Pulse-density modulation | EPFL Graph Search

Pulse-density modulation, or PDM, is a form of modulation used to represent an analog signal with a binary signal. In a PDM signal, specific amplitude values are not encoded into codewords of pulses of different weight as they would be in pulse-code modulation (PCM); rather, the relative density of the pulses corresponds to the analog signal's amplitude. The output of a 1-bit DAC is the same as the PDM encoding of the signal. In a pulse-density modulation bitstream, a 1 corresponds to a pulse of positive polarity (+A), and a 0 corresponds to a pulse of negative polarity (−A). Mathematically, this can be represented as where x[n] is the bipolar bitstream (either −A or +A), and a[n] is the corresponding binary bitstream (either 0 or 1). A run consisting of all 1s would correspond to the maximum (positive) amplitude value, all 0s would correspond to the minimum (negative) amplitude value, and alternating 1s and 0s would correspond to a zero amplitude value. The continuous amplitude waveform is recovered by low-pass filtering the bipolar PDM bitstream. A single period of the trigonometric sine function, sampled 100 times and represented as a PDM bitstream, is: 0101011011110111111111111111111111011111101101101010100100100000010000000000000000000001000010010101 Two periods of a higher frequency sine wave would appear as: 0101101111111111111101101010010000000000000100010011011101111111111111011010100100000000000000100101 In pulse-density modulation, a high density of 1s occurs at the peaks of the sine wave, while a low density of 1s occurs at the troughs of the sine wave. Delta-sigma modulation A PDM bitstream is encoded from an analog signal through the process of a 1-bit delta-sigma modulation. This process uses a one-bit quantizer that produces either a 1 or 0 depending on the amplitude of the analog signal. A 1 or 0 corresponds to a signal that is all the way up or all the way down, respectively. Because in the real world, analog signals are rarely all the way in one direction, there is a quantization error, the difference between the 1 or 0 and the actual amplitude it represents.

Dopaminergic modulation of cortical motor network lateralization

Michael Herzog, Bogdan Draganski, Maya Anna Jastrzebowska, Lester Melie Garcia, Renaud Marquis

Introduction Unilateral movements are primarily processed in contralateral cortical and subcortical areas and additionally in ipsilateral cerebellum, leading to an asymmetric pattern of neural activation. Decrease of lateralization is characteristic of aging (Naccarato et al., 2006; Wu et al., 2005), and disease, for example, in unilateral brain lesions or stroke (Carr et al., 1993; Rehme et al., 2011) and Parkinson's disease (PD; Wu et al., 2015). The explanation for imbalanced lateralization in drug-naive PD is an adaptive compensation, compatible with the finding that PD-associated deficient input from cortico-subcortical circuits is compensated by reduced cortical inhibition and increased cortical facilitation (Blesa et al., 2017). Here, we investigated the effect of dopamine depletion and substitution on cortical motor lateralization, with the hypothesis that lateralization decreases in advanced PD and that administration of levodopa, at least to a certain extent, reinstates lateralization. Methods We used fMRI to study motor activation in advanced PD patients and in healthy controls (HC) during unilateral upper and lower limb movements. Ten right-handed, left side symptom-dominant PD patients were tested in pseudo-randomized order after intake of their usual dopaminergic medication – 'ON' state – and after withdrawal of medication – 'OFF' state. Eighteen right-handed age-matched HC participated in a single session. We quantified activation lateralization using the average laterality index (AveLI; Matsuo et al., 2012) in three cortical motor regions of interest (ROIs): primary motor cortex (M1), supplementary motor area (SMA) and premotor cortex (PMC), during the four movement conditions. We compared AveLI between group pairs (PD OFF vs. HC, PD ON vs. HC, PD OFF vs. PD ON) within each ROI and movement condition. We estimated the effective connectivity between ROIs using bilinear dynamic causal modeling (DCM; Friston et al., 2003) and developed a measure to quantify the lateralization of the resulting connectivity networks to compare between groups. By constructing a group level parametric empirical Bayes (PEB) model (Friston et al., 2016) over all the subjects and conducting a search over nested models, we compared DCM parameter estimates between groups, thus providing the potential link between changes in motor lateralization and connectivity. Results In line with our predictions, motor activation lateralization as estimated with the AveLI showed a trend towards decrease in the PD OFF group compared to HC, in all three ROIs during left hand movement and in M1 during left foot movement (Fig. 1). Between-group differences were observed solely in conditions corresponding to movement of the more affected body side. Contrary to our hypothesis, dopamine substitution did not reinstate lateralization – in fact, AveLI in the PD ON group closely resembled that of the PD OFF group. Connectivity lateralization of input-specific modulation (DCM.B) networks was significantly lower in all conditions in the PD group as compared to HC. While on the body side more affected by PD, differences were found for both PD OFF and PD ON, input-specific modulation related to the less affected side was more altered in PD ON. PEB analysis revealed qualitatively more between-group differences in input-specific modulation on the more affected PD side and included many interhemispheric connections (Fig. 2). Conclusions Decreased lateralization is not only present in drug-naïve PD patients (Wu et al., 2015) but also in dopa-treated patients. Acute dopamine modulation does not alter lateralization. Decreased lateralization is evident in both fMRI activation amplitudes (as estimated with AveLI) and effective connectivity (as demonstrated through the DCM analysis).

2018

Dopaminergic modulation of cortical motor network lateralization

Michael Herzog, Bogdan Draganski, Maya Anna Jastrzebowska, Lester Melie Garcia, Renaud Marquis

2018