Renal Clearance Equations

00:01 What is clearance? Renal clearance refers to the volume of plasma that is completely cleared of a particular substance by the kidneys in a given period of time, and is usually measured in milliliters per minute.

00:15 It can help diagnose conditions such as chronic kidney disease short CKD.

00:20 It assists the efficiency of drug excretion by the kidneys, and is often calculated for substances such as creatinine and certain drugs or toxins.

00:28 The formula for calculating renal clearance is as follows.

00:32 Renal clearance equals urine concentration of substance X times urine flow rate divided by plasma concentration of substance X.

00:41 Urine concentration of substance X, abbreviated as UX, refers to the concentration of the substance X in the urine.

00:49 The urine flow rate U is the rate at which urine is produced in the kidneys. The plasma concentration of substance X, short Px, is the concentration of the substance X in the blood plasma. Let's look at an example.

01:02 What is the clearance of substance X? If the plasma concentration is 1mg/ml, the urine flow rate is one milliliter per minute and the urine concentration is 1mg/ml.

01:13 Here is what it looks like substituted into the formula.

01:17 Clearance equals 1mg/ml times one milliliter per minute divided by 1mg/ml.

01:24 We get a clearance of one milliliter per minute.

01:27 In other words, this means that one milliliter of plasma passing through the kidneys is cleared of the substance every minute.

01:34 We have a few other relationships that we need to bring out, and that is there are a number of factors that we need to try to calculate, and we can use various calculations in the renal system by using this clearance equation.

01:52 Now the clearance equation is looking at the concentration of a substance in the urine times the urine formation rate, which is v over the plasma concentration of the substance.

02:05 And that clearance equation won't change throughout our various substances that we're going to look at.

02:13 Interestingly though, you can pick a certain substance to look at that will give you insight into the function of the kidney.

02:20 Inulin is one of these substances.

02:23 We can use inulin as an index to measure glomerular filtration rate.

02:29 And how you do that is take glomerular filtration rate times the concentration of inulin in the urine, times the urine formation rate divided by the plasma concentration of inulin.

02:44 Creatinine is another way to measure glomerular filtration rate.

02:48 We utilize the very same equation.

02:51 The only thing we're doing is substituting creatinine for the x.

02:55 So here we have the urine concentration of creatinine times the urine formation rate divided by the plasma concentration of creatinine.

03:05 So both of these two substances can be utilized to measure glomerular filtration rate.

03:11 Inulin is a little bit more accurate.

03:14 But creatinine is made in the body and therefore is more functional.

03:19 So you can measure someone's creatinine much easier than you can induce or introduce inulin into someone.

03:27 The last substance that we can utilize in this kind of clearance equation is PAH.

03:34 PAH is utilized to help us for renal plasma flow.

03:38 We use the same equation.

03:40 All we're doing is substituting PAH for the x.

03:44 So here we have renal plasma flow equals the urine formation concentration of PAH times the urine formation rate divided by the plasma concentration of PAH.

03:59 A creatinine clearance measurement needs a 24 hour urine collection. If that's not possible, valuable information about the changes in the glomerular filtration rate can be obtained by measuring the plasma creatine concentration, which is inversely proportional to the GFR.

04:15 The graph on the right shows the approximate relationship between the glomerular filtration rate and the plasma creatinine concentration.

04:22 Note that decreasing the GFR by 50% of normal will double the plasma creatinine concentration, and decreasing the GFR to 25% of normal will increase the plasma creatinine concentration by about four times normal.

04:33 So let's now walk through these in a cartoon format.

04:38 In case you're one of those individuals that you struggle a little bit with equations.

04:42 So let's go through this in our picture form here.

04:47 So what happens to inulin.

04:49 Inulin as it travels through the afferent arteriole into the glomerular capillary is what we call freely filtered.

04:58 And what freely filtered means is it travels through that filtration barrier freely.

05:05 The filtration barrier doesn't block it or say, hold back.

05:09 It allows it to travel through.

05:13 Interestingly, inulin is not reabsorbed.

05:16 There are no specific transporters for inulin.

05:21 Inulin is also not secreted.

05:24 So all the inulin that is filtered is excreted into the urine.

05:28 There's no addition or subtraction to that volume.

05:35 Creatinine looks very similar.

05:38 It is also freely filtered.

05:41 It is not reabsorbed.

05:43 However, there is a tiny amount that is secreted.

05:46 So in this case that part is different than inulin.

05:50 Interestingly, though, since you know about how many transporters are there, people oftentimes use a fudge factor for that small amount of secretion.

06:00 That's why you can still use creatinine as a marker for glomerular filtration rate.

06:06 It is just a little less accurate because the secretion rate is not fully accounted for.

06:16 Properties of PAH.

06:18 It is also freely filtered.

06:21 Interestingly, it's still not reabsorbed.

06:24 And finally it is secreted fully, meaning that it is going to secrete as much or based upon a transport maximum across from the blood through the renal tubule cells into the tubule fluid. So in this case, you have both the freely filtered amount and the secreted amount that are measured in the urine.

06:50 The final components that we need to do is convert renal plasma flow into renal blood flow.

06:56 And how you do that is by taking into account the hematocrit.

07:01 Remember from the cardiovascular section that hematocrit is the amount of red blood cells in the blood.

07:08 So with this you take the renal plasma flow.

07:11 You divide it by one minus the hematocrit.

07:13 And that will yield renal blood flow.

07:17 Other important equations that we have in the kidney in terms of the system is the filtered load of a substance and what we mean by a filtered load, because this is kind of hard to think about, is the glomerular filtration rate multiplied by the plasma concentration of a substance. So if you take something like sodium, if you know the plasma concentration of sodium, you know the glomerular filtration rate, you can figure out how much, in terms of an absolute amount, a load that was delivered to the Bowman's space.

07:54 The last item that's important in renal physiology is the filtration fraction. The filtration fraction is the glomerular filtration rate divided by the renal plasma flow.

08:07 So what this is in practical terms is the amount of flow going in the afferent arteriole through the Bowman's capillaries and then out the efferent arterial.

08:19 How much of that flow was filtered.

08:22 So that is glomerular filtration rate.

08:24 You divide it by renal plasma flow.

08:27 I know we went through a lot of different equations, but these are important renal functions.

08:34 And if you understand these kinds of equations you'll be able to understand the concept that is behind them.