Research article Special Issues

Estimation of left ventricular parameters based on deep learning method


  • Received: 04 December 2021 Revised: 09 April 2022 Accepted: 19 April 2022 Published: 27 April 2022
  • Estimating material properties of personalized human left ventricular (LV) modelling is a central problem in biomechanical studies. In this work we use deep learning (DL) method to evaluating the passive myocardial mechanical properties inversely. In the first part of the paper, we establish a standardized geometric model of the LV. The geometric model parameters are optimized based on 27 different healthy volunteers. In the second part, we use statistical methods and Latin hypercube sampling (LHS) to obtain the geometric parameters data. The LV myocardium is described using a structure-based orthotropic Holzapfel-Ogden constitutive law. The LV diastolic pressure-volume (PV) curves are calculated by numerical simulation. Tn the third part, we establish the multiple neural networks to pblackict PV curve parameters. Then, instead of using constrained optimization problems to solve constitutive parameters, DL was used to establish the nonlinear mapping relationship of geometric parameters, PV curve parameters and constitutive parameters. The results show that the deep learning method can greatly improve the computational efficiency of numerical simulation and increase the possibility of its application in rapid feedback of clinical data.

    Citation: Li Cai, Jie Jiao, Pengfei Ma, Wenxian Xie, Yongheng Wang. Estimation of left ventricular parameters based on deep learning method[J]. Mathematical Biosciences and Engineering, 2022, 19(7): 6638-6658. doi: 10.3934/mbe.2022312

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  • Estimating material properties of personalized human left ventricular (LV) modelling is a central problem in biomechanical studies. In this work we use deep learning (DL) method to evaluating the passive myocardial mechanical properties inversely. In the first part of the paper, we establish a standardized geometric model of the LV. The geometric model parameters are optimized based on 27 different healthy volunteers. In the second part, we use statistical methods and Latin hypercube sampling (LHS) to obtain the geometric parameters data. The LV myocardium is described using a structure-based orthotropic Holzapfel-Ogden constitutive law. The LV diastolic pressure-volume (PV) curves are calculated by numerical simulation. Tn the third part, we establish the multiple neural networks to pblackict PV curve parameters. Then, instead of using constrained optimization problems to solve constitutive parameters, DL was used to establish the nonlinear mapping relationship of geometric parameters, PV curve parameters and constitutive parameters. The results show that the deep learning method can greatly improve the computational efficiency of numerical simulation and increase the possibility of its application in rapid feedback of clinical data.



    Vitamin B12, also known as cobalamin, plays an important role in the functioning of the brain and nervous system, and in the formation of red blood cells. Vitamin B12, occurring naturally in food, derives from bacterial synthesis and therefore occurs only in foods of animal origin. Small amounts can be found in plant products due to the presence of bacteria or due to microbial contamination. Plant food such as blue-green algae contains of pseudo vitamin B12 which is in active in humans. In foods, cobalamins are bound to proteins and glycoproteins and must be released by enzymatic and acid hydrolysis in the gut. Dairy foods, milk and milk products, eggs, meat and seafoods are the main natural sources in the diet. Tempeh, solid state boiled-dehulled soybean fermentation using starter culture of Rhizopus oligosporus, is rich of antioxidants and contains vitamin B12 [1,2]. Few scientific literatures mentioned the vitamin B12 values of tempeh. Areekul et al. [3] found between 0.18 and 4.1 Mcg vitamin B12 analogues per 100 g tempeh from tempeh sold in market in Jakarta, and tempeh sold in Toronto, Canada contained of 148 ng of vitamin B12 per g [4]. During the soybean fermentation, enzymatic activities of R. oligosporus leads to a significant increase in water-soluble nutrients, enhancing the biosynthesis of B vitamins and transformation of soy-isoflavones into antioxidant compounds. Soybean itself contains low or undetectable of vitamin B12, yet when soybeans are fermented to produce tempeh, a considerable amount of vitamin B12 was found, about 0.7 to 0.8 µg/100 g [5]. It is known that vitamin B12 contained in tempeh is synthesized by Klebsiella pneumoniae and Citrobacter freundii [6]. These bacteria were thought as the contaminating bacteria during processing of tempeh making. With these values of vitamin B12, tempeh may be as an additional diet of vitamin B12 from plant-derived food sources. The RDI of vitamin B12 for adults is set at 2.4 µg/day in Indonesia [7], and as well in The US and Japan (RDA) [8]. Recently, industrial production of vitamin B12 has been carried out through microbial fermentation, mostly use Pseudomonas denitrificans, Propionibacterium shermanii [9]; however, this process has some drawbacks such as a long fermentation process and expensive media requirements

    Consumption of soy based foods may have health benefits due to their functional ingredients, especially isoflavones. In soybeans, isoflavones are in the form of isoflavone glycosides. The two most widely studied of isoflavones from soybeans are daidzin and genistin, which are not easily absorbed by the intestinal absorptive cells because of their large hydrophilic structures [10,11]. However, hydrolytic enzyme-producing microorganisms can hydrolyze isoflavone glucosides by the enzyme β-glucosidase to form of aglicones, daidzein and genistein which have antioxidant properties. Hydrolysis of isoflavone glycoside, and variation of individual isoflavone aglycones are influenced by microbial types [12,13,14] reported that bacteria are more effective in converting daidzin and genistin into their aglycone forms than molds. Aspergillus and Streptomyces isolated from soybean fermented foods are known as best producer of ortho-dihydroxyisoflavone (ODI), hydroxylated isoflavones which is produced during fermentation of soybeans. This study conducted to analyze the vitamin B12 and the isoflavone aglycone contents produced during soybean fermentation using co-inoculated of R. oligosporus, S. cerevisiae, and Klebsiella sp as starter cultures.

    Starter cultures used in this study: Rhizopus oligoporus was isolated from tempeh, Saccharomyces cerevisiae isolated from commercial Fermipan dried yeast product, and Klebsiella sp non-pathogenic bacteria were isolated from the tempeh [15]. Except for Klebsiella sp which was cultured on nutrient agar and its stock culture was maintained at −20 ℃ in 20% glycerol, all the starter cultures were freshly prepared. For inoculums preparation, the bacteria and yeast were grown in nutrient broth at 37 and 32 ℃ respectively for 24 h. The cells were harvested and resuspended in sterile distilled water and properly adjusted to obtain a concentration of 105 and 105 CFU mL−1 respectively. For mold preparation, the mycelium was streaked on potatoes dextrose agar and grown at 27 ℃ for 120 h. The spores were harvested, resuspended in sterile distilled water and properly adjusted to obtain a concentration of 105 cell mL−1.

    The data obtained was analysed by the use of Excel Microsoft program 2016.

    Soybeans in this research were purchased in the Primkopti Bandar Lampung. Tempeh was produced in a microbiology laboratory as follows; 300 g of soybeans were soaked in clean water overnight at room temperature, and then dehulled manually. Dehulled soybeans were boiled in clean water with a ratio of 1:3 (soybeans: water) for 30 minutes, drained, air dried at room temperature, and then 100g aseptically inoculated with the cultures at defined number of cells which was 105, 105, and 105 CFU 100g−1 for R.oligosporus, S. cerevisiae, and Klebsiella sp, respectively. Inoculated soybeans were packed in perforated plastic packaging and incubated at 32 ± 2 ℃ for 40 hours. Five types of fermented soybeans with the addition of different inoculated cultures were produced in this study, namely (1) soybeans + R. oligosporus + Klebsiella sp (SRK), soybeans + R. oligosporus + S. cerevisiae (SRSc), soybeans + R. oligosporus + S. cerevisiae + Klebsiella sp. (SRScK), and Soybean + R. oligosporus (SR) and soybeans + Klebsiella sp. (SK). Separate soybeans were also fermented as a control without inoculation. The experiments were made in three replication.

    The measurement of pH was carried out with a pH meter model 501 (Crison, Barcelona, Spain). All samples were homogenized prior to pH measurements. Measurements were made three times for testing the accuracy then the mean was taken.

    Each of fermented soybeans was analyzed for its total number of bacteria, yeast and molds at the starting and the end of fermentation. A total of 15 g tempeh was taken, mixed with 135 mL of 0.1% peptone water, homogenized with a stomacher for 30 seconds, and a series of dilutions from 10−1 to 10−8 was made in duplicate. Then one mililiter is taken from certain dilutions for plating microorganisms done by spread plate method on EMB agar (BBL Microbiology Systems. Cockeysville, Md.), MEA (Difco), and PDA (Oxoid) for Klebsiella sp., S. cerevisiae, and R. oligosporus, respectively. Incubation of the plates was at 37, 27, 32 ℃ for Klebsiella sp., S. cerevisiae, and R. oligosporus respectively, for 24 to 48 hours.

    The method of vitamin B12 analysis was performed according to the procedure run by Lawrence [16] with small modification on the application of UAE. Sample preparation method applies water ultrasonic assisted extraction (UAE), in which ultrasonic water extraction was used for extraction. A total of 0.5 grams of ground tempeh was weighed and place into 100 mL Erlenmeyer containing of 20 mL of milli-Q water. Sample was extracted by using ultrasonic equipped with heater for 30 minutes. Then, sample volume was set for 25 mL by adding milli-Q-water, and centrifuged at 3000 rpm for 10 min. Supernatant was pipetted using syringe equipped with filter holder so that 2 mL of supernatant was obtained, and then filtered using paper filter of 13 mm in diameter and 0.2 µm pore size. The filtrate was then placed in the vial bottle. The sample was ready to be injected into the HPLC (Shimadzu, CBM-20A controller, LC 20AD solvent delivering unit, CTO 10A column oven, SPD M20-A photo diode array detector). HPLC running condition was using Agilent C-18 5 um (125 × 4.6 mm) column, column temperature of 35 ℃, mobile phase (water: acetonitrile: buffer phosphate 10 nM = 80:10:10), isocratic mobile phase method with flow rate 1 mL min−1, injection volume of 20 µL, wavelength detector 360 nm, and running time of 20 min.

    Standard solution was prepared as following, weigh 5 mg of standard cyanocobalamin, dissolve it in 100 mL of milli-Q-water so that a concentration of 50 µg.mL−1 is obtained. Then the standard was diluted into a working solution with a concentration of 0.5 µg.mL−1, 1 µg.mL−1, 2 µg.mL−1, and 4 µg.mL−1.

    For quantification of daidzein and genistein, fermented soybean samples were freeze-dried and stored at −20 ℃ until used. The extraction of isoflavones from fermented soybeans and unfermented soybeans, and their quantification by HPLC were assayed followed the procedures worked by El-Shazy et al. [17] with small modification and was assayed at the Centre Technology and Innovation Lab. Univ. of Lampung. HPLC-MWD instrument (Agilent 1200 series), Zorbax 5µm (4.6 mm × 150 mm) column, and UV detector (λmax = 254 nm). The mobile phase consisted of 100% methanol and 10 mmol L-1 of ammonium acetate buffer (60:40) containing 1 mL of trifluoro-acetic acid per liter of solvent mixture. This was set at a flow rate of 0.6 mL min−1. Standards of daidzein and genistein were obtained from Sigma. 1gram of the freeze-dried sample was added to 10mL of 80% (v v−1) aqueous methanol and extracted under agitation for 24 hours at room temperature. The homogenates were centrifugated at 15000rpm for 30min and the methanol obtained were used to determine daidzein and genistein concentrations. Injection volumes of isoflavone standards and of the samples were set at 100 µL throughout the run time of 30min. Single standards were also prepared for peak identification. Calculation of the isoflavone concentration was dry basis (µg g−1 fermented soybean).

    The number of R.oligosporus, S. cerevisiae, and Klebsiella sp inoculated into soybeans for tempeh production were 103, 105 and 103 cells g−1, respectively. Table 1 shows that the addition of S. cerevisiae and Klebsiella sp. either together or separately did not affect the growth of R. oligosporus. R oligosporus in tempeh is not a contaminant microorganism and instead it has to be deliberately added into the soybeans. It was possible that R. oligosporus played a role in supporting the growth of other microorganism in the soybeans fermentation, because during fermentation R. oligosporus produces several enzymes including lipase, protease, and phytase which hydrolyzes carbohydrate, lipid, and protein from the soybeans and produces fatty acids and amino acids which are then utilized by bacteria and yeast [18]. In addition, they also function as growth control of microorganisms in tempeh, preventing the tempeh consumer from diarrhea and flatulence. R.oligosporus produces antibiotics which actively kill certain bacteria in tempeh i.e. Staphylococcus aureus, Bacillus subtilis, and Clostridium sp which is known to produce gas in the intestines [19]. S. cerevisiae was able to grow together either with R. oligosporus or Klebsiella sp. during fermentation of tempeh making, it is possible to obtain carbon and nitrogen sources from soybeans as well as fatty acid and amino acids produced by R. oligosporus. Meanwhile, the wide pH tolerant and that Klebsiella is a bacterial contaminant in tempeh which may be the reason for the high number of Klebsiella found in tempeh. The pH of tempeh in this experiment was found between 6.60 to 7.40 (Tabel 2).

    Table 1.  The total number of microorganism in soy fermentation inoculated with various cultures.
    Type of isolates in soy fermentation Microbial number (CFU g−1) at
    0 h of fermentation 40 h of fermentation
    Ro Sc. K Ro Sc. K
    SR 2.6 × 103 ND ND 3.4 × 106 ND 2.0 × 108
    SRSc 2.8 × 103 3.6 × 103 ND 4.5 × 106 1.2 × 106 1.1 × 108
    SRScK 4.4 × 103 6.3 × 103 1.0 × 103 5.6 × 105 3.7 × 105 2.5 × 108
    SRK 5.0 × 103 ND 2.7 × 103 3.0 × 105 ND 1.9 × 108
    SK ND ND 2.1 × 103 ND ND 2.7 × 108
    Note: The data in the table were average value of three replications. ND not detected. SR is soy + R. oligosporus, SRSc is soy + R. oligosporus + S. cerevisiae, SRScK is soy + R. oligopsorus + S. cerevisiae + Klebsiella sp, SRK is soy + R.oligosporus + Klebsiella sp, SK is soy + Klebsiella sp. Ro is R. oligosporus, Sc is S. cerevisiae, K is Klebiella sp.

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    Table 2.  Effect of isolated cultures in producing vitamin B12, daidzein, and genistein during tempeh fermentation.
    Isolated culture Initial pH Final pH Water content (%) Vit B12 (Mcg100 g−1) Daidzein (Mcg g−1) Genistein (Mcg g−1)
    SR 6.2 6.40 65.1 ± 0.19 2.88 ± 0.50 276.17 ± 0.20 492.96 ± 1.0
    SRSc 6.2 6.10 65.23 ± 0.80 3.15 ± 0.70 224.37 ± 0.20 465.12 ± 0.90
    SRScK 6.2 6.60 65.14 ± 0.10 1.64 ± 0.9 753.96 ± 0.15 1072.87 ± 0.90
    SRK 6.2 6.60 65.24 ± 0.20 0.81 ± 2.00 781.76 ± 0.15 1071.85 ± 1.0
    SK 6.2 7.40 65.91 ± 0.50 0.39 ± 1.9 782.17 ± 0.30 1072.51 ± 0.70
    Soybean only 6.2 6.20 65.0 ± 0.50 0.36 ± 0.42 0.69 ± 0.20 0.25 ± 0.60
    Note: The data in the table were mean of three replications with standard deviation. SR is soy + R. oligosporus, SRSc is soy + R. oligosporus + S. cerevisiae, SRScK is soy + R. oligopsorus + S. cerevisiae + Klebsiella sp, SRK is soy + R.oligosporus + Klebsiella sp, SK is soy + Klebsiella sp.

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    Biosynthesis of vitamin B12 is limited to some bacteria and archaea, and its production depends on type of microorganisms involved during fermentation. Soybeans only used as control of the tempeh production in this experiment contained very little vitamin B12 that it would not be of nutritional significance. This finding (0.36 mg100g−1) was close with data reported by Liem et al. [4] and Areekul et al. [3], in which the amount was found to be 0.39 ng/g and 0.15 ng g−1, respectively. R. oligosporus was an essential microorganism in the production of tempeh, but when Klebsiella sp was used as culture to soybean fermentation, tempeh did not produce (Figure 1). When R. oligosporus was as an inoculum in soybean fermentation it yielded vitamin B12 of about 2.88 mg 100g−1, R. oligosporus co-inoculated with Klebsiella sp yielded lower vitamin B12 (0.81 mg 100g−1). The first data (2.88 Mcg 100 g−1) was close with the data reported by Liem et al. [4] which was 66.0 ng g−1. The presence of S. cerevisiae during tempeh fermentation was beneficial from the nutritional point of view. When S. cerevisiae co-inoculated with R. oligosporus, a high vitamin B12 was produced (3.15 Mcg100 g−1) in tempeh. S. cerevisiae is rich in cobalt and a vitamin B12 producer [20,21], which may contribute to an increase in vitamin B12 of the tempeh. In addition, S. cerevisiae co-inoculated with R. oligosporus in soybean fermentation produced tempeh that contain β-glucan [22] and a new aroma of yeasty which is preferred by some tempeh consumers [23]. Yeasty aroma of tempeh produced by alcohol, ester, and aromatic group such as styrene, caryophyllene, phenol, and maltol during fermentation.

    Figure 1.  The profile of tempeh produced by the use of different cultures. SR is soy + R. oligosporus), SRSc is soy + R. oligosporus + S. cerevisiae, SRScK is soy + R. oligosporus + S. cerevisiae + Klebsiella sp, SRK is soy + R.oligosporus + Klebsiella sp, SK is soy + Klebsiella sp. All of the tempeh except SK showed the white mycelium binds the beans into a compact, cake-like texture.

    The recommended dietary allowance of vitamin B12 is 2.4 µg/day for adults. When the concentration of vitamin B12 in tempeh was 3.15 Mcg100g−1, it becomes visible for the consumer to get his or her daily requirement of vitamin B12 by consumption of approximately 76.2 g of tempeh. The bioavailability of vitamin B12 in tempeh in this study was not investigated. Mo et al. [24] found the bioavailability of tempeh was 0.016–0.072 Mcg 100g−1 which is very low. This could be because they made tempeh from soybean fermentation with Rhizopus microsporus var. microsporus LU573 and did not use the vitamin B12 producing bacteria. However, Bor et al. [25] mentioned that a daily vitamin B12 intake of 6 Mcg is sufficient to maintain a steady-state concentration of plasma vitamin B12. Bioavailability of dietary vitamin B12, daily body loss of vitamin B12, and human healthiness of normal gastrointestinal function are important to consider for consumption of tempeh as a source of daily vitamin B12 intake. When compared to cooked lean meat which contains 33 µg 100g−1 of vitamin B12 and the bioavailability of vitamin B12 which is 0.9 µg from 100 g of mutton ground patties, tempeh can be a potential source of vitamin B12 from non-meat origin. Provided that the potential use of bacteria producing vitamin B12 or yeast in soy fermentation is attempted to increase the quantity of vitamin B12 to make tempeh a reliable source of vegetable vitamin B12.

    Recently Propionibacterium freundenreichii, the food grade producer of vitamin B12, has been used in co-culture with R. oryzae to enrich vitamin B12 in lupin tempeh [26]. An increase of vitamin B12 content (up to 0.97 μg100 g−1) was achieved in lupin tempeh and its texture, taste and overall acceptance were not affected by the bacterial co-inoculation [27]. Nevertheless, lupin tempeh have distinct flavour and aroma that may be unacceptable to consumers who are familiar with the taste of soy tempeh. Propionibacterium freundenreichii was usually used in the preparation of cheese making with its contribution to fat compounds, an important flavour in cheese [28]. Regardless of whether tempeh can be fermented with substantial amount of vitamin B12 producing bacteria, its overall digestibility, rich in protein content and antioxidant. This can make it potential meat alternative and functional food.

    In all, the tempeh that was analyzed showed that genistein was larger amount than daidzein (Table 2). Most of the inoculated cultures, R.oligosporus, S. cerevisiae and Klebsiella sp may effectively hydrolyze daidzin and genistin during the soy fermentation. In tempeh fermentation co-inoculated with Klebsiella sp, it was noticed that the amount of daidzein was three-fold, and genistein was doubled compared to that of without Klebsiella sp. Differences in the biotransformation of both daidzin and genistin were found when the addition of Klebsiella sp to the soy fermentation produced high amount of both daidzein and genistein. In addition, inoculation of the mold R. oligosporus into the soy fermentation produced low amount of either daidzein or genistein. Even though the activity of β-glucosidase was not analyzed in this study, the production of daidzein and genistein indicated that there was biotransformation of isoflavones catalysed by the β-glycosidase. Our results are not in agreement with the work done by El-Shazly et al. [17] where the amount of daidzein was larger than genistein in fermented soy flour with Bacillus licheniformis. The type of soybean fermentation applied to measure isoflavones, and the selective action of the β-glucosidase, might explain the different findings in this study. Solid state fermentation as a process in which microorganisms are grown in solid material without the presence of free liquid was applied in this study while submerge fermentation was applied in another study. According to Fang et al. [9], hydrolysis of soy isoflavones by microbial β-glucosidase depend on substrate specificity. Beside hydrolyzed from daidzin and genistin, daidzein and genistein may also be derived from formononetin and biochanin-A [29]. In addition, the bacterial-synthesized β-glucosidase can be bound to the cell walls or secreted into the periplasmic space [30]. Borges et al. [31] found that soaking, cooking and fermentation times in the tempeh making influenced the production of isoflavone, and the highest yield of genistein and daidzein was fermentation with R. oligosporus for18 hours, but the beans and the culture used were no cause for concern.

    R. oligosporus is the main isolated culture in tempeh production. Inoculation of Klebsiella to cooked dehulled soybean fermentation did not produce tempeh. S. cerevisiae is the most potential contributor of vitamin B12 in tempeh. Klebsiella sp. co-inoculation with either R. oligosporus or S. cerevisiae inhibit the production of vitamin B12 in tempeh, although it does not affect their growth. Klebsiella sp contributes to the production of daidzein and genistein in tempeh.

    This research was partly funded by the University of Lampung through the BLU-Fundamental Research, University of Lampung, 2019.

    All authors declare no conflict of interest.



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