1. PK/PD: an introduction with the case of antimicrobials
Veterinary Committee on Antimicrobial
Susceptibility Testing (VetCAST)
PK/PD: an introduction with the case of antimicrobials
P.L. Toutain
VMAS symposium/workshop
Uppsala 13 December 2017

2. 1-What is PK/PD approach for antibiotics?

3. What is the main goal of PK/PD for antibiotics
It is an alternative to dose-titration studies to discover an optimal dosage regimen:
For efficacy
For prevention of resistance

4. EMEA "Points to consider" July 2000
Inadequate dosing of antibiotics is probably an important reason for misuse and subsequent risk of resistance

5. 2-What is a dosage regimen for antimicrobials (AMD)

6. The elements of a dosage regimen
The dose:
Dose titration or PK/PD
The dosing interval
PK/PD
The treatment duration:
a clinical issue
When to start :
When to finish:
But PK for single dose of LA formulations

7. The three endpoints to consider in veterinary medicine
Efficacy in animal
Dose titration or PK/PD
No promotion of resistance in animal (target pathogen)
PK/PD and clinic
No promotion of resistance in man (commensal microbiota)
PK selectivity (gut microbiota)

8. 3-How to establish a dosage regimen for an antibiotics in veterinary medicine

9. EMA/CVMP 2015

10. How to find and confirm a dose (dosage regimen)
Dose determination
Dose titration
Experimental infectious model
Dose confirmation
Well controlled, naturally infected animals
PK/PD

11. The dose-titration

12. Dose titration: principle
An infectious model
Three dose-levels (including placebo)
Response: clinical and bacteriological
Statistical comparison

13. Parallel design for antibiotics: Statistical model
Response NS *
The null hypothesis
placebo = D1 = D2 = D3
The statistical linear model
Yj = wj + j
Conclusion
D3 = D2 > D1 > Placebo *
Selected dose
Dose 1 2 3
Placebo

14. The parallel design Advantages Disadvantages easy to execute
total study lasts over one period
approved by Authorities
Disadvantages
"local information" (response at a given dose does not provide any information about another dose)
no information about the distribution of the individual patient's dose response.

15. Why PK/PD approach is an ethical attractive alternative to the dose-titration?
Dose titration, not the PK/PD approach, require an experimental infectious model.
Infectious models are:
Severe
not representative of the real world
Prophylaxis vs. metaphylaxis vs. curative
power of the design generally low for large species
The pivotal PD parameter (MIC) reflecting the disease is easily obtained in vitro

16. PK/PD allows determination of a dosage regimen in healthy animals
The PK part of the model can be refined to take into account the disease : POP PK
The PD part of the model rely on the in vitro MIC that is assumed to “reflect” the major component of the disease

17. 4-An overview on the concept of PK/PD

18. Dose titration for antibiotic using infectious model
Response
clinical
Black box
Dose titration for antibiotic using infectious model
PK/PD PK PD
Body
pathogen
Dose
Response
Plasma
concentration

19. Why plasma concentration for antimicrobials

20. Where are located the pathogens
Extra Cellular Fluid
Most bacteria of clinical interest
- respiratory infection
- wound infection
- digestive tract inf.
Cell
(in phagocytic cell most often)
Legionnella spp
mycoplasma (some)
chlamydiae
Brucella
Cryptosporidiosis
Listeria monocytogene
Salmonella
Mycobacteria
Meningococci
Rhodococcus equi
Most pathogens of veterinary interest are extracellular

21. AUCfree plasma = AUC free ECF (biophase)
Free drug concentration is the driving force controlling AMD concentrations at the biophase level
1-ECF = biophase
PLASMA
Bound
Free
Bound
Free
Bug
Cell
Cytosol
Diffusion/permeability
AUCfree plasma = AUC free ECF (biophase)
Free serum concentrations is the best predictor of AB effect

22. How to assess the effective Free plasma concentration for an AMD?

23. MIC is a reasonable approximate of the order of magnitude of concentration of free drug needed at the site of infection to treat an animal

24. 5-How integrate PK and PD data (MIC) for antibiotics to find a dose

25. A fundamental PK/PD relationship
For all antibiotics, the in vivo MIC is directly related to the Therapeutic concentrations throughout the so-called PK/PD index !
A dose can be determined rationally using a PK/PD approach but the MIC is not the best candidate to be “the “ therapeutic concentration

26. Therapeutic concentration
The MIC itself is not directly use in the equation allowing to compute a dose for an AMD
The MIC is use indirectly throughout the so-called PK/PD indices, all of which are expressed in terms of MIC,

27. Practically, 3 indices cover all situations:
In order to use the MIC to determine a dose, It has been developed 3 surrogates indices (predictors) of antibiotic efficacy taking into account MIC (PD) and exposure antibiotic metrics (PK)
Practically, 3 indices cover all situations:
AUC/MIC
Time>MIC
Cmax/MIC

28. PK/PD predictors of efficacy
Cmax/MIC : aminoglycosides
AUC/MIC : quinolones, tetracyclines, azithromycins, florfenicol…
T>MIC : penicillins, cephalosporins,
Cmax
Cmax/MIC
AUC/ MIC
Concentrations
MIC
Time
24h
T>CMI

29. A fundamental PK/PD relationship using PK/PD index
When PK/PD index is AUC/MIC, it is equivalent to select a therapeutic concentration that is a multiple of the MIC
e.g. if the objective is an AUC/MIC=125h, the therapeutic concentration should be 125h/24h≈5XMIC

30. 6-Why these indices are termed PK/PD

31. PD parameter expressing antibiotic potency
AUC/MIC
PK parameter expressing capacity of the body to eliminate the antibiotic
PD parameter expressing antibiotic potency

32. Time > MIC
Half-life
concentrations
MIC
Time (h) 24 t2 t1

33. Cmax / MIC PK PD Bioavailability (%) Clearance Rate of absorption
Rate of elimination
Accumulation factor PD

34. PK/PD indices are hybrid parameters
For all indices:
the PD input is the MIC
the PK input is associated to the free plasma concentration

35. fAUC/MIC fTime>MIC fCmax/MIC
The PK input is associated to the free plasma: concentration and because MIC is homogeneous to a free plasma concentration, an f for free is often added to write the indices as
fAUC/MIC
fTime>MIC
fCmax/MIC

36. Comparative AUC/MIC computed with free and total concentrations for different macrolides, kétolides and clindamycin forS. pneumoniae All free AUC/CMI are very similar
Craig et al. 42nd ICAAC, 2002

37. PK/PD indices have a dimension (units)
AUC/MIC=h
Not very appealing
Often units are deleted
AUC/MIC divided by 24h give a scaling factor without units
E.g AUC/MIC=125h is equivalent to say that in steady state condition, the average plasma concentration should be equal to 125h/24h=5.2 times the MIC
Cmax/MIC: ratio (scalar)
Time>MIC: expressed as a % over the 24h dosage interval

38. To know more on the dimension of AUC/MIC and its consequences in veterinary medicine

39. 7-How were established these indices?

40. How were established these indices?

41. Search for the best correlation between the shape of the plasma antibiotic exposure and efficacy
A lung or thigh infectious challenge in neutropenic mouse
From 20 to 30 different dosage regimens (5 doses levels and 4-6 intervals of administration) are tested
Efficacy is measured in terms of reduction of Log10 CFU (bacteriological endpoint) or mortality (clinical endpoint) after 24h
Plot of results and computation of correlation between each putative PK/PD index (T>CMI, Cmax/CMI, AUC/CMI) and the outcome

42. Relationship between the different PK/PD indices and the effect of Cefotaxim against Klebsiella pneumoniae in a murine lung infectious model 3 10 30
100
300
1000
3000
24 h AUC/MIC ratio 5 6 7 8 9 20 40 60 80
Time above MIC (%)
R² = 94%
Peak MIC ratio 01 1
10000
Log10 CFU per lung at 24 h
Craig CID, 1998

43. Relationship between AUC/MIC and mortality rate for a fluoroquinolone against a Gram positive bacillus 3 10 30
100
300
1000 20 40 60 80
% Mortality
24 h AUC/MIC (h)

44. Appropriate PK/PD indices for the different antibiotics according to their bactericidal properties
Bactericidal pattern
Antibiotics
Therapeutic goal
PKPD
indices
Type I
Concentration dependant & persistent effect
Aminoglycosides
Fluoroquinolones
To optimize plasma concentrations
Cmax/MIC
24h-AUC/MIC
Type II
Time-dependent and no persistent effect
Penicillins
Céphalosporins
To optimize duration of exposure
T>MIC
Type III
Time-dependent and dose-dependent persistent effect
Macrolides
Tetracyclines
Florfenicol
To optimize amount (doses)

45. 6-What is the appropriate magnitude (size) of PK/PD indices to guarantee efficacy i.e. how establish PK/PD breakpoint values
To optimize efficacy
To minimize resistance

46. Determination of breakpoint value of PK/PD indices
In vitro or ex vivo (tissue cage)
in vivo
Prospectively from dose-titration
Retrospectively from meta-analysis of clinical trials

47. Preclinical determination of the magnitude of the PK/PD indices

48. Preclinical determination of the PK/PD size
In vitro
Static
Killing curves
Dynamic
Hollow fibers
Others

49. Bacterial growth in serum containing danofloxacin for incubation periods of 0.25 to 6h
Log cfu/ml
0.02
0.04
0.06
0.08
0.12
0.16
0.20
0.24
0.28
0.32
1.E+00
1.E+03
1.E+06
1.E+09 1 2 3 4 5 6
Incubation time (h)
Conc.
P. Lees

50. The tissue cage model Perforated hollow devices
Subcutaneous implantation
development of a highly vascularized tissue
fill up with a fluid with half protein content of serum (delay 8 weeks)

51. The hollow fiber

52. Sigmoidal Emax relationship for bacterial count vs. ex vivo AUC24h/MIC-7 -6 -5 -4 -3 -2 -1 1 50
100
150
200
250
300
AUC24h/MIC
Observed
Predicted
Bacteriostatic AUC24h /MIC= 18 h
Bactericidal AUC24h /MIC= 39 h
Elimination AUC24h/MIC = 90 h
Log cfu/ml difference
P. Lees

53. In vitro Data modelling for AUC/MIC
A classical Emax model
𝐸= 𝐸 𝐸 𝑚𝑎𝑥 × 𝑋 𝑁 𝐸𝐶 50 𝑁 + 𝑋 𝑁
E0 is the bacterial growth after 24 h incubation in the absence of drug, expressed as log10 cfu/mL subtracted from the initial inoculum log10 cfu/mL;
Emax is the maximum growth inhibition determined as the change from the initial count in log10 cfu/mL over 24 h incubation with the antibiotic;
X is the concentration term (expressed as AUC(0-24h)/MIC)
N is the Hill coefficient, which describes the slope of the AUC(0-24h)/MIC-effect curve;
EC50 is the AUC(0-24h)/MIC value providing 50% of the maximum antibacterial effect.
Solving the model to compute AUC//MIC to achieve bacteriostatic , bactericidal or eradication

54. Parameter Danofloxacin Marbofloxacin
Ex vivo AUC24h/MIC (h) values for danofloxacin and marbofloxacin in calf serum
Parameter Danofloxacin Marbofloxacin
Bacteriostatic 15.9 ± ± 6.9
Bactericidal 18.1 ± ± 6.8
Elimination 33.5 ± ± 10.9
Slope 17.3 ± ± 3.3
Values are mean ± sem (n=6)
P. Lees

55. A more advanced data analysis to establish PK/PD indices and their magnitude : semi-mechanistic models

56. Classical PK/PD indices vs. semi-mechanistic models
These semi-mechanistic models are able to predict the classical PK/PD indices and their breakpoint values.

57. PK/PD model for resistance and predicted bacterial time-kill curves
B1, compartment with drug sensitive bacteria;
B2, compartment with less drug-sensitive bacteria;

58. A major review

59. In silico dose fractionation using a mechanistic PK/PD model
Principle
A semi-mechanistic PD model (rather than a mouse) is used to predict the bacteriological effect of different dosage regimen ( different doses, and for a total given dose, splitted vs. non-splitted dose)
Classical Killing curves should be analyzed with the PD model then to compute PD parameters (EC50, Emax…) (see next section)
Then using simulations, the bacteriological effect of the AMD is predicted using its PK data

60. Classical PK/PD indices vs. semi-mechanistic models
However, they also predict that when the AM half-life is short, the best predictor is always T>MIC and when the half-life is long, the best predictor is always AUC/MIC whatever the antibiotic.
These kind of results are very important for veterinary medicine that uses many long-acting formulations and the use of AUC/MIC as a universal PK/PD index would greatly facilitate many tasks such as finding an optimal dosage regimen and fixing sound clinical breakpoints for susceptibility testing.

61. Same index or not?

62. 8-Clinical validation of the breakpoint values of PK/PD indices from (human) clinical trials

63. Comparison of the relationships between efficacy and 24-hr AUC/MIC for fluoroquinolones in animal models and infected patients
Seriously ill patients+Ciprofloxacin
AUC/MIC
24-Hr AUC/MIC

64. Relationship Between T>MIC and Efficacy for Carbapenems (Red), Penicillins (Aqua) and Cephalosporins (Yellow)

65. Efficacy index: clinical validation
Bacteriological cure versus time above MIC in otitis media (from Craig and Andes 1996)
100
S. pneumoniae
Penicillin
cephalosporins 50
Bacteriologic cure (%)
H. influenzae
Penicillin
cephalosporins 50
100
Time above MIC (%)
Free serum concentration need to exceed the MIC of the pathogen for 40-50% of the dosing interval to obtain bacteriological cure in 80% of patients

66. Efficacy index: clinical validation
Relationship between the maximal peak plasma level to MIC ratio and the rate of clinical response in 236 patients with Gram-negative bacterial infections treated with aminoglycosides (gentamicin, tobramycin, amikacin)
100 80
Response rate (%) 60 2 4 6 8 10 12
Maximum peak/MIC ratio
Moor et al J. Infect. Dis.

67. Breakpoint values for PK/PD indices
Pathogens
Breakpoint values
24h-AUC/MIC
Gram positive
~50h
Gram negative
~ h
T>MIC
~40-50% of the dosage interval
~100% of the dosage interval
Cmax/MIC
All pathogens 10

68. Universality of PK/PD breakpoint
Likely (because PK & PD)
Allow interspecific extrapolation

69. 9-PK/PD indices and the development of resistance

70. The mutant Selective Window (MSW)
Currently the MSW is the only PK/PD index that is use to mitigate the emergence of resistance

71. Traditional hypothesis on emergence of AMR
Concentration
MIC
Selective pressure for antibiotic concentration lower than the MIC
Time

72. Current view for the emergence and selection of resistance : situation II
No antibiotics & low inoculum size
Mutation rate10-8
105 CFU
Wild pop
No Mutant pop
With antibiotics
eradication
résistant
susceptible

73. Current view for the emergence and selection of resistance : situation II
No antibiotics & high inoculum
Mutation rate10-8
108 CFU
Mutant pop
5-10xMIC=MPC
Wild pop
With antibiotics
Mutation rate10-8
eradication
susceptible
Mutants population

74. The selection window hypothesis

75. The selection window hypothesis
Mutant prevention concentration (MPC)
(to inhibit growth of the least susceptible, single step mutant)
MIC
Selective concentration (SC)
to block wild-type bacteria
Mutant Selection window
Plasma concentrations
All bacteria inhibited
Growth of only the most resistant subpopulation
Growth of all bacteria

76. MIC & MPC for the main veterinary quinolones for E. coli & S. aureus

77. Comparative MIC and MPC values for 285 M
Comparative MIC and MPC values for 285 M. haemolytica strains collected from cattle
MIC50
MIC90
MPC50
MPC90
MPC/MIC
Ceftiofur
0.016 1 2
125
Enrofloxacine
0.125
0.25 8
Florfenicol 4
Tilmicosine 16
>32 ≈8
Tulathromycine
Vet Microbiol Blondeau JM

78. Firsov et al (2003). Antimicrob. Agents Chemother. 47, 1604
The MPC hypothesis for 4 Quinolones against S aureus
DRUGS
Cmax
AUC24/MIC (h)
Change in MIC
Gatifloxacin & Ciprofloxacin
>MIC
15 to 16
Slight increase
Moxifloxacin & Levofloxacin
MIC
13 to 17
None
All 4 drugs
24 to 62*
Greatest increase
107 to 123
Small increase
All drugs
>> MIC
201 to 244**
*Concentrations within MSW over most of dose interval
**Concentrations >MPC over most of dose interval
Firsov et al (2003). Antimicrob. Agents Chemother. 47, 1604

79. The mutant Selective Window
Currently the MSW is the only PK/PD index that is use to mitigate the emergence of resistance and it is recommended that a dosage regimen should limit the overall time spent in the MSW during a treatment

80. 11-How to compute an average dose using PK/PD indices and recommended breakpoint values

81. Determination of a dose for a quinolone
Breakpoint value
e.g. 125h PD
Bioavailability
Free fraction

82. Determination of a dose for a quinolone
This equation is exactly the same as the previous one but thanks to a dimensional analysis, the breakpoint value of the PK/PD indice (125h) has been replaces by a scaling factor (here 5)
Fore more explanation, download the following (free) article

83. Computation of an “average dose”
Computation of the dose with point estimates (mean clearance and F%, MIC90)
MIC90
(worst case scenario)
Breakpoint value
Mean value
Bioavailability
(Mean value)
Computation of an “average dose”

84. 14-How to compute a population dosage regimen using PK/PD indices and recommended breakpoint values

85. PK Variability
Doxycycline
n = 215

86. PD variability MIC distribution Pasteurella multocida40 35 30 25
Pathogens % 20 15 10
SUSCEPTIBLE 5
0.0625
0.125
0.25
0.5 1 2 4
MIC ( m
g/mL)

87. The so-called Probalility of target attainment (PTA)
The population PK/PD dosage regimen obtained by Monte Carlo simulations
What is the dose of an antibiotic to be administrated to a group of cattle to guarantee that at least 90% of these cattle will achieve an AUC/MIC ratio (the selected PK/PD index) value of 125 in the framework of an empirical antibiotherapy?
The so-called Probalility of target attainment (PTA)

88. Computation of the dose using Monte Carlo simulation (Point estimates are replaced by distributions)
Log normal distribution: 9±2.07 mL/Kg/h
Observed distribution
Breakpoint value
Dose to POC=0.9
Uniform distribution:

89. Dosage regimen: application of PK/PD concepts
The 2 sources of variability : PK and PD
PK: exposure
PD: MIC
Distribution of PK/PD surrogates (AUC/MIC)
Monte-Carlo approach

90. An add-in design to help Excel spreadsheet modelers perform Monte Carlo simulations
Others features
Search optimal solution (e.g. dose) by finding the best combination of decision variables for the best possible results

91. Dose to achieve a POC of 90% for a given
Dose distribution

92. Conclusions
PK/PD is a powerful tool allowing to arrive very quickly to a appropriate dosage regimen recommendation
PK/PD cannot replace confirmatory clinical trials of efficacy
Classical PK/PD indices as obtained over 24h are not enough to predict resistance