An intelligent cardiovascular disease (CVD) diagnosis system using hemodynamic parameters (HDPs) derived from sphygmogram (SPG) signal is presented to support the emerging patientcentric healthcare models. To replicate clinical approach of diagnosis through a staged decision process, the Bayesian inference nets (BIN) are adapted. New approaches to construct a hierarchical multistage BIN using defined function formulas and a method employing fuzzy logic (FL) technology to quantify inference nodes with dynamic values of statistical parameters are proposed. The suggested methodology is validated by constructing hierarchical Bayesian fuzzy inference nets (HBFIN) to diagnose various heart pathologies from the deduced HDPs. The preliminary diagnostic results show that the proposed methodology has salient validity and effectiveness in the diagnosis of cardiovascular disease.
Cardiovascular diseases (CVD) are known as the silent killers and often they may develop over time without being noticed until a critical stage is reached. Early diagnosis, care, and continuous monitoring are crucial in preventing heart failures. Thus, exploiting the benefit of multiple technological advancements, research over the past decade has focused on the development of various intelligent tools, to support healthcare professionals and promote CVD selfmonitoring. In the same vein, our research team has also been devoted to the research and development (R&D) of ehome healthcare system for CVD selfmonitoring [
Though the benefits of SPG and hemodynamic analysis have been well documented [
However, difficulty arises in constructing the BIN and quantifying the inference nodes to compute the inference through the nets and solve uncertainties. Many renowned researchers including Pearl [
In constructing a BIN, researchers first developed algorithms that learn the parameters from a large data set to optimally construct the graphical model. These were generally referred to as the learning models and were further distinguished into search and score based methods [
The alternative to the datadriven approach was the manual construction of BIN through knowledge acquisition from domain experts using various knowledge elicitation techniques [
To overcome the critical challenges, some unique benefits from datadriven and knowledge elicitation techniques are availed in this paper and a new approach to construct hierarchical multistage BIN and quantify the inference nodes is proposed. Function formulas in first order predicate logic form are derived to guide in constructing the hierarchical multistage BIN. Further, the FL technology is used to quantify dynamic statistical parameters to inference nodes. The proposed methodology is then applied to construct hierarchical multistage Bayesian fuzzy inference nets (HBFIN) to diagnose various heart pathologies based on HDPs. HBFIN is finally validated using sitemeasured medical data acquired from two hospitals in China.
HDPs derived from hemodynamic analysis of SPG signal can serve as powerful indices for prognosis of CVDs. There are various approaches to hemodynamic analysis [
Point and area based morphological features of a typical SPG signal.
Blood flow continuous equation is
Relation between pressure and blood flow is
Arterial pressurevolume equation is
Now, with (
Computing the integral of (
Auxiliary blood pressure index is
Stroke volume is
Auxiliary sphygmogram index is
Arterial compliance is
Peripheral resistance is
Similarly, with morphological features and deduced HDPs, various other HDPs can be generated.
The sitemeasured medical data consists of medical records of different samples, including each patient’s physiological attributes, original SPG waveforms, HDPs, and doctor’s clinical diagnostic results. Here, the medical symptom space is denoted by MSS
Moreover, a medical knowledge base was developed by acquiring information from various medical sources to analyze the relation between the derived HDPs and various pathological conditions of heart. Such medical knowledge base was then verified by doctors from two hospitals in China.
The key step in constructing inference nets is to define the function formulas in first order predicate logic form using the developed medical knowledge base.
Following equation shows an example of such defined function formula:
Condition values of symptoms (HDPs) for indicating pathological condition of heart.
Symptoms (units)  Conditions  



 
SP (mmHg)  ≥160  <90  =110~130 
DP (mmHg)  ≥95  =80~90  
MAP (mmHg)  >115  <65  =70~100 
MDP (mmHg)  >105  =66~96  
BV (L)  ≤{0.75 * Wt * 0.075}  ={0.75 * Wt * 0.075}~{1.25 * Wt * 0.075}  
PR (mmHg)  ≥104  <50  =60~100 
Wt (kg)  >20  =50~80  
SV (mL/stroke)  ≤{0.8 * (1 + 
≥{1.3 * 1.2 * (1 + 
≈{(1 + 
SI (mL/stroke/m^{2})  ≤0.8 * (1 + 
≥{1.3 * 1.2 * (1 + 
≈(1 + 
VPE (kg/stroke)  ≤{0.8 * 2 * (Wt + 45) * 0.0112}  ≥{1.2 * 2 * (Wt + 45) * 0.0112}  ≈(2 * Wt + 45) * 0.0112 
CI (mL/stroke/m^{2})  ≥2.2 
={(1 + 


≥{1.1 * 4}  ≤{0.85 * 3}  =3~4 
Yr (mpa·s)  ≥{1.1 * 4}  ≤{0.85 * 3}  =3~4 
AC ( 
≥1.2  ≥1.2  
FEK  ≥{0.9 * 0.25}  =0.35~0.55  
BLK  <{0.85 * 0.22}  =0.22~0.26 
Deriving from the medical knowledge base, the first order predicate logic formulas for diagnosing various other heart pathologies can be defined as follows:
The defined function formulas can then be used to guide in constructing the hierarchical multistage inference nets to diagnose various CVDs.
Based on the data distribution, various types of function such as Gaussian, triangle, highorder polynomial,
The general formula of
Based on statistical analysis of sitemeasured records, the MF for each plot of pair (symptom (HDP) versus membership grade of having specific CVD) is predefined. This therefore fixes all the parameters of (
Generation of highorder polynomial or quasiGaussian membership function for symptom
Partially constructed HBFIN for diagnosing heart pathologies with statistical parameters assigned for a sampled medical record.
Now, in HBFIN, when testing data
The coefficients
With the function formulas defined in (
It is worth emphasizing here that the partially constructed HBFIN in Figure
Generally, the inference nodes are quantified by static values of statistical parameters using subjective (experts’ estimation) approach. However, since confliction exists among experts’ opinions, defining appropriate static values of statistical parameters to inference nodes has always been a challenge. But, with the proposed methodology using FL technology, dynamic values of statistical parameters can be defined and assigned to inference nodes automatically.
Here, with a specific example, by testing a patient’s medical record (partially shown in Table
A patient’s partial medical record.
Symptoms (units)  Patient’s partial medical record 

SP (mmHg)  168 
DP (mmHg)  100 
MAP (mmHg)  130.98 
MDP (mmHg)  113.09 
BV (L)  3.5212 
PR (mmHg)  68 
Wt (kg)  49 
SV (mL/stroke)  63.81 
SI (mL/stroke/m^{2})  45.54 
VPE (kg/stroke)  2.18 
CI (mL/stroke/m^{2})  2.7 

3 
Yr (mpa·s)  3.8 
AC ( 
0.66 
FEK  0.11 
BLK  0.197 
*The expansion of symptom acronym is provided in Figure
The Bayesian inference nets generally form a static knowledge structure, in which the probability associated with each inference node consequently changes when the evidence is certain or uncertain. This change in probability is propagated up stage by stage through the hierarchical Bayesian inference nets to ultimately support or disprove the toplevel hypothesis/conclusion. In this paper, the following inference model is used to compute the inference through the nets. In this model, for addressing uncertainty in evidence, conditional independence of the evidence is assumed. Therefore, for partially known or uncertain evidence, according to its degree of belief, it is categorized as true or false and the inference through the nets is computed accordingly.
Prior odds of
Posterior odds of
Posterior probability of
Posterior probability of
If
If
For conjunction inference node,
For disjunction inference node,
The function and validity of partially constructed HBFIN are examined using the reserved testing samples. The number of samples used for testing and the obtained diagnostic accuracy are presented in Table
Diagnostic results of partially constructed HBFIN.
Person’s health status  Number of samples  Diagnostic accuracy (%) 

HT  53  78 
HPT  17  82 
Low_BE  13  76 
High_BE  17  82 
Low_CPP  10  80 
High_CPP  18  83 
HPV  8  87 
HV  13  84 
*The expansion of symptom acronym is provided in Figure
It is noteworthy that the partially constructed HBFIN in Figure
Overall diagnostic accuracy of HBFIN in CVD detection.
Person’s health status  Diagnostic accuracy (%) 

Healthy  91 
HT  78 
CHD  68 
AR  73 
PHD  65 
CIN  72 
HL  73 
Mixed CVD  58 
Considering that the diagnosis results are derived only from the HDPs and physiologic parameters in the proposed noninvasive approach, the above diagnostic accuracy is highly acceptable and therefore is suitable for ehome healthcare usage.
Furthermore, Table
Diagnostic accuracy of intelligent CVD diagnosis systems using adapted versions of AI technology.
CVD type  Adapted version of AI technology  

NN  FNN  HBFIN  
CHD  78  65 

HT  70  67 

HL  64  77 

Mixed CVD  —  40 

The diagnostic results in Table
An intelligent CVD diagnosis system based on HDPs derived from SPG signal is presented in this paper. By availing the benefit of some unique features of hybrid AI, BIN, and FL technologies, an intelligent CVD diagnosis system is proposed. A new approach for constructing hierarchical multistage BIN guided by function formulas defined in first order predicate logic form is proposed. A mathematical inference model using Bayesian theory is presented, and a method using FL technology to quantify dynamic values of statistical parameters to inference nodes is suggested. With the proposed methodology, HBFIN is constructed to diagnose various CVDs based on HDPs. The sitemeasured medical records from two hospitals of China have been used to design and validate the proposed HBFIN. For such a noninvasive diagnostic approach, the testing results with acceptable diagnostic accuracy in diagnosing six important CVDs prove the suitability of HBFIN for home healthcare usage.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This research was supported by Research Committee of University of Macau under Grant no. MYRG201400060FST and also by the Science and Technology Development Fund (FDCT) of Macau S.A.R with project reference no. 016/2012/A1.