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Good morning everybody, sorry for the delay.

I thought for the last week it might be a good idea to present also some of the recent research we did.

I'm going to talk about a topic where basically we are the first ones who do cardiac reconstruction, so motion compensated reconstruction of the coronary arteries.

I introduced already last week the basic concept here.

What we try to do is basically we have the C-arm device in the OR and the C-arm device rotates around the patient's head or around the patient's thorax.

That's a video that should run.

That's a video where the system rotates around the patient and acquires images and here you see during the intervention seven monitors.

You have the anesthesia devices and out of these 2D projections basically the task is to reconstruct three-dimensional information.

If the object is static we all know, at least those of us who attended the winter semester lecture, how to do the reconstruction of static objects from x-ray projections.

This for instance here is a vessel system in the brain where usually no motion happens.

We can say that the reconstruction of static objects is pretty okay.

I mean there are still people doing research on that and we also work on it.

But basically you can say that there are powerful reconstruction machines implemented in modern CT scanners and they work pretty well.

The current problem that we are facing is how can we reconstruct objects that are moving and where we don't know anything about the motion.

There are major changes that happened recently. For instance the detector technology used for x-ray imaging has improved and we are also able to do large object reconstruction.

The important thing that we now have to consider is how are 3D objects mapped to the 2D image plane.

As we are now educated with the contents of the summer semester lecture, images are no longer just matrices but images are 2D planes in a 3D space.

This is our image plane in the 3D space. What do we do?

We have a projection ray that propagates x-ray particles through the 3D object and maps a certain point or all points along this projection line onto this point in the image.

According to the physics that is involved we know that basically all the intensities where the x-ray particles are propagated through are integrated up.

Or in other words, depending on the material the x-ray particles go through, they are attenuated.

They lose energy. If it's a very hard object they lose more energy and if it's a very soft object they lose less energy.

Very roughly speaking.

What we observe down there is the i-th projection ray and here we have for instance a point along the projection ray and we observe here the 2D point U.

So aix is basically the forward projection operator.

Now do not feel stressed by the formulas here. Basically what we do now is we do a 3D reconstruction.

We reconstruct the original function by looking at the i-th projection ray that is forward projected and we integrate up with a certain rating function over all the forward projected rays.

So what we basically do and this is very roughly speaking for each projection point in the image we basically get a linear equation in terms of the function we want to reconstruct.

And reconstruction basically means that we have to solve a huge system of linear equations.

For the newcomers just associate with a reconstruction problem from a projection a system of linear equations that has to be solved.

And in terms of math it can also be rewritten as an integration combined with a convolution of the 2D signal with a high pass filter.

So the winter semester guys know what is actually written there.

All the others this is nothing else but a reconstruction module, a piece of software that reconstructs the three dimensional function from the 2D projections.

This is state of the art and this is what I explained last time already with the virtual detector.

And we are now looking at this particular problem. We see here the beating heart, we see here also the spine in the background, we see the coronary arteries how they spring up and down and we see that we rotate around the object.

And the task we are looking for now is how can we rewrite the reconstruction formulas on the five slides before including also the motion of the heart.

So we have three different types of motion. It is also something I have explained to you last time. We have the cardiac motion, we have the respine motion, the breathing motion and the patient can move during the procedure.

And we have to capture all this information and there are different ways to do so. First of all cardiac motion can be measured indirectly by using the ECG signal.

The respiratory motion can be measured by using a camera that acquires surface information and patient motion can also be measured by just looking at the patient how he moves and use image processing to remove it.

The first idea that was published in 2006 here by our partners, research partners, they were looking at the reconstruction problem.

First of all they started to look at low contrast reconstruction of the heart using a CR system. What is a low contrast object?

They were looking not at the coronary arteries that are filled with contrast agent but they were just looking at the heart muscle and they wanted to do a reconstruction of the heart muscle.

The idea was like modern cardiac CT scanners are doing it, the idea was to reduce the reconstruction problem of an object in motion to multiple reconstructions of static objects.

So if your heart is beating you say you try to acquire those projections that belong to the same heart state, you take them out as a subset of projections and then you do a reconstruction of a particular heart state.

And then you try to catch the next heart state, the next heart state, the next heart state. Then you do a static reconstruction.

The problem was basically can we identify those projections that belong to the same position of the heart by using for instance ECG measures.

If you go into the cardiac lab that's basically what is done. People get a beta blogger that the heartbeat goes down and it's very slowly beating.

Then you get an ECG and based on the ECG signal they can say these are the same points where the heart currently is based on the measurements.

Then they put together all the projections and do reconstructions of static objects.