pypharm 1.2.9

Module for solving pharmacokinetic problems

PyPharm

1) Установка пакета

pip install pypharm  

2) Пример использования пакета для модели, где все параметры известны

Задана двухкамерная модель такого вида

graph LR
D((Доза D)) --> V1[Камера V1]
V1 -- k12 --> V2[Камера V2]
V2 -- k21 --> V1
V1 -- k10 --> Out(Выведение)

При этом, нам известны параметры модели

V1	V2	k12	K21	K10
228	629	0.4586	0.1919	0.0309

Создание и расчет модели при помощи пакета PyPharm

from PyPharm import BaseCompartmentModel  
  
model = BaseCompartmentModel([[0, 0.4586], [0.1919, 0]], [0.0309, 0], volumes=[228, 629])  
  
res = model(90, d=5700, compartment_number=0)  

res - Результат работы решателя scipy solve_iv

3) Пример использования пакета для модели, где все параметры неизвестны

Задана многокамерная модель такого вида

graph LR
Br(Мозг) --'Kbr-'--> Is[Межклетачное пространство]
Is --'Kbr+'-->Br
Is--'Kis-'-->B(Кровь)
B--'Kis+'-->Is
B--'Ke'-->Out1((Выведение))
B--'Ki+'-->I(Печень)
I--'Ki-'-->Out2((Выведение))
B--'Kh+'-->H(Сердце)
H--'Kh-'-->B

При этом, известен лишь параметр Ke=0.077

Создание и расчет модели при помощи пакета PyPharm, используя метод minimize:

from PyPharm import BaseCompartmentModel
import numpy as np
matrix = [[0, None, 0, 0, 0],
[None, 0, None, 0, 0],
[0, None, 0, None, None],
[0, 0, 0, 0, 0],
[0, 0, None, 0, 0]]
outputs = [0, 0, 0.077, None, 0]

model = BaseCompartmentModel(matrix, outputs)

model.load_optimization_data(
	teoretic_x=[0.25, 0.5, 1, 4, 8, 24],
	teoretic_y=[[0, 0, 11.2, 5.3, 5.42, 3.2], [268.5, 783.3, 154.6, 224.2, 92.6, 0], [342, 637, 466, 235, 179, 158]],
	know_compartments=[0, 3, 4],
	c0=[0, 0, 20000, 0, 0]
)

x_min = [1.5, 0.01, 0.5, 0.0001, 0.1, 0.1, 4, 3]
x_max = [2.5, 0.7, 1.5, 0.05, 0.5, 0.5, 7, 5]
x0 = np.random.uniform(x_min, x_max)
bounds = ((1.5, 2.5), (0.01, 0.7), (0.5, 1.5), (0.0001, 0.05), (0.1, 0.5), (0.1, 0.5), (4, 7), (3, 5))

model.optimize(
	bounds=bounds,
	x0=x0,
	options={'disp': True}
)

print(model.configuration_matrix)

Или же при помощи алгоритма взаимодействующих стран

from PyPharm import BaseCompartmentModel
import numpy as np
matrix = [[0, None, 0, 0, 0],
[None, 0, None, 0, 0],
[0, None, 0, None, None],
[0, 0, 0, 0, 0],
[0, 0, None, 0, 0]]
outputs = [0, 0, 0.077, None, 0]

model = BaseCompartmentModel(matrix, outputs)

model.load_optimization_data(
	teoretic_x=[0.25, 0.5, 1, 4, 8, 24],
	teoretic_y=[[0, 0, 11.2, 5.3, 5.42, 3.2], [268.5, 783.3, 154.6, 224.2, 92.6, 0], [342, 637, 466, 235, 179, 158]],
	know_compartments=[0, 3, 4],
	c0=[0, 0, 20000, 0, 0]
)

model.optimize(
	method='country_optimization',
	Xmin=[0.5, 0.001, 0.001, 0.00001, 0.01, 0.01, 1, 1],
	Xmax=[5, 2, 2.5, 0.3, 1, 1, 10, 10],
	M=10,
	N=25,
	n=[1, 10],
	p=[0.00001, 2],
	m=[1, 8],
	k=8,
	l=3,
	ep=[0.2, 0.4],
	tmax=300,
	printing=True,
)

При оптимизации, вектор неизвестных это x = [configuration_matrix (неизвестные), outputs(неизвестные), volumes(неизвестные)]

4) Модель MagicCompartmentModel

Данная модель необходима нам для тех случаев, когда мы не знаем как именно стоит переводить входные единицы измерения в выходные.

В модель добавляется 2 дополнительных параметра:

• magic_coefficient - множитель преобразования входных единиц в выходные;
• exclude_compartments - список номеров камер, которые не подвергнутся преобразованию.

from PyPharm import MagicCompartmentModel  
  
model = MagicCompartmentModel([[0, 0.4586], [0.1919, 0]], [0.0309, 0], volumes=[228, 629], magic_coefficient=None, exclude_compartments=[2])  
  
res = model(90, d=5700, compartment_number=0)  

Параметр magic_coefficient может быть задан None, в таком случае он будет подвергнут оптимизации, в таком случае он будет браться из последнего значения в векторе переменных. Если оба параметра не заданы, то модель выраздается в простую BaseCompartmentModel.

5) Модель MagicCompartmentModel

Данная модель учитывает поправку на высвобождение ЛВ в модель вводятся дополнительные параметры:

• v_release - Объем гепотетической камеры из которой происходит высвобождение
• release_parameters - Параметры функции высвобождения
• release_compartment - Номер камеры в которую происходит высвобождение
• release_function - Функция высвобождения по умолчанию f(t,m,b,c) = c0 * c * t ** b / (t ** b + m)

При этом d и c0 теперь везде носят характер параметров камеры, из которой происходит высвобождение

from PyPharm import ReleaseCompartmentModel
import matplotlib.pyplot as plt

model = ReleaseCompartmentModel(
    6.01049235e+00,
    [4.56683781e-03, 1.36845756e+00, 5.61175978e-01],
    0,
    configuration_matrix=[[0, 1.18292665e+01], [3.02373800e-01, 0]],
    outputs=[5.00000000e+00, 0],
    volumes=[1.98530383e+01, 3.81007392e+02],
    numba_option=True
)
teoretic_t = [5/60, 0.25, 0.5, 1, 2, 4, 24, 48]
teoretic_c = [[3558.19,	508.49,	230.95,	52.05,	44.97,	36.52,	17.89,	10.36]]
d = 5 * 0.02 * 1000000
res = model(48, d=d)
plt.plot(teoretic_t, teoretic_c[0], 'r*')
plt.plot(res.t, res.y[0])
plt.grid()
plt.show()

Параметры release_parameters и v_release могут подвергаться оптимизации в таком случае, искомое нужно просто задать как None. Тогда вектор неизвестных это x = [configuration_matrix (неизвестные), outputs(неизвестные), volumes(неизвестные), release_parameters(неизвестные), v_release]

ENG documentation

1) Package Installation

pip install pypharm

2) An example of using a package for a model where all parameters are known

A two-chamber model of this type is given

graph LR
D((Dose D)) --> V1[Compartment V1]
V1 -- k12 --> V2[Compartment V2]
V2 -- k21 --> V1
V1 -- k10 --> Out(Output)

At the same time, we know the parameters of the model

V1	V2	k12	K21	K10
228	629	0.4586	0.1919	0.0309

Creating and calculating a model using the PyPharm package

from PyPharm import BaseCompartmentModel

model = BaseCompartmentModel([[0, 0.4586], [0.1919, 0]], [0.0309, 0], volumes=[228, 629])

res = model(90, d=5700, compartment_number=0)

res is the result of the scipy solve_iv solver

3) An example of using a package for a model where all parameters are unknown

A multi-chamber model of this type is given

graph LR
Br(Brain) --'Kbr-'--> Is[Intercellular space]
Is --'Kbr+'-->Br
Is--'Kis-'-->B(Blood)
B--'Kis+'-->Is
B--'Ke'-->Out1((Output))
B--'Ki+'-->I(Liver)
I--'Ki-'-->Out2((Output))
B--'Kh+'-->H(Heart)
H--'Kh-'-->B

At the same time, only the parameter Ke=0 is known.077

Creating and calculating a model using the PyPharm package using the minimize method:

from PyPharm import BaseCompartmentModel
import numpy as np
matrix = [[0, None, 0, 0, 0],
[None, 0, None, 0, 0],
[0, None, 0, None, None],
[0, 0, 0, 0, 0],
[0, 0, None, 0, 0]]
outputs = [0, 0, 0.077, None, 0]

model = BaseCompartmentModel(matrix, outputs)

model.load_optimization_data(
teoretic_x=[0.25, 0.5, 1, 4, 8, 24],
teoretic_y=[[0, 0, 11.2, 5.3, 5.42, 3.2], [268.5, 783.3, 154.6, 224.2, 92.6, 0], [342, 637, 466, 235, 179, 158]],
know_compartments=[0, 3, 4],
c0=[0, 0, 20000, 0, 0]
)

x_min = [1.5, 0.01, 0.5, 0.0001, 0.1, 0.1, 4, 3]
x_max = [2.5, 0.7, 1.5, 0.05, 0.5, 0.5, 7, 5]
x0 = np.random.uniform(x_min, x_max)
bounds = ((1.5, 2.5), (0.01, 0.7), (0.5, 1.5), (0.0001, 0.05), (0.1, 0.5), (0.1, 0.5), (4, 7), (3, 5))

model.optimize(
bounds=bounds,
x0=x0,
options={'disp': True}
)

print(model.configuration_matrix)

Or using the algorithm of interacting countries

from PyPharm import BaseCompartmentModel
import numpy as np
matrix = [[0, None, 0, 0, 0],
[None, 0, None, 0, 0],
[0, None, 0, None, None],
[0, 0, 0, 0, 0],
[0, 0, None, 0, 0]]
outputs = [0, 0, 0.077, None, 0]

model = BaseCompartmentModel(matrix, outputs)

model.load_optimization_data(
teoretic_x=[0.25, 0.5, 1, 4, 8, 24],
teoretic_y=[[0, 0, 11.2, 5.3, 5.42, 3.2], [268.5, 783.3, 154.6, 224.2, 92.6, 0], [342, 637, 466, 235, 179, 158]],
know_compartments=[0, 3, 4],
c0=[0, 0, 20000, 0, 0]
)

model.optimize(
method='country_optimization',
Xmin=[0.5, 0.001, 0.001, 0.00001, 0.01, 0.01, 1, 1],
Xmax=[5, 2, 2.5, 0.3, 1, 1, 10, 10],
M=10,
N=25,
n=[1, 10],
p=[0.00001, 2],
m=[1, 8],
k=8,
l=3,
ep=[0.2, 0.4],
tmax=300,
printing=True,
)

When optimizing, the vector of unknowns is x = [configuration_matrix (unknown), outputs(unknown), volumes(unknown)]

4) The MagicCompartmentModel model

We need this model for those cases when we do not know exactly how to convert input units of measurement into output units.

2 additional parameters are added to the model:

• magic_coefficient - multiplier for converting input units to output units;
• exclude_compartments - list of camera numbers that are not they will undergo a transformation.

from PyPharm import MagicCompartmentModel

model = MagicCompartmentModel([[0, 0.4586], [0.1919, 0]], [0.0309, 0], volumes=[228, 629], magic_coefficient=None, exclude_compartments=[2])

res = model(90, d=5700, compartment_number=0)

The magic_coefficient parameter can be set to None, in which case it will be optimized, in which case it will be taken from the last value in the vector of variables. If both parameters are not set, then the model is deleted into a simple BaseCompartmentModel.

5) The MagicCompartmentModel model

This model takes into account the release adjustment medicinal substance additional parameters are introduced into the model:

• v_release - The volume of the hepothetic chamber from which the release occurs
• release_parameters - Parameters of the release function
• release_compartment - The number of the camera into which the release takes place
• release_function - Default release function f(t,m,b,c) = c0 * c * t ** b / (t ** b + m)

At the same time, d and c0 are now everywhere in the nature of the parameters of the chamber from which the release occurs

from PyPharm import ReleaseCompartmentModel
import matplotlib.pyplot as plt

model = ReleaseCompartmentModel(
6.01049235e+00,
[4.56683781e-03, 1.36845756e+00, 5.61175978e-01],
0,
configuration_matrix=[[0, 1.18292665e+01], [3.02373800e-01, 0]],
outputs=[5.00000000e+00, 0],
volumes=[1.98530383e+01, 3.81007392e+02],
numba_option=True
)
teoretic_t = [5/60, 0.25, 0.5, 1, 2, 4, 24, 48]
teoretic_c = [[3558.19, 508.49, 230.95, 52.05, 44.97, 36.52, 17.89, 10.36]]
d = 5 * 0.02 * 1000000
res = model(48, d=d)
plt.plot(teoretic_t, teoretic_c[0], 'r*')
plt.plot(res.t, res.y[0])
plt.grid()
plt.show()

The release_parameters and v_release parameters can be optimized in this case, you just need to set the desired value as None. Then the vector of unknowns is x = [configuration_matrix (unknown), outputs(unknown), volumes(unknown), release_parameters(unknown), v_release]