Application of fractal dimension mapping in the MR assessment of microvasculature

Graeme M Wardlaw, McMaster University


It was hypothesised that quantification of the temporal structure of BOLD signals could help characterise the microvascular state. Temporal assessment was done using a fractal dimension (FD) approach which scales the signal between "periodic" and "chaotic". Signal FD values approaching 1.0 are suggested to have a high degree of periodicity. In physiological applications this may be due to low frequency vasoactive fluctuations or increased blood flow pulsatility. Conversely, FD values approaching 1.5 indicate uncorrelated or random signal change. Mapping FD values over an entire image provides unique image contrast and a potential alternative to dynamic Gadolinium contrast-enhanced methods. ^ To test the sensitivity of BOLD FD mapping to microvascular change, healthy muscle, pre and post-exercise was assessed, as exercise is known to induce vasodilation. In this study BOLD FD showed statistically significant shifts in the medial gastrocnemius following exercise at 50% of voluntary maximum. Based on a relative dispersion technique, FD was noted to have two components where values were calculated at slower (4-64s) and faster (0.25-2s) timescales. Statistically significant shifts were observed for both components, comparing pre vs. post exercise, where the shift direction (− or +) depended on pre-exercise conditions (mean BOLD). Based on this result it was postulated that BOLD signal temporal dynamics over different timescales could reflect differences in fast and slow twitch oxidative metabolism. ^ Following assessment of healthy muscle tissue, aberrant tumour microvasculature was investigated using BOLD FD mapping. It was found that FD maps identified intra-tumour regions with lower FD, or increased BOLD signal power at low frequencies (0.1 Hz). From previous studies on murine tumours and human brain hypercapnia BOLD signals show distinctive periodicity, and the associated low frequency power directly correlates with tumour blood oxygenation and flow measurements. Thus, in our study BOLD FD mapping likely identifies intra-tumour regions of potentially increased vasoactivity. ^ To more directly determine the relationship between BOLD FD and microvasculature a simple dceMRI logistic T2* weighted gadolinium bolus response curve model was developed. Images of logistic curve response parameters were generated from a small cohort of patients with clinically diagnosed rectal carcinoma. When compared to mean BOLD signal (qualitative indicator of overall flow/oxygenation) good correlation was noted in all cases between the baseline perfusion parameter P1 and wash-out (i.e. trailing slope) parameter, P5. Regions of elevated signal attenuation (wash-in) as exhibited by logistic parameter P4 were within tumour boundaries and close to elevated regions of increased wash-out (P5). In one case of complete response to adjuvant chemotherapy and radiation treatment, mean BOLD, logistic P1, P4 (contrast wash-in or signal attenuation constant) and P5 were almost juxtaposed. This overlap may indicate a more oxygenated environment with relatively mature vasculature and hence complete response to therapy (i.e. tumour response to adjuvant radiation therapy is directly related to oxygenation). ^ When BOLD FD maps were compared to logistic bolus response curve parametric maps regions of low FD were observed in regions of elevated rate of contrast attenuation or wash-in (P4). Furthermore, these also appeared in regions of highest signal amplitude decrease, as shown by others to be related to vascular hyperplasia, malignancy and approximate blood volume. Since parameters P 4 and P5 are typically related, correlation of low FD regions with areas of elevated contrast wash-out, or trailing slope, was also noted. Other less remarkable, yet notable correlations were seen in FD vs. time to minimum and percentage baseline signal loss. High grade, aggressive tumours have been associated with elevated baseline signal loss, hence again linking low BOLD FD with higher tumour vasoactivity. (Abstract shortened by UMI.)^

Subject Area

Biophysics, Medical

Recommended Citation

Graeme M Wardlaw, "Application of fractal dimension mapping in the MR assessment of microvasculature" (January 1, 2010). ETD Collection for McMaster University. Paper AAINR74086.