Answer
The biggest advantage of all of the listed methods is that they are relatively non-invaseive and so usable in human subjects, unlike our typical approaches in animal neuroscience, electrophysiology and calcium imaging.
Positron-emission tomography (PET) imaging has high spatial resolution but limited temporal resolution, high cost, and severe safety restrictions.
Electroencephalography (EEG) has excellent temporal resolution, low cost and no real safety restrictions, but poor spatial resolution and high noise.
Trans-cranial magnetic stimulation (TMS), unlike the other two methods, is an experimental manipulation, rather than a recording technique. As a reversible, time- and space-resolved manipulation of human neural function, it is invaluable. It is dogged, however, by safety and reproducibility concerns, and interpretation of results is challenging.
PET Imaging
PET Principles
The "P" in PET stands for positron – the antimatter version of an electron. PET works by introducing a radioactive isotope into the body. This isotope decays by emitting a positron, which almost immediately annihilates with an electron to produce a burst of gamma radiation – two high energy photons that have shorter wavelength even than X-Rays.
Because these photons travel in opposite directions from the annihilation event, these bursts can be localized precisely using radiation detectors placed on either side of the subject. The time difference between the two collisions, combined with the speed of light, can be used to find the spatial location of the annihilation event. As you might guess, this requires very precise timing – finer than nanoseconds!
This approach was pioneered in the detection and localization of cancers. The radioactive isotope is bound to a modified glucose molecule that can be taken up by cells but neither fully metabolized nor excreted. Because cancer cells typically get their energy from anaerobic glycolysis rather than the oxidative phosophorylation pathway, they consume glucose at a higher rate and so accumulate large quantitites of radioactive glucose. Tumors thus show up as "radiation hotspots".
A few of the concerns with PET should already be obvious. The detection equipment is bulky and has very tight engineering requirements, and so is expensive. Radioactive isotopes are also expensive and hard to come by. More subtly, there is a tradeoff between the shelf-life of the isotope and its expense: isotopes that decay on an appropriate time-scale to generate good images (many many events per second with a reasonable dose), will also decay rapidly if left sitting around. In the most extreme cases, usable quantities are only available "hot out of the oven" from a particle accelerator, which has obvious cost, complexity, and security issues.
Lastly, the generated gamma radiation can damage tissue, ironically placing the subject at increased risk of cancer. For a standard individual PET session, this is equivalent to two CAT scans, or one year in living at high altitude, or eating 140,000 bananas (don't try this at home!). Since basic scientific research is not medically necessary, multiple exposures are considered unethical, and data collection suffers as a result.
PET for Neuroscience
The remaining concerns about PET imaging are specific to its neuroscientific applications. For functional PET imaging, we are interested not in learning about spatial structure of tissue, but in learning about spatio-temporal patterns of neural activity. Functional PET, then, takes advantage of the same hemodynamic phenomena that are used for BOLD fMRI. In short, the vasculature of the brain responds fairly rapidly to changes in neural activity by changing blood flow, bringing oxygen and glucose to highly active neurons on a time scale of a few hundred milliseconds. This blog post on fMRI describes this process in detail.
For cognitive science applications of PET, this presents several issues:
- The signal is indirect.
As neuroscientists, we care about the behavior of neurons, since they are the functional unit of the brain. Vascular responses are epiphenomenal to neural function, just as the sounds of your car's engine are epiphenomenal to your car's function, and learning about function from an epiphenomenon is dangerous – consider what an auditory analysis of car function would tell you about a Prius or a Tesla.
- The signal is pooled across neurons.
The vasculature appears to respond at approximately the scale of a cortical column, or a square millimeter running perpendicular from the surface of the cortex to the interior. This corresponds to millions or hundreds of millions of neurons, and at best PET tells you the average activity level of this collection. In practice, PET spatial resolution is several times lower.
- The signal is smeared in time.
The hemodynamic response takes some time, meaning that our indirect, pooled signal is spread out by, or convolved with some wonky function. This signal must then be transmitted by changes in the radioactive decay pattern of our isotope, leading to another convolution. The result is poor temporal resolution, especially for discrete or "phasic" events.
Of course, every technique has its drawbacks – our gold-standard neuroscience techniques, like electrophysiology and calcium imaging, are total non-starters for human research, since they involve tissue damage. That doesn't mean they're bad techniques, it just means there are some questions they can answer, and some questions that they cannot.
PET used to be the best technique for observing hemodynamic responses in human brains, and so could be used to observe columnar-scale phenomena, like the retinal map in early visual cortex. This role has since been usurped by fMRI.
Unlike MRI, PET can be naturally combined with chemical techniques to determine both structure and chemistry at the same time. For example, if we attach our radioactive isotope to a neurotransmitter analogue that binds receptors without activating them, we can generate a map of receptor densities, helping us discover large-scale neurochemical networks in living humans.
EEG
Electroencephalography, as an examination of its etymological roots would show, involves measuring electrical activity on the head. Small electrodes are attached to the scalp, and the electrical fields generated by large networks of neurons firing relatively synchronous action potentials are detected.
EEG then, is a sort of distant cousin of extracellular electrophysiology, especially measurement of the local field potential. In all cases, the flow of ions causes distortions of the electric field that can be detected at a distance.
Some of the benefits of the invasive techniques transfer to electrophysiology. We're no longer considering an indirect signal, like blood flow in BOLD fMRI, but are instead looking at the electrical activity of neurons that leads to synaptic release and the cellular communication that underlies computation in the brain. Because these electrical changes are quick, we can get very fine time resolution, on the order of milli- or even micro-seconds.
Also unlike fMRI and PET, EEG equipment is cheap and easy to use: no multi-Tesla magnets or antimatter-producing radioisotopes required, just wires and signal processing gear.
However, EEG is plagued by an inverse problem. For any distribution of electrical field strengths detected on the scalp, there is a literal infinity of possible spatial patterns of electrical activity that could have generated it. This is exacerbated by the fact that the skull is a poor conductor, and so current tends to "splash off of it" and flow laterally, substantially reducing any potential spatial localization. Clever statistical models can make use of Bayes' Rule to try to get around this fact, but any added complexity in an analysis pipeline is bad, especially if it involves inferring a generative model.
TMS
Transcranial magnetic stimulation differs from our previous two methods of concern in that it is not a recording technique, but rather a manipulation, making its inclusion here somewhat strange. But I don't write the questions, I just answer them.
As discussed above under EEG, the electrical activity of neurons generates a fluctuating electrical field. You might wonder about the opposite direction: if we apply a fluctuating eletrical field to neurons, can we change their behavior?
The answer is yes, and the way we do that is with TMS. By running current through cleverly designed loopy wires, we can either activate or deactivate large groups of neurons without breaking the skin.
The potential importance of a non-invasive manipulation can't be over-stated. In short, any experiment based solely on observation falls prey to the fact that correlation does not equal causation, and any observed relation between two events that we observe could always be explained by another unobserved variable. For a bit on the math behind this, check out the section on Simpson's paradox in this blog post from Michael Nielsen on visualization.
If, however, we can directly change the putative causes we are tracking, then we can more confidently state a directional, causal relationship, passing over Hume's objections with a glance at Goodman's resolution of the problem of induction. TMS, by allowing us to modify human brain activity, rather than merely observe it, grants us this power.
With great power, of course, comes great responsibility. Any experimental manipulation of humans must be confirmed to be both temporary and safe. On both counts, there is much hope that TMS is superior to older methods of manipulation, like injecting pharmacological agents (click here for a neat video!). Despite research to the contrary, however, many psychologists and neuroscientists remain unconvinced that TMS is safe and reversible.
On a more direct scientific note, it remains unclear just exactly how TMS works, and so the results can be difficult to interpret mechanistically. Also, anatomical variations and monetary concerns lead most TMS labs to simply move the coils around by hand until they get the desired effect, which leads to difficulty establishing reproducibility, as is always the case when a critical piece of the experimental apparatus is the experimenter herself.