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# Urogenital Infections and Inflammations

T.E. Bjerklund Johansen, F. M.E. Wagenlehner, Y.-H. Cho, T. Matsumoto, J. N. Krieger, D. Shoskes, K. Naber

# Antibiotic therapy in patients with renal impairment

1 Department Internal Medicine 1, Nephrology, University Hospital Ulm, Ulm, Germany

## Abstract

Every second drug needs dose adjustment to kidney function. The Cockcroft and Gault formula gives an estimate of the individual kidney function whereas the CKD-EPI and other formulas state only the standardized GFR. Pharmacokinetics should be considered to avoid accumulation and toxic drug effects. Pharmacodynamics should be considered to avoid sub therapeutic under dosage. High peak concentrations are the target for antibiotics with a concentration-dependent action (gentamicin, amikacin, levofloxacin, ciprofloxicin, daptomycin, linezolid, colistin and most anti-fungal drugs). High trough concentrations are the target for antibiotics with  time-dependent action (ampicillin, piperacillin, cefazolin, ceftazidime, meropenem, clarithromycin, doxycycline, vancomycin and all anti-viral drugs). From such pharmacokinetic and pharmacodynamic principles the following recommendations might be derived for the adjustment of antimicrobial drugs to the kidney function.

1. Start anti-infective treatment within 1 hour.
2. Use a loading dose (Dstart) – at least the normal or even a higher bolus dose.
3. If the GFR is above 60 ml/min no dose adjustment is needed.
4. Dose adjustment (D) should follow not before day 3 of the antibiotic therapy.
5. If the estimated half-life is less than the normal administration interval no dose reduction should be made, but use at maximum the half-maximum standard dose.

After hemodialysis a supplementary dose should be given to replace the removed fraction. During continuous renal replacement therapy usually a normal or near normal dose might be advisable. In the most critical patients, the continuous infusion of anti-infective drugs might allow for higher and more efficacious dosing without an increased risk of toxicity (meropenem, piperacillin, oxacillin, vancomycin, acyclovir).

## Abbreviations

AUC: area under the concentration time curve (h x mg/l)
BSA: body surface area (sqm)
CE05: threshold concentration producing 5% of Emax
CE50: concentration producing 50% of maximum effect Emax
CE95: ceiling concentration producing 95% Emax
Cl: drug clearance (l/h)
CLCrea: creatinine clearance (ml/min)
Cpeak: peak steady state concentration (mg/l)
Ctrough: trough steady state concentration (mg/l)
D: dose (mg)
E: effect
F: bioavailable fraction
FR: fraction eliminated by hemodialysis
fren: fraction eliminated by renal route
GFR: glomerular filtration rate (ml/min)
IR: infusion rate (mg/h)
MIC: minimal inhibitory concentration (mg/l)
PB%: plasma protein binding (%)
R: accumulation factor
sCrea: serum creatinine (µmol/l)
t: time (h)
Tceiling-threshold: ceiling-to-threshold time (h)
T1/2: half-life (h)
Vd: volume of distribution (l)

## Summary of recommendations

For kidney failure with a GFR<60 ml/min the following recommendations could be made.

1. The individual GFR and the individual half-life should be estimated based on the fraction eliminated by the renal route (fren) – or even better, by interpolating between the half-life values for normal (T1/2norm) and failing (T1/2fail) kidney function.
2. The dose should be adjusted by using the eliminated fraction rule (Dettli 3). This means that the usual target is the normal peak.
3. Antibiotics with a concentration-dependent action need a high ceiling (CE95) meaning that peak concentrations (Cpeak) should be selected as the target but an extension of the administration interval is less critical
4. Antibiotics with a time-dependent action have a high threshold (CE05) meaning that a high trough concentration (Ctrough) should be selected as the target. Thus the administration interval must not be prolonged – at least not to more than one half-life. The dose should be reduced if the individual half-life is longer than the administration interval.
5. Most practically and according to Kunin, the maintenance dose is one half of the normal dose when the administration interval corresponds to one half-life.

Under renal replacement therapy the risk of insufficient under dosage is even higher than the risk of toxic overdose.

1. The antibiotic dose for continuous renal replacement therapy (D CRRT) should be derived from the total creatinine clearance (CLcrea). If kidney function is deteriorating or improving the kinetGFR could be used to give an estimate of how residual kidney function and renal replacement impact on drug kinetics.
2. For patients treated with intermittent hemodialysis the rule is to administer the antibiotics after dialysis (D HD) just to maintain effective drug levels also between the procedures. The dose after dialysis corresponds to the normal loading dose in most cases.
3. If the antibiotic is administered before dialysis a higher dose is needed that must preemptively replace the fraction removed by dialysis (FR).
4. In cases with suspected overdose an additional hemodialysis could be recommended to remove the excess amount from the body.

## 1 Introduction

In patients with impaired kidney function one must be aware of two errors when using antibiotics for treatment of infectious diseases. The first error emerges from drug toxicity due to excessive accumulation. One example is cefepime where neurotoxicity occurs in up to 20% of kidney patients – and some cases even die [1]. The other error results from underdosage due to overcautious dose adjustment. Former examples for underdosage were vancomycin and ciprofloxacin [2]. The dosing information of the producer in the package inserts follow often the proportional dose reduction rule by Dettli. Such dose recommendations may lead to inadequate exposures of ceftolozane-tazobactam, ceftazidime, cefotaxime, ciprofloxacin, erythromycin, imipenem, levofloxacin, and teicoplanin in patients with kidney dysfunction [3].

To avoid the first error, namely accumulation, one needs to apply pharmacokinetic principles. To avoid the second error, namely underdosage, one needs to apply pharmacodynamic principles. Both risks increase with the severity of the infectious affection. The main reason for drug accumulation is impaired kidney function. Kidney dysfunction can occur as a typical complication in the most critical cases under intensive care conditions. Mainly in the intensive care setting pharmacokinetic and pharmacodynamic considerations are helpful to improve antibiotic therapy.

## 2 Methods

A systematic literature search was continuously performed during the last 30 years in PubMed with the following keywords: pharmacokinetics, pharmacodynamics, clearance, volume, half-life, hemodialysis, hemofiltration and the following limitations: volunteers, patients, clinical studies. A total of 50,000 parameters were recorded from 10,000 publications in the NEPharm database [4]. The following statements on antibiotic dosing can be rated only with an evidence level LE of 3 or less and the strength of recommendations can be graded only with a C according to the system used in the EAU guidelines. In each patient, the decision about benefit or burden of the antibiotic dosing remains the responsibility of the treating physician.

### Kidney function

Drug elimination depends on kidney function. Therefore, an estimate of kidney function is needed to derive the appropriate dosage. The acute kidney injury (AKI) is distinguished from chronic kidney disease (CKD). For dose adjustment, not the creatinine but the glomerular filtration rate (GFR) gives the established measure in patients with kidney dysfunction.

The GFR can be used as a basis for estimating the effect of kidney dysfunction on drug pharmacokinetics. Today, the estimated GFR (ml/min) is provided by most clinical chemistry labs from the measured serum creatinine with the CKD-EPI formula. However, the output is a standardized eGFR in ml/min per 1.73 sqm body surface area. Accordingly, the individual GFR is less or more than the eGFR depending on the body surface area (BSA). That means the individual weight (kg) and height (cm) must be respected.

$GFR=eGFR*\frac{BSA}{1.73}$

$BSA=\frac{\sqrt{weight*height}}{60}$

Since the individual BSA is rarely calculated in the ICU, the advantage of the Cockcroft and Gault formula (C&G) can clearly be seen. The C&G equation considers not only the age (years) but also the weight (kg) to estimate the individual GFR. The most convenient C&G formula holds also for the new calibrated enzymatic creatinine (mcmol/l) and it is a coefficient-free version of the original C&G formula [5]. This GFR estimate can be easily memorized and calculated in mind.

$GFR=\frac{150-Age}{sCrea}*weight$

However, the acute kidney injury (AKI) is likely the bigger problem in the intensive care medicine than the CKD. The staging of CKD is based on GFR whereas the staging of AKI is based on the serum creatinine. It is a great advantage that also for AKI with changing kidney function as in the ICU a creatinine-based estimate of the GFR exists namely the kinetic GFR [6]. The kineticGFR is derived from creatinine production (GFR x sCrea = creatinine elimination), the creatinine distribution volume (Vd = 0.65 x Weight) and the maximum possible change in serum creatinine (delta Crea in µmol/l) within 24 hours (delta t in hours). Accordingly, a simplified version for the kinetGFR estimate can be derived from the C&G formula.

$kinetGFR=\frac{150-Age}{Crea_{i}}*weight-0.65*\frac{Crea_{i}-Crea_{i-1}}{t_{i}-t_{i-1}}$

If the creatinine rises every 12 hours by 50 µmol/l to 200 µmol/l, a 60 years old patient with a weight of 75 kg will have a decline in the kinetGFR from 65 to 43 ml/min. Conversely, if the creatinine improves every 12 hours by 50 µmol/l to 150 µmol/l, the kinetGFR rises from 36 to 48 ml/min.

Such a practical estimate of kidney function is helpful for drug dose adjustment in AKI. There is, however, not only the impaired kidney function due to AKI or CKD but also the case with overhydration and augmented renal clearance. The AKI and CKD usually need a drug dose reduction, but overhydration and augmented renal clearance need a higher dose. This is especially true for pregnant women, young patients with cystic fibrosis/ mucoviscidosis, patients with burns and patients in the hyperdynamic state of sepsis – usually temporary and variable conditions.

Augmented renal clearance only needs a higher maintenance dose. In contrast, the excessive volume expansion due to overhydration needs both, a higher loading dose and a higher maintenance dose – just as with weight-based dosing in children.

### Kidney dysfunction and pharmacokinetic parameters

To correlate drug elimination with kidney function, originally, a linear dependence of the elimination rate constant (Ke) from creatinine clearance has been demonstrated [7]. The elimination rate constant is the inverse half-life where it holds (ln(2)=0.693).

$T_{1/2}=\frac{0.693}{Ke}$

Today, such a linear dependence from kidney function (GFR), can be found for the clearance (Cl), the volume (Vd), the plasma binding (PB%) and the half-life (T1/2). If the specific parameters for the extremes of normal and failing kidney function have been determined, the respective individual parameter values can be estimated by interpolation.

$Cl=Cl_{fail}+\frac{Cl_{norm}-Cl_{fail}}{GFR_{norm}}*GFR$

$Vd=Vd_{norm}\pm&space;\frac{Vd_{fail}-Vd_{norm}}{GFR_{norm}}*GFR$

$PB\%&space;=PB\%&space;_{norm}\pm&space;\frac{PB\%&space;_{fail}-PB\%&space;_{norm}}{GFR_{norm}}*GFR$

$T_{1/2}=\frac{T_{1/2norm}}{1-\left&space;(&space;1-\frac{T_{1/2norm}}{T_{1/2fail}}&space;\right&space;)*\left&space;(&space;1-\frac{GFR}{GFR_{norm}}&space;\right&space;)}$

The changes in half-life and clearance are usually inversely proportional since changes in volume and binding are much less compared to changes in clearance and half-life.

$Cl=\frac{0.693*Vd}{T_{1/2}}\cong&space;\frac{const.}{T_{1/2}}$

If the clearance is reduced to 10 % the half-life will increase by the factor of 10 as can be seen with the example of amoxicillin.

### Accumulation kinetics

To derive dose adjustment rules, the accumulation kinetics must be considered: If a drug is given with a constant administration interval, the steady state will be reached after 4.32 half-lives (exactly to 95 %). In the steady state the concentrations will oscillate between the peak (Cpeak) and the trough concentrations (Ctrough) depending on half-life (T1/2) and administration interval (Tau).

$C_{peak}=\frac{C_{1}}{1-exp\left&space;(&space;-0.693*\frac{Tau}{T_{1/2}}&space;\right&space;)}$

$C_{trough}=\frac{C_{1}}{exp\left&space;(&space;0.693*\frac{Tau}{T_{1/2}}&space;\right&space;)-1}$

For repetitive dosing, the average concentration (Css=Caverage) is the steady state concentration which is the logarithmic mean of peak and trough values.

$C_{average}=\frac{C_{peak}-C_{trough}}{ln\left&space;(&space;C_{peak}&space;\right&space;)-ln\left&space;(&space;C_{trough}&space;\right&space;)}$

The average concentration can best be derived from the drug clearance (Cl) especially for the case of continuous infusion. The infusion rate (IR) is the dose (D) that is administered continuously within the time of infusion (T).

$IR=\frac{D}{T}$

$C_{average}=\frac{IR}{Cl}$

An example is meropenem, where the average concentration is the target concentration of 8 to 16 mg/l [8].

## 3 Results for dose adjustment

When treating patients with infection, it is important to start immediately and not to underdose as Paul Ehrlich already in 1913 stated: “Frapper vite et frapper fort”. If the clinical diagnosis of an infection has been made, the first step is to withdraw material for microbiology from urine and blood. But immediately after securing the material the antibiotic treatment should be initiated without a delay and within 60 minutes caled the “golden hour” [9]. The immediate therapy usually begins with an empirical or calculated antibiotic regimen depending on local experience. The specific antibiotic treatment can be modified later when the microbiological findings are available. The antibiotic treatment starts with a loading dose that primarily is the normal dose (Figure 1). However, in the intensive care medicine, patients frequently are overhydrated and need an even higher loading dose.

$D_{start}=D_{norm}*\frac{weight\left&space;(&space;kg&space;\right&space;)+water\left&space;(&space;l&space;\right&space;)}{65\left&space;(&space;kg&space;\right&space;)}$

Thus, also for normal kidney function the loading dose can be higher than the normal dose (e.g. teicoplanin). For kidney dysfunction, the loading dose (Dstart) must be derived from the accumulation factor (R) and normal dose (Dnorm).

$D_{start}=D_{norm}*R_{norm}$

$R_{norm}=\frac{1}{1-exp\left&space;(&space;-0.693*\frac{Tau}{T_{1/2}}&space;\right&space;)_{norm}}$

To adjust the maintenance dose, 3 different rules are available (Figure 2). Luzius Dettli was not only the first to show the linear dependence of drug elimination from kidney function. He also demonstrated how the drug dose can be adjusted in proportion to the reduced drug elimination. There are, however, two possibilities to proportionally adjust the dosing (Figure 1): one can either reduce the maintenance dose (Dettli 1) or extend the administration interval (Dettli 2).

Dettli derived the dose adjustment diagram from the nonrenal fraction (Qo). This Qo is complementary to the fraction eliminated be the renal rout (fren). The fren is found in the literature most easily since it must be stated before approval of a new drug by the authorities (FDA, EMA).

$fren=1-Q_{0}$

$fren=\frac{Cl_{ren}}{Cl_{norm}}$

The fraction eliminated be the renal route can be estimated from the amount eliminated in urine (A urine) under normal conditions.

$fren=\frac{A_{urine}}{D}$

This might help to predicting the individual kinetics of new drugs when more data are not available. It can be predicted that those drugs will need dose adjustment to kidney function where the fren is high since kidney dysfunction will impact the half-life (Figure 2). On the other side, it might be concluded that a dose adjustment generally will not be needed if the GFR is 60 ml/min or more. The most universal form of the Dettli dose adjustment rules can be derived from this fraction eliminated by the renal route (fren).

$\frac{D}{Tau}=\left&space;(&space;\frac{D}{Tau}&space;\right&space;)_{norm}*\left&space;[&space;1-fren*\left&space;(&space;1-\frac{GFR}{GFR_{norm}}&space;\right&space;)&space;\right&space;]$

This solution applies also to the case of augmented renal clearance.

$\frac{GFR}{GFR_{norm}}>&space;1.0$

$\frac{D}{Tau}>&space;\left&space;(&space;\frac{D}{Tau}&space;\right&space;)_{norm}$

The other, however, more frequent problem occurs when kidney function is impaired and one of the 3 Dettli rules applies. If data are available, the dose adjustment should be based on the real parameters estimated for normal (T1/2norm) and failing kidney function (T1/2fail) since the fren is a less reliable parameter.

$for:\frac{GFR}{GFR_{norm}}<&space;1.0$

Dettli 1: The dose is reduced in proportion to the reduced clearance or in reverse proportion to the half-life. Which approach is selected depends on the pharmacokinetic parameter that is available. A doubling of the half-life should have the consequence to reduce the dose to one half.

$Tau=Tau_{norm}=const.$

$D=D_{norm}\frac{Cl}{Cl_{norm}}$

$D=D_{norm}*\frac{T_{1/2norm}}{T_{1/2}}$

The new cephalosporin is ceftolozane + tazobactam with the normal dose of 1,000+500 mg every 8 hours. Since the half-life rises from 2.5 to 36 hours, the producer recommends to reduce the dose to 100+50 mg every 8 hours (Tau = const.). This dose is absurdly low especially if no loading dose and after hemodialysis no supplementary dose are given. Instead, for patients on continuous renal replacement therapy recently a dose of 1,000+500 every 8 hours has been recommend [10].

Dettli 2: Alternatively, the administration interval is extended in proportion to the half-life or inversely to the clearance (Figure 1).

$D=D_{norm}=const.$

$Tau=Tau_{norm}*\frac{T_{1/2}}{T_{1/2norm}}$

$Tau=Tau_{norm}*\frac{Cl_{norm}}{Cl}$

Another proportional dose reduction is the combined Dettli 1 and Dettli 2 rule that applies to continuous infusion. The infusion rate (IR) is the dose continuously administered within the time of infusion (T). If the infusion is performed for a sufficient period of time, a steady state occurs after 4.32 times the half-life, and this steady state produces the average steady state concentration (Caverage). Here the drug clearance gives a practical estimate of the elimination process since the average concentration is the ratio of infusion rate and clearance. If the average steady state concentration is the target, the infusion rate should be adjusted in proportion to the clearance.

$C_{average}=const.$

$IR=IR_{norm}*\frac{Cl}{Cl_{norm}}$

However, when the antibiotic is administered by continuous infusion there is no immediate and sufficient concentration established. The steady state takes 4.32 half-lives to occur (C → Caverage).

$C=C_{average}*\left&space;[&space;1-exp\left&space;(&space;-0.693*\frac{t}{T_{1/2}}&space;\right&space;)&space;\right&space;]$

Therefore, a loading dose is essential when giving the antibiotic by continuous infusion. This loading dose should be administered as a bolus within less than one hour. Frequently it has been proposed to derive the special loading dose (Dss) from the average steady state concentration. This needs the volume to be determined. Since 5 different volume terms can be identified the steady state volume (Vss) is preferred.

$D_{ss}=C_{average}*Vss$

But this loading dose (Dss) might be insufficient as can be shown with meropenem where the volume is 24 liters. The target steady state concentration should be 4 times the MIC [8], [11]. Accordingly, the target concentration is 8 to 16 mg/l and the respective loading dose (Dss) would only be 200 to 400 mg but never in the range of the normal dose of 1,000 mg (see below).

Kunin rule: A completely different solution for drug dose adjustment has been proposed by Calvin Kunin [12]. The treatment starts with a loading dose that is the product of the normal dose (Dnorm) and the normal accumulation factor (Rnorm). In doubt the loading dose is the normal dose. Since after one half-life the drug in the body will be reduced by one half, the adjusted maintenance dose is the half normal dose and the administration interval is one half-life time. This rule makes only sense, however, if the half-life is close to or even longer than the normal administration interval.

$D_{start}=D_{norm}*R_{norm}$

$\frac{D}{Tau}=\frac{1/2*D_{start}}{T_{1/2}}$

With the Kunin rule, the recommended dose for ceftolozane + tazobactam is a loading dose of 1,000+500 mg and a maintenance dose of 500+250 mg. But the administration interval should be extended to 24 hours since the half-life is 36 hours in renal failure. Since during continuous hemofiltration the half-life is 13 hours, a dose of 1,000+500 could be given every 12 hours (see Table 1 at the end of the chapter).

Dettli 3 (=David Czock rule): The most universal dose adjustment rule is the eliminated fraction rule that has been introduced by David Czock [3]. The eliminated fraction rule originally was proposed also by Luzius Dettli but he never has put this into an equation. The eliminated fraction depends on the half-life (Figure 3).

$D=D_{start}*\left&space;[&space;1-exp\left&space;(&space;-0.693*\frac{Tau}{T_{1/2}}&space;\right&space;)&space;\right&space;]$

$D_{start}=\frac{D_{norm}}{1-exp\left&space;(&space;-0.693*\frac{Tau}{T_{1/2}}&space;\right&space;)_{norm}}$

$D=D_{norm}*\frac{1-exp\left&space;(&space;-0.693*\frac{Tau}{T_{1/2}}&space;\right&space;)}{1-exp\left&space;(&space;-0.693*\frac{Tau}{T_{1/2}}&space;\right&space;)_{norm}}$

Primarily, Dettli 3 means that the peak concentration is the target and should be constant.

$C_{peak}=C_{target}=const.$

But Dettli 3 can be modified by defining the new target concentrations to derive an appropriate administration interval (Figure 2).

$Tau=\frac{T_{1/2}}{0.693}*ln\left&space;(&space;\frac{C_{peak}}{C_{trough}}&space;\right&space;)_{target}$

Dettli 3 corresponds to the Kunin rule for the case where the target is the peak and the administration interval is equal to one half-life. On the other side, the Dettli 3 rule corresponds to Dettli 2 for the case that both, the peak and the trough are unchanged and taken as the targets. Then the interval must be extended in proportion to the half-life. The Dettli 3 also corresponds to Dettli 1 if the constant area under the curve AUC is the target. With Dettli 1 the administration interval and the average steady state concentration are constant. Accordingly, the peaks are less but the troughs are higher than normal, where F is the bioavailable fraction after oral dose.

$AUC_{ss}=C_{average}*Tau=const.$

$C_{average}=\frac{F*D_{norm}}{Cl_{norm}}=\frac{F*D}{Cl}=const.$

$D_{startSS}=\frac{D_{norm}*\frac{T_{1/2norm}}{T_{1/2}}}{1-exp\left&space;(&space;-0.693*\frac{Tau_{norm}}{T_{1/2}}&space;\right&space;)}$

As with meropenem (see below), the immediate bolus loading dose (DstartSS) should be given simultaneously when starting the antibiotic administration by infusion. By this measure the average steady state concentration can immediately be established and continuously maintained. Thus, the adjusted maintenance dose (D) is the eliminated fraction of the specific loading dose that follows the Dettli 1 adjustment rule and Dettli 1 is also a special case of the Dettli 3 rule.

$C_{average}=\frac{D_{startSS}}{Vss}*exp\left&space;(&space;-0.693*\frac{t}{T_{1/2}}&space;\right&space;)+\frac{IR}{Vss}*\frac{0.693}{T_{1/2}}*\left&space;[&space;1-exp\left&space;(&space;-0.693*\frac{t}{T_{1/2}}&space;\right&space;)&space;\right&space;]$

$C_{average}\cong&space;const.$

$D_{start}>&space;D_{startSS}>&space;D_{ss}$

According to a most recent meta-analysis the continuous infusion of piperacillin or meropenem is superior to bolus administration with an evidence level of LE 1a and a grade A recommendation. Thus, the anti-infective response is improved, but simultaneously the mortality and stay in hospital are reduced [14]. The reason and an explanation can be demonstrated below with the pharmacodynamic principles.

### Pharmacodynamics

To decide on which one of the 3 Dettli rules should be applied (including Kunin and Czock) one must take into consideration also pharmacodynamic principles in addition to pharmacokinetic principles. There might be reason to speculate that some antimicrobial effects are irreversible and thus purely dose- or concentration-dependent. The irreversibility of the effect follows from the assumption that the antibiotic is killing the bacterial cells – the bactericidal effect is an irreversible process.

Most papers, however, describe the antimicrobial effect by the saturable Emax model and the sigmoid Hill equation that has been derived for receptor mediated effects [15]. Then, the effect depends on the concentration producing the half-maximum effect (CE50) and on the Hill coefficient (H). The Hill coefficient is a measure for the sigmoidicity of effect concentration curve (Figure 4).

$E=\frac{E_{max}}{1+\left&space;(&space;\frac{CE_{50}}{C}&space;\right&space;)^{H}}$

The concentration producing the half maximum effect gives an idea of the potency. The less the CE50 is that will be needed to already produce the half-maximum effect the higher is the potency of the drug.

$potency=\frac{1}{CE_{50}}$

The Hill coefficient indicates the sigmoidicity (Figure 4). Sigmoidicity means that at the beginning of the curve with low concentrations the effect only slightly increases and this increase is less than proportional to the rise in concentrations. Then at the CE50 there is an even over-proportionate increase, and this over proportional effect increase might make such antibiotics attractive. But for slightly higher concentrations the effect is already at maximum and saturated.

The transformed Hill equation allows to derive an exact definition of the threshold concentration (CE05) where the effect is only 5% of Emax and of the ceiling concentration (CE95) where the effect is already 95% of Emax since it holds (1.0/0.05–1.0=19).

$C=CE_{50}*\left&space;(&space;\frac{E_{max}}{E}&space;-1\right&space;)^{\frac{-1}{H}}$

$CE_{05}=CE_{50}*19^{}\frac{-1}{H}$

$CE_{95}=CE_{50}*19^{\frac{1}{H}}$

The target concentration range may be defined between the ceiling and the threshold concentration, and the time between ceiling and threshold (Tceiling-threshold) can be derived. It depends on the half-life and the Hill coefficient [4].

$T_{ceiling-threshold}=T_{1/2}*\frac{8.5}{H}$

This ceiling-to-threshold time is 13 hours for gentamicin since the Hill coefficient is 1.3 and the half-life is 2.0 hours. This ceiling to threshold time is also in agreement with the known postantibiotic effect of 10 to 18 hours [16]. It has long been speculated that the concentrations producing the half-maximum effect is correlated to the minimal inhibitory concentration in microbiology (CE50↔MIC). The probably more plausible concept is to identify the threshold concentration with the minimal inhibitory concentration (CE05 = MIC).

$MIC=CE_{05}$

The common practice is to set the target concentration for piperacillin, meropenem, or cefotaxim at 4 times the MIC. This would mean that the target concentration is 4-times the threshold concentration. If the Hill coefficient is H=2.13, the 4-fold threshold concentration is in the range of the concentration CE50 producing the half maximum effect.

$for:H=2.13$

$CE_{05}=CE_{50}*19^{\frac{-1}{2.13}}=0.25*CE_{50}=\frac{1}{4}*CE_{50}$

$4*MIC=4*CE_{05}$

The Hill coefficient gives a theoretical explanation for the empirical statement that the target should be 4 times the MIC. The Hill coefficient also explains the difference between antimicrobials with a time-dependent effect in contrast to antimicrobials with concentration-dependent action. Antibiotics with a time-dependent effect had a Hill coefficient of H=3.0 which is significantly higher than the Hill coefficient of H=1.9 for the antibiotics with concentration-dependent action [15]. For example, gentamicin, amikacin, levofloxacin, ciprofloxicin, daptomycin, linezolid, voriconazole or colistin are classified as drugs with a concentration-dependent action but ampicillin, piperacillin, cefazolin, ceftazidime, meropenem, clarithromycin, doxycycline or vancomycin are classified as drugs with time-dependent effects [17].

### Renal replacement therapy

Acute kidney injury and chronic kidney disease are frequently encountered in the intensive care unit. If conservative management fails, renal replacement therapy is required. Two different modalities of renal replacement therapy must be distinguished: continuous hemofiltration and intermittent hemodialysis. Both modalities have a considerable but different impact on drug pharmacokinetics and thus dose adjustment.

With hemofiltration as a continuous renal replacement therapy (CRRT) a measure is needed for the effect on drug elimination. The most evident approach is the total creatinine clearance since creatinine is eliminated by natural and artificial filtration.

$CLCrea_{tot}=Filtration_{kidney}+Filtration_{CRRT}$

Practically, the C&G derived kinetGFR gives a reliable estimate of the total creatinine clearance [6]. Thus, the kinetGFR indicates the impact on drug elimination for both possibilities of changing kidney function – worsening or improving and for renal replacement therapy (Figure 5).

$kinetGFR\leftarrow&space;CLCrea_{tot}$

$T_{1/2CRRT}=\frac{T_{1/2norm}}{1-\left&space;(&space;1-\frac{T_{1/2norm}}{T_{1/2fail}}&space;\right&space;)*\left&space;(&space;1-\frac{kinetGFR_{CRRT}}{GFR_{norm}}&space;\right&space;)}$

The colistin half-life rises from normal 3 hours to 24 hours in renal failure. When on continuous renal replacement therapy the kinetGFR of 35 ml/min might be estimated and the half-life of 7 hours can be predicted. Thus, the normal dose of 320 mg every 8 hours should be adjusted to 320 mg every 12 hours.

There are however some drugs that are eliminated be glomerular filtration but afterwards mainly reabsorbed by tubular uptake. One example is fluconazole where the half-life dramatically increases in renal failure from 25 to 110 hours. When the kinetGFR is 30 ml/min during CRRT, conversely, the filtration is nearly complete but no tubular reabsorption occurs. Thus, the half-life during CRRT is 30 hours or close to 25 hours and a normal dose is needed.

More complex are the kinetics when intermittent hemodialysis is performed (HD). The pharmacokinetic impact of hemodialysis can be quantitated by the fraction eliminated during one dialysis (FR). If hemodialysis is performed only for a short time period or less than 4 hours, a rebound of drug levels frequently is observed after dialysis. This rebound is due to a redistribution phenomenon of the drug from the tissue into the plasma. This rebound can lead to an overestimation of the effect of hemodialysis on drug elimination. If hemodialysis is performed for a time longer than 3 times the re-distribution alpha half-live, however, the redistribution from tissue is less than 10% and negligible.

Generally, the fraction removed by hemodialysis can be estimated from the elimination or beta half-life during dialysis (T1/2 HD).

$FR=1-exp\left&space;(&space;-0.693*\frac{t_{HD}}{T_{1/2HD}}&space;\right&space;)$

The effect of hemodialysis on drug kinetics must be replaced by the substitution dose or supplementary dose (Dsuppl). A common practice is to administer the dose after dialysis just to safekeeping the drug from wasting and just to guarantee sufficient drug levels during the interval between dialysis. Accordingly, the dose after hemodialysis (DHD) is both, the dose adjusted to kidney failure and the supplementary dose (Figure 6).

$D_{HD}=D_{fail}+D_{suppl}$

The supplementary dose replaces the amount of the drug that is eliminated during dialysis. This amount is a function of the removed fraction (FR), of the loading dose (Dstart) and of the dose adjusted to renal failure (Dfail). When hemodialysis is performed at the end of the administration interval the amount in the body is the difference between the loading dose (Dstart) and the maintenance dose (Dfail).

$D_{suppl}=FR*\left&space;(&space;D_{start}-D_{fail}&space;\right&space;)$

By transformation it can be shown that the dose after dialysis is often just the loading dose.

$D_{HD}=D_{start}*\left&space;[&space;1-exp\left&space;(&space;-0.693*\left&space;\{&space;\frac{t_{HD}}{T_{1/2HD}}+\frac{Tau}{T_{1/2fail}}&space;\right&space;\}&space;\right&space;)&space;\right&space;]$

The normal acyclovir half-life is 2.5 hours but 25 hours in renal failure. During 4 hour hemodialysis the removed fraction is 50% since the half-life on dialysis is 4 hours. The dose adjusted to renal failure is 360 mg every 24 hours but the dose after dialysis should be 560 mg. Since 25% of the loading dose will persist in the body, the dose after dialysis is 75% of the normal 750 mg dose. This solution can often be simplified and the dose after dialysis is the loading dose the longer (tHD>4 h) and more efficiently the dialysis is performed.

$D_{HD}\cong&space;D_{start}$

This advice applies for the recommendation to administer antibiotics after dialysis just to have antibiotic drug concentrations above the threshold for the complete time interval between the dialysis sessions. However, for aminoglycosides the recommendation has repetitively been made that for example gentamicin should be given immediately before dialysis to produce high peak concentrations [18]. This practice, however, works only if a gentamicin bolus dose is administered before dialysis that must be 4-times higher (320 mg) than the adjusted once-daily maintenance dose (80 mg). The fraction eliminated on dialysis is 75% for gentamicin (FR=0.75).

$D_{beforeHD}=\frac{D_{fail}}{1-FR}$

According to such a high pre-dialysis dose, the amount in the body after dialysis is still 80 mg producing gentamicin concentrations sufficiently high for the time period after dialysis until the next dose is given.

## 4 Further research: target concentration

A high Hill coefficient means that the threshold concentration is high and close to the concentration producing the half-maximum effect. At the same time – and this is not common knowledge – the ceiling concentration will be relatively low and only slightly higher than the CE50 when the Hill coefficient is high (Figure 4). The CE50 is independent from the Hill coefficient and can be estimated as either the geometric mean or the logarithmic mean of the threshold and of the ceiling concentrations.

$CE_{50}=\sqrt{CE_{05}*CE_{95}}$

$log(CE_{50})=\frac{log(CE_{05})+log(CE_{95})}{2}$

Time-dependent effect: Antibiotics with time-dependent action have a high Hill coefficient and a high threshold concentration. But simultaneously, the ceiling concentration is low. The consequence for drug dose adjustment is that the trough concentration must be high to stay above the threshold but the peak concentration is not critical since the ceiling is relatively low and easily obtained (Table 2). The vancomycin target is an AUC24 of 400 above the MIC. Consequently, the recommended trough concentration has been consistently elevated from 10 to 15 mg/l for vancomycin in the last 20 years.

 Concentration-dependent Time-dependent Hill coefficient H<2.0 H>2.0 Threshold concentration = CE05 CE05<>CE50 CE95>CE50 Target concentration range CE95/CE05>19 CE95/CE05<19 Dose adjustment D=const.Tau→extension Tau=const. D→reduction Target for dose adjustment Cpeak ↑ Ctrough ↑ Examples Aminoglycosides (Gentamicin) Quinolones Linezolid Daptomycin Colistin Penicillins Cefalosporins Meropenem Clarithromycin Vancomycin

Concentration-dependent effect: On the other side, there are antibiotics with concentration-dependent action which have a low threshold but a high ceiling concentration. Consequently, the peak concentration should be high for such antibiotics with concentration-dependent action since the ceiling concentration is much higher than the CE50. But the trough concentration is not so critical since the threshold is low (Figure 7).

This contrasts to the view that the time over MIC is the target (%T>MIC). With continuous infusion of piperacillin 8,000 mg per day the average steady state concentration is 25 mg/l and easily above the MIC of even 16 mg/l and achieves a 100%T>MIC for the complete treatment time [19]. But this regimen might be insufficient in patients with normal or even augmented renal clearance [20]. Therefore, one could think the other way that the average steady state concentration with continuous infusion should be 4xMIC. This targets the concentration CE50 producing the half-maximum effect (Caverage~CE50). Since impaired kidney function leads to longer half-life values, the drug kinetics are more similar to continuous infusion than to immediate bolus dosing. Consequently, the target is 4xMIC and not %T>MIC in kidney failure. Otherwise with intermittent dosing the target is a trough concentration above the MIC (Ctrough>MIC).

## 5 Conclusion

A therapeutic drug level monitoring (TDM) is also increasingly recommended (Table 3). This applies to aminoglycosides, to piperacillin, to meropenem, to vancomycin and to linezolid. However, the target concentrations are different in patients with kidney failure as compared to normal conditions. The peak could be the same and constant but the trough concentrations must be higher. If a TDM is established, one must be ready not only to reduce the dose when levels are too high; but also one must be ready to increase the dose if targets are defined but not yet met [11]. Based on the above principles, explicit dose adjustment recommendations can be made (Table 1).

 Target concentration Ctrough Caverage Cpeak Continuous infusion GFR normal GFR<15 ml/min Dose adjusted to GFR GFR normal GFR<15 ml/min Amikacin <10 mg/l 15 mg/l 50 mg/l 50 mg/l Cefazolin 20 mg/l 50 mg/l 200 mg/l 150 mg/l Gentamicin <2 mg/l 3–5 mg/l 10 mg/l 10 mg/l Linezolid 4–8 mg/l 4–8 mg/l 20–30 mg/l 20–30 mg/l Meropenem <4 mg/l 10 mg/l Target=4xMICMIC=2: Caverage=8 mg/lMIC=3: Caverage=12 mg/lMIC=4: Caverage=16 mg/l 40 mg/l 30 mg/l Piperacillin 15 mg/l 60 mg/l Caverage=25 mg/l 250 mg/l 250 mg/l Vancomycin 10 mg/l 15 mg/l Target 24-h AUC/MIC=400 h mg/lMIC=1.0: Css=17 mg/lMIC=2.0: Css=34 mg/lCave: Css>32 mg/l Nephrotoxicity 40 mg/l 30 mg/l
 Drug Brand name Half life [hours] Loading dose Normal kidney funktion [GFR=100 ml/min] Kidney impairment [GFR≈30 ml/min] Failure [GFR≤5 ml/min] & Hemodialysis Hemoflitration [2 L/h] or continuous dialysis Off dialysis day Dfail DHD=Dfail+Dsup Standard iv Route of administration Normal (metab) Failure (metab) Dstart [mg] Maintenance dose [mg] Dose interval [h] Maintenance dose [mg] Dose interval [h] Maintenance dose [mg] Interval [h] Post dialysis DHD [mg] Maintenance dose [mg] Dose interval [h] Abacavir (p.o.) Ziagen 1.5 2.1 600 600 12 600 12 600 12 Aciclovir (i.v.) Acic, Zovirax 2.5 25 750 750 8 500 12 375 24 750 750 24 Adefovir-Dipivoxil (p.o.) Hepsera 7.5/1.6 160 10 10 24 10 48 10 168 10 Albendazol (p.o.) Eskazole 8 8 400 400 12 400 12 400 12 Amantadin (i.v.) (p.o.) PK-Merz 1320 600610 200100 200100 812 200100 7272 200100 168168 200100 200 72 Amikacin Biklin 2 40 Norm/Failure1,500/750 1,500 24 500 24 250 24 750 750 24 Amoxicillin Amoxicillin p.o. 1.2 12 1,000 1,000 8 1,000 12 500 12 1,000 2,000 12 Amoxicillin + Clavulan i.v. Amoxiclav p.o. 1.2 +1.2 12 +4.3 500+125875+125 500+125875+125 88 500+125875+125 1212 500+125500+125 1212 500+125 500+125 12 Amphotericin B iv Amphotericin B 24(360) 35(360) 70 70 24 70 24 50 24 50 50 24 Amphotericin B liposomal AmBisome 24/92 24/160 200 200 24 200 48 200 24 200 200 24 Ampicillin+ Sulbactam Unacid, Ampicillin / Sulbactam 1 13 2,000 2,000 8 2,000 12 1,000 12 2,000 2,000 12 +1 +6.6 +1,000 +1,000 8 +1,000 12 +500 12 +1,000 +1,000 12 Amprenavir Agenerase 8 8 1,200 1,200 12 1,200 12 1,200 12 Anidulafungin Ecalta 26 26 200 100 24 100 24 100 24 100 100 24 Artesunat Artesunate 0.5 180 Atazanavir (p.o.) Reyataz 9 300 24 Atovaquon (p.o.) Wellvone 63 63 750 750 12 Atovaquon + Proguanil (p.o.) Malarone 6314 6323 250+100 250+100 24 250+100 24 250+100 24 Azidothymidin Retrovir 1 1.9(52) 200 200 8 100 8 100 8 200 200 24 Azithromycin po. Zithromax (p.o.) 39 40 1,000 500 24 500 24 500 24 500 – – Brivudin (p.o.) Zostex 14(144) 125 125 24 for 7d Caspofungin Cancidas 10 10 70 50 24 50 24 50 24 50 50 24 Cefaclor (p.o.) Cefaclor Acis 0.7 3 1,000 1,000 8 1,000 12 1,000 12 1,000 Cefazolin Cephazolin 2.2 34 2,000 2,000 8 2,000 12 500 12 1,500 1,000 12 Cefotaxim Cefotaxim 1.2 7(10) 2,000 2,000 8 2,000 12 1,000 12 2,000 2,000 12 Cefotiam Spizef 1 8 2,000 2,000 8 2,000 12 1,000 12 1,500 2,000 12 Ceftaroline - Fosamil Zinforo 27 6 600 600 12 600 12 600 12 600 600 12 Ceftazidim Ceftazidim 2.1 25 2,000 2,000 8 2,000 12 1,000 24 2,000 2,000 12 Ceftobiprol - Medocaril Zevtera 3.3 11 1,000 1,000 8 1,000 12 500 12 1,000 1,000 12 Ceftolozan + Tazobactam 2.5 36 1,000+500 1,000+500 8 500+250 8 500+250 24 1,000+500 1,000+500 12 Ceftriaxon Ceftriaxon 8 15 2,000 2,000 24 2,000 24 2,000 24 2,000 2,000 24 Cefuroxim Cefuroxim.i.v. Cefuroxim p.o. 1.1 18 1,500500 1,500500 88 1,500500 1212 750500 2424 1,500 1,500 12 Chinin=Quinin Chininum 13 15 600 600 12 600 12 600 12 600 600 12 Chloramphenicol Chloranic 2.5 7 1,000 1,000 8 1,000 8 1,000 12 1,000 1,000 12 Chloroquin Resochin 48/212 300 250 mg/8h 150 8 75 24 Cidofovir Vistide 3.4 45 375 mg/168h 375 336h=14d 70 336=14d 35 336=14d 70 140 336=14d Ciprofloxacin (i.v.)(p.o.) Ciprobay 4.4 10 400500 400500 1212 400500 1212 400500 2424 400 400 12 Clarithromycin Klacid (p.o.) 6.8 17 500 500 12 500 12 500 24 Clindamycin Sobelin 3 3 900 600 6–8 600 6–8 600 6–8 600 600 6–8 Colistin Colistimethat-Na InfectoPharm 3(9) 24(11) 480–720=9 Mio IE 240–480=3–6 MIO IE 8 240= 3 Mio IE 12 240= 3 Mio IE 24 240= 3 mio IE 320=4 Mio IE 12 Colistin p.o. Diaroent 3 16 160 mg= 2 Mio IE 2 Mio IE 12 Co-trimoxazol Cotrim, Bactrim 11/10 31/28 160/800 160/800 12 160/800 24 160/800 24 160/800 160/800 12 Dalbavancin Dalvance 336 1,000 500 168 Dapson (p.o.) Dapson Fatol 24 31 200 200 24 200 24 200 24 200 Daptomycin Cubicin 8 33 500 5006–10 mg/kg 24 5006–10 mg/kg 48 5006–10 mg/kg 48 5006–10 mg/kg 350 24 Darunavir (p.o.) Prezista 8 600 12 Delavirdin Rescriptor 5.8 400 8 Didanosin (p.o.) Videx 1.4 4.5 400 200 12 200 12 200 24 Doripenem Doribax 1 8 1,000 1,000 8 1,000 8 1,000 12 1,000 1,000 8 Doxycyclin Doxycyclin 15 23 200 100 24 100 24 100 24 100 100 24 Efavirenz (p.o.) Sustiva 47 47 600 600 24 600 24 600 24 Elbasvir 50 50 24 50 24 50 24 Emtricitabin (p.o.) Emtriva 8.7 36 200 200 24 200 48 200 72 Enfuvirtide Fuzeon 30 90 12 Entecavir (p.o.) Baraclude 24(138) 67(384) 1.0 1.0 24 0.5 48 0.5 72 0.5 Ertapenem INVANZ 4.1 14.4 1,000 1,000 24 1,000 24 1,000 24 1,000 1,000 24 Erythromycin Erycinum 2.3 5 1,000 1,000 8 1,000 12 1,000 12 1,000 1,000 8 Ethambutol (p.o.) (i.v.) Myambutol EMB-Fatol 3.1 9.6 1,60020 mg/kg 1,6001,400 2424 1,2001,000 2424 1,0001,000 4848 1,6001,400 1,6001,400 2424 Famciclovir (p.o.) Famvir Zoster 2.2 14 250 250 8 250 12 250 24 Flucloxacillin Fluclox 0.8 3 2,000 2,000 8 2,000 8 2,000 8 2,000 2,000 8 Fluconazol Diflucan 25 110 800 or 400 800 24 400 24 400 48 400 800 24 Flucytosin Ancotil 4 150 2,500 2,500 6 2,500 12 0 48 2,500 1,250 24 Fosamprenavir Telzir (p.o.) 19 700 700 12 700 12 Foscarnet Foscavir 4.5 100 6,000 6,0004,000 128 3,000 24 0 Post HD 4,000 3,000 12 Fosfomycin Infectofos, Monuril (p.o.) 1.5 20 5,0003,000 5,000single dose 8 5,000 24 2,500 24 5,000 5,000 12 Ganciclovir Cymeven 4.2 60 5005 mg/kg KG 500 12 250 12 200 24 400 200 12 Gentamicin Refobacin 2 48 Norm/fail240/160 240 24 120 24 400 2448 120320 before HD 120 24 Grazoprevir 20 100 100 24 100 24 100 24 Hydroxichloroquin Quensyl (p.o.) 400 200 8 Imipenem / + Cilastatin Zienam 0.9/0.9 3.3/13.8 1,000+1,000 1,000+1,000 8 1,000+1,000 12 500+500 12 1,000+1,000 1,000+1,000 12 Indinavir (p.o.) Crixivan 1.8 2.1 800 800 8 800 8 800 8 Isoniazid Isozid comp 1/3.3 5/12 300 300 24 300 24 300 24 300 300 24 Itraconazol (p.o.) Sempera 16 25 200 200 24 200 24 200 24 200 Ketoconazol (p.o.) Nizoral 3 2 200 200 12 200 12 200 12 200 Lamivudin (p.o.) Epivir, Zeffix 6.2 21 150 150 12 150 24 100 24 150 Levofloxacin Tavanic 7.3 35 750 500 12 500 24 250 24 500 500 12 Linezolid Zyvoxid 4.9 6.9 600 600 12 600 12 600 12 600 600 12 Lopinavir / Ritonavir (p.o.) Kaletra (p.o.) 7/3.7 7/6.3 400+100 400+100 12 400+100 12 400+100 12 Maraviroc (p.o.) Celsentri 36 36 300 300 12 300 12 300 12 Mebendazol (p.o.) Vermox forte 5 2x500 1,000 8 Mefloquin (p.o.) Lariam 336 340 250 250 168 250 168 250 168 Meropenem Meronem 1 9.7 1,000 1,000 8 1,000 12 1,000 12 1,000 1,000 12 Metronidazol Metronidazol Clont Metronidazol p.o. 10 11(34) 500400 500400 8 500400 12 500400 12 500 500 12 Micafungin Mycamine 13 14 100 100 24 100 24 100 24 100 Miconazol Daktar 24 24 1,200 1,200 24 1,200 24 1,200 24 1,200 Moxifloxacin Avalox 12 15 400 400 24 400 24 400 24 400 400 24 Nelfinavir (p.o.) Viracept 4.5 4 750 750 8 750 8 750 8 Nitrofurantoin Nifurantin (p.o.) 1.0 1.2 100 100 8 Nevirapin (p.o.) Viramune 28 22 200/24 200 12 200 12 200 12 Oritavancin OrbactivTM 336 1,200 Oseltamivir (p.o.) Tamiflu 7 (80) 75 75 12 30 24 0 75 Paromomycin Humatin (p.o.) 2 40 500 8 500 24 500 48 Penicillin G = Ben-zylpenicillin Infectocillin parenteral 0.5 10 10 mega 10 mega 8 10 mega 12 5 mega 12 5 mega 5 mega 8 Penicillin V (p.o.) Penhexal 0.6 4.1 1 mega 1 mega 8 1 mega 8 1 mega 12 Pentamidin Pentacarinat iv 60 96 300 300 24 300 24 300 24 Pentacarinat inhprophylactic 600300 600300 244 week Piperacillin + Sulbactam Pipril / Sulbactam 1.11 48 4,000500 4,000800 88 4,000500 1212 4,000500 1212 4,000500 4,000500 1212 Piperacillin + Tazobactam Piperacillin/ Tazobactam 1.11 48 4,000500 4,000500 88 4,000500 1212 4,000500 1212 4,000500 4,000500 1212 Posaconazol (p.o.) Noxafil 24 29 2x300 300 24 300 24 300 24 Primaquin (p.o.) Primaquine 6.3 6.4 30 30 24 30 24 30 24 Proguanil (p.o.) Paludrine 14 23 200 24 Propicillin (p.o.) Baycillin Mega 1 700=1 mega 700 8 Protionamid (p.o.) Peteha 1.5 1,000 1,000 24 500 24 250 24 500 ? ? Pyrazinamid (p.o.) Pyrafat 9.1 19 2,000 2,000 24 2,000 24 2,000 48 2,000 – – Pyrimethamin Daraprim (p.o.) 92 80 50 50 24 50 24 50 24 Pyrviniumembonat Molevac (p.o.) ? ? 50 single dosing Quinine Chininum 13 15 600 600 12 600 12 600 12 600 600 12 Raltegravir (p.o.) Isentress 5.5 2.5 400 400 12 400 12 400 12 Ribavirin aerosol Virazole 44 26 6,000 6,000 12 6,000 12 6,000 12 6,000 6,000 12 Ribavirin (p.o.)(i.v.) Rebetol, Virazole 4/250 24/672 6001,000 6001,000 128 200500 2412 200500 2448 400200 400200 7224 Rifabutin (p.o.) Mycobutin 25 37 600 600 24 300 24 300 24 Rifabutin + Clarithromycin Mycobutin+Klazid atyp Mycobact 256.8 3717 600300 600300 2424 600300 2424 300300 2424 Rifampicin (i.v.) (p.o.) Eremfat 4.5 4.5 600450 600450 2412 600450 2412 600450 2412 600 600 24 Rifaximin (p.o.) Xifaxan, Colidimin intestine unchan 400 200 8 200 8 200 8 Ritonavir (p.o.) Norvir 3.7 6.3 600 600 12 600 12 600 12 Roxithromycin po Rulid (p.o.) 12 15 300 300 24 300 24 300 24 – – – Saquinavir (p.o.) Invirase 7 13 2x500 1,000 12 1000 12 600 12 Stavudin (p.o.) Zerit 1.5 6.0 40 40 12 40 12 20 12 40 Sofosbuvir (p.o.) Sovaldi 1 (18) (50) 400 400 24 400 24 400 48 400 Streptomycin Strepto Fatol 2.6 100 1,000 1,000 24 500 48 250 72 250 500 24 Tedizolid Sivesxtro 11 200 200 24 200 24 Teicoplanin Targocid 52 348 3x (800/24) 1,200 24 400 24 400 48 800 400 24 Telavancin VIBATIF 7.3 25 750 750 24 500 24 250 24 500 750 24 Telbivudin (p.o.) Sebivo 22 600 600 24 Tenofovir (p.o.) Viread 14 28 245 245 24 245 24 245 48 245 Terbinafin (p.o.) Lamisil 16 16 250 250 24 250 24 250 24 Tetracyclin (p.o.) Tefilin, Tetracyclin 8.9 83 500 500 8 Tigecyclin Tygacil 40 47 100 50 12 50 12 50 12 50 50 12 Tipranavir + Ritonavir Aptivus 2.83.7 2.86.3 500+200 500+200 12 Tobramycin Gernebcin 2 48 Norm/Fail240/160 240 24 120 24 40 24 120 120 24 Trimethoprim (i.v.)(p.o.) Infectotrimet (p.o.)prophylactic 11 31 200100 150100 1224 150100 2424 150 24 – – – Trimethoprim + Sulfamethoxazol Cotrim 1110 3128 160+800 160+800 1212 160+800 2424 160+800 2424 160+800 160+800 1212 Trimethoprim + Sulfamethoxazol Cotrim Pneumocystis 1110 3128 400+2,000 400+2,000 88 320+1,600 1212 400+2,000 2424 400+2,000 400+2,000 1212 Valaciclovir (p.o.) Valtrex 2.5 25 1,000 1,000 8 500 8 500 12 1,000 Valganciclovir po Valcyte (p.o.) 3.0 68 900 900 12 450 24 450 72 900 Vancomycin Vancomycin 6 150 1,000 1,000 12 1,000 24 500 48–72 1,000 1,000 24 Voriconazol Vfend iv / p.o. 8 12 2x400/24 200 12 200 12 200 12 200 200 12 Zalcitabin (p.o.) HIVID 1.8 11 0.75 0.75 8 0.75 12 0.75 24 Zanamivir (inha.) Relenza 2.5 13.7 10 10 12 10 12 10 12 10 24 Zidovudin (p.o.) Retrovir 1 1.9(52) 200 200 8 100 8 100 8 200 200 12

## Acknowledgement

The support by Julia Langgartner, Intensive Care Medicine, Regensburg University was very helpful.

## Conflict of interest

Consultant: MSD Sharp & Dohme

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The ZB MED – Information Center for Life Sciences, Germany, together with the European Association of Urology (EAU) provided the opportunity to publish a “Living Textbook” on “Urogenital Infections and Inflammations” in an open access form. This “Living Textbook” represents also an update of the Textbook on Urogenital Infections published 2010 by the International Consultation on Urological Infections and the EAU: http://www.icud.info/urogenitalinfections.html.

The “Living Textbook” will cover infections and inflammations of the kidney, the urinary tract, as well as the male and female genital tract considering pathogenesis, diagnostics, treatment, prophylaxis and future aspects. The “Living Textbook” will be structured into about 26 Sections each with two section co-chairs responsible for peer review of the chapters of each section. Each chapter should reflect the background to the topic and highlight all of the critical evidence relating to the subject. The intention is to provide an up to date, concise synthesis of the literature on that topic, and for clinical topics also recommendations based on levels of evidence for contemporary clinical practice, as well as suggested research recommendations.

The editors hope that this “Living Textbook” may become a useful instrument for physicians of different specialties taking care about patients suffering from these diseases.

Truls E. Bjerklund Johansen (Norway),

Florian ME Wagenlehner (Germany),

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Daniel Shoskes (USA),

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### Support

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## General

The textbook will be structured in sections with two co-chairs each. Each section will start with an introductory chapter written by the two respective co-chairs presented like an editorial commentary in regard to the following chapters (see proposed contents of the book). The two co-chairs of each section will also peer review all chapters in their section and stimulate a consensus discussion within their section together with the authors and the main editors if needed.

## Chapters

Each chapter should reflect the background to the topic and highlight all of the critical evidence relating to the subject. The intention is to provide an up to date, concise synthesis of the literature on that topic, and for clinical topics also recommendations based on levels of evidence for contemporary clinical practice, as well as suggested research recommendations.

## Manuscript

Each manuscript should have up to approximately 3,000 words (excluding abstract, tables/figures and references). The abstract should count about 300 words.

## Structure

The outline of each chapter should be structured as follows (similar as in the edition 2010, which can be downloaded for free: http://www.icud.info/urogenitalinfections.html):

1. Abstract
2. Summary of recommendations*/key notes*
(*which ever term is more appropriate)
3. Introduction
4. Methods
5. Results
6. Further research
7. Conclusions
8. Acknowledgement
9. Conflict of interest of each author
10. References

### Citation style

As a citation style, the Vancouver style is preferred.

Please mark your references in the text with square brackets ([1], [2], ...).

## Summary of recommendations

We would like to have the Summary of recommendations at the beginning after the abstract (as in the edition 2010). However, we do not expect as in the edition 2010, that each recommendation is also specified according to Level of Evidence and Grade of Recommendation, because such a claim would not only need a systematic literature search (see below), but also a structured discussion in a defined group of experts.

## Systematic literature search

A systematic literature search should be performed, at least of PUBMED/MEDLINE but ideally of several relevant databases in addition (like Cochrane CENTRAL) to find recent, high quality systematic reviews and/or primary research studies. It is not expected to perform for all chapters a de novo systematic review, if such reviews are already published recently, but it still may be indicated for some items. For questions relating therapy, it should be focused on evidence from (systematic reviews of) randomized controlled trials if available.

The method of the systematic literature search needs to be fully described in the section “Methods”, e.g.:

“A systematic literature search was performed for the last ... (usually 10) years in MEDLINE, Cochrane etc. with the following key words ... and the following limitations: e.g. UTI, age (adult?), ... clinical studies ... English ... abstract available ... only peer reviewed ...

A total of ... publications were identified, which were screened by title and abstract ... After exclusion of duplicates ... a total of ... were included into the review (analysis), supplemented by citations or known to the authors ... ”.

## Clinical topics

Clinical topics should be focused on the importance to clinical practice according to the up to date scientific knowledge as presented in the literature. It should relate to questions/complaints/symptoms of patient/population concerning definition, diagnosis, therapy/prevention, intervention, and outcome in comparison, if different approaches are feasible. Please choose patient-important outcomes and focus on those, which you deem critical for decision-making.

## Level of evidence and grade of recommendations

Any recommendation should be based on the level of evidence and the grade of recommendation. For this purpose the following system, modified from the Oxford Centre for Evidence-based Medicine should be used (EAU guidelines 2015):

### Level of evidence (LE)

 Level Type of evidence 1a Evidence obtained from meta-analysis of randomised trials 1b Evidence obtained from at least one randomised trial 2a Evidence obtained from one well-designed controlled study without randomization 2b Evidence obtained from at least one other type of well-designed quasi-experimental study 3 Evidence obtained from well-designed non-experimental studies, such as comparative studies, correlation studies and case reports. 4 Evidence obtained from expert committee reports or opinions or clinical experience of respected authorities.

 Grade Nature of recommendations A Based on clinical studies of good quality and consistency addressing the specific recommendations and including at least one randomised trial B Based on well-conducted clinical studies, but without randomised clinical trials C Made despite the absence of directly applicable clinical studies of good quality

The aim of assigning a LE and grading recommendations is to provide transparency between the underlying evidence and the recommendation given.

It should be noted that when recommendations are graded, the link between the level of evidence and grade of recommendation is not directly linear. Availability of randomized controlled trials may not necessarily translate into a grade “A” recommendation where there are methodological limitations or disparity in published results.

Alternatively, absence of high level evidence does not necessarily preclude a grade A recommendation, if there is overwhelming clinical experience and consensus. In addition, there may be exceptional situations where corroborating studies cannot be performed, perhaps for ethical or other reasons and in this case unequivocal recommendations are considered helpful for the reader. The quality of the underlying scientific evidence - although a very important factor – has to be balanced against benefits and burdens, values and preferences and costs when a grade is assigned.

Since the same rating system should be used in all chapters, for the sake of brevity the same sentence could be used in “Methods” for all manuscripts, because the rating system will be described in details in the Preface of the book:

“The studies were rated according to the level of evidence and the strength of recommendations graded according to a system used in the EAU guidelines modified from the Oxford Centre for Evidence-based Medicine [1].”

## References

[1] European Association of Urology. Guidelines. Methodology section. 2015 ed. Arnhem: European Association of Urology; 2015. p. 3. ISBN/EAN: 978-90-79754-80-9. Available from: http://uroweb.org/wp-content/uploads/EAU-Extended-Guidelines-2015-Edn..pdf

### The Living Handbook of Urogenital Infections and Inflammations is issued by:

European Association of Urology
att. Maurice Schlief, EAU executive manager business affairs

P.O.Box 30016
NL-6803 AA Arnhem, The Netherlands

Phone: 0031-26-38.90.680
E-mail: m.schlief@uroweb.org

### Editor in Chief

#### responsible for the contents according to § 5 TMG and § 55 Abs. 2 RStV (Germany):

Kurt G. Naber, MD, PhD
Assoc. Professor of Urology

Technical University of Munich
Karl-Bickleder-Str. 44c
94315 Straubing, Germany

E-mail: kurt.naber@nabers.de

### John N. Krieger MD, PhD

University of Washington Section of Urology

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### Daniel Shoskes MD, PhD

Cleveland Clinic Glickman Urological and Kidney Institute

more

### Yong-Hyun Cho MD, PhD

St. Mary's Hospital, The Catholic University of Korea Department of Urology

more

### Tetsuro Matsumoto MD, PhD

University of Occupational and Environmental Health Department of Urology

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### Florian M. E. Wagenlehner MD, PhD

Justus-Liebig University of Giessen Clinic of Urology and Andrology

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### Truls Erik Bjerklund Johansen MD, PhD

Oslo University Hospital Urology Department

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### Kurt G. Naber MD, PhD

Technical University of Munich

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### Riccardo Bartoletti

University of Pisa
Department of Translational Research and New Technologies

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### Truls Erik Bjerklund Johansen MD, PhD

Oslo University Hospital
Urology Department

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### PD Dr. med. Gernot Bonkat

University Basel
alta uro AG, Merian Iselin Klinik, Center of Biomechanics & Calorimetry (COB)

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### Prof. Tommaso Cai MD

Santa Chiara Regional Hospital
Dept. of Urology

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### Dr Leyland Chuang

Ng Teng Fong Hospital, National University Health System
Department of Medicine

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### Prof. Milan Cizman

University Medical Centre
Department of Infectious Diseases

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### Alison Crawford MSc

Queen's University
Department of Psychology

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### Pfofessor Svetlana Dubrovina MD, PhD

Rostov Medical State University
Obstetrics and Gynaecology

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### Dr Valerie Huei Li Gan MBBS (S'pore), MRCS (Edin), MMed (Surg), FAMS (Urology)

Singapore General Hospital
Department of Urology

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### Philip Hanno

University of Pennsylvania

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### Ass prof MD Gundela Holmdahl

Queen Silvia Childrens Hospital, Sahlgrens Academy
Pediatric surgery and urology

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### Udo B. Hoyme

HELIOS Hospital Erfurt Ltd.
Department of Gynecology and Obstetrics

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Washington University School of Medicine
Pediatrics / Molecular Microbiology

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### Gitte M. Hvistendahl

Aarhus University Hospital

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### Prof. Michael KOGAN M.D., PhD

Rostov State Medical University
Department of Urology

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### Dr Akihiro Kanematsu

Hyogo College of Medicine
Department of Urology

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### Frieder Keller

University Hospital Ulm
Department Internal Medicine 1, Nephrology

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### Professor Katarzyna Kilis-Pstrusinska PhD, MD

Wroclaw Medical University
Department of Pediatric Nephrology

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### MD, PhD Tae-Hyoung Kim

Chung-Ang University
Urology

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### John N. Krieger MD, PhD

University of Washington
Section of Urology

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### Prof Ekaterina Kulchavenya

Novosibirsk Research TB Institute, Novosibirsk State Medical University

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### Dr Christina Kåbjörn Gustafsson

Ryhov Hospital Jönköping
Pathology

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### Dr. Bela Köves

South Pest Teaching Hospital
Department of Urology

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### Dr. med. Giuseppe Magistro

Ludwig-Maximilians-University of Munich
Department of Urology

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ASST-North
Urologic Clinic

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### András Magyar

South-Pest Hospital
Department of Urology

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### Professor Emeritus Brian Morris

University of Sydney
School of Medical Sciences

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### Baerbel Muendner-Hensen

ICA-Deutschland e.V.

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### Stephen F. Murphy

Feinberg School of Medicine, Northwestern University
Department of Urology

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### Kurt G. Naber MD, PhD

Technical University of Munich

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### Prof. Yulia Naboka

Rostov State Medical University
Department of Microbiology

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### Dr. J. Curtis Nickel MD

Queen's University
Department of Urology

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### Professor Ralph Peeker MD PhD

University of Gothenburg
Department of Urology

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### Tamara Perepanova

N.A. Lopatkin Research Institute of Urology and Interventional Radiology

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### Prof. Gianpaolo Perletti M. Clin. Pharmacol.

University of Insubria
Department of Biotechnology and Life Sciences

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### Felice Petraglia

Department of Biomedical, Experimental and Clinical Sciences, University of Florence
Obstetrics and Gynecology

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### Dr. Jörgen Quaghebeur PhD. Med. Sci.

University Hospital Antwerp and University Antwerp
Department of Urology

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### Yazan F. Rawashdeh

Aarhus University Hospital
Paediatric Urology Section, Department of Urology

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-
Urology

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### Matthew Roberts

The University of Queensland
Faculty of Medicine

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### PD Dr. med Guido Schmiemann MPH

Institut für Public Health und Pflegeforschung, Universität Bremen
Abteilung Versorgungsforschung

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### Prof. Dr. med. Peter Schneede

Klinikum Memmingen
Department of Urology

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### Aaron C. Shoskes

Des Moines University Medical College of Ostheopathic Medicine

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### Daniel Shoskes MD, PhD

Cleveland Clinic
Glickman Urological and Kidney Institute

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### Prof. Dr. Roswitha Siener

University of Bonn
University Stone Centre, Department of Urology

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### Sofia Sjöström

Queen Silvia Childrens Hospital, Sahlgrens Academy
Pediatric surgery and urology

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### Mathew Sorensen

University of Washington School of Medicine
Department of Urology

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### Prof. Dr. Dr. Walter Ludwig Strohmaier FEBU

Regiomed-Klinikum Coburg. Medical School Regiomed
Urology and Paediatric Urology

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### Satoshi Takahashi

Sapporo Medical University School of Medicine
Department of Infection Control and Laboratory Medicine

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### Professor Paul Anantharajah Tambyah

Yong Loo Lin School of Medicine, National University Hospital
Department of Medicine

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### Peter Tenke

South-Pest Hospital
Department of Urology

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### Praveen Thumbikat

Department of Urology

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### Dr. Jose Tiran Saucedo

Obstetrics and Gynaecology

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### Dominic Tran-Nguyen

Des Moines University

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### Dean Tripp

Queen's University
Psychology, Anesthesia & Urology

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### Prof. SEONGHEON WIE

The Catholic University of Korea, St. Vincent's Hospital
Division of Infectious Diseases, Department of Internal Medicine

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### Florian M. E. Wagenlehner MD, PhD

Justus-Liebig University of Giessen
Clinic of Urology and Andrology

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### Assoc. Prof. Christian Wejse

Aarhus University, Aarhus University Hospital
Department of Infectious Diseases/Center for Global Health, Dept of Public Health

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### Prof. Dr. Mete Çek

Trakya University, School of Medicine
Urology

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text:
# Central Limit Theorem

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The Central Limit Theorem identifies the distribution of the sample mean and is arguably the most important theorem in probability theory.

Let $X$ be a random variable, and let $X_1, X_2, \ldots , X_n$ be a random sample for $X$, such that each $X_i$ has a distribution identical to that of $X$ itself. Let $\overline{X}$ be the sample mean; in other words, let $\overline{X}$ be equal to $\frac{\sum X_i}{n}$. Because each $X_i$ is a random variable, $\overline{X}$ is also a random variable. The Central Limit Theorem observes several important facts about the distribution of $\overline{X}$:

1. The distribution of $\overline{X}$ is approximately normal, even when the underlying distribution $X$ is not.
2. The expected value of the $\overline{X}$ is equal to the expected value of $X$.
3. As the sample size $n$ increases, the variance of $\overline{X}$ approaches zero.

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text:
• ### Cyclical period changes in HT Cas: a clear difference between systems above and below the period gap(0711.3660)

Nov. 23, 2007 astro-ph
We report the identification of cyclical changes in the orbital period of the eclipsing cataclysmic variable HT Cas. We measured new white dwarf mid-eclipse timings and combined with published measurements to construct an observed-minus-calculated diagram covering 29 years of observations. The data present cyclical variations that can be fitted by a linear plus sinusoidal function with period 36 yr and semi-amplitude ~ 40 s. The statistical significance of this period by an F-test is larger than 99.9 per cent. We combine our results with those in the literature to revisit the issue of cyclical period changes in cataclysmic variables and their interpretation in terms of a solar-type magnetic activity cycle in the secondary star. A diagram of fractional period change (Delta P/P) versus the angular velocity of the active star (Omega) for cataclysmic variables, RS CVn, W UMa and Algols reveal that close binaries with periods above the gap (secondaries with convective envelopes) satisfy a relationship Delta P/P \propto Omega^{-0.7+/-0.1}. Cataclysmic variables below the period gap (with fully convective secondaries) deviate from this relationship by more than 3-sigma, with average fractional period changes ~ 5 times smaller than those of the systems above the gap.
• ### HS1857+5144: A hot and young pre-cataclysmic variable(0704.1780)

April 13, 2007 astro-ph
We report the discovery of a new white dwarf/M dwarf binary, HS1857+5144, identified in the Hamburg Quasar Survey (HQS). Time-resolved optical spectroscopy and photometry were carried out to determine the properties of this new cataclysmic variable progenitor pre-CV). The light curves of HS1857+5144 display a sinusoidal variation with a period of Porb=383.52 min and peak-to-peak amplitudes of 0.7 mag and 1.1 mag in the B-band and R-band, respectively. The large amplitude of the brightness variation results from a reflection effect on the heated inner hemisphere of the companion star, suggesting a very high temperature of the white dwarf. Our radial velocity study confirms the photometric period as the orbital period of the system. A model atmosphere fit to the spectrum of the white dwarf obtained at minimum light provides limits to its mass and temperature of Mwd=~0.6-1.0 Msun and Twd=~70000-100000 K, respectively. The detection of HeII 4686 absorption classifies the primary star of HS1857+5144 as a DAO white dwarf. Combining the results from our spectroscopy and photometry, we estimate the mass of the companion star and the binary inclination to be Msec=~0.15-0.30 Msun and i=~45-55 deg, respectively. We classify HS1857+5144 as one of the youngest pre-CV known to date. The cooling age of the white dwarf suggests that the present system has just emerged from a common envelope phase ~10^5 yr ago. HS1857+5144 will start mass transfer within or below the 2-3h period gap.
• ### SW Sextantis stars: the dominant population of CVs with orbital periods between 3-4 hours(0704.1129)

April 11, 2007 astro-ph
[Abridged] We present time-series optical photometry of five new CVs identified by the Hamburg Quasar Survey. The eclipses observed in HS 0129+2933, HS 0220+0603, and HS 0455+8315 provided very accurate orbital periods of 3.35129827(65), 3.58098501(34), and 3.56937674(26) h, respectively. HS 0805+3822 shows grazing eclipses and has a likely orbital period of 3.2169(2) h. Time-resolved optical spectroscopy of the new CVs (with the exception of HS 0805+3822) is also presented. Radial velocity studies provided an orbital period of 3.55 h for HS 1813+6122, which allowed us to identify the observed photometric signal at 3.39 h as a negative superhump wave. The spectroscopic behaviour clearly identifies these new CVs as new SW Sextantis stars. These new additions increase the number of known SW Sex stars to 35. Almost 40 per cent of the total SW Sex population do not show eclipses, invalidating the requirement of eclipses as a defining characteristic of the class and the models based on a high orbital inclination geometry alone. On the other hand, the predominance of orbital periods in the narrow 3-4.5 h range is becoming more pronounced. In fact, almost half the CVs which populate the 3-4.5 h period interval are definite members of the class. These statistics are confirmed by our results from the Hamburg Quasar Survey CVs. Remarkably, 54 per cent of the Hamburg nova-like variables have been identified as SW Sex stars with orbital periods in the 3-4.5 h range. The observation of this pile-up of systems close to the upper boundary of the period gap is difficult to reconcile with the standard theory of CV evolution, as the SW Sex stars are believed to have the highest mass transfer rates among CVs. Finally, we review the full range of common properties that the SW Sex stars exhibit.
• ### Cataclysmic variables from a ROSAT/2MASS selection I: Four new intermediate polars(astro-ph/0504460)

April 21, 2005 astro-ph
We report the first results from a new search for cataclysmic variables (CVs) using a combined X-ray (ROSAT) / infrared (2MASS) target selection that discriminates against background AGN. Identification spectra were obtained at the Isaac Newton Telescope for a total of 174 targets, leading to the discovery of 12 new CVs. Initially devised to find short-period low-mass-transfer CVs, this selection scheme has been very successful in identifying new intermediate polars. Photometric and spectroscopic follow-up observations identify four of the new CVs as intermediate polars: 1RXSJ063631.9+353537 (Porb~201min, Pspin=1008.3408s or 930.5829), 1RXSJ070407.9+262501 (Porb~250min, Pspin=480.708s), 1RXSJ173021.5-055933 (Porb=925.27min, Pspin=128.0s), and 1RXSJ180340.0+401214 (Porb=160.21min, Pspin=1520.51s). RXJ1730, also a moderately bright hard X-ray source in the INTEGRAL/IBIS Galactic plane survey, resembles the enigmatic AE Aqr. It is likely that its white dwarf is not rotating at the spin equilibrium period, and the system may represent a short-lived phase in CV evolution.
• ### The XMM-Newton/2dF survey IV. The X-ray spectral properties of the hard sources(astro-ph/0404048)

April 2, 2004 astro-ph
We present an analysis of the X-ray spectral properties of 61 hard X-ray selected (2-8 keV) sources from the bright ($f_{2-8 keV}>10^{-14}$ \funits) {\it XMM-Newton}/2dF survey. This comprises of 9 {\it XMM-Newton} pointings in the North Galactic Pole region ($\sim 1.6 \rm deg^2$) and overlaps with the SDSS, 2QZ and 2dFGRS surveys. Our sources contribute about 50 per cent of the 2-10 keV X-ray background down to the flux limit of $10^{-14}$ cgs. The hardness ratio distribution of the sample suggests a deficit of heavily absorbed sources. A spectral fit to the co-added total source spectrum yields a steep photon index, $\Gamma=1.83^{+0.04}_{-0.05}$. All but 8 sources have optical counterparts down to the SDSS photometric limit of $r\approx22.5$. Spectroscopic identifications exist for 34 sources. The vast majority are associated with Broad-Line (BL) AGN (24 sources) while only 7 present narrow or no emission lines. Five sources are probably associated with Galactic stars. Finally, for another 17 probable AGN we present photometric redshifts. The combined spectrum of the 24 spectroscopically identified BL AGN is steep ($\Gamma=2.02^{+0.04}_{-0.05}$), while that of the 7 AGN, which do not present broad lines is flatter with $\Gamma=1.64^{+0.11}_{-0.11}$. The spectrum of the 8 optically unidentified sources is flat with $\Gamma\approx 1.1$. Spectral fits to the individual BL AGN reveal large absorption (rest-frame column density $\rm>10^{22} cm^{-2}$) in only two cases. The individual spectra of the NL AGN present significant evidence for even a moderate absorption ($\rm 3\times 10^{21} cm^{-2}$) in only one case.
• ### 5 Poster Contributions in the MPA/ESO Conference "Evolution of large-scale structure", Garching, August 1998(astro-ph/9810504)

Oct. 30, 1998 astro-ph
Poster Titles: (1) Optical to IRAS galaxy bias factors using the Local Group Dipole (2) The X-ray Luminosity Function of Local Galaxies (3) The ROSAT X-ray Background Dipole (4) The Angular Correlation Function of RASS Extragalactic Sources (5) Galaxy Cluster Shapes