Difference between SPECT en PET

External radiation: X-ray, CT-scan

Internal radiation: SPECT or PET. This is also called ‘scintigraphy’.

SPECT: Single photon emission Computed tomography. An example is bone scintigraphy, where Technetium is utilized. This is a process based on gamma-decay, or the shooting out of a photon by decay. It is also used in the lungs for lung scintigraphy(ventilation/perfusion scan), to determine pulmonary emboli.

SPECT: Bone scintigraphy, myocardial perfusion scan, brain scan, parathyroid scan

PET: Positron emission tomography. This is based on beta positive decay, where a proton turns into a neutron, shooting out a positron. This positron annihilates with an electron and shoots two symmetrical gamma radiation in opposition directions.

Central is nuclear decay process.

SPECT is the older, cheaper technique. It has a lower resolution and is used in cardiological medicine and finding bone laesions in cancer.

SPECT scans are primarily used to diagnose and track the progression of heart disease, such as blocked coronary arteries. There are also radiotracers to detect disorders in bone, gall bladder disease and intestinal bleeding. SPECT agents have recently become available for aiding in the diagnosis of Parkinson’s disease in the brain, and distinguishing this malady from other anatomically-related movement disorders and dementias.

The major purpose of PET scans is to detect cancer and monitor its progression, response to treatment, and to detect metastases. Glucose utilization depends on the intensity of cellular and tissue activity so it is greatly increased in rapidly dividing cancer cells. In fact, the degree of aggressiveness for most cancers is roughly paralleled by their rate of glucose utilization. In the last 15 years, slightly modified radiolabeled glucose molecules (F-18 labeled deoxyglucose or FDG) have been shown to be the best available tracer for detecting cancer and its metastatic spread in the body.

Patients are given radioactive tracers. These tracers start to decay and emit radiation

Coordinate time is the hypotenuse of the triangle created by proper time and spatial distance

Coordinate time is the hypotenuse.

Proper time is one leg and spatial distance is another leg of the triangle.

Is proper time ‘perpendicular’ to space? Using the y-dimension as a surrogate/substitute for proper time.

Since the only difference between spatial dimensions is the fact that they are perpendicular to each other, and since time is on equal footing with space, time has to perpendicular to space. A better word instead of perpendicular would be orthogonal. This perpendicularity of space and time seems mystical, but we actually defined time to be perpendicular/orthogonal to space.

The definition: The amount of distance a lightbeam has travelled perpendicular to a moving object is proportional to the amount of time that has passed for that object. So we use a perpendicular spatial dimension as a measure of time. Since we define time to be proportional to the distance light has travelled perpendicular to the motion of an object, time is per definition perpendicular to space. I hope you see that you use the perpendicular ‘y-direction’ as a surrogate or substitute for the time direction. The amount of distance light has passed per your own time is the actual time in that reference frame.

I hope I can make this more clear in a different blog post. In the mean time, an often used derivation of the spacetime-interval shows the perpendicularity I mean. You use the perpendicular space direction as a surrogate for the amount of time that has passed.

Essential derivation of special relativity

 

Gramnegatives and grampositives

Why are grampositive bacteria often part of the skin flora and why are gramnegative bacteria often part of the gut flora?

I don’t get it. Hopefully in the future I will find out.

A hyperbolic rotation stretches out and compresses the coordinates.

Since moving object path in spacetime is hyperbolically rotated compared to your own path in spacetime, its coordinates with be stretched out(time dilation) and compressed (length contraction) with regards to you. See the following.

Relativity is just the study of wordlines in spacetime

Summary of side effects of commonly used antibiotics

In general for every antibiotic the following side effects are to be expected:

1. Anafylaxis (!)
2. Superinfections with fungi, such as oral candidiasis
3. Skinreactions such as toxicodermia and eosinofilia
4. Overgrowth of clostridium difficile, resulting in serious bloody diarrhea. This is called pseudomembraneus colitis and can be treated with stopping the antibiotic and starting metronidazol or vancomycin orally

In some cases ‘drug fever’, which should be considered in prolonged fever with resolving bacterie.

Specific side effects are:

Membrane maulers (penicillins, cefalosporins, carbapenems and vancomycin):

There is crosshypersensitivity between penicillins, cefalosporins and carbapenems.

Carbapenemens: livertoxicity

Vancomycin can cause ‘red man syndrome’ and hypotension. It consists of serious itching and red skin. It results because of too fast infusion of the antibiotic. Treatment consists of stopping antibiotic, treating hypotension with fluids and vasopressors if needed and an antihistamin against the pruritus.

Protein persecutors (Aminoglycosides, tetracyclines, macrolides and clindamycin):

Aminoglycosides can cause ototoxicity, dizziness and nephrotoxicity. The serum levels need to be monitored.

Tetracyclines cannot be given to pregnant women and children because of permanent discoloration of teeth. These antibiotics are also fotosensibilizers. They can be hepatotoxic.

Macrolides give a lot of gastrointestinal side effects and heighten the risk of cardial events. They change the taste perception. They can also alter vision.

Clindamycin gives gastrointestinal side effects.

Nucleic acid nukers (TMP/SMX, chinolones, metronidazol):

TMP/SMX: They inhibit folic acid metabolism and thus should not be given to pregnant women and babies. They mildly suppress the bonemarrow. Just like tetracyclines, they are fotosensibilizers.

Chinolones can rupture the achilles tendon, especially when given in conjunction with corticosteroïds. They are nefrotoxic, hepatotoxic and also are fotosensibilizers. Don’t give in pregnant women and babies because they have effects on cartilage.

Metronidozal: specific side effects are neuropsychological such as side effects.

Simple overview of commonly used antibiotics

Membrane maulers:

The antibiotics are listed in increasing broad spectrum activity.

1. Penicillines
2. Aminopenicillines (Amoxicillin)
3. Amoxicillin with Clavulanic acid
4. Piperacillin with Tazobactam
5. Carbapenem (meropenem, iminepem)

• Vancomycin is a specific membrane mauler, against Methicillin-Resistent S. Aureus. It is commonly used against endocarditis.

If patients are indicated to use a penicillin, but are allergic, they can use cefalosporins. There are 5 generations. The first generation barely has any activity against gramnegatives, but work good against grampositives. The higher the generation, the better the activity against gramnegatives and lesser activity against grampositives.

Protein prohibitors

In no general order

• Aminoglycosides (tobramycin, gentamicin, streptomycin)
• Tetracyclines (doxycyclin, tetracyclin)
• Macrolides (azithromycin, clarithromycin, erythromycin)
• Clindamycin

They inhibit protein synthesis by interfering with the bacterial ribosomes.

Nucleic acid nukers:

1. Chinolones (ciprofloxacin, levofloxacin, moxifloxacin)
2. Trimethoprim/Sulfamethoxazol (TMP/SMX or Co-trimoxazol)
3. Metronidazol

These antibiotics interfere with parts of the nucleic acid metabolism. Chinolones target the protein that unzips DNA-strands to copy them. TMP/SMX inhibit folic acid metabolism, which is used in the synthesis of nucleic acids. Metronidazol creates free radial oxygen species that damage the DNA.

Here is a great image of all the antibacterial drugs:

The left-hand-side of the Einstein Field Equations are hard.

I do not understand the left-hand-side(LHS) of the Einsteins Field Equations (EFE).

So in my eyes it goes like this:

First understand the christoffel symbols (?)

Then define the Riemann curvature tensor with the use of the Christoffel Symbols.

Then contract the Riemann curvature tensor to get the Ricci-tensor.

Calculate the Trace of the Ricci-tensor and you get the Ricci-scalar.

Combine the Ricci-scalar, the Ricci-tensor and the Riemann curvature tensor and you can describe the spacetime curvature with the LHS of the EFE.

I don’t know how the following is included in this analysis:

1. Parallel vector transport
2. Geodetic equation
3. Equivalence principle
4. Minkowski metric

You should start with the Euclidean plane in polar coordinates. You take a vector at some point (better not the origin) and transport it parallelly to some other point. Its polar coordinates will change (do this!). Christoffel symbols describe the infinitesimal rate of such changes for the parallel transport in different directions.

 

You live at some spot in an n dimensional Riemannian manifold and have a convenient coordinate system. Each of the indexes i, j, k and l take on one of n values; there are n⁴ such combinations and as many values for Rⁱ_jkl. For each such set of values Rⁱ_jkl can be evaluated by the following simple procedure. Travel in direction k until coordinate x^k is increased by dx^k. (You choose dx^k, but see guidance at end.) The other coordinates will not have changed. Next travel indirection l for distance dx^l. Now travel backwards in the k direction but a distance −dx^k. Then once more in the direction l for distance −dx^l. You will arrive back near to where you left. That was just practice.

Now travel the same route again but carry along a vector V that initially points in the direction j with magnitude dx^j. (You choose dx^j too.) At each step in the journey do not turn V that you carry, even though the coordinates may themselves turn which will cause the coordinate description of V to change. This would be a big effect if you were walking near the North pole. There are several ways that the meaning of this can be defined which we do not explore here. When you get back compare the V you carried with a copy that you left behind. The difference between the vector you started with and the one you brought back will be a new vector with components D¹, …Dⁿ.
Rⁱ_jkl = Dⁱ/(dx^jdx^kdx^l).

You must choose the size of dx^j etc. and this is a practical tradeoff—too small and D will be too small to measure, too large and your curvature result won’t really be local. If your manifold is mathematically defined then you should let the dx’s tend to zero and take the limit.

 

 

 

 

We measure space with light and time with radioactivity

The definition of a meter is the distance a lightbeam travels in a certain time limit.

The instrument of space is light, or electromagnetic force.

The definition of a second is period of a certain amount of radioactive decay of the cesium atom.

The instrument of time is radioactive decay, or the weak force.

—————————————————————————

This means that the theory of electroweak interaction defines spacetime. This is the only interaction that defies certain symmetries I believe… Interesting.

Shortest summary of relativity

The weird conclusions of relativity originates from the observations of electromagnetic behaviour and combining these with important statements in old mechanics. What is electromagnetism?

Electric fields: An object can have electrostatic charge, which is either + or -. Opposite charges attract, like charges repel. Charges create electric fields.

Magnetic fields: A moving electrostatic charge is attracted to like charges if they move in the same way. If they move in the opposite way it is repelled. Vice versa, opposite charges repel each other magnetically when moved in the same direction and attract each other when moving in the other direction.

Principle of relativity: Velocities are only relative. It cannot be determined which observer is actually moving!

The theory of electromagnetism:predicts that what one observer sees as an electric field, another moving observer will see as an electric field mixed with a magnetic field! Another prediction is that the speed of light only depends on the properties of space, and not on wether or not an observer is moving. This means that either space is absolute or that the speed of light is invariant. We found in experiments that the latter is true, thus leading to special relativity. Philosophically and theoretically it also makes more sense, since the notion of absolute space is considered absurd:

The laws of physics transform from one inertial frame to another according to Galilean relativity, leading to the following objections to absolute space, as outlined by Milutin Blagojević:

• The existence of absolute space contradicts the internal logic of classical mechanics since, according to Galilean principle of relativity, none of the inertial frames can be singled out.
• Absolute space does not explain inertial forces since they are related to acceleration with respect to any one of the inertial frames.
• Absolute space acts on physical objects by inducing their resistance to acceleration but it cannot be acted upon

Special relativity:

The speed of light is for every observer the same, regardless of relative velocities.

This means that every observer will measure the same lightspeed. This leads to three important conclusions:

1. Time dilation/stretching
2. Length contraction
3. Loss of causality

These conclusions can be summed up as the notion that space and time can be interchanged. Distances in space and time are not absolute, only the distance in spacetime is absolute. Just like the loss of absolute distances in space and time, there is a loss of the corresponding conservations laws: conservation of momentum (which corresponds with space) and conservation of energy (which corresponds with time). These are replaced with the more general conservation of energy-momentum (or it is actually called 4-momentum). Considering this, we conclude that energy has inertia or that energy is equal to mass in that sense. This last sentence is the starting point of General Relativity, or understanding better the nature of gravity.

General relativity

Since Energy is equal to mass, it has to be susceptible to gravity and also produce gravity! This means the following statement is true, and it is the starting point for General relativity:

Electromagnetic radiation (or light) produces and reacts to gravitational fields.

This leads to the following conclusions:

1. Lightpath bend because of gravity
2. Light loses energy and thus frequency/wavelength when moving away from a mass and vice versa.

Equivalence principle: there is no difference between an acclerating inertial frame and a gravitatinoal field. This leads to the fact that there is no difference between a fictitious force in an accelerating frame of reference and a gravitational force in a gravitational field.

Since fictitious forces arise because objects are only moving in a straight path because of their inertia, gravitional forces could arise because objects are only moving in a straigh path because of their inertia in spacetime.

Fictitious forces also vanish in a certain reference frame, just like gravitational fields.

Special relativity implies that an accelerating frame has non-Euclidean geometry (ehrenfast paradox).

The equivalence principle says that there is no distinction between accelerating frame and a gravitational field.

Combining these two statements leads to the observation that there is a non-Euclidean geometry in a gravitational field.

The equivalence principle implies that an accelerating frame has non-Euclidean geometry.

 

Inertial objects maximize their proper time. Since proper time is maximized closer to massess, objects move towards it.

Parrellel vector transport quantifies curvature

The stress-energy tensor notes the 4-momentum current.

 

(To be continued)