We develop a method of magnetic resonance (MR) image analysis able to provide parameter(s) sensitive to bone microarchitecture changes in aging, and to osteoporosis onset and progression. The method has been built taking into account fractal properties of many anatomic and physiologic structures. Fractal lacunarity analysis has been used to determine relevant parameter(s) to differentiate among three types of trabecular bone structure (healthy young, healthy perimenopausal, and osteoporotic patients) from lumbar vertebra MR images. In particular, we propose to approximate the lacunarity function by a hyperbola model function that depends on three coefficients, alpha, beta, and gamma, and to compute these coefficients as the solution of a least squares problem. This triplet of coefficients provides a model function that better represents the variation of mass density of pixels in the image considered. Clinical application of this preliminary version of our method suggests that one of the three coefficients, beta, may represent a standard for the evaluation of trabecular bone architecture and a potentially useful parametric index for the early diagnosis of osteoporosis.

Osteoporosis represents one major health condition for our growing elderly population. It accounts for severe morbidity and increased mortality in postmenopausal women and it is becoming an emerging health concern even in aging men. Screening of the population at risk for bone degeneration and treatment assessment of osteoporotic patients to prevent bone fragility fractures represent useful tools to improve quality of life in the elderly and to lighten the related socio-economic impact. Bone mineral density (BMD) estimate by means of dualenergy X-ray absorptiometry is normally used in clinical practice for osteoporosis diagnosis. Nevertheless, BMD alone does not represent a good predictor of fracture risk. From a clinical point of view, bone microarchitecture seems to be an intriguing aspect to characterize bone alteration patterns in aging and pathology. The widening into clinical practice of medical imaging techniques and the impressive advances in information technologies together with enhanced capacity of power calculation have promoted proliferation of new methods to assess changes of trabecular bone architecture (TBA) during aging and osteoporosis. Magnetic resonance imaging (MRI) has recently arisen as a useful tool to measure bone structure in vivo . In particular, high-resolution MRI techniques have introduced new perspectives for TBA characterization by non-invasive non-ionizing methods. However, texture analysis methods have not found favor with clinicians as they produce quite a few parameters whose interpretation is difficult. The introduction in biomedical field of paradigms, such as theory of complexity, chaos, and fractals, suggests new approaches and provides innovative tools to develop computerized methods that, by producing a limited number of parameters sensitive to pathology onset and progression, would speed up their application into clinical practice. Complexity of living beings and fractality of several physio-anatomic structures suggest fractal analysis as a promising approach to quantify morphofunctional changes in both aging and pathology. In this particular context, fractal lacunarity seems to be the proper tool to characterize TBA texture as it is able to describe both discontinuity of bone network and sizes of bone marrow spaces, whose changes are an index of bone fracture risk. In this paper, an original method of MRI texture analysis, based on TBA fractal lacunarity is described and discussed in the light of new perspectives for early diagnosis of osteoporotic fractures.

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Alzheimer’s disease (AD) represents one major health concern for our growing elderly population. It accounts for increasing impairment of cognitive capacity followed by loss of executive function in late stage. AD pathogenesis is multifaceted and difficult to pinpoint, and understanding AD etiology will be critical to effectively diagnose and treat the disease. An interesting hypothesis concerning AD development postulates a cause-effect relationship between accumulation of mitochondrial DNA (mtDNA) mutations and neurodegenerative changes associated with this pathology. Here we propose a computerized method for an easy and fast mtDNA mutations-based characterization of AD. The method has been built taking into account the complexity of living being and fractal properties of many anatomic and physiologic structures, including mtDNA. Dealing with mtDNA mutations as gaps in the nucleotide sequence, fractal lacunarity appears a suitable tool to differentiate between aging and AD. Therefore, Chaos Game Representation method has been used to display DNA fractal properties after adapting the algorithm to visualize also heteroplasmic mutations. Parameter β from our fractal lacunarity method, based on hyperbola model function, has been measured to quantitatively characterize AD on the basis of mtDNA mutations. Results from this pilot study to develop the method show that fractal lacunarity parameter β of mtDNA is statistically different in AD patients when compared to age-matched controls. Fractal lacunarity analysis represents a useful tool to analyze mtDNA mutations. Lacunarity parameter β is able to characterize individual mutation profile of mitochondrial genome and appears a promising index to discriminate between AD and aging.

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