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Equations Flashcards

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1
Q

Starling’s forces

A

Filtration (Jv) = Kf [(Pc-Pif)- σ (πc- πif)]

Kf – capillary filtration coefficient/permeability (capacity of the membrane to filter water at a given net filtration pressure) (ml/min/mmHg)
- Kf is 100x greater in kidney than systemic capillaries

σ – osmotic reflection coefficient (the fraction of the total potential osmotic pressure exerted by the solute in question)
- Glomerular capillary is essentially 1

Pc = capillary hydrostatic pressure
Pif = interstitial hydrostatic pressure

πc =plasma oncotic pressure
πif= interstitial oncotic pressure

Jv = net capillary filtration

Also used to determine GFR (bowman’s space = interstitium)

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2
Q

Free water deficit (L)

A

0.6 x BW (kg) x ([patient Na+]/[normal Na+] – 1)

Quick formula: 3.7mls/kg/hr of D5W
*calculated to change Na by 1 mEq/hr

If severe (>180meq/L), then replace at a rate of 0.5mEq/L/hr with D5W or oral hourly water administration (if drinking or by NG tube)

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3
Q

Estimated ∆ Na with 1 L fluid

A

Change in serum [Na]= ([Nafluids]-[Naserum]) / [(0.6 x kg) + 1]

Sodium deficit should be calculated from the minimum safe sodium: 12mEq/L

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4
Q

Na+ deficit in hyponatremia

A

Na deficit (mmol) = 0.6 x BW (kg) x (Normal Na - Pts Na)

●Sodium deficit should be calculated from the minimum safe sodium : 120 mEq/L

● Do not exceed 0.5 mEq/L/hr or no more than 12 mEq/L/day
● If severe symptoms, may increase sodium more quickly 1.5-2.0 mEq/L/hr for 3-4 hours

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5
Q

Corrected Chloride

A

Pts Chloride x (Norm Na/Pts Na)

Corrects for free water deficit

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6
Q

Plasma/serum osmolality

A

Plasma/serum osmolality (mmol/L) = 2(Na + K) + (BUN/2.8) + (glucose/18)

*2 x (Na + K) to account for Cl and HCO3
*Divide to convert between mg/dL to mmol/L

Dog: 290-310 mOsm/kg
Cat: 290-330 mOsm/kg

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7
Q

Effective osmolality

A

2(Na+K) + (glucose/18)

Because urea is not an effective osmole

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8
Q

Osmolal gap

A

Measured osmolality – calculated osmolality

  • If measured >10mOsm/kg over calculated there are unmeasured solutes present
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9
Q

GFR (ml/min)

A

(Volume/time)
= Clearance of inulin (filtered but not reabsorbed or secreted)
= Same as clearance, thus saying that the clearance of creatinine equals GFR
- This equation works because there is no tubular reabsorption or section or metabolism of creatinine (-ish) and would work for any other substance like that (inulin)

GFR = (U{Crea} X V ) / P{Crea}

Either inulin or creatinine clearance rate may be used for GFR

U{Crea} = urinary concentration of creatinine
V = urine flow rate
P{Crea} = arterial plasma concentration of Crea

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10
Q

Albumin deficit (grams) = _____________

A

10 x (desired alb - patient alb) x Kg x 0.3

Or

Using 25% Human serum albumin (HAS) (25g/100mL)
2ml/kg x 2hr then 0.1-0.2mL/kg/hr x 10hr = total 2g/kg

FFP = 3g/100mL
Whole blood = 1.4g/100mL
CSA = variable

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11
Q

Normal COP in dogs and cats:
Plasma: _____
Whole blood: _______
Sick patients: ______ (+ Goal)

A

Plasma dogs: 21-25mmHg
Plasma Cats: 23-35mmHg
Whole blood Dogs: 10 +/- 2mmHg
Whole blood Cats: 25 +/- 4mmHg
Sick patients: ~14 +/- 3mmHg
Goal of 16mmHg

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12
Q

Henderson-Hasselback Equation

A

pH= 6.1 x log [ (HCO3) / (0.03 x PCO2) ]

6.1 = pH in bodily fluids
HCO3 -> mEq/L or mmol/K
0.03 = solubility coefficient of CO2 in plasma
PCO2 -> mmHg

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13
Q

Carbonic Acid Equation

A

CO2 + H2O <—> H2CO3 <—> H (+) + HCO3 (-)

Carbonic anhydrase catalyzes first half (intracellularly)

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14
Q

Base excess
Vs
Base deficit

A

Base excess = (+) number
Base deficit = (-) number

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15
Q

Corrected Sodium

A

Na[corrected] = Na[p] + 1.6 [(BG[p] - BG[n]) / 100]

Or

1.6mEq/L decrease in Na for every 100mg/dL increase in glucose or mannitol

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16
Q

Anion Gap =

A

Anion Gap = (Na + K) - (Cl + HCO3)

                = UA (variable)  - UC (not variable)
  • not reliable if patient is hypoalbuminemic

Dogs: 12-24mEq/L
Cat: 17-31mEq/L

AG alb (dog) = AG + 0.42 x (3.77 - alb)
AG alb (cat) = AG + 0.41 x (3.3 - alb)

AG phos = AG + (2.52 - 0.58 x Pi)

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17
Q

Expected compensation for simple acid base disorders:

A

Acute Resp Acidosis: ⬆️ 1mmHg PCO2 = 0.15mEq/L HCO3 ⬆️ +/- 2
Acute Respiratory Alkalosis: ⬇️ 1mmHg PCO2 = 0.25 mEq/L HCO3 ⬇️ +/- 2
Chronic Respiratory Acidosis: ⬆️ 1mmHg PCO2 = 0.35 mEq/L HCO3 ⬆️ +/- 2
Chronic Respiratory Alkalosis: ⬇️ 1mmHg PCO2 = 0.55mEq/L HCO3 ⬇️ +/- 2

*Metabolic Acidosis: ⬇️ 1mEq/L HCO3 = 0.7mmHg PCO2 ⬇️ +/- 3
*Metabolic Alkalosis: ⬆️ 1mEq/L HCO3 = 0.7mmHg PCO2 ⬆️ +/- 3

  • Not really a thing in cats
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18
Q

Sodium Bicarb Dose =

A

NaHCO3 (mmol/L) = 0.3 x kg x Base deficit (mmol/L)
= 0.3 x kg x (normal HCO3 - patient HCO3)

0.3 is approximate distribution of bicarb
This dose will return bicarb to normal, so only give a fraction
8.4% NaHCO3 = 2000mOsm/L so dilute 1:3 with water for injection
Don’t push or risk hypovolemia/Increased ICP

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19
Q

Stewart Approach

A

Strong ion difference (SID) = Na + K + Ca + Mg - (Cl + other strong anions)
Most simplified SID = (Na) - (Cl)
ATOT (aka total of weak acids) = Alb + Phos
* SIG = SID - (HCO3 + ATOT)

*its like AG for traditional, but less effected by albumin
*Normal SIG should be zero

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20
Q

Steward Semi-quantitative approach

A

Shorthand formulas:
N= normal value
P= patient or measured value

1) Free water effect = (Na[p] - Na[n]) / 4
Hypernatremia -> alkalosis

Corrected chloride = Cl[p] x (Na[n] / Na[p])
2) Chloride effect = Cl[n] - Cl[corrected]

3) Albumin effect = (Alb[n] - Alb[p]) x 4
Hypoalbuminemia -> alkalosis

4) Phosphate effect = (Phos[n] - Phos[p]) / 2

5) Lactate effect = Lact[p] x (-1)

Add all together to = Sum
XA (unmeasured) = Base excess - Sum

(+) value is alkalosis
(-) value is acidosis

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21
Q

Na Deficit example:
20kg dog with a Na of 120mmol/L (normal 145mmol/L)

Calculate the Na deficit.
Give plan to correct over 10hrs.

A

Na deficit (mmol) = (145-120) x (20 x 6)
Na deficit = 300mmol Na

Correct over 10 hr:
30mmol Na/hr
If you use 3% HTS = 513mmol Na/L or 0.513mmol Na/mL
30/0.513 =58ml/hr of 3% HTS

Or

1) Calculate: Change in serum sodium = (Fluid Na - Patients Na) / [(0.6 x kg) + 1]
- Fluid Na options include: 3% HTS = 513mmol/L, 5% HTS = 856mmol/L, 7.2% HTS = 1283mmol/L, 23.4% HTS = 4004mmol/L
- JVECCs Review suggests adding K into the equation bc any K supplementation will activate NaKATPase and will cause Na to leave the cell and increase Na -> change in serum sodium = [(Fluid Na + K) - Patients Na] / [(0.6 x kg) + 1]
2) Determine: fluid rate (ml/hr) = (1000 x rate of Na correction in mmol/L/hr)/Change in serum sodium
- Rate of Na correction should be 0.4mmol/L/hr (= 9.6mmol/L in 24 hr)
- so that you do not correct > 10mmol in 24 hr.
3) Throw away: Na deficit calculation -> you don’t need it

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22
Q

Pseudohyponatremia

A

Na dilution due to increased osmolality, most often hyperglycemia (also retained mannitol)

For every 100mg/dL increase in glucose above normal = 1.6-2.4meq/L decrease in Na
Not linear relationship, more hyperglycemia, larger the Na drop

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23
Q

Phosphate

A

3.1mg/dL = 1mmol/L = 1.8mEq/L

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24
Q

APP = _____

A

Abdominal perfusion pressure (mmHg) = MAP - IAP
Goal APP > 60mmHg

IAP = Intra-abdominal pressure
IAH = intra-abdominal hypertension (sustained pressure > 12mmHg)
ACS = abdominal compartment syndrome (sustained increase > q-mmHg that is associated with new organ dysfunction or failure)

1mmHg = ~ 1.4cmH2O

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25
APP/IAP Grading scale:
1mmHg = ~1.4cmH2O - Normal = less than 0-5 cm H2O (0-3.6mmHg) 1) IAP 16-20cmH2O or 12-15mmHg 2) IAP 21-27cmH2O or 16-20mmHg : might need fluid resuscitation 3) IAP 28-34cmH2O or 21-25mmHg : Consider decompression 4) IAP >35cmH2O or >25mmHg : needs decompression - Normal muscle pressure in dogs = 5.7 +/- 5mmHg
26
Kt/v
- Unitless - Describes efficacy of dialysis with 1.2 as a minimum recognized standard adequacy - K = dialyzer clearance of urea (rate of blood passing through dialyzer) - t = dialysis treatment time - v = volume of distribution of urea (kg x 0.6) - assume single pool fixed volume model with 0.6 as TBW distribution Ex: K = 300ml/min dialyzer clearance t = 180 min session v = 70kg pt -> (70 x 0.6) = 42L 300ml/min x 180min = 54,000mL or 54L 54L / 42L or 1.3
27
URR = ____________
Urea Reduction Ration % (URR) = (BUNpre - BUNpost) / BUNpre x 100 URR = pre-dialysis vs post dialysis urea concentrations Ex: Cat Pre-dialysis Urea 100mg/dL Post dialysis Urea 8mg/dL -> removed 92mg/dL urea (100-8) / 100 x 100 = 92%
28
URR reference ranges:
Small/medium animals can reach 95% Med/Large animals can reach 80-85% Humans can reach 60-65%
29
Extraction Ratio
Extraction Ratio (%) (ER) = (Cone In - Cone Out) / Cone In ER = percentages of a substance removed in a single pass through the dialyzer or device, measure in blood entering and then leaving the system Conc = the substance being measured
30
Clearance of a dialyzer
(mL/min) - Volume of blood completely cleared of a certain solute during a single pass through the device (identical to concept of clearance in the kidney) Clearance (mL/min) = Blood flow rate (Qb) x ER = Qb x ER = Qb x [(Conc In - Conc Out) / Conc In] Common substances used: urea, creatinine, phosphorous, Vit B12, inulin
31
Urinary Free water clearance
Urinary Free water Clearance (%) = 1 - [(Urine Na + Urine K) / Urine Na] - Uses urine cations rather than osmolality - Can only be performed when urine sodium concentration is > 20meq/L
32
Fraction Excretion of Sodium (FE[na]) = __________
FE[na] = 100 x [(Urine Na x Plasma Crea) / (Plasma Na x Urine Crea)] - Can really be the fractional excretion of anything
33
Clearance
(Volume/time) = a volume of plasma from which all the substance has been removed and excreted in the urine per unit time .. it is an idealized volume, basis on which GFR is calculated C{x} = (U{x} x V) / P{ax} C{x} = clearance of x U{x} = urinary concentration of x V = urine flow rate P{ax} = arterial plasma concentration of x
34
Filtration fraction
FF (volume/time) Filtration Fraction = GFR/RPF - not all blood that goes to the kidney is filtered across the glomerulus - Generally in humans, only 15-20% of the plasma that enters the glomerulus is actually filtered - Dogs: 32-36% - Cats: 22-42%
35
RPF
= Renal Plasma Flow (vol/time) = clearance of PAH (both filtered an unfiltered) - PAH is commonly used - PAH - p-aminohippuric acid - not made in the body, freely filtered, does not effect blood flow. Also, excreted by the renal tubules RPF = (U{x} x V) / P{x} Normal: Dogs: 7-20ml/min/kg Cats: 8-22ml/kg/min
36
RBF
RBF = Renal Blood flow (volume/time) RBF = RPF / (1 - HCT)
37
Functional Clearance (FC)
FC = Clearance{x} / Clearance{creat}
38
Filtered load
Filtered load = GFR x plasma
39
Excretion rate
Excretion rate = urine flow rate x urine
40
Reabsorption rate
Reabsorption rate = filtered load - excretion rate
41
Secretion rate
Secretion rate = excretion rate - filtered load
42
CaO2
CaO2 = Carrying capacity of O2 (mL O2/dL) CaO2 = bound O2 + dissolved O2 CaO2 = (1.34 x HgB x SaO2) + (0.003 x PaO2) With units: CaO2 = (1.34mL O2/g x HgB g/dL x SaO2 %) + (0.003mL O2/dL/mmHg x PaO2 mmHg) 1.34mL O2/g =56.699/oz normal oxygen carrying capacity of HgB Hgb g/dL = hemoglobin (normal 14g/dL) 0.003 (mL O2/dL/mmHg) = solubility coefficient of oxygen at body temp Normal = ~ 18mL O2/dL
43
CO
Cardiac Output (CO) = volume of blood transferred to systemic circulation over time CO = SV x HR Dogs: 125-200mL/kg/min -> technically a CI because its calculated with respect to patient size Cats: 120ml/kg/min
44
Cardiac Index
Cardiac index (CI) = correlates CO with respect to patients body surface area = CO/BSA in m*2 or CO/kg Dog: 3.5-5.5 L/min/m*2
45
Fick’s Oxygen consumption method of determining CO
CO = VO2 / (CaO2 - CvO2) “What went in minus what came out must equal what was left behind”
46
Fick’s Principle applied to CO2 for CO determination
CO = CO2 production / (CvCO2 - CaCO2)
47
Calculating CO from Trans-esophageal echo
- Need LVOT diameter and aortic blood velocity to calculate stroke volume, use that x HR = CO - Difficult to obtain accurate LVOT measurement even for experienced operators
48
Pressure variation (either systolic PV, pulse PV, or stroke volume V)
Variation = (Max - Min) / Average x 100 <13% =is normal /not fluid responsive
49
Caudal Vena cava collapsibility index or CVC-CI
CVC-CI = (Max - Min) / Max x 100 <20% variation, then hypervolemic If >60% variation, then hypovolemic
50
MAP
MAP = diastolic + [(systolic - diastolic) / 3] MAP = CO x SVR
51
DO2
Delivery of oxygen (DO2) = CO x CaO2 CaO2 = arterial O2 content
52
VO2
Oxygen Consumption (VO2) = CO x (CaO2 - CvO2) Tissue O2 uptake/consumption Normal 110-160ml/kg/min
53
OER
Oxygen extraction ratio (OER) O2ER = VO2/DO2 O2ER = (SaO2 - SvO2) / SaO2 O2 ER = (CaO2 - CvO2) / CaO2 Normal is ~ 25% Can go up to as much as 60% (critical point)
54
SVR index
Systemic vascular resistance index (SVR) Units: ml/kg/min Or m*2 SVR = MAP - CVP x 80 Or SVR = (MAP - CVP) / CI
55
CoPP
Coronary perfusion pressure (CoPP) Also called myocardial perfusion pressure = Diastolic aortic pressure - right atrial diastolic pressure
56
Ohm’s Law
ΔP = Q x R Change in pressure (P) = Flow (Q) x Resistance (R)
57
Pouiseulle’s Law
Q = (π x P x r*4) / (8 x ή x l) Q = flow P = pressure r = radius η = fluid viscosity l = length of tubing The reason why you’re shorter length, larger bore IVC has faster flow rates
58
FS
Fractional shortening % FS % = [(LVIDd - LVIDs) / LVIDd] x 100 LVID = left ventricular internal diameter Normal: Dogs: 35-45% Cats: 40% M mode measurement
59
EF
Ejection Fraction (EF %) EF % = [(LVEDV - LVESV) / LVEDV] x 100 SV expressed as percentage of left ventricular diastolic volume
60
Simplified Bernoulli Equation
ΔP = 4v*2
61
Calculating PH based on simplified Bernoulli equation
Pulmonary artery pressure = 4 x (peak velocity of the pulmonary regurgitation flow) *2 + RA pressure OR PAP = 4 x (TR)^2 Severity of PH: Mild = 20-40mmHg Moderate = 41-55mmHg Severe = >55mmHg
62
Heart Chamber pressures
(Rounded numbers for easy memorization) RA = mean 5mmhg RV = 25/5 PA = 25/10 LA = mean 5-10 LV = 125/10 Ao = 125/80
63
Law of Laplace
Wall tension = Pressure x radius / wall thickness
64
Fick’s law of gas diffusion
Volume of gas per unit time = area/thickness x diffusion constant x partial pressure difference Diffusion constant = solubility / ✅MW
65
Shifts in O2 saturation curves:
Left (more affinity): - alkaline pH (low H or CO2) - cold - low 2,3 DPG (fetus) - CO Right (more offloading): - acidic pH (increased H or CO2) - hot - Elevation (increased 2,3 DPG)
66
A-A gradient
PAO2 - PaO2 PAO2 = FiO2 decimal (barometric pressure - 50) - (PaCO2 x 1.1) Sea level barometric pressure = 760 So short formula = 150 - PaCO2 x 1.1 Normal A-A gradient = <15
67
P:F ratio
PaO2 should be 5x the FiO2 Normal P/F = 500 (using the decimal FiO2)
68
Haldane effect
Offloading of O2 allows for more CO2 carrying
69
Bohr effect:
Increased CO2 decreases the affinity for O2
70
Bohr equation for dead space
Vd/Vt = [(PaCO2 - PEtCO2) / PaCO2] To assess physiologic dead space Fowler method would assess more an atomic dead space Can substitute PaCo2 Normal 0.25-0.3
71
Compliance
= Δvolume / Δpressure
72
Elastance
= Δpressure / Δvolume
73
Airway pressure during inspiration
ΔPressure = (ΔTidal volume / compliance) + (resistance x Δflow)
74
Equation of motion (ventilator):
Pressure = (Tidal volume / compliance) + (resistance x flow) Pressure = Muscle pressure + ventilator pressure
75
Whole blood transfusion calculation
(Desired PCV - patient PCV) x kg x 2mL
76
PRBC transfusion calculation
(Desired PCV - patient PCV) x kg x 1.5mL
77
Any blood transfusion calculation
(Desired PCV - patient PCV) x (90mL / donor PCV) x kg
78
Nutrition RER
RER = 30 x kg + 70 Or RER = (70 x Kg)*0.75
79
TPN calculations:
Dog protein requirement: 4-5g/100kcal Cat protein requirement: 6-8g/100kcal Dextrose for 30-50% of remaining calories 50% dextrose is 1.7%kcal/mL Lipid for 50-70% of remaining calories 20% lipid is 2kcal/mL
80
Uroabdomen ratio of fluids
Creatinine of abd fluid >/= 2x that of serum creatinine K of abd fluid >/= 1.4x that of serum K
81
Bile peritonitis ratio for fluids
Tbili of abd fluid >/= 1.2x Tbili of serum
82
Septic abdomen ratio for fluids
Glucose of abd fluid <20 than serum glucose Lactate of abd fluid > 2 than serum lactate
83
Sensitivity
= ability to correctly ID those with the disease True positive/all with the disease = true positive / (true positive + false negative)
84
Specificity
= Ability to correctly ID those without disease True negative/all those without the disease = true negative / (true negative + false positive)
85
PPV
Positive predictive value = likelihood that patient with positive results has the disease True positive/all test positive = true positive / (true positive + false positive)
86
NPV
Negative predictive value = likelihood that patient with negative results has the doesn’t have the disease True negative/all test negative = true negative / (true negative + false negative)
87
Accuracy
# test correct / all = (true positive + true negative) / (true positive + false positive + false negative + true negative) = (sensitivity x prevalence) + [specificity x (1 - prevalence)]
88
Likelihood ratio
= How much more likely it is that a patient with a positive test has disease compared to a patient with a negative test LR = sensitivity / (1 - specificity)
89
CPP
Cerebral perfusion pressure (CPP) = MAP - ICP Normal ICP = 5-12mmHg Normal CPP = 50-90mmHg
90
K - shift
0.6mEq increase for each 0.1 unit decrease in pH (and vise versus) - metabolic process only, mineral not organic acidosis
91
Protein:Creatinine Ratio
= Clearance{prot} / Clearance {Crea} = (U{prot}/P{prot}) / (U{Crea}/P{crea}) = roughly U{prot} / U{crea} = roughly equal to ex creation rate ratio Normal: <0.5 Borderline: 0.5-1 Abnormal: > 1
92
Transmural pressure = _____
= P{inside} - P{outside} - Positive tends to expand volume - Negative decreases volume
93
P{alv}
P{alv} = P{el} + P{pl} P{el} is elastic recoil pressure
94
Alveolar ventilation
Alveolar ventilation (VA) = F (Vt - Vd)
95
Reynold’s number
Reynolds number = [2 (radius)(density)(Velocity)] / (viscosity) Laminar vs turbulent flow
96
Henry’s law
the amount of gas dissolved is proportional to the partial pressure
97
Alveolar gas equation
PAO2 = FiO2 (P{atm} - P{h2o}) - PACO2/ R PAO2 = 150 - PaCO2/0.8 Only when on room air Normal <15mmHg For each 10% in FiO2 the A-a would increase by 5-7 mmHg
98
Dynamic compliance
= TV/PIP - PEEP
99
Static complianace
TV/Plat - PEEP
100
Shunt equation
Qs/Qt = (CcO2 - CaO2) / (CcO2 - CvO2) CcO2 = end capillary O2 content Normal shunt fraction is 10% of CO 0-5% in awake 5-10% in anesthetized
101
Starling Landis Equation
JV = LpA [(Pv - Pi) - σ (π{v} - π{subg})]
102
PAP
Pulmonary arterial pressure (PAP) = CO x PVR
103
Stroke volume
SV = CO/HR 40-60ml/beats/kg
104
Stroke volume index
SV/BSA
105
Systemic volume resistance
= MAP - RAP / CI 0.5-0.8mmhg/ml/kg/min
106
PVR
Pulmonary vascular resistance (PVR) = Mean PAP - Mean PAOP / CI 0.04-0.06 mmHg/mL/kg/min
107
SID Apparent
= (Na + K) - (Cl + Lac)
108
SID effective
Bicarb + alb eff + phos eff
109
SIG
= SID app - Sid eff Dog: Alb x 4.8 - AG Cat: Alb x 7.4 - AG Normal: -5 to 5 AG (P adj) = AG + (2.52 - [0.58 x P]) P in mg/dL
110
SID
Na - Cl corrected Normal: Dog = 36 Cat = 29 + strong ion alkalosis - Strong ion acidosis
111
Temperature conversion: C -> F
C (9/5) + 32
112
Temperature conversion: F-> C
(F - 32) x 5/9
113
1mmHg = ___________ cmHg
1mmHg = 1.36cmH2O
114
RQ
Respiratory quotient (RQ) = VCO2 / VO2
115
120 Rule
PaO2 + PaCO2 > or = 120 If less, then venous admixture exists Normal about 140 +/- 10, assumes 21% FiO2 at sea level with normal alveolar nitrogen and water vapor
116
P/F ratio
PaO2/FiO2 ratio P/F > 400 = WNL P/F: 300-399 = mild ARDS P/F: 200-299 =moderate ARDS P/F: <200 = Severe ARDS Severe lung disease if PaO2 is <2s FiO2
117
Fowler’ s method
Measure of an atomic dead space (volume of conducting airway) Use volumetric expired nitrogen concentration graph after taking 1 breath of 100% O2

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