Fractal discrimination of random fractal aggregates and its application in biomarker analysis for blood coagulation

A recent rheological study has established that the fractal dimension, d _f, of an incipient clot, formed at the Gel Point (sol-gel transition) of coagulating blood is a significant new biomarker of haemostasis. In whole healthy blood, incipient clots show a clearly defined value of d _f = 1.7 within a narrow range, which represents a new 'healthy index' for normal clotting. The addition of unfractionated heparin significantly prolongs the onset of clot formation with a corresponding reduction of d _f as a function of heparin dose. However, as clots mature they exhibit (i) an expected increase in d _f and (ii) a significant increase to spread of these values, i.e. d _f's in the range 2.0-2.5, limiting the use of d _f as a discriminant of clot microstructure. The present study, details how and why the spectral dimension, d _s, can be used to accommodate this shortcoming and allow discrimination of mature forms of clot microstructure in indistinguishable in terms of their fractal dimension. To elucidate why d _s permits discrimination a numerical experiment was conducted on computationally generated random fractal aggregates (RFAs) with a priori set value of d _f. Starting from RFAs with a d _f of 1.7, mature RFAs are evolved from these incipient templates by two differing growth processes achieving a final d _f of 2.1. Fractal and statistical analysis of the mature RFAs reveals, for the first time, that their differing internal structure is manifest in the magnitude of d _s. The potential clinical significance of these findings is discussed in terms of the possibility of exploiting the incipient clot's ability to template the internal arrangement of the mature clot to better predict long term clot susceptibility to lysis.