quantitation of renal function1

8/4/2019 Quantitation of Renal Function1

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A PROGRAMMED INTRODUCTION TO THE

QUANTITATION OF RENAL FUNCTION

by Nora Laiken, PhD

Many aspects of renal function can be quantitatively analyzed. In

fact, a firm understanding of the quantitation of renal function is an

essential prerequisite for the study of renal physiology and

pathophysiology. This lesson is designed to help you acquire such an

understanding and develop skills in solving typical renal function problems.

Table of Contents

A. Basic definitions and fundamental equations . . . . . . . . . 2

B. General excretion models and their quantitation. . . . . . . 7

C. Fractional excretion, fractional delivery, and

fractional reabsorption . . . . . . . . . . . . . 28

Revised, September 2008


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A. Basic definitions and fundamental equations.

1. The purpose of this section is to define several important terms used in the

quantitation of renal function and then to combine these terms to form a set

of fundamental equations that describe the basic functions of the kidneys.

2. PX represents the concentration of a substance X in plasma. Commonly

used units for PX include mg/ml, mg/dl (i.e., mg/100 ml; also called mg %),

mosmol/liter, mmol/liter (mM), and (for electrolytes) meq/liter. For

example, typical normal PX values for some important plasma constituents

are as follows:

PNa = 140 mM PG = 80 mg/dl (G=glucose, fasting value)

PK = 4 mM PCr= 1 mg/dl (Cr = creatinine)

PCl = 110 mM

PHCO3 = 24 mM

3. UX represents the concentration of a substance X in urine. Commonlyused units for UX, as for PX, are ____. Because UX for a given substance

can vary markedly depending upon the diet, fluid intake, and physiological

state of the individual, it is impossible to list meaningful normal values;

however, many examples will be encountered in the problems presented

throughout this lesson.

mg/ml, mg/dl,mosmol/liter,

mmol/liter (mM),

meq/liter

4. V represents the volume of urine excreted per unit time, i.e., the urine

flow rate.1 Commonly used units for V are ml/min or liters/day. Although

V can vary from less than 0.5 ml/min to greater than 15 ml/min, depending

upon the diet, fluid intake, and physiological state of the individual, a

typical normal value for V

is 1 ml/min or 1.5 liters/day.

5. GFR represents the glomerular filtration rate and is defined as the

volume of plasma filtered (i.e., the volume of plasma passing from the

glomerular capillaries into Bowmans space) per unit time. Commonly used

units for GFR are ml/min and liters/day. In humans, a typical normal GFR

is 125 ml/min or 180 liters/day.

__________1Frequently, the symbol V is used instead of V, or V is called the urine volume instead of the urine flow rate. However,

the symbol V and the term urine flow rate are preferable.


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6. RPF represents the renal plasma flow and is defined as the volume of

plasma flowing to the kidneys through the renal arteries per unit time.1

Commonly used units for RPF, as for GFR, are _____ . In humans, a

typical normal RPF is 625 ml/min or 900 liters/day.

ml/min, liters/day

7. FF represents the filtration fraction and is defined as the fraction of the

RPF that is filtered into Bowmans space. Thus

FF = GFR (A-1)

RPF

Using the typical normal values for GFR and RPF listed in questions 5 and

6, a typical normal FF is ____. 0.2

8. TX represents the rate of tubular transport and is defined as the amount

of a substance X transported across the tubular epithelium per unit

time. Commonly used units for TX are mg/min, mmol/min, or (for

electrolytes) meq/min. Note that the term TX is used foreitherthe rate ofreabsorption (i.e., the rate of transport from the _____ fluid to the _____

capillaries) orthe rate of secretion (i.e., the rate of transport from _____

capillaries to the _____ fluid); the direction of transport must be specified

when the parameter is used, if not obvious from the context (sometimes, TXrand TXs are used to represent the rate of tubular reabsorption and the rate of

tubular secretion, respectively). TX values for several substances will be

calculated in Section B.

tubular

peritubular

peritubular

tubular

__________1RPF should not be confused with RBF, the renal blood flow. RPF and RBF are related as follows:

RBF = RPF

1 - Hct

where Hct represents the hematocrit.


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9. Summary of basic terms used in the quantitation of renal function:

Definition Commonly Used Units Typical Normal Values

PX Concentration of X in plasma mg/ml, mg/dl, mmol/liter (mM),

mosmol/liter, meq/liter

PNa = 140 mM, PK= 4 mM,

PCl = 110 mM, PHCO3 = 24 mM

UX Concentration of X in urine mg/ml, mg/dl, mmol/liter (mM),mosmol/liter, meq/liter

Varies markedly with diet, fluidintake, physiological state

V Urine flow rate ml/min, liters/day Varies markedly with diet, fluid

intake, physiological state, but

typically 1 ml/min or 1.5

liters/day

GFR Glomerular filtration rate ml/min, liters/day 125 ml/min or 180 liters/day

RPF Renal plasma flow ml/min, liters/day 625 ml/min or 900 liters/day

FF Filtration fraction 0.2

TX Rate of tubular transport(reabsorption orsecretion)

mg/min, mmol/min, meq/min See Section B for examples

In the remainder of this section, the above terms will be combined to form a set

of fundamental equations that describe the basic functions of the kidneys.

10. For any substance X that is freely filtered from the glomerular capillaries

into Bowmans space,1 the amount filtered per unit time is given by

Amount filtered per unit time = PXGFR (A-2)

The amount filtered per unit time often is loosely referred to as the amount

filtered. However, in this lesson, the term filtered load will be used when

referring to the quantity PXGFR.

__________1A freely filtered substance is one whose concentration in the filtrate is equal to its concentration in plasma

([filtrate]/[plasma] ratio = 1.0). Freely filtered substances include any water-soluble molecule that has the following two

properties: (1) it has a molecular weight < 5000 Da; as the molecular weight increases above 5000 Da, the

[filtrate]/[plasma] ratio gradually decreases (for example, myoglobin {17,000 Da} has a [filtrate]/[plasma] ratio of 0.75,

while serum albumin {69,000 Da} has a [filtrate]/[plasma] ratio of 0.01); and (2) it is not significantly bound to plasma

proteins. In general, if a substance is said to be filtered, it can be assumed that the substance is freely filtered unless

otherwise noted.


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11. For any substance X, the amount excreted per unit time is given by1

Amount excreted per unit time = UXV (A-3)

The amount excreted per unit time often is loosely referred to as the

amount excreted. However, in this lesson, the termrate of excretion will

be used when referring to the quantity UXV.

12. The clearance of any substance X, CX, is defined as

CX = UXV (A-4)

PX

Note that this definition of CX is valid for all X exceptH2O and electrolyte-

free H2O (EFW). As the clearance concept is an important one in renal

physiology, it will be discussed in more detail in the following question.

13. You have learned that the rate of excretion of a substance X is given byUXV

. Note that UXV describes the renal excretion of X from the urines

perspective. For example, if UX = 80 mg/ml and V = 0.5 ml/min, from the

urines perspective the renal excretion of X is best described as _____ . But

from the plasmas perspective, it might be more relevant to ask what

volume of plasma supplied the X that was excreted. Since volume =

amount/concentration, then:

Volume of plasma needed per = Amount of X excreted per unit time

unit time to supply excreted X Plasma concentration of X

= UXV

PX

For example, if 40 mg of X is excreted per min (UXV = 40 mg/min) and PX

= 2 mg/ml, then the volume of plasma needed per min to supply the

excreted X is _____. Note that the volume of plasma that supplies the

excreted X is thereby stripped orcleared of its X, i.e.,

Volumeof plasma needed per = UXV = Volume of plasma cleared

unit time to supply excreted X PX of X per unit time

Thus, the quantity UXV/PXrepresents the volume of plasma cleared of X

per unit time and is called the clearance of X (CX; cf. equation A-4). Note

that since CX represents a volume per unit time, its units are _____.

UXV = 40 mg/min

20 ml/min

ml/min, liters/day

__________1It is important to distinguish between excretion (the elimination of a substance in urine) and

secretion (the transport or diffusion of a substance from the peritubular capillaries or

epithelial cells into the tubular fluid).


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14. To consolidate your understanding of the concepts presented in this section,

complete the following table. The data were obtained from a patient with

GFR = 120 ml/min and V= 1 ml/min.

Filtered Rate of

PX UX Load Excretion CX

PXGFR UXV CX

mmol/min ml/min

or

mg/min

Na+ 140 mmol/liter 70 mmol/liter 16.8 0.07 0.5

K+ 4 mmol/liter 35 mmol/liter 0.48 0.035

8.75

Cl- 110 mmol/liter 70 mmol/liter 13.2 0.07 0.64

HCO3- 25 mmol/liter 1.4 mmol/liter 3.0 0.00

1

0.056

Creatinine 1 mg/dl 125 mg/dl 1.2 1.25 125

Glucose 70 mg/dl 0 84 0 0

Urea1 30 mg/dl 1500 mg/dl 36 15 501Actually, PUrea and UUrea are most commonly expressed as blood urea nitrogen (BUN) and urine urea

nitrogen (UUN), respectively. Urea has a mw of 60 Da, of which 28 is nitrogen, i.e., on a weight basis,

urea is 2 nitrogen. Thus, PUrea = 30 mg/dl is equivalent to BUN 15 mg/dl, while UUrea = 1500

mg/dl is equivalent to UUN 750 mg/dl.

15. In Section B of this lesson, the handling of certain substances by the kidney

will be summarized using graphs that illustrate the effect of plasma

concentration (PX) on four of the important quantities defined in this

section. Specifically, for each of these substances, fourrenal function vs.

PX curves will be shown:

(1) Filtered load ( ____ ) vs. PX

(2) Rate of excretion ( ______ ) vs. PX

(3) Rate of tubular transport ( ____ ) vs. PX

(4) Clearance ( ____ ) vs. PX

Note that the filtered load, rate of excretion, and rate of tubular transport all

share the same units (e.g., ____ ). Thus, the first three curves generally are

plotted on a single graph. It also should be noted that since these curves

typically are plotted at constant GFR, the filtered load vs. PX curve is a

straight line with slope ____ .1

PXGFR

UXV

TX

CX

mg/min, mmol/min

GFR

__________1This may not be true if the substance is bound to plasma proteins, as the extent of binding will depend on the plasma

concentration of the substance. However, this effect of protein binding will not be considered here.


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B. General excretion models and their quantitation.

1. Different substances are handled by the kidney in different ways. On the

macroscopic level, five general excretion models are possible:

(1) No filtration or secretion(2) Filtration only; no reabsorption or secretion

(3) Filtration and reabsorption

(4) Filtration and secretion

(5) Filtration, reabsorption, and secretion

Each of these models will be described in this section. More specifically,

for each model equations for the rate of excretion and clearance will be

derived. In addition, renal function vs. PX curves will be shown for several

important substances.

2. No filtration or secretion. A substance that is neither filtered nor added to

the tubular fluid by secretion cannot be excreted. Therefore,

Rate of excretion = UXV = 0 (B-1)

and

CX = UXV = 0 (B-2)

PX

Such substances are either (i) too large to cross the filtration barrier (e.g.,

the [filtrate]/[plasma] ratio for serum albumin, mw 69,000 Da, is 0.01; see

footnote 1, p 4); or (ii) tightly bound to plasma proteins (e.g., unconjugated

bilirubin is virtually absent from tubular fluid and urine because of its tightbinding to serum albumin).

3. Filtrationonly, no reabsorption or secretion. For a substance that is

freely filtered1 but neither reabsorbed nor secreted

Rate of excretion = Filtered load

i.e.,

UXV = PXGFR (B-3)

Examples of such substances are inulin (a fructose polymer with mw 5000

Da) and mannitol (a hexose that is neither found in nor metabolized by the

body).__________1The term freely filtered is defined in footnote 1, p 4.


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4. You have learned that the clearance of a substance X, CX, is defined by the

equation CX = UXV/PX. However, for a substance that is freely filtered but

neither reabsorbed nor secreted, such as inulin (equation B-3)

UInV = PIn GFR

so that

CIn = UInV/PIn = PIn GFR/PIn

or

CIn = GFR (B-4)

Equation B-4 makes sense: if inulin is freely filtered but neither reabsorbed

nor secreted, the volume of plasma that is cleared of inulin per unit time

(CIn) will equal the volume of plasma that is filtered per unit time (GFR); no

inulin is addedto the tubular fluid by secretion (in which case the volume

of plasma cleared of inulin per unit time would be greaterthan the GFR)

and no inulin is removedfrom the tubular fluid by reabsorption and returned

to the plasma (in which case the volume of plasma cleared of inulin perunit time would be less than the GFR). In fact, in quantitative discussions of

renal function, GFR and CIn often are used interchangeably. Furthermore,

since CIn can be obtained from readily measurable parameters, _____ , this

means that GFR can be measured noninvasively.1

UIn, V, PIn

5. GFR can be equated to the ____ of any substance that is ____ ____ , but

neither _____ nor _____ , such as the polysaccharide ____ , i.e., GFR =

____ . However, this polysaccharide must be infused IV in order to obtain

the latter quantity and therefore is not used routinely to determine GFR in

humans. Instead, for clinical purposes, GFR is estimated using the

endogenous substance creatinine, as described below (see question 20).

clearance

freely filtered

reabsorbed

secreted

inulin

CIn

6. The renal handling of a substance that is freely filtered but neither reab-

sorbed nor secreted can be conveniently summarized with renal function vs.

PX curves (question A-15), using inulin as an example. The data needed to

construct these curves are obtained by completing the table below:

__________1In addition to being freely filtered but neither reabsorbed nor secreted, inulin is

physiologically inert (most importantly, it does not alter renal function) and is easily

measured. Any substance used for the determination of GFR must satisfy these criteria as

well as the criterion of being freely filtered but neither reabsorbed nor secreted.


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PIn UIn V

CIn (= GFR) Filtered Rate of

mg/dl mg/ml ml/min Load Excretion

50 60 1.0

100 160 0.75

150 225 0.8

200 240 1.0

150

100

50Clearance(ml/min)

10050 150 200

PIn (mg/dl)

200

100

50RateofE

xcretion

(mg/min)

10050 150 200

PIn (mg/dl)

150

FilteredLoad(mg/min)

CIn PInGFR UInV

ml/min mg/min mg/min

120 60 60

120 120 120

120 180 180

120 240 240

(1) Filtered load (= ____ ) vs. PIn. Since GFR (= CIn) is constant, this

plot is a ____ ____ with slope ____ (see question A-15).

(2) Rate of excretion (= ____ ) vs. PIn. Since the rate of excretion

equals the ____ ____ for a substance that is filtered only (equation

B-3), this curve is identical to the _____ curve.

(3) Clearance vs. PIn. Since CIn = GFR and GFR is constant, CIn is

independentof PIn.

PInGFR

straight line

GFR (120 ml/min)

UInV

filtered load

filtered load vs. PIn

7. Filtration and reabsorption. For a substance that is filtered and

reabsorbed

Rate of excretion = Filtered load Rate of tubular reabsorption

so that

UXV

= ____

____

Examples of such substances are glucose, amino acids, sodium, chloride,

and phosphate.

PXGFRTX


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8. For a substance that is filtered and reabsorbed

UXV = PXGFR TX (B-5)

Since CX = UXV/PX, this means that

CX = PXGFR TXPX

= GFR TX /PX

or CX = CIn TX /PX (B-6)

Note, therefore, that for a substance that is filtered and reabsorbed

CX < CIn (B-7)

This result is expected: if a substance is filtered and reabsorbed (i.e., ifsome

of the filtered substance is returned to the _____ ), a smaller volume of____ will be cleared per unit time compared to the volume cleared if a

substance is filtered only (so that none of the filtered substance is returned

to the _____ ).

plasmaplasma

plasma

9. While a detailed description of the reabsorption processes in the kidney is

beyond the scope of this lesson, it is important to note that for many

reabsorbed substances, the reabsorption process is Tm-limited, i.e., it has a

maximum rate Tm (Tm = transport maximum).1 Glucose, amino acids,

and phosphate are among the substances whose reabsorption is Tm-limited.

Furthermore, many important substances that exhibit Tm-limited

reabsorption (including glucose, amino acids, and phosphate) also exhibit

the so-called threshold phenomenon. This means that the affinity of thetransport mechanism for the substance is so high that the reabsorption of the

substance from the tubular fluid is virtually complete when the filtered load

does notexceed Tm, i.e., when PXGFR TmX, then the entire filtered load

is reabsorbed

TX = PXGFR (B-8)

so that

UXV = PXGFR TX = PXGFR PXGFR

i.e., UXV = 0 (B-9)

which means that

__________1It is important to note that the Tm for some substances is subject to physiological regulation, i.e., only under a given

set of physiological conditions can it be regarded as afixedmaximum rate of reabsorption. For example, the Tm for

phosphate is decreasedby parathyroid hormone (PTH).


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CX = UXV

= 0 (B-10)

PX

When the filtered load exceeds Tm (i.e., when the transport mechanism is

saturated), the excess load will be excreted. Thus, when PXGFR > TmX, the

rate of reabsorption TX is fixed at its maximum value TmX

TX = TmX (B-11)

and the remaining X is excreted

UXV= PXGFR TmX (B-12)

so that CX = UXV = PXGFR TmX

PX PX

= GFR TmX/ PX

or

CX = CIn TmX/ PX (B-13)

i.e., some _____ is cleared of X (CX is _____ than 0). However, because

some X is returned to the _____ by _____ , the volume of _____ cleared

per unit time is ____ than the volume of _____ filtered per unit time (CX is

_____ than CIn [GFR]). Note that it is possible to define a plasma

concentration PThX, the so-called renal threshold for X, at which the

substance first appears in the urine. Theoretically (see question 11 below),

PThX represents that plasma concentration at which the filtered load exactly

saturates the transport mechanism (for a given GFR)

PThXGFR = TmX

orPThX = TmX/GFR (B-14)

The normal plasma concentrations of glucose and amino acids are well

below their respective renal thresholds, so that these substances normally

are absentfrom urine (see question 10 below). In contrast, the normal

plasma phosphate concentration generally is above the renal threshold for

phosphate, so that some phosphate normally is excretedin the urine (see

question 12 below).1

plasma

greater

plasma

reabsorption

plasma

less

plasma

less

__________1Since PTH decreases Tm for phosphate (see footnote 1, p 10), it also decreases PTh for

phosphate.


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10. The renal handling of substances that exhibit Tm-limited reabsorption and

the threshold phenomenon can be conveniently summarized with renal

function vs. PX curves, using glucose as an example. The data needed to

construct these curves can be obtained by completing the table below.

During the time period that the data were obtained, CIn was noted to have a

constant value of 125 ml/min.

PG UG V Filtered Rate of Rate of CG

mg/dl mg/ml ml/min Load Excretion Tubular

Reabs

50 0 1.0

150 0 0.8

250 0 0.8

300 tr. 0.75

350 70 0.9

400 125 1.0

500 250 1.0

150

100

50Clearan

ce(ml/min)

200 400 600

PG

(mg/dl)

400

200

100RateofExcr

etion

(mg/min)

PG

(mg/dl)

300

FilteredL

oad(mg/min)

RateofTubularR

eabsorption

(mg/min)

Inulin

200 400 600

500

600

nl

PXGFR UXV

TX CG

mg/min mg/min mg/min ml/min

63 0 63 0

188 0 188 0

313 0 313 0

375 Tr. 375 tr.

438 63 375 18

500 125 375 31

625 250 375 50

(1) Filtered load vs. PG. Since GFR (= CIn) is constant, a ____ ____ is

obtained with slope ____ (see question A-15).

straight line

GFR

(2) Rate of excretion vs. PG.

(3) Rate of tubular reabsorption vs. PG.

Taken together, curves (2) and (3) illustrate both the Tm-limitednature of glucose reabsorption and the threshold phenomenon:


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For PG ____ mg/dl, the transport mechanism (with its high

____ for glucose) is able to reabsorb the entire filtered load,

i.e., TG = ____ and UGV = ____ (equations B-8 and B-9).

For PG > ____ mg/dl, the filtered load exceeds the maximum

rate of tubular reabsorption, TmG (= ____ ), and the excessfiltered load is excreted. PG = ____ mg/dl therefore represents

PThG, the ____ ____ for glucose at this GFR. Note that for PG >

PThG, the rate of excretion vs. PG curve parallels the ______

curve, i.e., it is a ____ ____ with slope ____ , as predicted by

equation B-12.

(4) Clearance vs. PG.

For PG PThG, CG = ____ (equation B-10).

For PG > PThG, CG increases, and if additional data were

available CG would asymptotically approach CIn (which has

been included on the graph as a reference line). This ispredicted by equation B-13 and makes sense: when PG is very

high, the filtered load PGGFR is so much greater than TmG that

the rate of excretion UGV is approximately equal to PGGFR, as

predicted by equation B-12 when PGGFR >>> TmG. Thus, at

very high PG, glucose behaves approximately like a substance

such as inulin that is ______ only, and CG approaches _____.

Note that when PG is in the normal range, indicated by the bracket below the

abscissa, PG < PThG, so that UG = ____ and CG = ____ (equations B-9 and B-

10).

300 mg/dl

affinity

PGGFR

0

300 mg/dl

375 mg/min300 mg/dl

renal threshold

filtered load vs. PG

straight line

GFR

0

filtered

CIn

0

0

11. It should be noted that the data and glucose titration curves presented in theprevious question are somewhat idealized, as the curves for rate of excretion

vs. PG, rate of tubular reabsorption vs. PG, and clearance vs. PG show an

abruptchange when the rate of tubular reabsorption reaches its maximum

value. Actual glucose titration curves show a more gradual change in this

region:


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150

100

50Clearance(ml/min)

200 400 600

PG (mg/dl)

400

200

100RateofExcretion

(mg/m

in)

PG (mg/dl)

300


RateofTubularReabsorption

(mg/min)

Inulin

200 400 600

500

600

This feature of renal titration curves is called splay.1 Note that because of splay, PThG (defined as the

value of PG at which glucose first appears in urine) is 200 mg/dl insteadof 300 mg/dl, even though

the transport mechanism does notbecome saturated (i.e., TG does notreach TmG) until PG 300

mg/dl (see question 10). PG = 300 mg/dl therefore only can be regarded as the theoretical renalthreshold for glucose.

__________1Two explanations for splay commonly are offered:

(1) Reaction of glucose with the Na+-glucose cotransporter. Using the symbol R for the Na+-glucose cotransporter,

the reaction between glucose and the cotransporter can be written as

GR G + R

and

K = [G] [R]

[GR]

where K is the dissociation constant for the glucose-cotransporter complex. Even if K is very small (i.e., if the

affinity of the cotransporter for glucose is very large), a finite concentration of glucose must be present in thetubular fluid in order to saturate the cotransporter. Hence, some glucose will be excreted before the theoretical

renal threshold (= TmG /GFR; see equation B-14) is reached.

(2) Nephron heterogeneity. Considerable heterogeneity in the filtration capacity of glomeruli and the reabsorption

capacity of renal tubules is believed to exist. For example, some nephrons may produce average volumes of

filtrate but have subnormal reabsorption capacities; these nephrons are likely to excrete glucose at a lower PG

than the average nephron. In contrast, other nephrons may produce small volumes of filtrate but have high

reabsorption capacities; these nephrons are likely to excrete glucose at a higher PG than the average nephron.


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12. To consolidate your understanding of Tm-limited

reabsorption and the threshold phenomenon, use the

data below to construct renal titration curves for

phosphate. During the time period that the data

were obtained, CIn was noted to have the constant

value of 120 ml/min.

PP UP V Filtered Rate of Rate of CP

mmol/l mmol/l ml/min Load Excretion Tubular

Reabs

0.2 0 0.8

0.4 0 0.75

0.6 tr. 1.0

0.7 7.5 0.8

0.8 17.3 0.75

1.0 25 1.0

1.2 40 1.1

1.5 66.7 1.2

2.0 140 1.0

PPGFR UPV TP CP

mmol/min mmol/min mmol/min ml/min

0.024 0 0.024 0

0.048 0 0.048 0

0.072 tr. 0.072 tr.

0.084 0.006 0.078 8.6

0.096 0.013 0.083 16

0.120 0.025 0.095 25

0.144 0.044 0.1 37

0.180 0.080 0.1 53

0.240 0.140 0.1 70

150

100

50Clearance(ml/min)

1.0 2.0

PP (mmol/liter)

0.2

0.1

RateofExcretion

(mmol/min)

PP (mmol/liter)

FilteredLoad(mmol/min)


(mmol/min)

Inulin

1.0 2.0

0.3

nl

150

100

50Clearance(ml/min)

1.0 2.0

PP (mmol/liter)

0.2

0.1

RateofExcretion

(mmol/min)

PP (mmol/liter)

FilteredLoad(mmol/min)


(mmol/min)

Inulin

1.0 2.0

0.3

nl


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The basic features of the curves are similar to those for glucose (questions

10 and 11). PThP, the plasma phosphate concentration at which phosphate

first appears in the ____ , is approximately ____ mmol/liter, while TmP , the

_____ , is approximately ____ . Like the glucose titration curves in

question 11, and in contrast to the idealized curves in question 10, the

changes in the region at which the rate of tubular reabsorption reaches its

maximum value are gradual, i.e., the curves exhibit ____ ; thus, phosphateappears in the ____before the rate of tubular reabsorption reaches TmP.

Note that when PP is in the normal range, indicated by the bracket below the

abscissa, PP > PThP, so that UPV > ____ and CP > ____ (equations B-12 and

B-13).

urine

0.6 mmol/liter

transport maximum

for phosphate

0.1 mmol/minsplay

urine

0

0

13. Filtration and secretion. For a substance that is filtered and secreted

Rate of excretion = Filtered load + Rate of tubular secretion

i.e.,1

UXV

= ____ + ____

Examples of such substances are organic acids (e.g., penicillin, para-aminohippuric acid [PAH], furosemide, uric acid) and organic bases (e.g.,

creatinine, cimetidine, trimethoprim).2

PXGFR

TX

14. For a substance that is filtered and secreted

UXV = PXGFR + TX (B-15)

Since CX = UXV/PX, this means that

CX = PXGFR + TX

PX

= GFR + TX /PX

or

CX = CIn + TX /PX (B-16)

__________1Note that TX is used to represent the rate of tubular reabsorption (question 7) as well as the rate of tubular secretion (see

question A-8). The direction of transport must be specified when the parameter is used, if not obvious from the context.2It should be noted that many substances that are secreted are partially bound to plasma proteins and therefore are not

freely filtered (see footnote 1, p 4). For such substances, the filtered load is more accurately given by PXGFRF, where F

is the fraction of the substance in plasma that is freely filterable (i.e., unbound). However, since the purpose of this

lesson is to provide a general introduction to the quantitation of renal function, the effects of protein binding will not be

considered further here.


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17

Thus, for a substance that is filtered and secreted

CX > CIn (B-17)

This result is expected: if a substance is filtered and secreted (i.e., if some of

the substance that was notfiltered from the _____ capillaries into _____

space leaves the _____ capillaries and is added to the _____ _____ ), alarger volume of ____ will be cleared per unit time compared to the

volume cleared if a substance is filtered only.

glomerular

Bowmansperitubular

tubular fluid

plasma

15. A detailed description of the secretory processes in the kidney is beyond the

scope of this lesson. However, it should be noted that certain secreted

substances exhibit Tm-limited secretion, a phenomenon that is completely

analogous to Tm-limited reabsorption; such substances have a maximum

rate of secretion, Tm (Tm = ____ ____ ).1 PAH and creatinine are

examples of substances whose secretion is Tm-limited. Some secreted

substances, most notably PAH, also exhibit a phenomenon that is somewhat

analogous to the threshold phenomenon for reabsorption (question 9).Specifically, for a substance like PAH, the affinity of the transport

mechanism for the substance is so high that essentially all of the substance

in the peritubular capillaries is secreted into the tubular fluid as long as the

rate of delivery of the substance to the peritubular capillaries does not

exceed Tm. As a first approximation (see question 16 below), any part of

the RPF that does not get filtered enters the efferent arterioles and

peritubular capillaries, so that the rate of plasma flow through the

peritubular capillaries can be equated to RPF GFR and the rate of delivery

of a substance to the peritubular capillaries can be equated to PX(RPF

GFR). Thus, for a substance like PAH, as long as PX(RPF GFR) does not

exceed Tm, the entire amount delivered to the peritubular capillaries is

secreted, i.e.,

TX = PX (RPF GFR) (B-18)

Therefore

UXV = PXGFR + TX = PXGFR + PX (RPF GFR)

= PXRPF (B-19)

and

CX = UXV = RPF (B-20)

PX

i.e., the entire RPF is cleared of X. Equation B-20 makes sense: ifessentially all of the X delivered to the peritubular capillaries is secreted,

transport maximum

__________1Note that the symbol Tm is used to represent the transport maximum for reabsorption (question 9)

as well as the transport maximum for secretion.


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18

any plasma that is not cleared of X by filtration will be cleared of X by

secretion. In contrast, if PX(RPF GFR) exceeds Tm, so that the transport

mechanism is ____

TX = TmX (B-21)

so that

UXV = PXGFR + TmX (B-22)and1

CX = CIn + TmX/PX (B-23)

saturated

Because some X is secreted, the volume of _____ cleared of X per unit

time is ____ than the volume of _____ filtered per unit time (CX is _____

than CIn [GFR]). However, because some X remains in the peritubular

capillaries, the RPF is notcompletely cleared of X (CX is _____ than

RPF).

plasma

greater

plasma

greater

less

16. In the previous question, it was noted that the ____ of the transport

mechanism for substances such as PAH is so high that essentially all of the

substance in the ____ ____ is secreted into the ____ ____ as long as thetransport mechanism is not ____ . It was shown that under such conditions

CX = RPF (equation B-20), or, considering PAH as an example

CPAH = RPF (B-24)

As noted above, equation B-24 makes sense: if essentiallyall of the PAH in

the ____ ____ is secreted into the ____ ____ . any plasma that is not

cleared of PAH by filtration should be cleared of PAH by _____ , so

that the entire _____ is cleared of PAH. According to equation B-24, it

should be possible to determine the RPF noninvasively, from readily

measurable parameters ( _____ ). However, in actuality the RPF is not

completely cleared of PAH, even when the transport mechanism is not _____ , i.e., equation B-24 should be written as CPAH RPF. This is

because 10% of the RPF supplies portions of the kidney that cannot

remove PAH (e.g., the renal medulla [via the vasa recta capillaries], capsule,

and pelvis, the perirenal fat), i.e., 10% of the RPF does notflow through

the glomerular and/or peritubular capillaries and therefore cannotbe

cleared of PAH by filtration and secretion. The rate of plasma flow to

regions of the kidney that can remove PAH often is termed the effective

renal plasma flow (ERPF). Thus, the rate of plasma flow through the

peritubular capillaries is most accurately expressed as ERPF GFR, i.e.,

when the rate of PAH delivery does not exceed Tm (compare to equations

B-18 to B-20)

affinity

peritubular capstubular fluid

saturated

peritubular caps

tubular fluid

secretion

RPF

UPAH, V, PPAH

saturated

__________1While it is possible to define a plasma concentration at which the rate of delivery to the peritubular capillaries exactly

saturates the transport mechanism (at a given GFR and RPF), in analogy to PThX (equation B-14), this seldom is done, as

the term renal threshold refers specifically to the plasma concentration at which a substance first appears in the urine.


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19

TPAH = PPAH (ERPF GFR) (B-25)

so that

UPAHV = PPAH ERPF (B-26)

and

CPAH = ERPF (B-27)

In other words, while CPAH provides a good estimate of the RPF, it actuallymeasures the ERPF. For clinical purposes, the approximate RPF values

obtained by CPAH measurements are quite useful. If an accurate

determination of RPF is needed, the Fick principle can be used, as discussed

in the following question.

17. Because the rate of plasma flow through the peritubular capillaries is most

accurately expressed as ERPF GFR, where ERPF represents the ____

RPF, CPAH provides an accurate measurement of ERPF (as long as the

transport mechanism is not ____ ), but only an estimate of RPF. While

such an estimate is quite useful for clinical purposes, it is possible to obtain

an accurate RPF value with the Fick principle

RPF = UPAH V (B-28)

PPAH PRV,PAH

where PRV,PAH represents the concentration of PAH in the renal vein, so that

PPAH PRV,PAH represents the renal arterio-venous plasma concentration

difference for PAH.1 Thus, since ERPF = CPAH = UPAHV/PPAH

ERPF = RPF (PPAH PRV,PAH) (B-29)

PPAH

or

ERPF = RPF EPAH (B-30)

where EPAH represents the extraction ratio for PAH, defined as (PPAH

PRV,PAH)/PPAH. When the transport mechanism is not saturated, EPAH 0.90.2

effective

saturated

__________1Note that the renal vein must be catheterized to obtain PRV,PAH . Also note that many substances

other than PAH can be used when determining RPF with the Fick principle.2If PAH were completely cleared or extracted by the kidneys, PRV,PAH would equal 0 (i.e., PAH

would be completely absent from the renal vein) and EPAH would equal 1.0 .


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20

18. The renal handling of substances that exhibit Tm-limited secretion and that are almost completely

removed from the peritubular capillaries if the transport mechanism is not saturated can be

conveniently summarized with renal function vs. PX curves, using PAH as an example. The data

needed to construct these curves can be obtained by completing the table below. Data also are

included to allow the rate of PAH delivery to the peritubular capillaries to be calculated. During the

time period that the data were obtained, CIn was noted to have a constant value of 120 ml/min.

[Important note : Answers are provided at the bottom of the page, notin an answer column along theright margin, and the renal function vs. PX curves are shown on p 21.]

PPAH UPAH V Filtered Rate of Rate of CPAH ERPF Rate of PAH

mg/dl mg/ml ml/min Load Excretion Tubular Delivery to

Secretion Perit Caps

4 40 0.6

8 60 0.8

12 72 1.0

16 120 0.8

18 102 1.0 - - 1 - - 1

20 130 0.8 - - - -

24 136 0.8 - - - -

30 116 1.0 - - - -1The ERPF can be equated to CPAHonly when the transport mechanism is notsaturated. Hence, ERPF and the rate of

PAH delivery to the peritubular capillaries cannot be calculated from the data provided when PPAH > 16 mg/dl.

_________________________________________________________________________________Answers

Filtered Rate of Rate of CPAH ERPF Rate of PAH

Load Excretion Tubular ml/min ml/min Delivery to

mg/min mg/min Secretion (= CPAH) Perit Caps

mg/min mg/min

PPAH(ERPF-GFR)

4.8 24 19 600 600 19

9.6 48 38 600 600 38

14 72 58 600 600 58

19 96 77 600 600 77

22 102 80 567 - - - -

24 104 80 520 - - - -

29 109 80 454 - - - -

36 116 80 387 - - - -


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21

600

400

200Clearance(m

l/min)

PPAH (mg/dl)

80

40

RateofExcretion

(mg/min)

PPAH (mg/dl)

FilteredLoad(m

g/min)

RateofTubularSecr

etion

(mg/min)

Inulin

10 20

120

30 10 20 30

The important features of these renal function vs PX curves are as follows:


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22

(1) Filtered load vs. PPAH. Since GFR (= CIn) is constant, a ____ ____

is obtained with slope ____ .

(2) Rate of excretion vs. PPAH.

(3) Rate of tubular secretion vs. PPAH.

Taken together, curves (2) and (3) illustrate the Tm-limited nature

of PAH secretion and the ability of the transport mechanism toremove essentially all of the PAH delivered to the _____ capillaries

if it is not saturated:

For PPAH _____mg/dl, the transport mechanism (with its high

____ for PAH) is able to secrete essentially all of the PAH

delivered to the _____ capillaries. Thus, TPAH (calculated from

the data as follows: _____ ) equals the rate of PAH delivery to

the _____ capillaries (calculated from the data as follows:

_____ ).

For PPAH > _____ mg/dl, the rate of PAH delivery to the _____

capillaries exceeds the maximum rate of tubular secretion,

TmPAH ( = ____ ). PPAH ____ mg/dl therefore represents theplasma PAH concentration at which the transport mechanismis

saturated at this GFR and ERPF. Note that for PPAH > ____

mg/dl, the rate of excretion vs. PPAH curve parallels the _____

curve, i.e., it is a _____ _____ with slope ____ , as predicted

by equation B-22.

(4) Clearance vs. PPAH.

For PPAH ____ mg/dl, CPAH = ERPF (equation B-27).

For PPAH > ____ mg/dl, CPAH decreases, and if additional data

were available CPAH would asymptotically approach CIn (which

has been included on the graph as a reference line). This ispredicted by equation B-23 and makes sense: when PPAH is

very high, the filtered load PPAHGFR is so much greater than

TmPAH that the rate of excretion UPAHV is approximately equal

to PPAHGFR, as predicted by equation B-22 when PPAH >>>

TmPAH. Thus, at very high PPAH, PAH behaves approximately

like a substance such as inulin that is _____ only, i.e., CPAHapproaches _____.

It should be noted that the above curves exhibit a gradual change as the rate

of tubular secretion reaches its maximum level. An analogous gradual

change was seen in the renal titration curves for glucose (question 11) and

phosphate (question 12) and is called ____ . The latter term also can beapplied to the PAH curves.1

straight line

GFR

peritubular

16 mg/dl

affinity

peritubular

UPAHV PPAHGFR

peritubular

PPAH(ERPF GFR)

16 mg/dl

peritubular

80 mg/min

16 mg/dl

filtered load vs.

PPAH

straight line

GFR

16 mg/dl

16 mg/dl

filtered

CIn

splay

__________1The explanations offered for the splay in the PAH curves are analogous to those presented in

footnote 1, p 14 for the splay in the glucose titration curves.


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23

19. To consolidate your understanding of Tm-limited secretion and the removal

of secreted substances from the peritubular capillaries, use the data below to

construct renal titration curves for diodrast, a contrast agent used in

radiology whose renal handling is similar to PAH. During the time period

that the data were obtained, CIn was noted to have a constant value of 125

ml/min. [Important note: Answers are provided at the bottom ofpage 24,notin an answer column along the right margin.]

PD UD V Filtered Rate of Rate of CD ERPF Rate of D

mg/dl mg/ml ml/min Load Excretion Tubular Delivery to

Secretion Perit Caps

4 25 1.0

6 37.5 1.0

8 62.5 0.8

10 60.5 1.0 - - 1 - - 1

12 74.4 0.9 - - - -

16 77 1.0 - - - -

20 102.5 0.8 - - - -

30 94.5 1.0 - - - -1The ERPF can be equated to CDonly when the transport mechanism is notsaturated. Hence, ERPF and the rate of

diodrast delivery to the peritubular capillaries cannot be calculated from the data provided when PD > 8 mg/dl.

600

400

200Clearance(ml/min)

PD (mg/dl)

80

40

RateofExcretion

(mg/min)

PD (mg/dl)


RateofTubularSecretion

(mg/min)

Inulin

10 20 30 10 20 30


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24

The basic features of the curves are similar to those for PAH (question 18).

TmD, the ______ , is approximately ____ , and the transport mechanism

becomes saturated at PD ____ mg/dl. That the transport mechanism is

able to remove essentially all of the diodrast from the ____ ____ when the

transport mechanism is not _____ is shown by the fact that TD (calculated

from the data as follows: _____ ) equals the rate of diodrast delivery to the

_____ _____ (calculated from the data as follows: _____ ). Like the PAHtitration curves, the changes in the region where the rate of tubular secretion

reaches its maximum level are gradual, i.e., the curves exhibit ____.

transport maximum

for diodrast

57 mg/min

10 mg/dl

peritubular caps

saturated

UDV PDGFRperitubular caps

PD(ERPF GFR)

Splay

20. As noted in question 13, creatinine is an organic base that is filtered and

secreted. However, normally in humans the amount secreted is only about

10 to 15% of the amount filtered. This means that as an approximation

Rate of excretion Filtered load

or

UCrV PCrGFR (B-31)

________________________________________________________________Answers for p 23 Filtered Rate of Rate of CD ERPF Rate of D

Load Excretion Tubular ml/min ml/min Delivery to

mg/min mg/min Secretion Perit Caps

mg/min mg/min

5 25 20 625 625 20

7.5 37.5 30 625 625 30

10 50 40 625 625 40

12.5 60.5 48 605 - - - -

15 67 52 558 - - - -

20 77 57 481 - - - -

25 82 57 410 - - - -

37.5 94.5 57 315 - - - -

600

400

200Clearance

(ml/min)

PD

(mg/dl)

80

40

RateofExcretion

(mg/min)

PD

(mg/dl)

FilteredLoa

d(mg/min)

RateofTubularS

ecretion

(mg/min)

Inulin

10 20 30 10 20 30


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25

20. (cont.)

Hence, as an approximation, creatinine behaves like a substance that is

filtered only, such as the polysaccharide ____ , and its clearance can be

used to determine the GFR (see question 4 above):

CCr = UCrV GFR (B-32)

PCr

In fact, for clinical purposes, creatinine is preferable to the polysaccharide

____ , even though the resulting GFR value will be an approximation.1

This is because creatinine is an endogenous molecule that is produced from

muscle protein metabolism at a relatively constant rate, whereas the

polysaccharide ____ must be _____ in order to determine GFR (see

question 5 above).

inulin

inulin

inulin

infused IV

21. At this point, it may be helpful to briefly summarize the use of clearance

measurements for the determination of hemodynamic parameters in the

kidney:

Most Accurate Useful ApproximationDetermination for Clinical Purposes

GFR CIn CCr

RPF Fick principle CPAH

Furthermore, recalling that the filtration fraction, FF, is defined as

GFR/RPF (question A-7):

FF CInRPF from Fick

CCr

CPAH

__________1Because a small amount of creatinine is secreted in humans, the GFR will be slightly overestimated when determined

from CCr. However, the overestimate is at least partly corrected because PCrvalues, as measured in clinical laboratories,

tend to be too high (since the colorimetric methods for the determination of PCrmeasure other chromagens as well).


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22. Filtration, reabsorption, and secretion. For a substance that is filtered,

reabsorbed, and secreted

Rate of excretion = Filtered load Rate of tubular reabsorption

+ Rate of tubular secretion

For quantitative purposes, a substance that is filtered, reabsorbed, andsecreted usually is treated according to whether there is netreabsorption or

netsecretion:

If there is net reabsorption (i.e., if the rate of excretion is ____ than

the filtered load), the substance is treated as if it were filtered and

reabsorbed (see question 7 above), even though secretion also has

occurred. Thus, the rate of excretion can be described by the

equation _____ (with TX referring to the netrate of ____ ____),

and the clearance of the substance is ____ than CIn.

If there is net secretion (i.e., if the rate of excretion is ____ than the

filtered load), the substance is treated as if it were filtered and

secreted (see question 13 above), even though reabsorption also

has occurred. Thus, the rate of excretion can be described by the

equation _____ (with TX referring to the netrate of ____ ____),

and the clearance of the substance is ____ than CIn.

Examples of substances that are filtered, reabsorbed, and secreted include

potassium, urea, and uric acid.Note that while bicarbonate normally is filtered andreabsorbed, under conditions of extreme alkalosis it can be filtered, reabsorbed, and secreted(although in the latter case, there is netbicarbonate reabsorption).

less

UXV = PXGFR

TX

tubular

reabsorption

less

greater

UXV = PXGFR +

TX

tubular secretion

greater


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27

23. Summary of general excretion models:

Model Examples Rate of Excretion Clearance Other Remarks

No filtration or

secretion

Plasma proteins,

substances that are

tightly bound to

plasma proteins

UXV = 0 CX = 0

Filtration only Inulin, mannitol UXV = PXGFR CX = GFR CIn used for non-

invasive measure-

ment of GFR

Filtration and

reabsorption

Special case: Tm-

limited reabsorption,

threshold phenomenon

Glucose, amino

acids, sodium,

chloride, phosphate

Glucose, amino

acids, phosphate

UXV = PXGFR TX

If PXGFR TmX,

UXV = 0

If PXGFR > TmX,

UXV

=PXGFR

TmX

CX = CIn TX /PX

(i.e., CX < CIn)

If PXGFR TmX,

CX = 0

If PXGFR > TmX,

CX = CIn

TmX/PX

Filtration and secretion

Special case: Tm-

limited secretion with

complete clearance

from peritubular caps

when transport

mechanism is notsaturated

Organic acids,

organic bases

PAH

UXV = PXGFR + TX

If rate of delivery to

perit caps TmX,

UXV PXRPF

= PXERPF


perit caps > TmX ,

UXV=PXGFR+TmX

CX = CIn + TX /PX

(i.e., CX > CIn)


perit caps TmX,

CX RPF

= ERPF


perit caps > TmX,

CX=CIn + TmX /PX

Because Cr secr is

minor, CCris used

for noninvasive

estimation of GFR

CPAH is used for

noninvasive mea-

surement of ERPF

and noninvasive

estimation of RPF

Filtration, reabsorption,

and secretion

Potassium, urea,

uric acid

Ifnetreabsorption,

same as for filtration

and reabsorption

Ifnetsecretion, same

as for filtration and

secretion

Ifnetreabsorption,

same as for filtration

and reabsorption

Ifnetsecretion, same

as for filtration and

secretion


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C. Fractional excretion, fractional delivery, and fractional reabsorption.

1. The fractional excretion, fractional delivery, and fractional reabsorption are

quantities with numerous applications in renal physiology. This section will

define these quantities and introduce the equations used in their calculation.

2. The fractional excretion(FE) can be defined as the fraction of a filteredsubstance that is excreted in the urine

FE = amount excreted

amount filtered

Dividing both numerator and denominator by time

FE = amount excreted per unit time

amount filtered per unit time

= rate of excretion

filtered loadi.e.,

FEX = ______

Snce CX = UXV/PX, FEX also can be written as

FEX = ______

Furthermore, since GFR = CIn and GFR CCr, additional equations for

FEX are

FEX = ______

FEX ______

UXV

PXGFR

CX

GFR

CX/CIn

CX/CCr

3. The fractional excretion can be calculated using any of the following

equations:

FEX = UXV (C-1)

PXGFR

FEX = CX (C-2)

GFR

FEX = CX (C-3)

CIn

FEX CX (C-4)

CCr


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Two additional equations for fractional excretion also are important.

Substituting CIn = UInV/PIn for GFR in equation C-1 gives

FEX = UX/PX (C-5)

UIn/PIn

and using CCr = UCrV/PCr as an approximation for GFR in equation C-1gives

FEX UX/PX (C-6)

UCr/PCr

Thus, equations C-5 and C-6 allow FEX to be calculated withoutmeasuring

____. Note that the quantity UX/PXby itselftells nothing about how much of

the filtered X is excreted because the value of UX/PX will vary depending on

the amount of water that is reabsorbed. Dividing UX/PX by UIn/PIn (or

UCr/PCr) corrects for water reabsorption (see below).

V

4. Of the equations for FEX, those in which U/P concentration ratios appear are

of particular interest (equations C-5 and C-6). One feature is that theyallow FEX to be calculated withoutmeasuring ____ , as noted above. An

additional feature can be appreciated with the aid of a terminology

switch: instead of using the term fractional excretion (FEX), we can use the

alternative term fractional delivery (FDX) because the fraction of the

filtered X that is excreted in the urine also represents the fraction of the

filtered X that is delivered to the urine. Thus, FDX can be substituted for

FEX in equations C-5 and C-6. Now, imagine moving from the urine up into

the tubule, sampling tubular fluid instead of urine. We could then substitute

tubular fluid concentration values (TF) for urine concentration values (U) in

equations C-5 and C-6:

FDX = TFX/PX (C-7)TFIn /PIn

and

FDX TFX/PX (C-8)

TFCr /PCr

These equations can be used to calculate the fraction of the filtered X that is

delivered to the point in the tubule from which the tubular fluid sample

was obtained (in experimental studies of renal function, such samples are obtained

by micropuncture). Note that the quantity TFX/PXby itselftells nothing about

how much of the filtered X is delivered to some point in the tubule

because the value of TFX/PX will vary depending on the amount of water

that is reabsorbed. Dividing TFX/PX by TFIn/PIn (or TFCr/PCr) corrects forwater reabsorption (see below).

V


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30

5. The fractional reabsorption (FR) can be defined as the fraction of a

filtered substance that has been reabsorbed. Once the fractional excretion

has been determined (by any equation in the C-1 to C-6 set), the fractional

reabsorption can be calculated easily, since

FRX = 1 FEX (C-9)

Similarly, once the fraction of a filtered substance that has been delivered

to some point in the tubule has been determined (using equation C-7 or C-

8), the fraction of the filtered substance reabsorbed from the tubular fluid

during its journey from Bowmans space to that point is given by

FRX = 1 FDX (C-10)

6. Summary of equations for fractional excretion, fractional delivery, and

fractional reabsorption:

Fractional Excretion

(FEX)

Fractional Reabsorption

(FRX)

UXV

PXGFR

CX

GFR

CX

CIn

CX

CIn

UX /PX

UIn/PIn

UX /PX

UCr/PCr

1 FEX

Fractional Delivery to

Point of Sample

(FDX)

Fraction Reabsorbed up to

Point of Sample

(FRX)

TFX /PX

TFIn/PIn

TFX /PX

TFCr/PCr

1 FDX


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7. To consolidate your understanding of fractional excretion, fractional

delivery, and fractional reabsorption, complete the following table:

Inulin Potassium

Low K+ Diet Normal Diet Vegetarian Diet

PX

TFX

end of proximal tubule

macula densa

UX

0.5 mg/ml

1.5 mg/ml

6 mg/ml

50 mg/ml

4 mM

4 mM

4.8 mM

20 mM

4 mM

4 mM

4.8 mM

80 mM

4 mM

4 mM

4.8 mM

640 mM

Fractional delivery to

point of sample


macula densa

Fractional excretion

Fraction reabsorbed up

to point of sample


macula densa

Fractional reabsorption - - 1

1.0

1.0

1.0

0

0

0

0.33

0.1

0.05

0.67

0.9

0.95

0.33

0.1

0.2

0.67

0.9

0.8

0.33

0.1

1.6

0.67

0.9

-- 1

1Since the fractional excretion exceeds 1.0, the amount excreted is greater than the

amount filtered, i.e., net secretion has occurred.

8. Equations for the fractional excretion, fractional delivery, and fractional

reabsorption of a substance now have been derived. However, it should be

noted that the fractional excretion, fractional delivery, and fractional

reabsorption of water also are important quantities, particularly when the

discussing the urinary concentration and dilution mechanisms. The

equations for water (which have many similar features to the equations in

the table on p 30; see question 12 below) are derived in the following

questions.


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9. The fractional excretion of water (FEH2O) can be defined as the fraction of

filtered water that is excreted

FEH2O = amount excreted

amount filtered

Dividing both numerator and denominator by time

FEH2O = amount excreted per unit time

amount filtered per unit time

= V (C-11)

GFR

A more useful equation for FEH2O is obtained by substituting CIn = UInV/PIn

for GFR

FEH2O = 1 (C-12)

UIn/PIn

Equation C-12 makes sense: since inulin is filtered but neither reabsorbed

nor secreted, the difference between UIn and PIn can be attributed exclusively

to the reabsorption of water. For example, if U In = 10PIn, ___ % of the

filtered water must have been reabsorbed, ____ % is excreted; this intuitive

result also is predicted by equation C-12. Another very useful equation for

FEH2O is obtained by substituting CCr = UCrV/PCras an approximation for

GFR in equation C-11

FEH2O 1 (C-13)

UCr/PCr

Note that equations C-12 and C-13 allow FEH2O to be calculated without

measuring ____ . Another important feature of equations C-12 and C-13 is

discussed in the following question.

90%

10%

V

10. Of the equations for FEH2O, those in which U/P ratios appear (equations C-

12 and C-13) are particularly useful. One feature is that they allow FEH2O to

be calculated withoutmeasuring ____ , as noted above. An additional

feature can be appreciated with the aid of the same terminology switch

that was introduced when FEX was discussed above (question 4): instead of

using the term fractional excretion of water (FEH2O), we can use the

alternative term fractional deliveryof water (FDH2O)because the fraction

of the filtered water that is excreted in the urine also represents the fractionof the filtered water that is delivered to the urine. Thus, FDH2O can be

substituted for FEH2O in equations C-12 and C-13. Now, imagine moving

from the urine up into the tubule, sampling tubular fluid instead of urine.

We could then substitute tubular fluid concentration values (TF) for urine

concentration values (U) in equations C-12 and C-13

V


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33

FDH2O = 1 (C-14)

TFIn/PIn

and

FDH2O 1 (C-15)

TFCr/PCr

Thus, the ratios TFIn/PIn and TFCr/PCr are very useful in discussions of the

urinary concentration and dilution mechanisms, since the fraction of filtered

water delivered to various points in the tubule are important in such

discussions (see question 14 below).

11. The fractional reabsorption of water (FRH2O) can be defined as the

fraction of filtered water that has been reabsorbed. Once the fractional

excretion of water has been determined (by any equation in the C-11 to C-

13 set), the fractional reabsorption can be calculated easily, since

FRH2O = 1 FEH2O (C-16)

Similarly, once the fraction of filtered water that has been delivered to

some point in the tubule has been determined (using equation C-14 or C-

15), the fraction of filtered water reabsorbed from the tubular fluid during

its journey from Bowmans space to that point is given by

FRH2O = 1 FDH2O (C-17)

12. Summary of equations for fractional excretion, fractional delivery, and

fractional reabsorption of water:


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34

Fractional Excretion of Water

(FEH2O)

Fractional Reabsorption of Water

(FRH2O)

V

GFR

1UIn/PIn

1

UCr/PCr

1 FEH2O

Fractional Delivery of Water

to Point of Sample

(FDH2O)

Fraction of Water Reabsorbed

up to Point of Sample

(FRH2O)

1

TFIn/PIn

1TFCr/PCr

1 FDH2O

13. Having derived the above equations for FEH2O, FDH2O, and FRH2O, it should

be noted that the same equations also could be obtained from the equations

for FEX, FDX, and FRX (question 6) by setting UX/PX (or TFX/PX) equal to

1.0 . This substitution is valid because UH2O/PH2O and TFH2O/PH2Odo equal

1.0: the concentration of water is 55 mol/liter in plasma, urine, and tubular

fluid.


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14. To consolidate your understanding of FEH2O, FDH2O, and FRH2O, complete

the following table:UCSD Medical Student UCSD Medical Student

during a Santa Ana after a Post-OP

Condition Beer Binge

PIn

TFIn


tip of papilla

macula densa

end of cortical CD

middle of medullary CD

UIn

0.1 mg/ml

0.3 mg/ml

1.2 mg/ml

1.2 mg/ml

2.0 mg/ml

10 mg/ml

20 mg/ml

0.1 mg/ml

0.25 mg/ml

0.8 mg/ml

0.8 mg/ml

0.8 ml/ml

0.8 mg/ml

0.8 mg/ml

Fraction of filtered H2O delivered

to point of sample


tip of papilla

macula densa

end of cortical CD


FEH2O

Fraction of filtered H2O reabsorbed

up to point of sample


tip of papilla

macula densa

end of cortical CD


FRH2O

0.33

0.083

0.083

0.05

0.01

0.005

0.67

0.917

0.917

0.95

0.99

0.995

0.4

0.125

0.125

0.125

0.125

0.125

0.6

0.875

0.875

0.875

0.875

0.875

quantitation of renal function1

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