# Fractal Features of Muscle to Quantify Fatty Infiltration in Aging and Pathology
###### Abstract  
The physiological loss of muscle mass and strength with aging is referred to as \"sarcopeniaa\", whose combined effect with osteoporosis is a serious threat to the elderly, accounting for decreased mobility and increased risk of falls with consequent fractures. In previous studies, we observed a high degree of inter-individual variability in paraspinal muscle fatty infiltration, one of the most relevant indices of muscle wasting. This aspect led us to develop a computerized method to quantitatively characterize muscle fatty infiltration in aging and diseases. Magnetic resonance images of paraspinal muscles from 58 women of different ages (age range of 23-85 years) and physio-pathological status (healthy young, pre-menopause, menopause, and osteoporosis) were used to set up a method based on fractal-derived texture analysis of lean muscle area (contractile muscle) to estimate muscle fatty infiltration. In particular, lacunarity was computed by parameter \(\beta\) from the GBA (gliding box algorithm) curvilinear plot fitted by our hyperbola model function. Succolarity was estimated by parameter \(\mu\), for the four main directions through an algorithm implemented with this purpose. The results show that lacunarity, by quantifying muscle fatty infiltration, can discriminate between osteoporosis and healthy aging, while succolarity can separate the other three groups showing similar lacunarity. Therefore, fractal-derived features of contractile muscle, by measuring fatty infiltration, can represent good indices of sarcopenia in aging and disease. Keywords:aging; biocomplexity; biomarkers; fractal; fatty infiltration; lacunarity; magnetic resonance imaging; muscle; sarcopenia; succolarity +
Footnote †: journal: Medical  
recently, sarcopenia has been defined as \"a syndrome characterized by a progressive and generalized loss of skeletal muscle mass and strength with a risk of adverse outcomes such as physical disability, poor quality of life and death\" [10; 11]. Past the age of 50 years, the rate of muscle loss ranges within 1-2% a year. It accounts for 25% and 40% sarcopenia people after the age of 70 and 80 years, respectively [12; 13]. The term myopia has been proposed to define a clinically relevant degree of muscle wasting characterized by a rapid loss of muscle mass in a short time (i.e., more than 5% in 6-12 months) associated with harmed functional capacity and increased risk of morbidity and mortality [14]. Several aspects other than muscle size lead to the loss of physical activity strength in the etiology of disability. Both neurological and muscular factors lead to the decline of muscle strength [15; 16; 17; 18]: muscle atrophy, reduced contractile quality induced by impaired myofibrillar machinery, and fatty infiltration of contractile muscle [3; 4; 15; 19]. Among several techniques proposed for muscle assessment [20], three main medical imaging systems are normally employed in the evaluation of muscle mass variation with aging: computer tomography (CT), magnetic resonance imaging (MRI), and dual-energy X-ray absorptiometry (DXA). Although CT and MRI represent the gold standards for muscle mass estimate, their application has been limited to the research field, while DXA has been chosen for clinical use [21; 22]. In fact, DXA, in spite of supplying surrogate estimates of both regional and whole-body skeletal muscle mass, is widely diffused as it is cheap and enables limited radiation exposure. Ultrasonography (US) is another imaging technique widely used for qualitative and quantitative assessment of muscle. US is a portable, non-ionizing and non-invasive cheap technique for muscle properties' estimation showing positive correlation with muscle measurements obtained by the other imaging techniques. Nevertheless, US presents the limitations of poor reproducibility and accuracy [23]. Both CT and MRI represent imaging techniques very precise in differentiating fat from other soft tissues; however, MRI has been recognized as the best tool for fatty infiltration assessment [24].