Patient Calculations

Data Validation

Parameter	Condition	Value(s)
Weight	in range	`1` to `300`
Height	in range	`60` to `250`
Age	in range	`0.25` (3 months) to `120`
SCr	in range	`0.1` to `20`
Sex	one of	`M` `m` `F` `f`

Age

Conversion to Years

If entered as #d → age = d ÷ 365.25
If entered as #m → age = m ÷ 12
If entered as #m#d → age = (m ÷ 12) + (d ÷ 365.25)

Age Context

(for determining which fields to show or hide)

Condition	Age Context
If age < 1 year	infant
Else if age < 18 years	child
Else	adult

Body Mass Index

$$\mathrm{BMI}=\frac{\mathrm{wt}}{\left(\frac{\mathrm{ht}}{100}\right)^2}$$

wt : weight in kg

ht : height in cm

Ideal Body Weight

$$\mathrm{IBW_{male}}=50+\left[ 2.3\times\left(\mathrm{ht}-60 \right )\right]$$

$$\mathrm{IBW_{female}}=45.5+\left[ 2.3\times\left(\mathrm{ht}-60 \right )\right]$$

ht : height in inches

AdjBW

Use ABW if ABW ≤ IBW, otherwise...

$$\mathrm{AdjBW}=\left[ 0.4\times \left(\mathrm{ABW}-\mathrm{IBW} \right ) \right ]+\mathrm{IBW}$$

Percent Over or Under IBW

$$\mathrm{OverUnder}=\left(\frac{\mathrm{ABW}}{\mathrm{IBW}}-1 \right )\times 100%$$

Lean Body Weight

$$\mathrm{LBW_{male}}=9270\times \left(\frac{\mathrm{ABW}}{6680+\left(216\times \mathrm{BMI} \right )} \right )$$

$$\mathrm{LBW_{female}}=9270\times \left(\frac{\mathrm{ABW}}{8780+\left(244\times \mathrm{BMI} \right )} \right )$$

Body Surface Area

$$\mathrm{BSA}=\sqrt{\frac{\mathrm{ht}\times\mathrm{wt}}{3600}}$$

wt : weight in kg

ht : height in cm

CrCl

Cockroft-Gault

$$\mathrm{CrCl}=\frac{\left(140-\mathrm{age} \right )\times\mathrm{wt}}{\mathrm{SCr}\times 72}\ \ \ \mathrm{\ }\times0.85\mathrm{\ if\ female\ }$$

wt : weight in kg

Schwartz

$$\mathrm{CrCl}_{\mathrm{Schwartz}}=\frac{\mathrm{k}\times\mathrm{ht}}{\mathrm{SCr}}$$

ht : height in cm

Condition	k value
if age ≤ 1 and term infant	k = 0.45
else if age ≤ 1 and LBW infant	k = 0.33
else if age ≥ 13 and sex = M	k = 0.7
else	k = 0.55

Protocol CrCl

Condition	Equation to Use
If age < 18	use Schwartz
Else if actual weight < IBW	use C-G(actual)
Else if overUnder > 30	use C-G(adjusted)
Else	use C-G(ideal)

Vancomycin Protocol Dosing

Configuration

Maximum Doses

Parameter	Value
Max initial TDD (non-HD)	4500 mg
Max MD for HD patient	2000 mg
Max MD for PD patient	2000 mg

Data Validation

Parameter	Condition	Value(s)
Dose	in range	`250` to `3000`
Frequency	in range	`6` to `48`
Level	in range	`3` to `100`
Time level drawn after dose	in range	`0` to `36`

Loading Dose

Pediatric (non-obese):

"Loading dose not recommended in non-obese pediatric patients"

Pediatric with BMI > 95th percentile for age:

"Consider loading dose of 20 mg/kg × ABW mg (BMI ≥ 95th percentile for age)"

Adults (calculated using ABW)

Adults	Loading Dose (ABW)	Max LD
Default	25 mg/kg	3 g
Severe sepsis	25-35 mg/kg	3 g
HD	25 mg/kg	2 g
PD	25 mg/kg	2 g
CRRT	20-25 mg/kg	3 g
SLED	20-25 mg/kg	3 g

Dose Rounding

Age ≥ 18: round to nearest 250 mg

Age < 18: round to nearest 25 mg for doses < 250 mg, otherwise round to nearest 250 mg

Infusion Time

Dose	Infusion Time ($\mathrm{T}$)
if dose > 2500	3 hours
else if dose > 2000	2.5 hours
else if dose > 1500	2 hours
else if dose > 1000	1.5 hours
else	1 hour

Maintenance Dose

Non-Dialysis

CrCl	Age	Recommendation
(any)	< 12 years	`60-80 mg/kg/day divided q6h`
(any)	< 18 years	`60-70 mg/kg/day divided q6h` or `60-70 mg/kg/day divided q8h`
≥ 75	< 40 years	`15-20 mg/kg q8h`
≥ 75	< 80 years	`15-20 mg/kg q12h`
≥ 75	≥ 80 years	`10-15 mg/kg q12h`
50-75	< 70 years	`15-20 mg/kg q12h`
50-75	70-79 years	`10-15 mg/kg q12h`
50-75	≥ 80 years	`15-20 mg/kg q24h`
35-49	< 70 years	`15-20 mg/kg q24h`
35-49	70-79 years	`10-15 mg/kg q24h`
35-49	≥ 80 years	`10 mg/kg q24h`
15-34	< 80 years	`10 mg/kg q24h`
15-34	≥ 80 years	`7.5 mg/kg q24h`
< 15	> 18 years	`15-20 mg/kg x1`*

*Consider checking level in 24-48 hours. Repeat dose when level ≤ 15 (≤ 20 for septic shock/CNS/meningitis)

Maximum initial maintenance dose: 4.5 g/day

Dialysis

HD: 10 mg/kg (ABW) after the first HD (max 1.5 g)

PD: 10-15 mg/kg when level is < 15 mcg/mL (max 2 g)

CRRT: 7.5-10 mg/kg q24h (max 4.5 g/day)

SLED: 15-20 mg/kg after each session (max 4.5 g/day)

Strategy, Target, and Monitoring

flowchart LR
  HDq[Dialysis?]:::gray -->|No| AKIq
  
  AKIq[AKI?]:::gray --> |No| InsightRx:::blue
  InsightRx --> insightInd[CNS/meningitis?]:::gray
  insightInd --> |No| AUC
  insightInd --> |Yes| Trough15

  Trough15 --> outlier[PK Outlier?]:::gray
  AUC --> outlier
  outlier --> |Yes|outlierLevel
  outlierLevel[24-48 hours, then 24-48 hours later]:::green
  outlier --> |No|standardLevel
  standardLevel[First level in 72 hours]:::green
  
  
  AKIq --> |Yes| WB[Weight-based]:::blue --> wtInd
  wtInd[CNS/meningitis?]:::gray
  wtInd --> |No| Trough10
  wtInd --> |Yes| Trough15W

  Trough15[Trough 15-20]:::calc 
  Trough15W[Trough 15-20]:::calc 
  Trough10[Trough 10-15]:::calc 
  AUC[AUC 400-600]:::calc

  Trough10 ---> akiLevel
  Trough15W ---> akiLevel
  akiLevel[First level in ~12 hours]:::green

  HDq ---> |Yes| HDW[Weight-based]:::blue
  HDW --> HDInd[SSTI or UTI?]:::gray
  HDInd --> |No| HD15[Trough 15-20]:::calc
  HDInd --> |Yes| HD10[Trough 10-15]:::calc
  HD15 --> HDType[Type of dialysis?]:::gray
  HD10 --> HDType
  HDType --> |HD| iHD
  HDType --> |PD| PD
  HDType --> |CRRT| CRRT
  HDType --> |SLED| SLED

  iHD[Before every HD, start w/ 2nd after LD]:::green
  PD[q24-48h]:::green
  CRRT[q24h]:::green
  SLED[before each run]:::green


  classDef gray fill:#dedede,stroke:#333,color:black
  classDef calc fill:#FFE5B4,stroke:#FFA500,color:black
  classDef start fill:#a9e695,stroke:#2e691a,color:black
  classDef blue fill:#95dcfa,stroke:#1D7EA8,color:black
  classDef green fill:#d5f291,stroke:#63870e,color:black
  classDef final fill:#ececff,stroke:#c7b5ed,color:black

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Vancomycin Dosing Equations

Initial Dosing (Trough Method)

Volume of Distribution (Vd)

If BMI < 40: Vd = ABW x 0.5

If BMI ≥ 40: Vd = ABW x 0.7

Vancomycin Clearance (CL)

using protocol CrCl

$$\mathrm{CL}=\left [ \left (0.695 \times \mathrm{CrCl} \right ) + 0.05\right ]\times 0.06$$

Elimination Rate Constant ($ke$)

$$ke=\frac{\mathrm{CL}}{\mathrm{V_{d}}}$$

Halflife ($t_\frac{1}{2}$)

$$\mathrm{t}_{\frac{1}{2}}=\frac{\ln(2)}{ke}$$

Suggested Interval ($τ$)

Condition	Value
if halflife < 7	q6h
else if halflife < 10	q8h
else if halflife < 15	q12h
else if halflife < 21	q18h
else if halflife < 36	q24h
else	q48h

Peak and Trough

Calculate for each possible dose (500-2000 mg):

$$\mathrm{C_{max}}=\frac{\mathrm{D}}{\mathrm{T}}\times\frac{1-e^{-ke\times \mathrm{T}}}{\mathrm{V_{d}}\times ke \times \left ( 1-e^{-ke\times \tau } \right )}$$

$$\mathrm{C_{min}}=\mathrm{C_{max}}\times e^{-ke: \times, (\tau - T)}$$

Suggested dose is the lowest dose where the predicted trough is greater than or equal to the low end of goal range and less than or equal to the high end of the goal range. Uses the goal from the “monitoring” section above. If the goal is an AUC range, uses trough 10-20 for this determination (10-15 for peds).

Dose Revision

Linear

New Dose

$$\mathrm{D}{2}=\left ( \frac{\mathrm{D}{1}}{\mathrm{C}{1}}\times\mathrm{C}{2} \right )+125$$

$C_2$ : Desired trough = middle of selection range

Expected Trough

$$\mathrm{C}{2}=\frac{\mathrm{D}{2}}{\mathrm{D}{1}}\times\mathrm{C}{1}$$

Single Level (Trough) Revision (Non-HD)

Calculated Elimination Rate Constant (ke)

$$ke=\frac{\ln\left(\frac{\left[\left(\frac{\mathrm{dose}}{\mathrm{V_{d}}} \right ) + \mathrm{C}{\mathrm{result}}\right ]}{\mathrm{C{result}}} \right )}{\left(\tau -\mathrm{T_{trough}} \right )}$$

$\mathrm{T}_\mathrm{trough}$ : hours drawn before next infusion

Estimated Trough

$$\mathrm{C_{est.trough}}=\mathrm{C_{result}}\times e^{-ke;\times,\mathrm{T_{trough}}}$$

Estimated Peak

$$\mathrm{C_{est.peak}}=\frac{\mathrm{C_{est.trough}}}{e^{-ke;\times,\left(\tau -\mathrm{T_{inf}}-\mathrm{T_{trough}} \right )}}$$

Halflife ($t_\frac{1}{2}$)

$$\mathrm{t}_{\frac{1}{2}}=\frac{\ln(2)}{ke}$$

Recommended New Frequency

$$\tau_{\mathrm{new}}=\mathrm{T_{inf}}+ \left ( \frac{\ln\frac{\mathrm{C_{trough.goal}}}{\mathrm{C_{peak.goal}}}}{-ke} \right )$$

Uses fixed goal peak of 35 mcg/mL

$\tau_\mathrm{new}$	Round to
< 7	q6h
< 10	q8h
< 16	q12h
< 21	q18h
< 36	q24h
else	q48h

Remainder of calculations

Use calculated ke in same equations/process as initial PK dosing

Single Level (Trough) Revision (HD)

Dose adjustment for HD patient requires goal trough of 10-15 or 15-20 to be selected.

Level Timing	Target (mcg/mL)	Level (mcg/mL)	Recommendation
Pre-HD	10-15	> 20	hold
Pre-HD	10-15	15-20	7.5 mg/kg
Pre-HD	10-15	10-15	10 mg/kg
Pre-HD	10-15	< 10	15-20 mg/kg
Pre-HD	15-20	> 25	hold
Pre-HD	15-20	20-25	7.5 mg/kg
Pre-HD	15-20	15-20	10 mg/kg
Pre-HD	15-20	< 15	15-20 mg/kg
Post-HD	10-15	> 15	hold
Post-HD	10-15	10-15	7.5 mg/kg
Post-HD	10-15	< 10	10 mg/kg
Post-HD	15-20	> 20	hold
Post-HD	15-20	15-20	7.5 mg/kg
Post-HD	15-20	< 15	10 mg/kg

"Hold dose and order trough before next HD"
or
"Give ABW x dose recommendation mg (dose recommendation mg/kg) after HD"

Two-Level PK

Elimination Rate Constant (ke)

$$ke=\frac{e^{\frac{\mathrm{C}_1}{\mathrm{C}_2}}}{\mathrm{T}_1-\mathrm{T_2}}$$

Remainder of calculations

Use calculated ke in same equations/process as initial PK dosing

AUC Calculation - Current Dose

$$ke=\frac{-e^{\frac{\mathrm{C_{max}}}{\mathrm{C_{min}}}}}{\mathrm{T_{min}}-\mathrm{T_{max}}}$$

$$\mathrm{C_{true,max}}=\frac{\mathrm{C_{max}}}{e^{-ke;\times,\left(\mathrm{T_{max}}-\tau \right )}}$$

$$\mathrm{C_{true,min}}=\mathrm{C_{min}\times e^{-ke;\times,\left(\tau -\mathrm{T_{min}} \right )}}$$

$$\mathrm{AUC_{inf}}=\left(\mathrm{C_{true,max}+\mathrm{C_{true,min}}} \right )\times\frac{\mathrm{T}}{2}$$

$$\mathrm{AUC_{elim}}=\frac{\mathrm{C_{true,max}-\mathrm{C_{true,min}}}}{ke}$$

$$\mathrm{AUC}{24}=\left(\mathrm{AUC{inf}} + \mathrm{AUC_{elim}} \right )\times \frac{24}{\tau}$$

$$\mathrm{V_d}=\frac{\mathrm{dose}}{\mathrm{T}}\times\frac{1-e^{-ke;\times,\tau}}{ke\times \left[\mathrm{C_{true,max}} -\left(\mathrm{C_{true,min}\times e^{-ke;\times,\tau}} \right )\right ]}$$

AUC Calculation - New Dose

$$\mathrm{AUC}=\mathrm{AUC_{24}}\times\frac{\mathrm{TDD_{new}}}{\mathrm{TDD_{old}}}$$

$$\mathrm{C_{max}}=\frac{\mathrm{D}}{\mathrm{T}}\times \frac{1-e^{-ke\times,\mathrm{T}}}{\mathrm{V_d}\times ke\times\left(1-e^{-ke;\times,\tau} \right )}$$

D : new dose

$$\mathrm{C_{min}}=\mathrm{C_{max}}\times e^{-ke;\times,\left(\tau -\mathrm{T} \right )}$$

Aminoglycoside Dosing

Dosing Weight

Adjusted weight is the standard AdjBW, using factor of 0.4)

Condition	Weight to Use
if age < 15	n/a - guideline does not apply
else if overUnder > 20	use adjusted wt
else if actual wt < ideal wt	use actual wt
else	use ideal weight

Alternate Aminoglycoside Dosing Weight

Used for patients with cystic fibrosis or who are pre- or postpartum.

Condition	Weight to Use
if age < 15	n/a - guideline does not apply
else if overUnder > 20	use adjusted wt
else	use actual wt

Extended Interval Dosing

Standard (non-Cystic Fibrosis) Calculations

Infusion time $T$ assumed to be 1 hour
Time to complete distribution assumed to be 1.7 hours
Goal trough is:
- 2 mcg/mL for gentamicin and tobramycin
- 4 mcg/mL for amikacin

flowchart LR
  D[[Dose]]:::dose <-->|True peak offset| TP((Peak)):::conc
  TP <-->|2.7 hours| L1[[Level 1]]:::level
  D <-.->|Show warning if < 2.7| L1
  L1 <-->|Calculate ke| L2[[Level 2]]:::level
  L2 <-->|Time to trough| T((Trough)):::conc
  L2 <-->|Time to redose| RD 
  T <-->|Post antibiotic effect| RD[/Redose/]:::dose

  classDef dose fill:#55a63a,stroke:black,color:white
  classDef conc fill:#27aae1,stroke:black,color:white
  classDef level fill:#a2d035,stroke:black,color:white

Loading

Calculated ke: $\frac{\ln{\left(\frac{\mathrm{level}_1}{\mathrm{level}_2}\right)}}{\mathrm{time\ between\ levels}}$

Estimated Vd: $\frac{\mathrm{dose}}{\mathrm{true\ peak}}$

Calculated (true) peak: $\frac{\mathrm{level}_1}{e^{-(\mathrm{time}_1-2.7)\ \times \ ke}}$

Time to goal trough (MIC): $\frac{\ln{\left(\frac{\mathrm{level}_1}{\mathrm{level}_2}\right)}}{-ke}$

Level at redose point: $e^{-ke \times \left( \mathrm{Time\ to\ goal\ trough}+\mathrm{Post\ antibiotic\ effect}\right)}\times\mathrm{level}_2$

Peak to trough time: $\frac{\ln{\left(\frac{\mathrm{goal\ trough}}{\mathrm{goal\ peak}}\right)}}{-ke}$

New dose to redose time: Peak to trough time + Post antibiotic effect + 2.7

Recommended dose: $\frac{\mathrm{goal\ peak}}{\mathrm{true\ peak}}\times\mathrm{dose}$

Recommended frequency: Round New dose to redose time to nearest 12 hours

Point level estimate: $e^{-ke \times \left( \mathrm{Time\ from\ level_2\ to\ custom\ time}\right)}\times\mathrm{level}_2$

Cystic Fibrosis Calculations

Infusion time $T$ assumed to be 1 hour
Goal trough is: Undetectable
Goal Peak is:
- 20-30 mcg/mL for tobramycin
- 35-50 mcg/mL for amikacin
Goal AUC is:
- < 101 mg·hr/L for q24h tobramycin
- n/a for amikacin and other tobramycin frequencies

Calculated ke: $\frac{\ln{\left(\frac{\mathrm{level}_1}{\mathrm{level}_2}\right)}}{\mathrm{time\ between\ levels}}$

Halflife: $\frac{0.693}{ke}$

Predicted peak: $\mathrm{level_1}\div e^{-ke\times\left(\mathrm{time_1}-T\right)}$

$\mathrm{time_1}$ : time from dose to first level

Predicted trough: $\mathrm{level_2}\times e^{-ke\times\left(\tau-\mathrm{time_2}\right)}$

$\mathrm{time_2}$ : time from dose to second level
$\tau$ : frequency

Calculated AUC: $\frac{\mathrm{predicted\ peak}-\mathrm{predicted\ trough}}{ke}$

Corrected QT Interval

Calculation Process

Adjust for prolonged QRS interval
- If QRS > 120, use Modified Bogossian formula to correct the above (QT or average QT)
Calculate QTc using the formula determined by the heart rate
- If HR < 50, use the Fridericia formula
- If HR 50-70, use the Bazett formula
- If HR > 70, use the Framingham formula

Variables

QT : QT Interval (from EKG)
QRS : QRS Interval (from EKG)
HR : Heart rate (bpm)
RR : $60\div\mathrm{HR}$

Formulas

Formula	Equation
Modified Bogossian	$QT-0.5(\mathrm{QRS})$
Fridericia	$\frac{QT}{\sqrt[3]{RR}}$
Bazett	$\frac{QT}{\sqrt{RR}}$
Framingham	$QT+154(1-RR)$

Diagram

flowchart LR
  QRS[QRS?]:::start -->|<120 msec| NL
  NL[Use QT from EKG]:::green --> HR
  QRS -->|>=120 msec| NH
  NH[Correct QT using Mod. Bogossian]:::blue --> HR
  HR[Determine which<br>formula to use]:::gray -->|HR < 50| F[use Fridericia formula]:::final
  HR -->|HR 50-70| G[use Bazett formula]:::final
  HR -->|HR >70| H[use Framingham formula]:::final

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  classDef calc fill:#FFE5B4,stroke:#FFA500,color:black
  classDef start fill:#a9e695,stroke:#2e691a,color:black
  classDef blue fill:#95dcfa,stroke:#1D7EA8,color:black
  classDef green fill:#d5f291,stroke:#63870e,color:black
  classDef final fill:#ececff,stroke:#c7b5ed,color:black

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Patient Calculations

Data Validation

Age

Conversion to Years

Age Context

Body Mass Index

Ideal Body Weight

AdjBW

Percent Over or Under IBW

Lean Body Weight

Body Surface Area

CrCl

Cockroft-Gault

Schwartz

Protocol CrCl

Vancomycin Protocol Dosing

Configuration

Maximum Doses

Data Validation

Loading Dose

Dose Rounding

Infusion Time

Maintenance Dose

Non-Dialysis

Dialysis

Strategy, Target, and Monitoring

Vancomycin Dosing Equations

Initial Dosing (Trough Method)

Volume of Distribution (Vd)

Vancomycin Clearance (CL)

Elimination Rate Constant ($ke$)

Halflife ($t_\frac{1}{2}$)

Suggested Interval ($τ$)

Peak and Trough

Dose Revision

Linear

New Dose

Expected Trough

Single Level (Trough) Revision (Non-HD)

Calculated Elimination Rate Constant (ke)

Estimated Trough

Estimated Peak

Halflife ($t_\frac{1}{2}$)

Recommended New Frequency

Remainder of calculations

Single Level (Trough) Revision (HD)

Two-Level PK

Elimination Rate Constant (ke)

Remainder of calculations

AUC Calculation - Current Dose

AUC Calculation - New Dose

Aminoglycoside Dosing

Dosing Weight

Alternate Aminoglycoside Dosing Weight

Extended Interval Dosing

Standard (non-Cystic Fibrosis) Calculations

Cystic Fibrosis Calculations

Corrected QT Interval

Calculation Process

Variables

Formulas

Diagram