Developments in Monte Carlo Methods for Medical Imaging

1. One of the main limitations of ray-tracing algorithms used in medical imaging is that they:

a. Require too much RAM memory and other expensive computational resources

b. Do not intrinsically model scattered radiation

c. Can be used only to model simple geometric objects

d. Simulate images with lower resolution than clinical systems

e. Require execution times that are too large for routine clinical use

Answer: b – Ray tracing algorithms only model the trajectories of x-rays that do not interact with the objects. Computational resources, speed, geometric complexity and resolution are typically not a problem.

2. Monte Carlo simulation algorithms can reproduce many physical effects that are observed in real CT scans, but one of the following effects is not directly modeled by Monte Carlo transport:

a. Motion blurring

b. Beam hardening

c. Quantum noise

d. Multiple scattering

Answer: a – Motion blurring caused, for example, by the patient heartbeat and other time- dependent events do not affect the individual x-ray movement and therefore are not directly modeled by Monte Carlo algorithms. However, multiple simulations with slightly different geometries could be combined to reproduce blurring.

3. Graphics Processing Units (GPU) are able to significantly speed up Monte Carlo simulation codes because they:

a. Have much faster access to the main video memory than the CPU to the RAM memory

b. Are programmer-friendly and much easier to program than CPUs

c. Use the Many Integrated Core Architecture with 61 computing cores that work in parallel and communicate at fast speed

d. Have thousands of computing cores that can work in parallel, although some groups of cores have to execute the same instruction each time interval Answer: d – GPUs have many SIMD microprocessors that contain thousands of separate computing cores. Option C describes another useful co-processors accelerator: the Intel Xeon Phi

4. Consider a VR technique where at each Compton interaction, a virtual scattered photon is created and then tracked to a fixed detector cell. Let  be the total cross section for Compton interaction, ∂/∂ Ω be the differential cross section for the direction towards the center of the detector cell (assumed constant across the cell) and ∆Ω be the solid angle covered by the detector cell as seen from the point of interaction. What weight needs to be assigned to the virtual photon to avoid bias in the resulting scatter distribution:

a) No weight

b) ∂/∂ Ω  ∆Ω c) Bias cannot be avoided by weighting

d)  / ∆Ω

e) -1  ∂/∂ Ω  ∆Ω

Answer: e – -1  ∂/∂ Ω  ∆Ω

Ref: J. F. Williamson, Monte Carlo evaluation of kerma at a point for photon transport problems, Med Phys 14, 567 (1987), C. J. Leliveld, A fast Monte Carlo simulator for scattering in X-ray Computerized Tomography, PhD Thesis, TU Delft, Netherlands, (1996).

5. Consider an unaccelerated MC simulation with a runtime of 300 sec. and two VR techniques: technique A reduces the variance (for the same signal level) by a factor of 2 with a runtime of 600 sec, and technique B reduces the variance by a factor of 3 with a runtime of 1000 sec. Which of the statements is true:

a) Technique A improves efficiency compared to unaccelerated MC

b) Technique B improves efficiency compared to unaccelerated MC

c) Neither of the VR techniques improves efficiency over unaccelerated MC.

d) Both VR techniques provide the same efficiency

e) Technique B has higher efficiency than technique A

Answer: c – Neither of the VR techniques improves efficiency over unaccelerated MC.

Ref: In the talk, we will discuss the following simple definition of efficiency: 1/(variance * runtime) – see e.g. C. J. Leliveld cited above.

6. Which of these acceleration methods are NOT considered MC Variance Reduction Techniques: f) Forced Detection g) Projection Denoising h) Interaction Splitting i) Interaction Forcing j) Woodcock Tracking Answer: b – Projection Denoising. Ref: Lack of mechanism for avoiding bias in the estimates is the problem here - see e.g. R. S. Thing and E. Mainegra-Hing, Optimizing cone beam CT scatter estimation in egs_cbct for a clinical and virtual chest phantom, Med Phys 41, 071902 (2014) .

7. The Oak Ridge National Laboratory (ORNL) series of computational phantoms represent which phantom format type and morphometric category?

A. Type – Voxel Category – Patient-Specific

B. Type – Stylized Category – Patient-Dependent

C. Type – Voxel Category – Reference

D. Type – Voxel Category – Patient-Sculpted

E. Type – Stylized Category – Reference

Answer: E (Stylized reference phantoms of different ages)

8. The ICRP Publication 110 male and female computational phantoms represent which phantom format type and morphometric category?

A. Type – Voxel Category – Patient-Specific

B. Type – Stylized Category – Patient-Dependent

C. Type – Voxel Category – Reference D. Type – Voxel Category – Patient-Sculpted

E. Type – Stylized Category – Reference

Answer: C (Voxel reference phantoms for the adult male and adult female)

9. Which anatomic sources is least useful in developing a computational voxel phantom for Monte Carlo radiation dosimetry and imaging studies?

A. Head and torso CT images

B. Head and torso MR images

C. Color photographs of cadaver tissue sections

D. Torso ultrasound images

E. Head and torso SPECT/CT images

Answer: D (All other types can and have been used in phantom development)

10. When replicating an experiment, which of the following simulation conditions needs to be accurately replicated?

a. Source description

b. Geometry definitions

c. Material definitions

d. Scoring details

e. All of the above

Answer: e – All of the above

11. Given the correct replication of conditions, what difference should be expected when performing the same simulations with different Monte Carlo software packages?

a. Always within the statistical uncertainty of the simulations b. Mostly within the statistical uncertainty, and a few results within <10% of each other

c. All results within <20% of each other

d. All results within <50% of each other, if you’re lucky!

Answer: b - Mostly within the statistical uncertainty, and a few results within <10% of each other

12. Why is the method called “Monte Carlo”?

a. For the Monte Carlo Casino, due to the random nature of the method

b. For James Bond, due to his ability to solve any problem!

c. For the Monte Carlo Opera, where the inventor of the method, Stanislaw Ulam, used to sing when he was younger.

d. For the Monte Carlo Beach hotel, where we would all prefer to be right now…

Answer: a - For the Monte Carlo Casino, due to the random nature of the method