Fancies and Fallacies of Spatial Sampling With Transcranial Magnetic Stimulation (TMS)

Frontiers in Psychology

Luigi Cattaneo¹ 

关键词: magnetic stimulation;    non-invasive brain stimulation;    aliasing;    anti-aliasing;    Nyquist;    spatial resolutions;    sampling frequency;    brain mapping;   

DOI  :  10.3389/fpsyg.2018.01171

学科分类：心理学（综合）

来源: Frontiers

【 摘 要 】

Once established that spatial sampling with TMS requires dense grids of TMS spots, a spontaneous question arises: how dense is dense? In other words, what is the adequate spatial sampling frequency? We know there is a maximal sampling frequency corresponding to around 1.5 spot/cm, that is dictated by spatial resolution that is inherent to TMS, but the highest sampling frequency I not necessary more efficient. In fact, there is no correct answer, it depends on the maximal signal's spatial frequency. The brain, up to the level of single cortical columns, is rich in spatial frequencies so high that it can be assimilated for our purposes to an analogic image. It is impossible to use TMS sampling frequencies adequate to the fine granularity of brain functions. The solution to this apparently unsolvable problem is band-limiting the signal. Let us get some help on this discussion on spatial sampling from an extraordinarily elaborate analogic picture, Pieter Bruegel the elder's “Netherlandish proverbs” (Figure ​(Figure1A,1A, left), that I will use as an analogy of the brain surface that we want to map. A hypothetical grid of the painting's coverage at a given sampling frequency is represented in Figure ​Figure1A,1A, right. Remember once more that TMS does not produce data by itself, we must therefore choose what characteristics of the signal (painting) to sample. Figure ​Figure1B1B represents 3 examples of sampling choices: animals (including humans), proverbs with positive meaning (such as “to have the roof tiled with tarts”, versus negative proverbs such as “to be a pillar-biter”) and buildings. It is visually immediate that the three categories of interest have a different spatial frequency in the native space (left row). The spatial sampling (middle row) is then used to reconstruct the image (right row). The goodness of the sample-and-reconstruct procedure is testified by how similar the reconstructed image is to the raw image. It is evident that the procedure fails in the case of animals but is acceptable in the case of positive proverbs and buildings. However, the original image did not change (the painting). What changed was the category that we decided to sample, the question that was asked at every spot: “is there an animal in this spot?” or “is there a positive proverb in this spot?” or “is there a building in this spot.” Let us now switch from the pictorial analogy to the TMS/brain system. TMS does not produce data by itself, the type of data is up to the experimenter's choice and depends strictly on the behavioral measurement. For example, I may choose to record response times (RTs) to a somatosensory stimulus to the left IV finger or to the whole upper limb. In the first case, even the maximal TMS sampling frequency will be probably insufficient for the signal's spatial frequency. In the second case, a 0.5 spots/cm sampling frequency will probably be optimal. Concluding, the spatial frequency of the brain signal is dependent exclusively on the behavioral task that I chose to explore the effects of TMS. Our choice of behavioral measures IS an operation of spatial low-pass filtering.

【 授权许可】

CC BY