Nonlinear wave-wave interactions in the brain.

Neural field theory of the corticothalamic system is used to analyze nonlinear wave-wave interactions in steady state visual evoked potential responses. The nonlinear power spectrum is analytically calculated by convolving the linear power spectrum with itself and other factors. Periodic sine and square wave stimuli are used to generate steady state visual evoked potential responses and to study stimulus-driven nonlinear corticothalamic dynamic interactions. Moreover, we use dual sine drives to analyze the driven dynamics. Numerical analysis shows that the nonlinear power spectrum embodies key nonlinear features, including harmonic and subharmonic generation, entrainment of the alpha rhythm to periodic stimuli at the drive frequency, sum and difference frequencies due to wave-wave coalescence and decay. Further, the scaling properties of the key phenomena observed in nonlinear interactions are studied, verifying some of the theoretical predictions for these being generated by three-wave processes.

Nonlinear harmonic generation in the corticothalamic system.

Neural field theory of the corticothalamic system is applied to quantitatively analyze harmonic generation in normal sleep and wake states. The linear power spectrum is derived analytically via the transfer function and is then convolved with itself and other factors to calculate the nonlinear power spectrum analytically via a recent perturbation expansion. Analysis shows that strong spectral peaks generate a harmonic at twice the original frequency with peak power proportional to the square of that of the original peak. Fits to the data enable absolute normalization to be determined, with the conclusion that the experimentally observed spindle harmonic peak is nonlinear. Using this normalization, the same analysis is applied to the wake state and nonlinear contributions to the alpha and beta peaks are quantified.

Subchondral tibial bone texture predicts the incidence of radiographic knee osteoarthritis: data from the Osteoarthritis Initiative.

OBJECTIVES: To evaluate whether trabecular bone texture (TBT) parameters measured on computed radiographs (CR) could predict the onset of radiographic knee osteoarthritis (OA). MATERIALS AND METHODS: Subjects from the Osteoarthritis Initiative (OAI) with no sign of radiographic OA at baseline were included. Cases that developed either a global radiographic OA defined by the Kellgren-Lawrence (KL) scale, a joint space narrowing (JSN) or tibial osteophytes (TOS) were compared with the controls with no changes after 48 months of follow-up. Baseline bilateral fixed flexion CR were analyzed using a fractal method to characterize the local variations. The prediction was explored using logistic regression models evaluated by the area under the receiver operating characteristic curves (AUC). RESULTS: From the 344 knees, 79 (23%) developed radiographic OA after 48 months, 44 (13%) developed progressive JSN and 59 (17%) developed osteophytes. Neither age, gender and BMI, nor their combination predicted poorer KL (AUC 0.57), JSN or TOS (AUC 0.59) scores. The inclusion of the TBT parameters in the models improved the global prediction results for KL (AUC 0.69), JSN (AUC 0.73) and TOS (AUC 0.71) scores. CONCLUSIONS: Several differences were found between the models predictive of three different outcomes (KL, JSN and TOS), indicating different underlying mechanisms. These results suggest that TBT parameters assessed when radiographic signs are not yet apparent on radiographs may be useful in predicting the onset of radiological tibiofemoral OA as well as identifying at-risk patients for future clinical trials.

Subchondral tibial bone texture analysis predicts knee osteoarthritis progression: data from the Osteoarthritis Initiative: Tibial bone texture & knee OA progression.

OBJECTIVES: To examine whether trabecular bone texture (TBT) parameters assessed on computed radiographs could predict knee osteoarthritis (OA) progression. METHODS: This study was performed using data from the Osteoarthritis Initiative (OAI). 1647 knees in 1124 patients had bilateral fixed flexion radiographs acquired 48 months apart. Images were semi-automatically segmented to extract a patchwork of regions of interest (ROI). A fractal texture analysis was performed using different methods. OA progression was defined as an increase in the joint space narrowing (JSN) over 48 months. The predictive ability of TBT was evaluated using logistic regression and receiver operating characteristic (ROC) curve. An optimization method for features selection was used to reduce the size of models and assess the impact of each ROI. RESULTS: Fractal dimensions (FD's) were predictive of the JSN progression for each method tested with an area under the ROC curve (AUC) up to 0.71. Baseline JSN grade was not correlated with TBT parameters (R < 0.21) but had the same predictive capacity (AUC 0.71). The most predictive model included the clinical covariates (age, gender, body mass index (BMI)), JSN and TBT parameters (AUC 0.77). From a statistical point of view we found higher differences in TBT parameters computed in medial ROI between progressors and non-progressors. However, the integration of TBT results from the whole patchwork including the lateral ROIs in the model provided the best predictive model. CONCLUSIONS: Our findings indicate that TBT parameters assessed in different locations in the joint provided a good predictive ability to detect knee OA progression.