A novel machine-learning based optimization: identifying new treatment regimens for tuberculosis

Maral Budak; Pariksheet Nanda; Denise Kirschner

doi:10.3934/naco.2025025

Article Contents

2026, Volume 18: 116-145. Doi: 10.3934/naco.2025025

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A novel machine-learning based optimization: identifying new treatment regimens for tuberculosis

1.
Dept. of Microbiology and Immunology, University of Michigan Medical School, 48109-5620, Ann Arbor, MI, United States

^*Corresponding author: Denise Kirschner
^*Corresponding author: Denise Kirschner

Received: March 2025

Revised: August 2025

Early access: September 15, 2025

Published online: September 15, 2025

The paper is handled by Zhisheng Shuai as the guest editor.

Abstract / Introduction Full Text(HTML) Figure(7) / Table(4) Related Papers Cited by

Abstract

Identifying optimization in a system from any discipline requires identifying ways to either maximize or minimize objectives of interest—or even trade-offs between these choices where goals must be balanced. Traditionally, optimal control theory has been used specifically for applications that are represented by ordinary differential equations. Here, we introduce a new approach to optimization that can be applied not only to ordinary differential-equation based systems, but importantly to other more complex models, such as agent-based model systems. To this end, we create a novel machine learning optimization pipeline that uses a Kriging-based surrogate model to predict objective functions. We use a Pareto optimization algorithm to identify regimens that maximize improvement to the predicted optimal set and then rank these findings. As an example, we apply this to a model system that captures drug treatment of hosts during infection with Mycobacterium tuberculosis. Typically for treatment of tuberculosis, a multiple drug regimen is used where four antibiotics are administered for a lengthy time frame of 6–9 months. We apply our new method to optimize treatment in the face of many choices for drugs, combinations and dosages and link for the first time with rankings to the optimized set of outcomes.

Keywords:

Mathematics Subject Classification: Primary: 37N40; Secondary: 92-10, 92C45.

Citation:

Full Text(HTML)

Figure 1. The optimization pipeline for non-ODE systems. The optimization pipeline starts with (1) simulating granulomas in GranSim and (2) simulating PK/PD for each antibiotic to be included. Model output of interest is: (3a) treatment time needed to sterilize granulomas (t_ster) (i.e. get rid of all bacteria). The optimization objectives are: (3b) reducing t_ster and total dose d. We build (3c) a Kriging-based surrogate model to predict objective functions for varying dosages using simulation output. (3d) A Pareto optimization algorithm identifies regimen(s) that maximize improvement in the Pareto set, i.e., the set of optimal regimens. After 20 cycles of surrogate-assisted optimization step, our algorithm predicts the Pareto set. We then rank the optimal regimens using (4) AUSC-based ranking. (n: number of simulated granulomas per regimen. t_{ster_i}: time to sterilization for granuloma i, N: number of antibiotics in a combination regimen, D_i: the dose of the antibiotic i, t_{i_max}: the maximum allowed dose of antibiotic i). See Methods for specific details of each calculation

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Figure 2. Overview of the pharmacokinetics (PK)/pharmacodynamics (PD) model that simulates tuberculosis drug regimen treatments in a granuloma. The model starts with a 2-compartment plasma PK model with 2 transit compartments that represent the digestive system (i.e., stomach, gut etc.) and the drug is dosed into Transit 1 (and Transit 2 if needed for some drugs). The drug in the plasma compartment permeates into the lung tissue through blood vessels represented in GranSim, our agent-based model simulating granulomas. Once in the lung, the drug diffuses, binds to the caseum and is taken up by macrophages. A Hill equation represents the pharmacodynamics of drugs, i.e., the killing rate of drugs depending on drug concentration and bacterial phenotype. If multiple drugs are present, we modify the killing rate based on the type of interaction (higher killing for synergistic and lower killing for antagonistic drugs). ($C_{t1(2)}$: drug concentration in Transit 1(2), $C_{Pe}$: drug concentration in peripheral tissue, $C_{P}$: drug concentration in plasma, $k_{a}$: absorption rate constant, Q: intercompartmental clearance, CL: plasma clearance, $V_{P}$: plasma volume, $V_{Pe}$: volume of peripheral tissue, $C_{V}$: concentration at the vascular source on GranSim, P: vascular permeability, $A_V$: area of the vascular source, $k_{P}$: permeability coefficient, D: diffusivity, $C_{free}$: concentration of free (unbound) drug, $f_{ub}$: caseum unbound fraction, $C_{extra}$: extracellular drug concentration, a: cellular uptake, $C_{intra}$: intracellular drug concentration, $k_{i}$: antibiotic killing rate constant for the i^th location where i is intracellular, extracellular, or caseum, $E_{max}$: maximum killing rate constant, C50: concentration needed to achieve $E_{max}$/2, h: Hill coefficient)

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Figure 3. Pharmacokinetic (PK)/pharmacodynamic (PD) calibrations for rifapentine (RPT). (A–H) PK calibrations using temporal data from rabbits [54] after (A–D) multiple (20mg/kg dosing every 3 hours, 4 times) and (E–H) single dosing (30mg/kg) in (A and E) plasma, (B and F) cavity caseum, (C and G) cellular lesion and tissue surrounding lesion, and (D and H) uninvolved lung. Black lines represent simulated concentrations in (A and E) plasma, (B and F) caseum, (C and G) granuloma, and (D and H) uninvolved lung. Green dots represent rabbit data and red dots represent the median of the data. (I–K) PD calibrations for (I) nonreplicating, (J) intracellular, and (K) extracellular Mtb. Data in (I) is from bactericidal assays using homogenized caseum [1]. Data in (J) and (K) are from [33], red circles are obtained using Mtb in butyrate, blue circles in (J) are obtained using Mtb in acidic condition, blue circles in (K) are obtained using Mtb in high cholesterol

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Figure 4. Identification of 1331 improved regimens for TB over the standard regimen. The heatmap shows the number of regimens that have shorter sterilization times and lower total doses than the standard regimen, HRZE (denoted with a red 'X'). 1331 regimens in total are improved regimens. The red 'X' denotes the CDC-recommended dose of the standard regimen HRZE based on its simulated sterilization time and dosage. The colors on the heatmap represent numbers of regimens corresponding to their sterilization time and dose that are more optimal that HRZE

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Figure 5. Optimized regimens compared to the standard when examining the antibiotics most often optimal. (A) Dots are referred to as the Pareto sets of all 4-way combinations of drugs that are > 40% present in improved regimens, H, R, M, Pa, and P (CDC-recommended dose of HRZE marked with an X). Regimens within the gray rectangle box each have optimized overall objective values for both t_ster and total dose. (B) Average sterilization times and total doses of regimens in the gray rectangle that are optimal over standard. The legend shows the regimen colors for the different doses and sterilization times

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Figure 6. Ranking of the optimized regimens. Rankings of the various dosages of the 6 optimal combinations (HRMPa, HMRP, HPaRP, HMPaP, and MPaRP) against the standard regimen HRZE based on minimizing sterilization times. Each combination regimen has 60 potential dosages determined in the optimization pipeline (6 × 60 = 360 total ranks). Colors indicate the ranks of each regimen: blue being the lowest ranking and yellow is the highest. Note that lower rankings are optimal

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Figure Suppl. Figure 1. Novel Pareto front optimization to identify optimal dose and sterilization times for HRZE. red dots represent non–dominating optimal regimens that belong to the Pareto set whereas black dots are the regimens that are not optimal based on the objectives. (see Methods for details)

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Table 1. ABC calibration priors and fitted estimates for each rifapentine (RPT) drug parameter. See Figure 3 for corresponding model outputs for the sample chosen; note that the sample chosen column correctly lists two parameters outside the 95% CI, namely, vascular permeability and permeability coefficient. CI = Bayesian credible interval; parameter values use scientific e notation

Parameter name (units)	Prior distrib. (log-uniform)	Fitted 95% CI	Sample chosen
Degradation rate on the grid (1/(60 s))	[1e-8, 1e-3]	[4.3e-6, 3.3e-4]	1.6e-4
Intracellular degradation rate (1/(30 s))	[1e-8, 1e-3]	[1.2e-7, 2.6e-4]	7.0e-5
Diffusivity (cm²/s)	[1e-9, 1e-6]	[1.8e-9, 1.7e-7]	6.4e-8
Cellular uptake (unitless)	[1e-1, 1e+2]	[1.9e-1, 7.1e+1]	3.8e+1
Vascular permeability (cm/s)	[1e-8, 1e-6]	[1.8e-7, 4.8e-7]	9.5e-8
Permeability coefficient (unitless)	[1e-1, 5e+1]	[1.4e+0, 5.5e+0]	1.1e+1
Caseum unbound fraction (unitless)	[1e-4, 2e-1]	[6.7e-4, 3.7e-2]	1.8e-1
Association constant for binding epithelium cells (unitless)	[1e-2, 1e+2]	[3.6e-2, 1.5e+1]	2.6e+0

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Table 2. Pharmacodynamic parameters for RPT

Parameter name (units)	Value
Maximum killing rate for intracellular bacteria (1/(10 min))	0.0073
Maximum killing rate for extracellular bacteria (1/(10 min))	0.0051
Maximum killing rate for nonreplicating bacteria (1/(10 min))	0.0036
C50 (concentration needed to reach half maximal killing rate) for intracellular bacteria (mg/L)	0.0042
C50 (concentration needed to reach half maximal killing rate) for extracellular bacteria (mg/L)	0.49
C50 (concentration needed to reach half maximal killing rate) for nonreplicating bacteria (mg/L)	1.57
Hill coefficient for intracellular bacteria (unitless)	1.3
Hill coefficient for extracellular bacteria (unitless)	1.1
Hill coefficient for nonreplicating bacteria (unitless)	1.7

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Table 3. The percentage of each drug present in the improved regimen set that perform better than the CDC-recommended dose of the standard regimen (HRZE). The drugs in red are present in more than 40% of the regimens within the improved regimen set

Drug	Percentage of regimens containing drug (%)
RPT	65.89
RIF	47.18
INH	43.28
MXF	43.13
PTM	42.6
BDQ	35.54
LZD	31.71
EMB	28.47
PZA	21.79

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Table Suppl. Table 1. Doses and ranks generated for the 9 drugs in combination in our regimens. We consider here 4-drug regimen sets. Our ranking method predicts these rankings based on drug efficacy for the following regimens and corresponding doses: HRZE, HRMPa, HMRP, HPaRP, HMPaP, and MPaRP simulated in our optimization pipeline

Reference Regimen	Doses (mg/l)							Rank
Reference Regimen	INH (H)	RIF (R)	PZA (Z)	EMB (E)	MXF (M)	PTM (Pa)	RPT (P)	Rank
MPaRP	0.00	19.52	0.00	0.00	9.55	31.90	59.06	1
MPaRP	0.00	18.41	0.00	0.00	9.79	38.31	58.83	2
MPaRP	0.00	18.46	0.00	0.00	10.77	20.51	53.85	3
HMRP	4.10	17.95	0.00	0.00	12.92	0.00	47.69	4
MPaRP	0.00	19.76	0.00	0.00	13.68	6.85	42.57	4
HMRP	5.64	20.00	0.00	0.00	12.56	0.00	55.38	6
MPaRP	0.00	18.97	0.00	0.00	12.56	22.56	10.77	7
MPaRP	0.00	19.49	0.00	0.00	13.64	37.95	29.23	7
MPaRP	0.00	4.10	0.00	0.00	8.97	28.72	24.62	9
MPaRP	0.00	14.45	0.00	0.00	12.61	21.99	49.78	10
MPaRP	0.00	10.33	0.00	0.00	7.06	39.76	44.80	10
MPaRP	0.00	14.36	0.00	0.00	11.13	13.33	35.38	12
MPaRP	0.00	20.00	0.00	0.00	7.90	35.90	55.38	12
MPaRP	0.00	9.23	0.00	0.00	13.28	5.13	56.92	12
HMRP	0.51	14.87	0.00	0.00	11.49	0.00	36.92	15
MPaRP	0.00	2.05	0.00	0.00	12.21	15.38	46.15	15
HMRP	4.36	10.26	0.00	0.00	12.21	0.00	40.00	17
MPaRP	0.00	16.41	0.00	0.00	12.92	12.31	16.92	17
HMRP	7.18	17.44	0.00	0.00	13.64	0.00	38.46	19
HMPaP	4.10	0.00	0.00	0.00	12.92	35.90	47.69	19
HMPaP	5.64	0.00	0.00	0.00	12.56	40.00	55.38	19
MPaRP	0.00	17.44	0.00	0.00	10.05	38.97	38.46	19
MPaRP	0.00	5.18	0.00	0.00	12.42	15.84	21.44	19
HMPaP	9.74	0.00	0.00	0.00	13.28	38.97	29.23	24
HMPaP	3.98	0.00	0.00	0.00	11.02	26.50	49.01	24
MPaRP	0.00	7.69	0.00	0.00	8.62	9.23	60.00	26
HMRP	9.74	19.49	0.00	0.00	13.28	0.00	29.23	27
HMRP	3.77	17.11	0.00	0.00	13.20	0.00	59.79	27
MPaRP	0.00	19.99	0.00	0.00	7.20	8.56	59.05	27
HMRP	8.84	16.71	0.00	0.00	8.92	0.00	46.94	30
HMPaP	0.43	0.00	0.00	0.00	7.89	22.01	58.51	30
MPaRP	0.00	11.79	0.00	0.00	11.85	7.18	41.54	30
HMRP	4.03	19.14	0.00	0.00	12.65	0.00	20.21	33
HMPaP	7.18	0.00	0.00	0.00	13.64	34.87	38.46	33
HMPaP	0.51	0.00	0.00	0.00	11.49	29.74	36.92	33
MPaRP	0.00	12.82	0.00	0.00	10.41	17.44	32.31	36
MPaRP	0.00	2.56	0.00	0.00	9.69	24.62	50.77	36
HMPaP	6.56	0.00	0.00	0.00	7.00	36.83	59.03	38
MPaRP	0.00	1.54	0.00	0.00	14.00	19.49	27.69	38
MPaRP	0.00	10.26	0.00	0.00	6.10	34.87	40.00	38
MPaRP	0.00	19.98	0.00	0.00	5.06	18.49	59.26	38
HMRP	5.24	17.77	0.00	0.00	10.54	0.00	56.95	42
MPaRP	0.00	2.70	0.00	0.00	13.10	23.52	17.60	42
HRMPa	7.18	19.49	0.00	0.00	12.21	25.64	0.00	44
HMPaP	2.05	0.00	0.00	0.00	11.85	16.41	33.85	45
HMPaP	0.01	0.00	0.00	0.00	12.14	17.20	30.61	45
MPaRP	0.00	0.37	0.00	0.00	13.97	30.25	1.56	45
HMRP	9.96	19.68	0.00	0.00	9.91	0.00	16.98	48
HMPaP	2.44	0.00	0.00	0.00	8.59	36.89	45.00	48
MPaRP	0.00	9.74	0.00	0.00	7.18	23.59	52.31	48
MPaRP	0.00	18.71	0.00	0.00	6.38	34.74	3.75	51
MPaRP	0.00	17.95	0.00	0.00	5.74	36.92	47.69	52
MPaRP	0.00	1.81	0.00	0.00	7.67	39.22	4.52	52
HRMPa	5.64	17.95	0.00	0.00	14.00	36.92	0.00	54
HRMPa	6.77	19.69	0.00	0.00	10.12	21.41	0.00	54
HMPaP	5.13	0.00	0.00	0.00	8.26	19.49	52.31	54
HMPaP	7.69	0.00	0.00	0.00	7.18	36.92	53.85	54
MPaRP	0.00	0.20	0.00	0.00	9.63	13.62	21.43	54
HRMPa	8.97	11.28	0.00	0.00	13.28	7.18	0.00	59
HMRP	2.05	8.21	0.00	0.00	11.85	0.00	33.85	59
HMPaP	4.36	0.00	0.00	0.00	12.21	20.51	40.00	59
HMPaP	4.00	0.00	0.00	0.00	8.41	39.55	32.32	59
HMPaP	2.82	0.00	0.00	0.00	10.41	17.44	7.69	63
HMPaP	1.28	0.00	0.00	0.00	11.13	7.18	43.08	63
HMRP	7.69	18.46	0.00	0.00	7.18	0.00	53.85	65
HMRP	3.59	6.67	0.00	0.00	8.97	0.00	58.46	65
HRMPa	0.51	16.41	0.00	0.00	10.41	24.62	0.00	67
HRMPa	8.47	19.82	0.00	0.00	6.92	31.49	0.00	67
HMPaP	1.03	0.00	0.00	0.00	10.77	33.85	21.54	67
HMPaP	3.59	0.00	0.00	0.00	8.97	13.33	58.46	67
HMPaP	7.47	0.00	0.00	0.00	10.42	36.59	24.59	67
HRMPa	7.86	16.13	0.00	0.00	9.50	33.32	0.00	72
HMRP	1.03	16.92	0.00	0.00	10.77	0.00	21.54	72
HMRP	1.28	3.59	0.00	0.00	11.13	0.00	43.08	72
HMRP	5.13	9.74	0.00	0.00	8.26	0.00	52.31	72
HMRP	4.20	19.04	0.00	0.00	6.93	0.00	32.37	72
HMPaP	7.44	0.00	0.00	0.00	6.10	25.64	32.31	72
HMPaP	8.97	0.00	0.00	0.00	7.90	37.95	10.77	72
HMPaP	0.00	0.00	0.00	0.00	9.69	12.31	18.46	72
HMPaP	5.02	0.00	0.00	0.00	11.93	0.53	45.52	72
HMPaP	5.22	0.00	0.00	0.00	5.96	31.24	59.98	72
HMPaP	2.04	0.00	0.00	0.00	6.63	25.55	59.64	72
MPaRP	0.00	1.03	0.00	0.00	11.49	26.67	1.54	72
MPaRP	0.00	6.67	0.00	0.00	5.03	25.64	58.46	72
MPaRP	0.00	12.41	0.00	0.00	6.18	5.22	56.01	72
HRMPa	4.36	17.44	0.00	0.00	7.18	26.67	0.00	86
HMPaP	7.95	0.00	0.00	0.00	4.67	28.72	35.38	86
HMPaP	0.30	0.00	0.00	0.00	9.18	25.93	0.99	86
MPaRP	0.00	5.64	0.00	0.00	8.26	21.54	6.15	86
HMRP	4.90	0.23	0.00	0.00	11.92	0.00	32.34	90
HRMPa	1.03	15.38	0.00	0.00	11.85	14.36	0.00	91
HMPaP	2.56	0.00	0.00	0.00	5.74	24.62	44.62	91
HMPaP	6.92	0.00	0.00	0.00	8.62	5.13	50.77	91
HMPaP	4.19	0.00	0.00	0.00	10.50	30.98	18.69	91
MPaRP	0.00	15.38	0.00	0.00	6.82	1.03	49.23	91
HRMPa	9.74	18.97	0.00	0.00	13.64	19.49	0.00	96
HMPaP	4.70	0.00	0.00	0.00	4.16	39.47	59.98	97
HMRP	9.76	7.04	0.00	0.00	7.00	0.00	58.27	98
HMPaP	6.41	0.00	0.00	0.00	10.05	8.21	24.62	99
HMRP	8.97	18.97	0.00	0.00	7.90	0.00	10.77	100
HRMPa	5.00	15.03	0.00	0.00	8.98	10.97	0.00	101
HRMPa	0.04	18.36	0.00	0.00	12.03	10.48	0.00	101
HRMPa	0.56	19.88	0.00	0.00	5.68	18.36	0.00	101
HMRP	6.92	2.56	0.00	0.00	8.62	0.00	50.77	101
HMPaP	0.43	0.00	0.00	0.00	11.19	1.39	42.14	101
HRMPa	4.10	18.46	0.00	0.00	12.56	31.79	0.00	106
HMRP	9.03	7.04	0.00	0.00	11.35	0.00	17.54	107
HMPaP	9.23	0.00	0.00	0.00	4.31	32.82	16.92	107
HMRP	7.44	12.82	0.00	0.00	6.10	0.00	32.31	109
HRMPa	2.66	12.70	0.00	0.00	10.50	23.16	0.00	110
MPaRP	0.00	12.17	0.00	0.00	3.05	39.32	59.22	110
HRMPa	0.28	15.71	0.00	0.00	10.00	19.77	0.00	112
HMPaP	3.54	0.00	0.00	0.00	6.96	1.52	59.66	113
MPaRP	0.00	8.72	0.00	0.00	3.95	29.74	7.69	113
HRMPa	5.13	11.79	0.00	0.00	6.82	34.87	0.00	115
HRMPa	2.05	16.92	0.00	0.00	5.74	22.56	0.00	115
HRMPa	7.98	15.02	0.00	0.00	13.77	20.02	0.00	115
HMRP	9.43	10.02	0.00	0.00	5.08	0.00	59.98	115
HMPaP	4.58	0.00	0.00	0.00	7.72	4.92	29.97	115
HMPaP	5.90	0.00	0.00	0.00	7.54	11.28	6.15	120
HRMPa	7.95	6.67	0.00	0.00	10.05	23.59	0.00	121
HMRP	6.41	4.10	0.00	0.00	10.05	0.00	24.62	121
HRMPa	7.69	10.26	0.00	0.00	12.92	35.90	0.00	123
MPaRP	0.00	10.77	0.00	0.00	9.33	18.46	0.00	123
HRMPa	3.59	12.82	0.00	0.00	4.67	38.97	0.00	125
HMRP	0.00	6.15	0.00	0.00	9.69	0.00	18.46	125
MPaRP	0.00	4.62	0.00	0.00	7.54	10.26	4.62	127
HRMPa	9.23	6.15	0.00	0.00	11.49	11.28	0.00	128
HMRP	2.56	12.31	0.00	0.00	5.74	0.00	44.62	129
HRMPa	9.92	19.15	0.00	0.00	5.43	6.25	0.00	130
HMRP	7.36	13.69	0.00	0.00	6.91	0.00	15.76	131
HMRP	3.50	4.85	0.00	0.00	5.45	0.00	58.34	132
HMPaP	10.00	0.00	0.00	0.00	6.82	3.08	27.69	133
HRMPa	2.56	8.21	0.00	0.00	8.62	29.74	0.00	134
HRMPa	1.84	19.91	0.00	0.00	4.53	30.03	0.00	134
HMRP	8.90	2.55	0.00	0.00	4.87	0.00	59.30	136
HRMPa	7.44	8.72	0.00	0.00	8.97	21.54	0.00	137
HRMPa	0.11	12.58	0.00	0.00	5.40	36.24	0.00	137
MPaRP	0.00	12.31	0.00	0.00	3.59	16.41	44.62	139
HMRP	10.00	1.54	0.00	0.00	6.82	0.00	27.69	140
HRMPa	0.00	13.85	0.00	0.00	4.31	12.31	0.00	141
HRMPa	8.46	3.59	0.00	0.00	8.26	27.69	0.00	142
HMPaP	8.72	0.00	0.00	0.00	5.38	4.10	46.15	142
HRMPa	5.26	10.78	0.00	0.00	4.98	21.77	0.00	144
HMRP	8.72	2.05	0.00	0.00	5.38	0.00	46.15	145
HMPaP	0.45	0.00	0.00	0.00	8.76	7.78	5.84	145
HMRP	1.70	7.85	0.00	0.00	7.02	0.00	26.09	147
HMRP	3.59	0.66	0.00	0.00	8.14	0.00	24.82	148
HMRP	7.95	14.36	0.00	0.00	4.67	0.00	35.38	149
HMRP	2.82	8.72	0.00	0.00	10.41	0.00	7.69	149
HMPaP	0.26	0.00	0.00	0.00	3.95	14.36	23.08	149
MPaRP	0.00	8.12	0.00	0.00	8.15	2.46	13.49	149
HRMPa	2.82	14.87	0.00	0.00	6.10	5.13	0.00	153
MPaRP	0.00	8.21	0.00	0.00	2.87	33.85	33.85	153
HMRP	5.10	1.54	0.00	0.00	6.89	0.00	28.35	155
HRMPa	6.15	4.62	0.00	0.00	5.38	40.00	0.00	156
MPaRP	0.00	11.28	0.00	0.00	4.31	4.10	30.77	157
MPaRP	0.00	0.00	0.00	0.00	2.51	40.00	9.23	157
MPaRP	0.00	13.85	0.00	0.00	6.46	2.05	12.31	159
HMRP	1.79	0.00	0.00	0.00	14.00	0.00	9.23	160
HMPaP	1.79	0.00	0.00	0.00	14.00	0.00	9.23	160
HRMPa	6.41	14.36	0.00	0.00	2.87	16.41	0.00	162
HMPaP	6.15	0.00	0.00	0.00	3.23	15.38	60.00	162
HRMPa	9.49	2.56	0.00	0.00	6.46	37.95	0.00	164
HRMPa	0.26	5.64	0.00	0.00	5.03	15.38	0.00	165
HRMPa	1.28	15.90	0.00	0.00	2.51	28.72	0.00	166
HMPaP	8.46	0.00	0.00	0.00	2.51	23.59	41.54	167
MPaRP	0.00	3.08	0.00	0.00	3.23	14.36	15.38	168
HRMPa	7.26	2.23	0.00	0.00	5.29	17.07	0.00	169
HMRP	9.23	16.41	0.00	0.00	4.31	0.00	16.92	169
HRMPa	4.62	1.03	0.00	0.00	9.69	8.21	0.00	171
MPaRP	0.00	0.51	0.00	0.00	4.67	8.21	13.85	171
HRMPa	6.67	9.23	0.00	0.00	7.54	0.00	0.00	173
HMPaP	2.31	0.00	0.00	0.00	5.03	6.15	15.38	174
HMPaP	0.77	0.00	0.00	0.00	2.15	31.79	3.08	175
MPaRP	0.00	5.13	0.00	0.00	5.38	3.08	20.00	176
HRMPa	3.08	2.05	0.00	0.00	7.90	20.51	0.00	177
HMRP	6.67	10.77	0.00	0.00	6.46	0.00	0.00	178
HMRP	6.15	7.69	0.00	0.00	3.23	0.00	60.00	179
HRMPa	4.85	0.91	0.00	0.00	12.60	20.19	0.00	180
HRMPa	6.92	12.31	0.00	0.00	1.79	33.85	0.00	181
HRMPa	2.85	1.95	0.00	0.00	5.68	28.13	0.00	182
MPaRP	0.00	3.59	0.00	0.00	1.79	31.79	43.08	183
HRMPa	6.47	0.18	0.00	0.00	12.48	29.66	0.00	184
HRMPa	4.87	0.51	0.00	0.00	10.77	32.82	0.00	185
HMPaP	8.21	0.00	0.00	0.00	9.33	2.05	1.54	186
HRMPa	5.90	10.77	0.00	0.00	3.95	4.10	0.00	187
HMPaP	9.49	0.00	0.00	0.00	1.79	18.46	56.92	187
HRMPa	3.85	1.54	0.00	0.00	3.59	13.33	0.00	189
HMPaP	5.38	0.00	0.00	0.00	3.59	9.23	4.62	190
HMRP	8.46	11.79	0.00	0.00	2.51	0.00	41.54	191
HMRP	5.90	5.64	0.00	0.00	7.54	0.00	6.15	192
HPaRP	4.10	17.95	0.00	0.00	0.00	36.92	47.69	193
MPaRP	0.00	16.92	0.00	0.00	1.44	30.77	21.54	194
HMRP	8.21	1.03	0.00	0.00	9.33	0.00	1.54	195
HPaRP	9.74	19.49	0.00	0.00	0.00	37.95	29.23	196
HMRP	0.26	7.18	0.00	0.00	3.95	0.00	23.08	197
HPaRP	8.03	10.72	0.00	0.00	0.00	33.84	21.93	198
HPaRP	5.05	16.28	0.00	0.00	0.00	35.00	46.28	199
HPaRP	7.18	17.44	0.00	0.00	0.00	38.97	38.46	200
HPaRP	5.64	20.00	0.00	0.00	0.00	35.90	55.38	200
HPaRP	1.06	16.51	0.00	0.00	0.00	35.39	44.98	202
HRMPa	8.72	7.69	0.00	0.00	1.44	30.77	0.00	203
MPaRP	0.00	0.37	0.00	0.00	3.24	0.67	38.48	204
HPaRP	2.05	8.21	0.00	0.00	0.00	33.85	33.85	205
HPaRP	4.36	10.26	0.00	0.00	0.00	34.87	40.00	206
HPaRP	3.59	6.67	0.00	0.00	0.00	25.64	58.46	207
HPaRP	3.66	6.72	0.00	0.00	0.00	37.42	33.68	208
HPaRP	9.73	18.23	0.00	0.00	0.00	34.13	2.98	208
HPaRP	5.13	9.74	0.00	0.00	0.00	23.59	52.31	210
HPaRP	1.03	16.92	0.00	0.00	0.00	30.77	21.54	211
HPaRP	0.51	14.87	0.00	0.00	0.00	32.82	36.92	211
HPaRP	1.09	9.55	0.00	0.00	0.00	37.51	24.59	211
MPaRP	0.00	13.33	0.00	0.00	2.15	0.00	26.15	211
MPaRP	0.00	5.06	0.00	0.00	2.14	13.40	0.56	211
HMPaP	3.08	0.00	0.00	0.00	1.44	22.56	30.77	216
HMRP	2.31	3.08	0.00	0.00	5.03	0.00	15.38	217
HPaRP	5.57	9.81	0.00	0.00	0.00	37.51	14.36	218
HPaRP	1.28	3.59	0.00	0.00	0.00	31.79	43.08	219
HRMPa	2.31	7.18	0.00	0.00	2.15	10.26	0.00	220
HPaRP	8.97	18.97	0.00	0.00	0.00	22.56	10.77	221
HPaRP	9.99	4.37	0.00	0.00	0.00	37.33	46.20	221
MPaRP	0.00	1.35	0.00	0.00	0.01	40.00	35.71	221
HPaRP	7.69	18.46	0.00	0.00	0.00	20.51	53.85	224
HPaRP	6.92	2.56	0.00	0.00	0.00	24.62	50.77	224
HPaRP	7.44	12.82	0.00	0.00	0.00	17.44	32.31	226
HPaRP	9.23	16.41	0.00	0.00	0.00	12.31	16.92	226
HPaRP	6.41	4.10	0.00	0.00	0.00	28.72	24.62	226
HPaRP	0.00	6.15	0.00	0.00	0.00	27.69	18.46	226
HPaRP	2.82	8.72	0.00	0.00	0.00	29.74	7.69	226
HPaRP	7.95	14.36	0.00	0.00	0.00	13.33	35.38	226
HPaRP	0.19	1.74	0.00	0.00	0.00	35.19	16.16	226
HPaRP	0.10	17.49	0.00	0.00	0.00	36.32	0.25	226
HRMPa	0.77	3.08	0.00	0.00	11.13	2.05	0.00	234
MPaRP	0.00	14.87	0.00	0.00	0.72	32.82	36.92	235
HPaRP	8.46	11.79	0.00	0.00	0.00	7.18	41.54	236
HPaRP	5.90	5.64	0.00	0.00	0.00	21.54	6.15	236
HMRP	9.49	9.23	0.00	0.00	1.79	0.00	56.92	238
HPaRP	6.15	7.69	0.00	0.00	0.00	9.23	60.00	238
HPaRP	10.00	1.54	0.00	0.00	0.00	19.49	27.69	240
HPaRP	2.56	12.31	0.00	0.00	0.00	16.41	44.62	240
HMPaP	4.87	0.00	0.00	0.00	0.36	30.77	49.23	240
HPaRP	8.72	2.05	0.00	0.00	0.00	15.38	46.15	243
HPaRP	6.45	18.27	0.00	0.00	0.00	5.09	28.47	243
HPaRP	9.49	9.23	0.00	0.00	0.00	5.13	56.92	245
HPaRP	0.12	0.02	0.00	0.00	0.00	30.08	39.13	246
HPaRP	1.79	0.00	0.00	0.00	0.00	40.00	9.23	247
MPaRP	0.00	6.15	0.00	0.00	0.00	27.69	18.46	248
HPaRP	6.67	10.77	0.00	0.00	0.00	18.46	0.00	249
HPaRP	0.20	17.20	0.00	0.00	0.00	24.76	0.47	249
HPaRP	9.99	19.69	0.00	0.00	0.00	9.79	3.83	251
HPaRP	8.21	1.03	0.00	0.00	0.00	26.67	1.54	252
HPaRP	0.83	0.32	0.00	0.00	0.00	19.99	19.70	253
HPaRP	3.08	11.28	0.00	0.00	0.00	4.10	30.77	254
HRMPa	5.38	5.13	0.00	0.00	3.23	3.08	0.00	255
HMPaP	1.54	0.00	0.00	0.00	0.00	26.67	26.15	256
HMPaP	6.67	0.00	0.00	0.00	6.46	21.54	0.00	256
HRMPa	1.54	0.00	0.00	0.00	9.33	17.44	0.00	258
HPaRP	2.31	3.08	0.00	0.00	0.00	14.36	15.38	258
HRMPa	10.00	9.74	0.00	0.00	1.08	18.46	0.00	260
HPaRP	0.26	7.18	0.00	0.00	0.00	11.28	23.08	261
HRZE	9.99	19.75	49.74	39.76	0.00	0.00	0.00	262
HMPaP	4.62	0.00	0.00	0.00	0.72	27.69	12.31	263
HPaRP	4.87	15.38	0.00	0.00	0.00	1.03	49.23	264
HRZE	9.74	18.97	48.72	19.49	0.00	0.00	0.00	265
HMRP	0.08	17.70	0.00	0.00	0.23	0.00	54.21	265
MPaRP	0.00	7.18	0.00	0.00	0.36	11.28	23.08	267
HPaRP	3.33	0.51	0.00	0.00	0.00	8.21	13.85	268
HRZE	9.99	19.94	35.42	36.59	0.00	0.00	0.00	269
HRZE	7.18	19.49	43.59	25.64	0.00	0.00	0.00	270
HPaRP	5.38	4.62	0.00	0.00	0.00	10.26	4.62	271
HRZE	8.77	14.92	45.66	37.95	0.00	0.00	0.00	272
HMRP	4.87	15.38	0.00	0.00	0.36	0.00	49.23	273
HRZE	7.30	17.08	47.33	28.39	0.00	0.00	0.00	274
HMRP	3.08	11.28	0.00	0.00	1.44	0.00	30.77	274
HRZE	5.64	17.95	50.00	36.92	0.00	0.00	0.00	276
HMPaP	3.85	0.00	0.00	0.00	1.08	10.26	20.00	276
HPaRP	4.62	13.85	0.00	0.00	0.00	2.05	12.31	278
HRZE	4.10	18.46	44.87	31.79	0.00	0.00	0.00	279
HPaRP	0.77	15.90	0.00	0.00	0.00	6.15	3.08	280
HPaRP	3.85	5.13	0.00	0.00	0.00	3.08	20.00	281
HRZE	7.24	17.25	41.75	39.16	0.00	0.00	0.00	282
HPaRP	1.54	13.33	0.00	0.00	0.00	0.00	26.15	282
HRZE	7.46	19.98	23.32	26.50	0.00	0.00	0.00	284
HRZE	9.98	14.63	37.55	13.45	0.00	0.00	0.00	285
HRZE	8.37	13.99	43.74	21.26	0.00	0.00	0.00	285
HRZE	8.97	11.28	47.44	7.18	0.00	0.00	0.00	287
HRMPa	1.79	20.00	0.00	0.00	0.00	6.15	0.00	288
HMRP	3.33	0.51	0.00	0.00	2.87	0.00	13.85	289
HMPaP	3.33	0.00	0.00	0.00	2.87	1.03	13.85	289
HRZE	8.34	19.96	26.60	19.68	0.00	0.00	0.00	291
HRMPa	6.98	0.58	0.00	0.00	1.67	4.36	0.00	292
HRZE	9.80	19.71	12.75	39.62	0.00	0.00	0.00	293
HRZE	4.36	17.44	25.64	26.67	0.00	0.00	0.00	293
HMRP	5.38	4.62	0.00	0.00	3.59	0.00	4.62	295
HRZE	7.69	10.26	46.15	35.90	0.00	0.00	0.00	296
HMRP	1.54	13.33	0.00	0.00	0.00	0.00	26.15	296
HRZE	3.84	17.86	31.69	1.51	0.00	0.00	0.00	298
HRMPa	3.33	4.10	0.00	0.00	0.36	9.23	0.00	299
HPaRP	4.80	1.01	0.00	0.00	0.00	7.19	0.18	299
HRZE	5.95	13.55	38.55	39.22	0.00	0.00	0.00	301
MPaRP	0.00	15.90	0.00	0.00	1.08	6.15	3.08	302
HRZE	9.23	6.15	41.03	11.28	0.00	0.00	0.00	303
HRZE	0.51	16.41	37.18	24.62	0.00	0.00	0.00	304
HPaRP	7.57	4.51	0.00	0.00	0.00	0.28	8.82	304
HRZE	1.03	15.38	42.31	14.36	0.00	0.00	0.00	306
HRMPa	6.95	1.65	0.00	0.00	0.56	6.31	0.00	307
HRZE	7.44	8.72	32.05	21.54	0.00	0.00	0.00	308
HMRP	0.77	15.90	0.00	0.00	2.15	0.00	3.08	309
HRZE	7.95	6.67	35.90	23.59	0.00	0.00	0.00	310
HRZE	5.13	11.79	24.36	34.87	0.00	0.00	0.00	311
HRZE	2.05	16.92	20.51	22.56	0.00	0.00	0.00	311
HMRP	3.85	5.13	0.00	0.00	1.08	0.00	20.00	313
HRZE	2.82	14.87	21.79	5.13	0.00	0.00	0.00	314
HMRP	4.62	13.85	0.00	0.00	0.72	0.00	12.31	314
HRZE	6.41	14.36	10.26	16.41	0.00	0.00	0.00	316
HRMPa	8.21	13.33	0.00	0.00	0.72	1.03	0.00	316
HPaRP	7.77	2.69	0.00	0.00	0.00	1.16	3.53	318
HRZE	5.90	10.77	14.10	4.10	0.00	0.00	0.00	319
HMPaP	5.85	0.00	0.00	0.00	0.48	5.11	5.30	319
HRZE	8.46	3.59	29.49	27.69	0.00	0.00	0.00	321
HRZE	9.49	2.56	23.08	37.95	0.00	0.00	0.00	322
HRZE	8.21	13.33	2.56	1.03	0.00	0.00	0.00	322
HRZE	6.92	12.31	6.41	33.85	0.00	0.00	0.00	322
HRZE	2.56	8.21	30.77	29.74	0.00	0.00	0.00	325
HRZE	6.67	9.23	26.92	0.00	0.00	0.00	0.00	326
HRZE	3.59	12.82	16.67	38.97	0.00	0.00	0.00	327
HRZE	1.79	20.00	0.00	6.15	0.00	0.00	0.00	327
HRZE	10.00	9.74	3.85	18.46	0.00	0.00	0.00	327
HPaRP	1.31	1.46	0.00	0.00	0.00	2.05	4.62	327
HMRP	3.39	0.22	0.00	0.00	4.66	0.00	0.77	331
HRZE	6.15	4.62	19.23	40.00	0.00	0.00	0.00	332
HRZE	1.28	15.90	8.97	28.72	0.00	0.00	0.00	332
HPaRP	3.01	9.90	0.00	0.00	0.00	0.56	0.56	332
HRZE	0.83	18.22	0.84	2.34	0.00	0.00	0.00	335
HRZE	4.87	0.51	38.46	32.82	0.00	0.00	0.00	336
HRZE	4.62	1.03	34.62	8.21	0.00	0.00	0.00	337
HRZE	8.72	7.69	5.13	30.77	0.00	0.00	0.00	337
HRZE	5.00	8.01	8.27	2.59	0.00	0.00	0.00	339
HRZE	0.77	3.08	39.74	2.05	0.00	0.00	0.00	340
HRMPa	2.85	0.31	0.00	0.00	0.63	3.46	0.00	341
HRZE	0.00	13.85	15.38	12.31	0.00	0.00	0.00	342
HRZE	3.08	2.05	28.21	20.51	0.00	0.00	0.00	343
HMPaP	4.32	0.00	0.00	0.00	0.28	2.44	4.85	343
HRZE	5.38	5.13	11.54	3.08	0.00	0.00	0.00	345
HRZE	1.54	0.00	33.33	17.44	0.00	0.00	0.00	346
HRZE	1.53	11.36	3.49	1.11	0.00	0.00	0.00	347
MPaRP	0.00	1.86	0.00	0.00	0.36	2.59	0.01	348
HRZE	2.31	7.18	7.69	10.26	0.00	0.00	0.00	349
HMPaP	1.24	0.00	0.00	0.00	0.08	0.51	7.31	350
HRZE	0.26	5.64	17.95	15.38	0.00	0.00	0.00	351
HRZE	3.85	1.54	12.82	13.33	0.00	0.00	0.00	351
HMRP	0.02	3.87	0.00	0.00	0.08	0.00	4.86	353
HRZE	0.79	7.08	7.19	0.31	0.00	0.00	0.00	354
HRZE	3.44	4.74	2.52	2.63	0.00	0.00	0.00	355
HRZE	3.33	4.10	1.28	9.23	0.00	0.00	0.00	356
HMRP	0.28	2.25	0.00	0.00	0.19	0.00	3.53	357
HRZE	1.40	4.40	4.43	1.86	0.00	0.00	0.00	358
HRZE	2.78	0.06	1.98	5.43	0.00	0.00	0.00	359
HRZE	0.79	3.22	0.47	1.09	0.00	0.00	0.00	360

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