Vessel wall monitoring apparatus

1. A vessel wall monitoring apparatus comprising:

a first detecting unit which detects vessel diameter information based on first biological information obtained from a subject;

a first producing unit which differentiates the vessel diameter information detected by the first detecting unit, to produce a vessel diameter function;

a second detecting unit which detects blood pressure based on second biological information obtained from the subject;

a second producing unit which performs a logarithmic operation on the blood pressure detected by the second detecting unit, to produce a logarithmic blood pressure function; and

an outputting unit which produces an impedance model expression by using: the vessel diameter function; the logarithmic blood pressure function; and mechanical characteristic values including a stiffness, viscosity, and inertia in a mechanical impedance model of a vessel wall, and which calculates and outputs at least one of a stiffness, viscosity, and inertia of a vessel wall of the subject based on the produced impedance model expression.

2. The vessel wall monitoring apparatus according to claim 1 , wherein the first detecting unit detects the vessel diameter information based on the first biological information obtained by an ultrasonic diagnostic apparatus using an ultrasonic echo.

3. The vessel wall monitoring apparatus according to claim 1 , wherein

the vessel diameter information includes a plethysmogram, and

the first detecting unit detects the plethysmogram based on the first biological information obtained by a photoelectric sensor or a strain gauge.

4. The vessel wall monitoring apparatus according to claim 1 , wherein

the first producing unit uses the vessel diameter information detected by the first detecting unit based on the first biological information obtained at a reference appearance timing and a next reference appearance timing of a blood pressure waveform,

the second producing unit uses the blood pressure detected by the second detecting unit based on the second biological information obtained at the reference appearance timing and the next reference appearance timing of the blood pressure waveform, and

each of the reference appearance timing and the next reference appearance timing is obtained from an inflection point of the blood pressure waveform.

5. The vessel wall monitoring apparatus according to claim 4 , wherein the logarithmic blood pressure function includes

dP b ( t )=ln( P b ( t ))−ln( P b ( t 0 )), and

the vessel diameter function includes:

ε( t )=( r ( t )− r ( t 0 ))/ r ( t 0 );

ε′(t) which is a first derivative of ε(t); and

ε″(t) which is a second derivative of ε(t),

where t 0 indicates the reference appearance timing, t indicates a time period from the reference appearance timing to the next reference appearance timing, P b (t) indicates a blood pressure value at t, and r(t) indicates a vessel diameter at t, and

the impedance model expression includes

dP b (t)=ln(P b (t))−ln(P b (t 0 ))=βε(t)+ηε′(t)+με″(t), where β indicates the stiffness, η indicates the viscosity, and μ indicates the inertia, on which a recurrent calculation is performed to output the at least one of the stiffness, the viscosity, and the inertia.

6. The vessel wall monitoring apparatus according to claim 5 , wherein the outputting unit detects a time difference τ between an appearance timing of the inflection point in dP b (t) and an appearance timing of the inflection point in ε(t), and the outputting unit corrects dP b (t) to dP b (t−τ) and corrects dP b (t 0 ) to dP b (t 0 −τ).

7. The vessel wall monitoring apparatus according to claim 4 , wherein the logarithmic blood pressure function includes

dP b ( t )=ln( P b ( t ))−ln( P b ( t 0 )), and

the vessel diameter function includes:

dP 1 ( t )=( P 1 ( t )− P 1 ( t 0 ));

dP 1 ′(t) which is a first derivative of P 1 (t); and

dP 1 ″(t) which is a second derivative of P 1 (t),

where t 0 indicates the reference appearance timing, t indicates a time period from the reference appearance timing to the next reference appearance timing, P b (t) indicates a blood pressure value at t, and P 1 (t) indicates a plethysmogram at t, and

the impedance model expression includes

dP b (t)=ln(P b (t))−ln(P b (t 0 ))=βdP 1 (t)+ηdP 1 ′(t)+μdP 1 ″(t), where β indicates the stiffness, η indicates the viscosity, and μ indicates the inertia, on which a recurrent calculation is performed to output the at least one of the stiffness, the viscosity, and the inertia.

8. The vessel wall monitoring apparatus according to claim 7 , wherein

the outputting unit detects a time difference τ between an appearance timing of the inflection point in dP b (t) and an appearance timing of the inflection point in dP b (t), and

the outputting unit corrects dP b (t) to dP b (t−τ) and corrects dP b (t 0 ) to dP b (t 0 −τ).

9. The vessel wall monitoring apparatus according to claim 1 , wherein

the first producing unit uses the vessel diameter information detected by the first detecting unit based on the second biological information obtained at a reference appearance timing and a next reference appearance timing of a blood pressure waveform,

the second producing unit uses the blood pressure detected by the second detecting unit based on the second biological information obtained at the reference appearance timing and the next reference appearance timing of the blood pressure waveform, and

each of the reference appearance timing and the next reference appearance timing is obtained from an R-wave of an electrocardiogram.

10. The vessel wall monitoring apparatus according to claim 9 , wherein the logarithmic blood pressure function includes

dP b ( t )=ln( P b ( t ))−ln( P b ( t 0 )), and

the vessel diameter function includes:

ε( t )=( r ( t )− r ( t 0 ))/ r ( t 0 );

ε′(t) which is a first derivative of ε(t); and

ε″(t) which is a second derivative of ε(t),

where t 0 indicates the reference appearance timing, t indicates a time period from the reference appearance timing to the next reference appearance timing, P b (t) indicates a blood pressure value at t, and r(t) indicates a vessel diameter at t, and

the impedance model expression includes

dP b (t)=ln(P b (t))−ln(P b (t 0 ))=βε(t)ηε′(t)+με″(t), where ε indicates the stiffness, η indicates the viscosity, and μ indicates the inertia, on which a recurrent calculation is performed to output the at least one of the stiffness, the viscosity, and the inertia.

11. The vessel wall monitoring apparatus according to claim 10 , wherein

the outputting unit detects a time difference τ between an appearance timing of an inflection point of the blood pressure waveform in dP b (t) and an appearance timing of the inflection point of the blood pressure waveform in ε(t), and the outputting unit corrects dP b (t) to dP b (t−τ) and corrects dP b (t 0 ) to dP b (t 0 −τ).

12. The vessel wall monitoring apparatus according to claim 9 , wherein the logarithmic blood pressure function includes

dP b ( t )=ln( P b ( t ))−ln( P b ( t 0 )), and

the vessel diameter function includes:

dP 1 ( t )=( P 1 ( t )− P 1 ( t 0 ));

dP 1 ′(t) which is a first derivative of P 1 (t); and

dP 1 ″(t) which is a second derivative of P 1 (t),

where t 0 indicates the reference appearance timing, t indicates a time period from the reference appearance timing to the next reference appearance timing, P b (t) indicates a blood pressure value at t, and P 1 (t) indicates a plethysmogram at t, and

the impedance model expression includes

dP b (t)=ln(P b (t 0 ))−ln(P b (t 0 ))=βdP 1 (t)+ηdP 1 ′(t)+μdP 1 ″(t), where β indicates the stiffness, η indicates the viscosity, and μ indicates the inertia, on which a recurrent calculation is performed to output the at least one of the stiffness, the viscosity, and the inertia.

13. The vessel wall monitoring apparatus according to claim 12 , wherein the outputting unit detects a time difference τ between an appearance timing of an inflection point of the blood pressure waveform in dP b (t) and an appearance timing of the inflection point of the blood pressure waveform in dP 1 (t), and

the outputting unit corrects dP b (t) to dP b (t−τ) and corrects dP b (t 0 ) to dP b (t 0 −τ).

14. The vessel wall monitoring apparatus according to claim 1 , wherein the outputting unit calculates the stiffness and the viscosity and calculates and outputs a ratio of the stiffness and the viscosity.