Notes:a Model of gas Exchange for hyperpolarized Xe (129) Magnetic Resonance of the Lung

Notes:a Model of gas Exchange for hyperpolarized Xe (129) Magnetic Resonance of the Lung

Background knowledge:

Gas exchange is the essential function of the lung.  In general, a lung can be viewed as a porous medium (porous media) consisting of capillary (capillary) circuits with blood flowing inside. The blood flows is separated from the air spaces by several layers of tissues, including epithelium (tissue skin cell), endothelium (endothelial), and interstitium (small gap). These tissues together is called air–blood barrier.(air blood fence). At equilibrium, gas molecules in theAlveolar spaces(alveolar space)is under constant exchange with those dissolved in the barrier and capillary blood.

Remark: gas from the alveolar diffusion concentration from high to low, equilibrium state, at constant rate and dissolved in tissue and capillary vessel gas exchange .

Almost all pulmonary diseases can is attributed to deficient gas exchange or delivery in the lung.

Insufficient or excessive gas exchange can cause lung disease, which is linked to 5 key lung parameters.

Prob:how measure gas exchange?

Ans:however, none of the established imaging techniques provides direct measurement of gas exchange!!!

There is no direct method of indirect experimentation.

EXP.1 Computerized tomography (tomography technology) measures tissue density

EXP.2 Magnetic resonance Imaging of hyperpolarized (HP)

He ( ultra-polarized helium ) images The air spaces in the lung.

EXP.3 MR of HP Xe is capable of providing direct measurements of gas exchange in the lung. As a contrast

Agent, not only does xenon yield dramatically enhanced

MR signals in the air spaces, but it also dissolves into lung tissue and blood. As the dissolved xenon in blood follows the same physiological pathways of the normal blood gases (i.e., O2,co2) ( see below Face of the image )

Quantization:

Quantification of dissolved Xenon dynamics would leads to a quantified understanding of lung function.

(How?) M.R. Experiment)

Principle:

A particular feature of xenon that permits such a study, was that the xenon dissolved into human lung exhibits both large ch Emical shifts from the resonance frequency(Resonant frequency)of the free Xenon Gas-One at 197 ppm(Parts per million), for xenon in lung tissue and blood plasma(plasma)(TP Xenon), the other at 217 ppm, for the xenon in the red blood cells (RBC Xenon)

RBC :Red Blood Cell

Tp:tissue and Plasma(tissue and plasma)

Xenon----> Dissolved Xenon +free Xenon

dissolved Xenon = TP Xe + PBC XE

197ppm:xenon in lung tissue and blood plasma(plasma)

217ppm:the Xenon in the red blood cells

NMR specific experimental techniques are unknown.

CSSR have been used frequently, over the past years in various lung diseases, including fibrosis (fibrous degeneration) and emphysema (emphysema) c1>.

Despite the previous applications of CSSR, there have not been a satisfactory theory to interpret xenon uptake dynamics for Both dissolved xenon peaks in the lung.

Density m_d within the septum(diaphragm), perpendicular(vertical) to the blood flow

M_d is density of dissolved xenon

M_f is the density of free xenon gas (at 0 ppm) in the air spaces

D is the diffusion coefficient of dissolved xenon

\lambda is the Ostwald solubility of xenon in lung parenchyma (soft Cell tissue)

Prob:how to define the boundary value conditions?

Apply Fourier ' s separation of variable obtain series solution:

Where T is the Xenon-exchange time constant in the lung

(That's par.4)

Proof:

。。。。。。。。

Numerical solution of initial boundary value problem (Zhang Wensheng book):

Progression Solution Asymptotic :

Assume:

S_a is the total surface area of air space

V_g is all volume of the air spaces in the lung

The dissolved xenon signal is proportional to m_d *S_A/2

The free xenon gas signal are proportional to M_f * v_g

The normalized signal distribution s_d (x, T) for dissolved xenon can is written as (why? Normalized)

and (4) contrast compare with (4).

s_d= M_d Svr/2m_f

S_a/v_g is the surface-area-to-volume ratio

(That's Par.1 SVR)

S_D1 (t): The total Signal from the Tissue

( Xenon Signal in the organization)

It isn't difficult to derive (6)---> (7),. Calculated as the spatial integral of s_d in eq.6 over the the NS from (0) to (\delta) and from (d-\delta) to (d).

Where,B is the normalization factor (dimensionless), and \delta/d are what we call Barrier-to-septum Rati O.

(That's par.2 BSR)

The dissolved xenon signal from the blood (' Blood xenon ') are more difficult to calculate owing to flow.

S_D2 (s): The total Signal from Blood (No-flow & Flow)

( Xenon signal in total blood )

No flow:integral of S_d at (\delta, D-\delta)

How is consider blood flow? (Key)

The total xenon signal from the blood is:

Where t_x is pulmonary capillary transit time

(Par.5 Transit time )

To calculate the xenon signal in tissue and blood plasma, e.g., TP Xenon signal s_tp (t) at 197 ppm, and signal of RBC Xeno n S_RBC (t) at 217 ppm, we-let H denote the fraction of RBC xenon relative-total xenon in blood

S_PBC = h * s_d2

S_blood plasma = (1-h) * S_D2

S_TP = S_d1 + (1-h) * s_d2(tissue and plasma signals)

The Hematocrit (HCT) can be calculated from H using

(Par.3 Blood cell volume )

Where \LAMBDA_RBC and \lambda_p is Ostwald solubilities of xenon in RBCs and plasma, respectively.

Remark:how calculate h? MR of HP Xe

The theoretical model established above, the experimental signal can be observed (different lung disease), and then fit the required five parameters with the normal comparison???

The paper chooses the lungs to be in four different states.

Remark:

COPD (Chronic obstructive pulmonary disease) chronic obstructive pulmonary disease

Fibrosis Fibrous lesions

Anemia anemia

Parameters of the normal healthy person:

\LAMBDA 0.2

\delta 2

D 10

SVR 250

T 40

\eta 0.5

T_X 1.6