Table 1.
Parameter estimates.
| Variable (programming language) | Symbol (mathematical variable) | Description | Unit | Fixed Effects | SE Lin | RSE (%) | IIV (SD) | SE Lin | RSE (%) |
|---|---|---|---|---|---|---|---|---|---|
| Frxn_0abs_pop | F0-abs | Fraction of benazepril zero-order absorbed | – | 0.695 | 0.024 | 3.5 | 0.606 | 0.078 | 12.9 |
| F_bio_pop | F | Bioavailability of benazepril | – | 0.883 | 0.022 | 2.5 | 0.451 | 0.200 | 44.4 |
| Frxn_ACE_fr_pop | FACE fr | Fraction of ACE in free circulation compartment | – | 0.035 | 0.006 | 17.1 | – | – | – |
| delta_24hr_pop | δ24hr | Scale of renin production variance due to chronobiology | – | 0.292 | 0.032 | 11.3 | 0.768 | 0.133 | 17.3 |
| Vpl_pop | Vpl | Volume of plasma compartment | L | 48.5 | 4.2 | 8.7 | 0.298 | 0.047 | 15.7 |
| Vts_pop | Vts | Volume of tissue compartment | L | 0.965 | 0.221 | 22.9 | 1.4 | 0.163 | 11.7 |
| Vns_pop | Vns | Volume of non-specific binding for benazepril | L | 23.6 | 6.1 | 25.7 | 0.824 | 0.122 | 14.8 |
| Vrn_pop | Vrn | Volume of kidney compartment | L | 4.3 | 0.587 | 13.8 | 0.030* | – | – |
| Qfr_ns_pop | Qfr, ns | Intercompartmental transfer rate between free circulation and non-specific binding compartment | L/h | 85.1 | 32.2 | 37.8 | – | – | – |
| Qfr_ts_pop | Qfr, ts | Intercompartmental transfer rate between free circulation and tissue compartment | L/h | 2.0** | – | – | 1.4 | 0.168 | 12.5 |
| Qrn_pop | Qrn | Intercompartmental transfer rate between plasma and kidney compartment | L/h | 12.3 | 2.6 | 20.8 | 0.030* | – | – |
| ACE_total_pop | [ACE] | Total number of ACE enzymes | pmol | 0.00021 | 5E−05 | 21.3 | 0.231 | 0.182 | 78.5 |
| Shcc_pop | S0 | The concentration of angiotensin I (1–10) at time 0 | pmol/L | 93.3 | 4.4 | 4.7 | 0.355 | 0.039 | 10.8 |
| Phcc_pop | P0 | The concentration of angiotensin II (1–8) at time 0 | pmol/L | 56.7 | 2.4 | 4.2 | 0.274 | 0.040 | 14.7 |
| Ang17hcc_pop | Ang(1–7)0 | The concentration of angiotensin (1–7) at time 0 | pmol/L | 33.7 | 1.7 | 5.0 | 0.332 | 0.047 | 14.2 |
| AngIIIhcc_pop | AngIII0 | The concentration of angiotensin III (2–8) at time 0 | pmol/L | 5.0 | 0.372 | 7.4 | 0.324 | 0.103 | 31.8 |
| AngIVhcc_pop | AngIV0 | The concentration of angiotensin IV (3–8) at time 0 | pmol/L | 9.1 | 0.540 | 5.9 | 0.287 | 0.077 | 26.9 |
| ka1_pop | ka1 | First-order analog absorption rate | 1/h | 0.0148 | 0.002 | 14.3 | 0.030* | – | – |
| ka_pop | ka | Zero–order analog absorption rate | 1/h | 1.5 | 0.137 | 9.1 | 0.560 | 0.066 | 11.8 |
| Cl_pop | ClI | Clearance rate of benazeprilat | L/h | 27.3 | 2.4 | 8.6 | 0.030* | – | – |
| ClP_pop | ClP | Clearance rate of angiotensin II (1–8) | L/h | 118 | 16.1 | 13.6 | 0.214 | 0.137 | 63.8 |
| ClS_pop | ClS | Clearance rate of angiotensin I (1–10) | L/h | 6.4 | 2.1 | 33.4 | 0.030* | – | – |
| ClAng17_pop | ClAng(1–7) | Clearance rate of angiotensin I (1–7) | L/h | 98.1 | 12.2 | 12.5 | 0.030* | – | – |
| ClAngIII_pop | ClAngIII | Clearance rate of angiotensin III (2–8) | L/h | 250** | – | – | – | – | – |
| ClAngIV_pop | ClAngIV | Clearance rate of angiotensin IV (3–8) | L/h | 165 | 47.6 | 28.9 | – | – | – |
| kd_pop | kd | Ratio of enzyme substrate association rate to angiotensin II (1–8) catalysis in vivo | – | 39.3 | 9.1 | 23.0 | – | – | – |
| k1_s_pop | k1s | Rate of ACE-angiotensin I (1–10) dissociation in vivo, scaled | 1/s | 3.0** | – | – | – | – | – |
| k2_s_pop | k2s | Rate of angiotensin II (1–8) catalysis from ACE-angiotensin I (1–10) enzyme–substrate complex in vivo, scaled | 1/s | 2.9* | – | – | – | – | – |
| k3_s_pop | k3s | Rate of ACE-benazeprilat dissociation in vivo, scaled | 1/s | 7.0 | 1.3 | 19.3 | – | – | – |
| kI_17_pop | kI, (1–7) | Overall in vivo conversion rate of angiotensin I (1–10) to angiotensin (1–7) | 1/h | 0.347 | 0.042 | 12.1 | 0.254 | 0.057 | 22.5 |
| kII_17_pop | kII, (1–7) | Overall in vivo conversion rate of angiotensin II (1–8) to angiotensin (1–7) | 1/h | 0.344 | 0.063 | 18.3 | 0.189 | 0.470 | 249 |
| kII_III_pop | kII, III | Overall in vivo conversion rate of angiotensin II (1–8) to angiotensin III (2–8) | 1/h | 6.0 | 1.0 | 17.3 | 0.231 | 0.047 | 20.5 |
| kIII_IV_pop | kIII, IV | Overall in vivo conversion rate of angiotensin III (2–8) to angiotensin IV (3–8) | 1/h | 5.2 | 0.859 | 16.5 | 0.030* | – | – |
| PRA_pop | PRA | Time of peak angiotensin I (1–10) production during 24 h cycle | – | 8.4 | 1.1 | 12.7 | 1.2 | 0.145 | 11.9 |
| r_S_pop | rS | Relative rate of angiotensin I (1–10) production | pmol/h | 0.0117 | 0.0012 | 10.4 | 0.335 | 0.041 | 12.5 |
| bAngI_1to10 | bAngI | Proportional measurement error of angiotensin I (1–10) | – | 0.535 | 0.029 | 5.3 | – | – | – |
| bAngII_1to8 | bAngII | Proportional measurement error of angiotensin II (1–8) | – | 0.263 | 0.0005 | 0.205 | – | – | – |
| bAngIII_2to8 | bAngIII | Proportional measurement error of angiotensin III (2–8) | – | 0.454 | 0.0102 | 2.2 | – | – | – |
| bAngIV_3to8 | bAngIV | Proportional measurement error of angiotensin IV (3–8) | – | 0.226 | 1E−5 | 0.007 | – | – | – |
| bAng_1to7 | bAng(1–7) | Proportional measurement error of angiotensin (1–7) | – | 0.306 | 0.0003 | 0.083 | – | – | – |
| bconcentration | bbenazeprilat | Proportional measurement error of benazeprilat | – | 0.292 | 4.E−09 | 1.4E−06 | – | – | – |
The full table of parameter estimates. In the first column, the name of the parameter used in the computer code is given. Then, the variable name for the mathematical equations is given. A description of the parameter and units are given in the next two columns. Finally, the actual value of the estimate along with error estimate, gamma (standard deviation) estimate, and the error of the standard deviation estimate. Low residual error estimates on the table of parameters indicate that the model is not over-parameterized and the identification of parameters is precise. **: fixed typical value estimate; *: random effect fixed to an arbitrary small value.