# Tutor profile: Taylor B.

## Questions

### Subject: MATLAB

How do I know when to use a for loop or a while loop?

A while loop enables you to execute a statement an undetermined number of times until a conditional is satisfied, so this loop is really good to use in scenarios when you don't know how many times an operation will have to be completed to reach your desired condition. When using a while loop it is really important to set your condition before starting the loop! If you don't you may end up in an infinite loop that has been known to crash your MATLAB. On the other hand, a for loop is used when you know the exact number of times you want to execute a set of statements.

### Subject: Calculus

What is the first derivative?

The first derivative of a function, f(x), is simply the slope of the tangent line to the function at a point x. From the first derivative we can determine whether or not the function is increasing or decreasing and the amount by which it is changing. One example we can use to visualize this concept is by thinking about distance, time, and velocity. Say we are walking and keeping track of the time it takes for us to get from point A to point B. If we plot the distance with respect to time (x-axis: Distance, y-axis: Time) we will see a pretty nice line. Our velocity is the slope of that line (i.e. the first derivative of distance with respect to time). If our velocity is greater than 0 that means we walked faster over time; a velocity less than 0 means we slowed down over time; a velocity of 0 means we kept the same pace over time.

### Subject: Biomechanical Engineering

Why do implanted biomaterials with micromotion typically form larger fibrotic capsules?

Micromotion continuously damages the tissue surrounding the implanted biomaterial which causes the wound healing process to be continually activated. When the wound healing process is activated macrophages and foreign-body giant cells travel to the site to form fibrotic tissue as a way to protect the body from the invasive "attacking" object. Over time these cells form a thick capsule around the object sealing it off. This is an example of extreme healing and can be really detrimental to an implant because it can no longer perform its intended function and most likely will require invasive removal.

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