lac changes, smaller than the sensitivity threshold (i.e. estimated at 0.1–0.2 μmol/g at 3 T), cannot be detected by MRS. Our study does, however, argue against a significant switch to non-aerobic glucose metabolism during long-lasting PS of the visual cortex in MwoA patients

Magnetic resonance imaging phantoms for quality-control of myocardial T1 and ECV mapping: specific formulation, long-term stability and variation with heart rate and temperature

Background: Magnetic resonance imaging (MRI) phantoms are routinely used for quality assurance in MRI centres; however their long term stability for verification of myocardial T1/ extracellular volume fraction (ECV) mapping has never been investigated. Methods: Nickel-chloride agarose gel phantoms were formulated in a reproducible laboratory procedure to mimic blood and myocardial T1 and T2 values, native and late after Gadolinium administration as used in T1/ECV mapping. The phantoms were imaged weekly with an 11 heart beat MOLLI sequence for T1 and long TR spin-echo sequences for T2, in a carefully controlled reproducible manner for 12 months. Results: There were only small relative changes seen in all the native and post gadolinium T1 values (up to 9.0 % maximal relative change in T1 values) or phantom ECV (up to 8.3 % maximal relative change of ECV, up to 2.2 % maximal absolute change in ECV) during this period. All native and post gadolinium T2 values remained stable over time with <2 % change. Temperature sensitivity testing showed MOLLI T1 values in the long T1 phantoms increasing by 23.9 ms per degree increase and short T1 phantoms increasing by 0.3 ms per degree increase. There was a small absolute increase in ECV of 0.069 % (~0.22 % relative increase in ECV) per degree increase. Variation in heart rate testing showed a 0.13 % absolute increase in ECV (~0.45 % relative increase in ECV) per 10 heart rate increase. Conclusions: These are the first phantoms reported in the literature modeling T1 and T2 values for blood and myocardium specifically for the T1mapping/ECV mapping application, with stability tested rigorously over a 12 month period. This work has significant implications for the utility of such phantoms in improving the accuracy of serial scans for myocardial tissue characterisation by T1 mapping methods and in multicentre work